Shock Temperatures of Materials: Experiments and Applications to the High Pressure Equation of State - CaltechTHESIS

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Shock Temperatures of Materials: Experiments and Applications to the High Pressure Equation of State
Citation
Lyzenga, Gregory Allen
(1980)
Shock Temperatures of Materials: Experiments and Applications to the High Pressure Equation of State.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/VSBK-ZA43.
Abstract
The experimental determination of temperatures in the high-pressure shocked state of condensed matter provides a useful supplement to equation-of-state models derived from Hugoniot measurements. An optical pyrometry technique has been developed to obtain temperature measurements during impact-driven shock wave experiments with solid and liquid samples at pressures near 100 GPa. Experimental results confirm that throughout moderate ranges of shock pressure amplitude, transparent dielectrics emit thermal radiation from the region of the shock front, with a spectrum which is characteristic of the Hugoniot state temperature. Shock temperatures in sodium chloride crystals have been measured in the pressure range 70-105 GPa. The observed temperatures, between 4000 and 8000 K, are in agreement with the results of earlier determinations and with calculations assuming the occurrence of shock-induced melting. Results of experiments to measure shock temperatures in metallic silver include a successful measurement of 5950 K at a pressure of 185 GPa. This result is consistent with the melting of silver under shock, with a melting pressure dependence described by the Lindemann criterion.
Shock temperature measurements in silica (SiO2) have produced anomalous results suggestive of melting occurring in the stishovite phase near 100 GPa pressure and 4700 K temperature. Experimental measurements with [alpha]-quartz and fused silica samples extend from pressures of approximately 60 GPa to 140 GPa, with shock temperatures between approximately 4500 K and 7000 K. The experimental data allow quantification of the thermodynamic relations among silica phases, including heats of transition and the Gruneisen parameter. Shock temperatures in single crystal forsterite (Mg2SiO4) between pressures of 150 GPa and 175 GPa range from 4500 K to 4950 K, a result which is consistent with occurrence of a polymorphic solid state transition accompanied by a substantial heat of transition (~1.5 MJ/kg). These results have potentially important implications for solid earth geophysics, and knowledge of the melting curves of candidate minerals of the earth's mantle provides some constraints on the geotherm.
Hugoniot temperatures have been measured in liquid water between approximately 50 GPa and 80 GPa, with results ranging from 3500 K to 5400 K. The observed temperatures are well reproduced by theoretical calculations assuming a constant specific heat model, but further work is required to characterize fully the thermal variation of H2O properties at high temperature. Compression measurements in pressure-volume states other than Hugoniot shock states and, in particular, in states of compression at constant entropy can provide both independent thermal equation-of-state information and the properties of high-density condensed phases inaccessible to shock wave experiments. Numerical calculations have been carried out for hypothetical experiments on water as well as carbon dioxide and liquid molecular hydrogen. The results of these calculations indicate that various experimental impact configurations may be employed to convert shock compression into isentropic compression, with pressures on the order of 100 GPa attained via impact velocities of a few kilometers per second. In the case of water, a net entropy production of a few percent of the Hugoniot entropy at the same pressure is predicted on the basis of these calculations.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
(Applied Physics) ; dynamic compression; geophysical equation of state; Hugoniot; shock equation of state; shock temperature
Degree Grantor:
California Institute of Technology
Division:
Geological and Planetary Sciences
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Ahrens, Thomas J.
Thesis Committee:
Unknown, Unknown
Defense Date:
19 May 1980
Record Number:
CaltechETD:etd-08032004-150047
Persistent URL:
DOI:
10.7907/VSBK-ZA43
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3001
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SHOCK TEMPERATURES OF MATERIALS:
EXPERIMENTS AND APPLICATIONS TO THE

HIGH PRESSURE EQUATION OF STATE

Thesis by

Gregory Allen Lyzenga

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology
Pasadena, California
1980

(Submitted May 19, 1980)

-ii-

ACKNOWLEDGMENTS

I express my sincere gratitude to Thomas J. Ahrens for his invaluable
support and guidance throughout all phases of this research. I also am
extremely grateful for the generous support of the Fannie and John Hertz
Foundation during my graduate residence. I have benefited greatly from
my associations and discussions with the faculty and students of the Insti-
tute; and, in particular, the help of Raymond Jeanloz and Ian Jackson, in
addition to that of T. J. Ahrens, is gratefully acknowledged. The experi-
mental work presented here has been made possible through the expert
assistance of the staff members of the Seismological Laboratory, and I
am grateful to E. Gelle, C. Hudson, J. Long, M. Long, N. Motta, E. Steffen-
sen and R. Wickes for their efforts. J. K. Erickson and his colleagues at
the Jet Propulsion Laboratory have contributed to the success of this work
as well.

The experiments of this research program have been largely supported
by the facilities and personnel of Lawrence Livermore Laboratory, and I
am very grateful for this opportunity and for the valuable advice and
assistance of A. C. Mitchell, W. J. Nellis and M. Van Thiel. The tech-
nical assistance of D. Bakker, E. Jerbic, H. Martinez, J. Samuels, and
C. Wallace of LLL is greatly appreciated. Thanks are extended to J. W.
Shaner of Los Alamos Scientific Laboratory for motivating advice and
valuable collaborations, I am most grateful to Helen F. White and Laszlo
Lenches for extraordinary help in the preparation of this thesis. In

addition to the support from DOE through Lawrence Livermore Laboratory,

-iii-
the financial support of the National Science Foundation and NASA is
gratefully acknowledged.
The support and understanding of my wife, Mary White Lyzenga, and
of my families have ranged from technical and financial to spiritual

backing, and it is to them that this work is dedicated.

-iv-

ABSTRACT

The experimental determination of temperatures in the high-pressure
shocked state of condensed matter provides a useful supplement to equation-
of-state models derived from Hugoniot measurements. An optical pyrometry
technique has been developed to obtain temperature measurements during
impact-driven shock wave experiments with solid and liquid samples at
pressures near 100 GPa. Experimental results confirm that throughout
moderate ranges of shock pressure amplitude, transparent dielectrics emit
thermal radiation from the region of the shock front, with a spectrum
which is characteristic of the Hugoniot state temperature. Shock tempera-
tures in sodium chloride crystals have been measured in the pressure range
70-105 GPa. The observed temperatures, between 4000 and 8000 K, are in
agreement with the results of earlier determinations and with calculations
assuming the occurrence of shock-induced melting. Results of experiments
to measure shock temperatures in metallic silver include a successful
measurement of 5950 K at a pressure of 185 GPa. This result is consistent
with the melting of silver under shock, with a melting pressure dependence
described by the Lindemann criterion.

Shock temperature measurements in silica (Si0,) have produced anoma—
lous results suggestive of melting occurring in the stishovite phase near
100 GPa pressure and 4700 K temperature. Experimental measurements with
a-quartz and fused silica samples extend from pressures of approximately

60 GPa to 140 GPa, with shock temperatures between approximately 4500 K

~y-
and 7000 K. The experimental data allow quantification of the thermo-
dynamic relations among silica phases, including heats of transition and
the Griineisen parameter. Shock temperatures in single crystal forsterite
(Mg,Si0,) between pressures of 150 GPa and 175 GPa range from 4500 K to
4950 K, a result which is consistent with occurrence of a polymorphic
solid state transition accompanied by a substantial heat of transition
(~1.5 MJ/kg). These results have potentially important implications for
solid earth geophysics, and knowledge of the melting curves of candidate
minerals of the earth's mantle provides some constraints on the geotherm.
Hugoniot temperatures have been measured in liquid water between
approximately 50 GPa and 80 GPa, with results ranging from 3500 K to
5400 K. The observed temperatures are well reproduced by theoretical
calculations assuming a constant specific heat model, but further work
is required to characterize fully the thermal variation of H,0O properties
at high temperature. Compression measurements in pressure~volume states
other than Hugoniot shock states and, in particular, in states of compres-
sion at constant entropy 'can provide both independent thermal equation-of-
State information and the properties of high-density condensed phases
inaccessible to shock wave experiments. Numerical calculations have been
carried out for hypothetical experiments on water as well as carbon dioxide
and liquid molecular hydrogen. The results of these calculations indicate
that various experimental impact configurations may be employed to convert
shock compression into isentropic compression, with pressures on the order
of 100 GPa attained via impact velocities of a few kilometers per second.
In the case of water, a net entropy production of a few percent of the
Hugoniot entropy at the same pressure is predicted on the basis of these

calculations.

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Appendix I

Appendix ITI

-vi-

TABLE OF CONTENTS

SHOCK TEMPERATURES AND THE
THERMAL EQUATION OF STATE

THE OPTICAL PYROMETRY TECHNIQUE
IN SHOCK COMPRESSION EXPERIMENTS

RESULTS AND APPLICABILITY OF
SHOCK PYROMETRY EXPERIMENTS

SHOCK TEMPERATURES OF SiO, AND Mg,Si0,:
EXPERIMENTAL RESULTS AND GEOPHYSICAL
IMPLICATIONS ,

SHOCK TEMPERATURE MEASUREMENTS IN H,0

ISENTROPIC COMPRESSION FROM SHOCKS
IN CONDENSED MATTER

DESIGN AND EXECUTION OF SHOCK
PYROMETRY EXPERIMENTS

EXPERIMENTAL SPECTRAL RADIANCE MEASUREMENTS
USED IN SHOCK TEMPERATURE DETERMINATIONS

25

45

76

123

141

185

201

Chapter 1

SHOCK TEMPERATURES AND THE

THERMAL EQUATION OF STATE

The Hugoniot Shock State and Thermal Pressure in Solids

The compression of condensed materials by passage of a steady, one-
dimensional shock wave through macroscopic specimens is a useful technique
for the study of equations of state as well as the structure and chemical
properties of matter at high pressures. The theory of the formation and
propagation of shocks in matter is the subject of a large body of litera-—
ture in gasdynamics and hydrodynamics. The present study considers the
application of these results to the study of solids, and what follows is a
brief sketch of the development of some of the useful results.

In general, a compressive disturbance of finite pressure amplitude
in a homogeneous medium does not propagate with a constant profile, since
the compressibility (and therefore the sound speed) of real substances
changes with increasing pressure. For most materials, the adiabatic com-
pressibility increases with pressure so that infinitesimal acoustic dis-
turbances propagate at ever higher velocities as the pressure increases
in the material. As discussed in the review material of [1], an initial
pressure pulse of arbitrary spatial profile will, as time progresses,
steepen in its pressure gradient as later, higher pressure disturbances
overrun the beginning of the wave. For such a material, in which

(3*P/av?) > 0 (the Bethe-Weyl condition for stability of weak shocks),

-2-
the wave steepens and stabilizes as a single shock transition, which is a
nearly discontinuous pressure profile of the kind illustrated in Figure 1-1.
The processes within the narrow region of the shock front are important
to a consideration.of the final compressed material state or Hugoniot state.
As the gradients of pressure and density in a steepening wave become very
large, dissipative effects of viscosity and heat conduction become impor-
tant in the flow, and these effects result in the net production of entropy
in the final state. Zel'dovich and Raizer [1] discuss the role of dissi-
pative processes in the shock front, demonstrating that while the net
entropy difference between the initial and final states is independent
of the details of these processes, the spatial width and structure of the
front depend upon the viscosity and thermal conductivity of the fluid.
In particular, the viscous shock front width is proportional to the coeffi-
cients of viscosity and thermal conductivity, each of which is proportional
to molecular mean free path in the limit of gas or dilute fluid behavior.
For the practical purposes of most experimental measurements of pres-
sure and density, the shock front is treated as a simple surface of dis-
continuity in the properties of the material. The present study considers
the applications of shocks in solids, in which the details of the scale
and mechanism of the shock front rise may differ from the gasdynamic case.
In typical experiments with solids, the shock front may be as narrow as
several atomic lattice spacings, or much larger if rate-limiting structure
changes occur. Nevertheless, the stability of the quasi-discontinuous
steady shock outlined above allows the final states of pressure, density
and energy to be determined from considerations independent of the details

of the front. The locus of such final states will be referred to as the

) TOA
-) |
@ -~ H———# shock velocity, u
5 particle | Ys
74 velocity,
2 Up |
a |
LF Po al
final initial
statei state O
Distance —>

Figure 1-1. Schematic profile of pressure and flow in steady
shock front. Shock front propagates into undis-
turbed material at velocity u,, leaving material
at pressure P, and moving with mass velocity Up:
Dashed lines represent boundaries fixed in the
material and moving with the mass velocity.

-4-
Hugoniot or shock adiabat of a given material.

In considering the motion of mass under the influence of a shock wave
moving into undisturbed material at velocity us» the final velocity of
material behind the front or the particle velocity will be denoted by a.
Vv denotes the specific volume of a given state and is the reciprocal of
the density p. The conservation of mass in the flow of material through
the shock front as shown in Figure 1-1 requires that the flux of mass
into the leading edge of the front equals the flux of mass emerging in
the final state. That is,

Pou, = py (u.-u)). (1)

Now consider the region between the dashed lines in Figure 1-1
including the shock front. The net stress on the cross section of this
region must equal the rate of momentum per unit area appearing within the

boundaries. This gives rise to the second conservation equation,

sp
Finally, the rate at which work is done on the moving boundary is

equal to the time rate of change of the kinetic plus internal energy of

the material within the region. Therefore,
= 2 ~
Puy, Pou, lu5/2 + (E,-E))], (3)

where E is the internal energy per unit mass. These three equations
involve the five quantities Us» Up» Pi Py and E, appropriate to the
final state. This means that specification of any two of these quanti-
ties suffices for a complete description of the Hugoniot state, and in

particular, an experimental measurement of the kinematic parameters us

and 4, for a shock wave, allows the direct calculation of pressure,

-5-
density and internal energy in the Hugoniot state.

Rearrangement of the three conservation relations yields

- Py-Po
us — Yo Vyo-v, ° (4)
ue ¥(P{-Po) (Vo-Vi) (5)
and
E - Ey = $(P,4P9) (Vo-V2) (6)

which are the familiar forms of the Rankine-Hugoniot relations. While

the shock compression process is adiabatic, it is not isentropic since

it is accompanied by a large amount of irreversible heating. This is
evident not only from a consideration of the discontinuous shock transi-
tion but also upon examination of the internal energy rise given in
equation (6). As illustrated graphically in Figure 1-2, the internal
energy jump, which is numerically equal to the area of the shaded triangle,
is greater than the area under any hypothetical adiabat (fav) connecting
the initial and final states.

The above derivation has referred throughout to the hydrostatic pres-
sure P, appropriate to an ideal fluid with no shear strength. It should
be emphasized that the Rankine-Hugoniot equations apply with equal validity
for solids as well as fluids of arbitrary rheological properties. When
the stress component along the direction of shock propagation replaces the
hydrostatic pressure, the above derivation remains valid. The one-dimen-
sional symmetry of the assumed flow causes this stress component to be the
only component which enters into the mass flow, momentum or energy of the

final strained state. As a matter of practical application, the pressures

-6-

considered in the present study (105-108 bars) are so large compared with
the yield strengths of solids that the difference between the Hugoniot and
the hydrostat is negligible. Thus, in the treatment that follows, the
distinction between the pressure P and the dynamic stress will be ignored.

As seen in Figure 1-2, the actual compression isentrope of a material
lies everywhere at lower pressures than the Hugoniot at the same density,
the pressure offset between the two being determined by the difference in
thermal energy between the two states. For this reason, the pressure dif-
ference AP is called the thermal pressure difference between the two
states. The zero point of thermal pressure at a given volume lies on the
cold compression isotherm at absolute zero temperature, since the pressure
on this zero isotherm is due to the elastic deformation of the cold crystal
lattice with no thermal component (except for pressure arising from the
volume dependence of zero-point quantum oscillations).

Obtaining the high-pressure equation of state of a given solid then
reduces to the separate problems of the nonthermal elastic pressure com-
ponent and the thermal ptessure. In experimental practice, the compression
isotherm is difficult to obtain except at relatively modest pressures,
while the Hugoniot curve is routinely measured for most solids to pressures
of several megabars (1 megabar = 100 GPa ~ 10° atmospheres). Therefore,
in characterizing the complete equation of state of a solid, we need to
determine the relationship between thermal pressure and thermal energy at
a given volume. In short, a thermal equation of state of the form

Pe P thermal ©=*¥) + Pero) (7)
is sought.

Consider a crystalline solid which consists of N atoms within a total

Pressure, P

- Hugoniot

isentrope

isotherm

Figure 1-2.

Specific volume, V

Relation of shock adiabat (Hugoniot) to equilibrium
curves of isothermal and isentropic compression.
Hugoniot energy 1/2 P, (Vy-V,) is given by area of
shaded triangle. AP denotes pressure difference
due to thermal contribution.

~g-
volume v. The solid may vibrate with 3N normal mode frequencies in the
semiclassical harmonic oscillator model. The solid may then be described
as an ensemble of quantum oscillators, characterized by 3N quantum num-
bers ny for the mode frequencies V5 The total internal energy of
this solid is

3N

u=u,+ } njhv; ; (8)

jel

where Uy is the cold compression energy of the lattice at absolute zero,

plus the zero-point quantum oscillator energy
U7 L Fh, - (9)

Here and below, h is equal to Planck's constant.
The statistical mechanical partition function for this system is
given by a sum of the terms exp (~€ ;/kT) for e; the energy of the qth

microstate accessible to the system. Thus,
z=) ye. J exp(-)n hv, /kT) exp (-Uy /kT) . (10)
Ry Np 13N j
Expressing this sum as the product of each of the independent sums over

the ys

Z = exp(-Up/kT) } exp(-nyhv,/kT) + + +} (-ngyhvay/kT). (11)
my 13N

Each of these sums is evaluated as a geometric series, yielding

3N
Z = exp(-U,/kT) T [1 - exp(-hv,/kT)]"*. (12)
j=l
Given this partition function, we may write an expression for the

Helmholtz free energy,

F = -kT &nZ =U, + ) kT en[1 - exp(-hv,/kT)]. (13)

The entropy is given by

s=- Gl (14)

Vv

and the internal energy is U=F+TS. Thus we obtain

hy,
us uO + } exp (hv, /kT) -1

(15)

for the internal energy of the solid in thermal equilibrium at temperature T.

Similarly, the pressure may be evaluated from F using

=. (oF
pP=- (J) (16)
which gives -h V5)
dU av
Prova Tt L exp(hv,/kT) - 1 (17)
or
1 hy,
Pe Pero’) + vi v5 exp (hv, /kT) - 1 (18)
where
y v4 d &£nv,
V5 on i ~~ G &nv ) ° (19)

The approximation which was originally suggested by Griineisen [2,3] is
that each of the V5 undergoes the same fractional change for a change

in volume. Note that for a perfectly harmonic solid, all the V5 vanish
and there is no thermal pressure or thermal expansion. In this sense, the

V5 are a measure of the anharmonicity of the solid.

If the Griineisen assumption is made and the V; are all equal, they
factor out of the summation, yielding a simple relationship between thermal
pressure and thermal energy. In this approximation,

Y hvy
P =!t}
thermal v F exp (hv, /kT) - 1

(20)

-10-
and we obtain

- = 7
Vv Vv E

P thermal ~ yy thermal ~ (21)

thermal
which is the Mie-Griineisen equation of state. In the Mie-Griineisen formu-
lation, y is assumed to be a function only of volume, so that the ther-
mal pressure of a solid is assumed to be directly proportional to the
thermal internal energy at fixed volume.

This equation of state is widely used as a description of the solid
at high pressures, with y treated as an empirically determined parameter.
Within the assumption that Mie-Griineisen is valid, y may be derived from

thermodynamic properties of the solid. If equation (21) is valid, then
-vfoh) -
y(V) = VGe oVK,/C.. (22)

This is a straightforward application of thermodynamic identities, where

o is the thermal coefficient of volume expansion, K, is the isothermal
bulk modulus, and V_ and Cy are the specific volume and heat capacity
per unit mass respectively. Thus the formal Griineisen parameter is deriv-
able from macroscopic material properties that are easily measurable, at
least at standard conditions of pressure and temperature.

In practice, the Mie-Griineisen equation is commonly assumed to hold
for general substances, even in the case of liquids for which any argument
about vibrational modes breaks down. It is interesting to note that for-
mally the Mie-Griineisen equation of state holds for the ideal gas, with
Y equal to a constant whose magnitude depends upon the ratio of specific
heats. The Mie-Gruneisen equation breaks down when the thermal pressure
exhibits other than a simple proportionality to internal energy, and this

failure is sometimes expressed by allowing a temperature (or energy)

-1li-
dependence for y.

In applying these results to the shock wave equation of state, it is
apparent that a knowledge of y(V) allows the calculation of the pressure
offset between the Hugoniot and the isentrope, since the internal energies
along each of these curves is known as a function of V. Similarly, given

a compression isotherm, its internal energy is given by

Vv
ye,
E - Ey = | (Ty vr - P)dv (23)
Vo

from a TdS thermodynamic relation.

Theoretical Shock Temperatures

It is apparent from the above discussion that the temperature of a
Mie-Griineisen material in a state on the Hugoniot curve will depend upon
the energy difference between the Hugoniot state and the isothermal state
at the same volume, with this difference depending upon Y. Furthermore,

C_, the specific heat at constant volume, will determine the Hugoniot

Wy?
temperature, given this energy difference.

The simplest scheme for performing this calculation, which was given
by Walsh and Christian [4], requires the imposition of some restrictions
on Y and C,, and it is limited in the range of conditions under which
it is applicable. The Walsh and Christian analysis begins with the thermo-
dynamic identities,
TdS = CAT + ne dv, (24)

and

TdS = dE + Pdv. (25)

~12-
Now for states on the Hugoniot,

BE - Ey = 5 PCVp-¥), (26)

where the initial pressure Py) is taken as zero. If equation (25)
describing the first law of thermodynamics is integrated from the initial
state (zero subscripts) along the path described by the Hugoniot to an

ultimate state of P, V, and S, we have

S Vv
| Tas =< P(Vy-V) + | Pav. (27)
So Vg
Differentiating with respect to V, we define
= | Tas = $ S P(v)(vy-v) +5 PCY) = EW), (28)
So

which is a function of V obtained directly from the Hugoniot curve, P(V).

Now if the specific heat may be regarded as constant, equation (24) yields

S T V C
_ Vv
fras= oc, [ ar+ | m 7 dv, (29)
So To Vo
and
yc
d _ _ aT v
av | TdS = f(V) = C, av + 7 T. (30)

This is a first-order ordinary differential equation for T(V), whose

solution is given by

V v v'
T(V) = exr(-| (y/v')av')} {T, + | ie expt| (y/v)dv]dv"}. (31)
Vo v Vo

-13-

An additional result of the Walsh and Christian formulation is inde-
pendent of restrictive assumptions about cy. If y(V) is correctly given
by the Mie-Griineisen equation, then the temperature gradient measured along
the Hugoniot curve is

Vv

dv

(32)

1 dP] 1
E (Vo-V) wl, an

The final term within the brackets which involves y is typically small
(~10%) compared with the first two pressure terms, so it is apparent that
under most circumstances, the effect of Cy on the slope of the tempera-
ture Hugoniot is considerably greater than that of y.

The Walsh and Christian scheme for calculation of shock temperatures
is applicable for cases in which the quantities in equation (31), including
vy; the Hugoniot pressure, and its derivative are continuous properties
of a single phase. If the material under consideration undergoes a shock-
induced transformation to a new phase, the above derivation breaks down.

As illustrated in Figure 1-3, when a phase transition occurs under
shock wave loading, the locus of final shocked states passes through a
region of mixed phases over a range of pressures (and temperatures). This
contrasts with the behavior observed during isothermal compression, in
which case the passage through the mixed phase regime occurs at constant
pressure. Under isothermal compression, the path through the mixed phase
region represents a locus of equilibrium states between two coexistent
phases at constant T. The Gibbs phase rule thus requires the pressure
to remain fixed as the mole ratio of phase A to phase B varies. The
Hugoniot curve, however, does not describe an isothermal or even an

equilibrium path, but merely a locus of final shocked states, so that a

-14-

A \ Hugoniot

oO
”~ \
@®
me }
@ phase B
QO isentrope
or
isotherm

vi V,

Specific volume, V

Figure 1-3. Hugoniot curve with phase transition. High-pressure
phase has metastable zero-pressure specific volume
of V,.

~15-
finite range of pressures occurs over which the Hugoniot energy induces
only partial transformation from initial phase A to final phase B. A more
detailed description of this behavior under various conditions of density
contrast and latent heat between phases is given by McQueen et al. [5].
Since continuous integration along the Hugoniot through the mixed
phase regime is not applicable, an alternate approach to the calculation
of Hugoniot temperatures is required. As illustrated schematically in
Figure 1-3, we may construct, at least in principle, an isotherm or isen-
trope of compression of the high-pressure phase from a metastable state
at standard pressure and temperature, and specific volume Vo- Given such
a reference curve for the high-pressure phase (denoted by the subscript
"R"), the Mie-Griineisen equation gives the energy difference between the

Hugoniot and reference curve at a given volume as,

=” _
Ey - ER = 7 (Py PR: (33)
The temperature Th in the Hugoniot state is then obtained by solving
Ty
BE, - ER = | C dT. (34)
TR

Here, C, and Y assume values appropriate to the new phase and are
assumed known. When the reference curve is the isotherm, the reference
temperature IR is simply Tp), the standard state temperature (usually

298 K). In the case that the isentrope of compression is used as a refer-

ence curve, TR becomes Vv

T, = To exo (-| (y/v) dv) , (35)

which is obtained by setting TdS = 0 in equation (24).

-16-

Since in the vast majority of cases, the Hugoniot curve is the only
experimentally determined equation of state at very high pressures, the
reference curve (either isotherm or isentrope) must be calculated. We will
consider first the calculation of the isentrope, assuming that y(V) for
the high-pressure phase is a known function. Equating the Hugoniot. energy
at some arbitrary volume with the energy of isentropic compression along
the unknown adiabat P,(V) plus the energy of heating the material at

constant volume to the Hugoniot pressure Pov) »

Vv
tp w-v) = E - | Poav + (PLP). (36)
2H’ 9 tr _3 -Y “HOS
Vo
Here, E represents the specific energy added to the stable low-pressure

tr

phase in order to transform it into the high-pressure phase at &.T.P. This
integral equation for the unknown curve P,(V) may be solved numerically,
for example, by approximating it with a centered difference equation after
the manner of McQueen et al. [5]. Alternatively, differentiation of this

equation yields

dP dP
dv dv Vv

dPy

dV
avi re

Vv _ on -
avy) Py?) + malse v)

- PL - 2°, . (37)
This ordinary differential equation for P,(V) is readily solved by numeri-
cal integration techniques, for example the Runge-Kutta method, and such
methods are well suited to computer or calculator solution.

A practical complication presents itself in the actual calculation of
a high-pressure isentrope in this manner. In most cases (for example, see
the calculations for SiO, and MgySi0,) the zero-pressure volume of the

metastable phase is at a larger volume than the beginning of the high-

pressure phase region of the Hugoniot curve. This means that unless

-17-

equation (37) is integrated from a sufficiently high starting pressure,
the integration is performed through a region where PA Cv) describes the
mixed phase regime, and equation (36) is no longer valid.

This problem is avoided by replacing the Hugoniot POY)» which is
centered on the initial low-pressure phase, with the metastable Hugoniot
PCV). This is the locus of shocked states that would be achieved if the
initial material was metastable high-pressure phase. This metastable
Hugoniot is calculable from the principal Hugoniot by a straightforward
application of the Mie-Griineisen equation and a knowledge of y(V) and
AE This calculation is detailed by McQueen et al. [5,6], but for the
present discussion we will specialize to a particular case. Once the
metastable Hugoniot is determined, calculation of the isentrope from
equation (37) may proceed unhindered, since PCV) now refers strictly
to the phase of interest.

It will be convenient to consider the special case of a metastable
Hugoniot curve for material which is in the transformed phase (of specific
volume Vj) but which has been given an initial porosity so that its bulk
volume equals V), the specific volume of the low-pressure phase. In
this special case, the pressure offset between the principal Hugoniot
and its metastable counterpart assumes a particularly simple forn.

Referring to Figure 1-4, the energy of a state on the principal
Hugoniot (state 1) is simply

E,(1) = 5 Py(L) (Vp-¥)- (38)

On the other hand, the energy of a sample which has been prepared in the
high-pressure phase and shocked from a porous initial volume Vp) is

Ey(2) = Epp + 5 Py (2) (Vo-V). (39)

Pressure, P

-18-

principal Hugoniot, PR

metastable Hugoniot, P,

Figure 1-4.

Vo Vo

Specific volume, V

Metastable high-pressure phase Hugoniot derived from
principal experimental Hugoniot. When metastable
initial phase has porous volume Vj), the pressure
offset Pa - P, is simply proportional to the
transition energy Ey

-19-

Taking the difference between these energies and equating it to the Mie-
Griineisen offset, we obtain an expression which solved for the pressure
difference gives

' -~ ¥ ¥ _ -1
Py Py wy Beg ~ 3 [(V0/M) - 1. (40)

Since the principal Hugoniot P is experimentally measured, -appli-

cation of equation (40) allows the direct conversion of this curve into
Pr The metastable Hugoniot Pa passes in principle through zero pressure
at volume Vo> since negligible pressure is required to collapse the pore
space and bring the material to normal density. The effect of the initial
porosity is instead manifested in the subsequent compression and its
higher thermal pressure (see, for example, Al'tshuler [7]).
Recapitulating, the metastable Hugoniot obtained as described above
and fit with an appropriate analytic interpolation formula is used in
equation (37) to solve for the high-pressure isentrope P.(V). Ete enters
directly into Pe and this transition energy thus has an immediate and
important effect upon the position of the calculated isentrope. With
this isentrope in hand, it is finally a simple matter to apply equations
(33) and (34) with a suitable model for the specific heat C_ to obtain
the Hugoniot temperature Th at each value of V in the phase of interest.
The foregoing discussion applies with equal validity to materials which
do not undergo a shock-induced phase change, but since this derivation is
based upon the same Mie-Griineisen assumptions as the single-phase Walsh
and Christian calculation, their results are identical in that application.
For the sake of completeness, the following equation replaces (36)

in the case that the reference curve is an isotherm instead of an adiabat.

The differential equation for the isotherm is derived from

-20-

1» (v,-v) = AE lew vy wy al py (41)
2 “HH. 0 tr , or ov y HT? —
Vo

where the subscript "I" indicates the isotherm. The remaining analysis
proceeds by analogy with the isentropic case. The temperature of an
equilibrium Hugoniot state in the mixed phase region may be calculated
assuming that the reference isotherms of the low- and high-pressure phases
have already been determined. As detailed by Ahrens et al. [8], two
independent equations in the two component phases are derived which may be
solved for the unknowns T,, and the mass fraction of material transformed

to the high-pressure phase.

Experimental Shock Temperatures

As indicated in the above derivations, knowledge of the parameters
of the thermal equation of state and heat capacity of a given material
allow the calculation of shock temperatures for a variety of phase rela-
tionships. Conversely, experimental measurement of temperatures along
the Hugoniot may be used to characterize the equation of state, beyond
the pressure-volume information obtained from conventional Hugoniot
measurements.

As pointed out earlier in this chapter, the measured temperature
gradient along the Hugoniot provides a strong constraint on the specific
heat Cc, of the phase in question, while y is not so well bounded. On
the other hand, information about the magnitude and variation of the
Griineisen parameter may be derived indirectly from shock temperature
measurements. The case of Si0, (Chapter 4) illustrates this possibility,

as the configuration of phase boundaries and transition energies in the

-21-

silica system, found through Hugoniot temperature measurements, have allowed
correct values of y in the stishovite and newly identified liquid phases
to be estimated. Furthermore, in cases for which y has been previously
evaluated under the assumptions of the Mie-Griineisen equation, experimental
temperatures can provide a check on the consistency of these assumptions
with the actual case. Departures from ideal Mie-Grtineisen behavior may be
thus detected through anomalous temperature dependence in y, as is dis-
cussed in the case of shock temperature results for liquid H,0 (Chapter 5).

Not to be neglected is the importance of Hugoniot temperature measure-
ments in the detection and characterization of first-order phase trans-
formations, including polymorphic solid-solid transitions, as well as shock
induced melting and freezing. The standard condition free energy differ-
ence E+ between competing phases quantitatively influences the position
of the measured temperature Hugoniot, and the existence of phase equili-
brium boundaries can profoundly affect the qualitative nature of the
observed temperature trajectories. In some cases, the temperature sig-
nature associated with the heat of transition is the only observable indi-
cation of the phase change under the difficult measurement conditions of
the shock wave experiment.

The nature of shock wave experiments make the task of temperature
measurement a formidable one. The short time scales involved (typically
107” seconds or less) present a problem for thermometry or thermocouple
techniques which require an appreciable time to reach thermal equilibrium.
Furthermore, in many cases, the presence of an in situ gauge for tempera-—
ture measurement in the shock-compressed material can give rise to

reflected shocks and rarefactions which seriously disturb the desired

~22—

state (and temperature) in the material for the length of the experiment.
For these reasons, the approach to temperature measurement in high-pressure
shock experiments has been predominantly through the measurement of thermal
radiation.

Shock-wave investigators have long observed that transparent dielec-—
trics shocked to sufficiently high pressures will become self-luminous in
the compressed region behind the shock front. This radiation escapes
through the transparent unshocked layers of the sample, and in many cases
the spectrum of emitted light is continuous and characteristic of a thermal
(blackbody) source. Early experiments designed to use this radiation for
Hugoniot temperature determinations were performed by Kormer [9,10], using
alkali halide crystal specimens. These temperature determinations were
made by measuring the radiation intensity versus time at two visible wave-
lengths. The Kormer analysis necessarily assumed the blackbody nature of
the radiation, but the results obtained were internally consistent and
indicative of the validity of the optical pyrometry technique.

Considerable interest has also centered on the problem of shock tem-
perature measurements in opaque specimens, and experimental research in
this direction has been along two lines. The first has been the measure-
ment of residual post-shock temperatures at the free surfaces of opaque
samples subjected to shock loading and subsequently released to zero
pressure. This work was done by Raikes [11] for a variety of metals and
silicate minerals, and the degree of residual temperature rise was used
to estimate indirectly the thermal nature of the shock compressed state.
The second line of experiments has examined the thermal radiation from

the impedance-matched interface between an opaque (metallic) sample and

-23-

a transparent "window" layer. The function of the transparent window is
to allow radiation from the shocked metal layer to be detected, while
retaining the sample in its elevated pressure state. This work has been
described by Grover and Urtiew [12,13] and forms the basis of some of the
present series of experiments, as described further in Chapter 3.

The present chapter is intended as an introduction and to provide
motivation for the measurement of shock temperatures. The succeeding
chapters will discuss the techniques and results coming from this research,
discussing their implications both for the physics and chemistry of high-
pressure shock phenomena generally, and for the properties of the specific
materials studied here, including those materials which are of importance

in geophysics.

3.

10.

li.

12.

13.

-24-

REFERENCES

Zel'dovich, Ya. B., and Yu. P. Raizer, Physics of Shock Waves and
High-Temperature Hydrodynamic Phenomena, edited by W. D. Hayes
and R. F. Probstein, Academic Press, New York (1966).

Grimeisen, E., Handbuch der Physik, 10, 22 (1926).

Slater, J. C., Introduction to Chemical Physics, p. 219, McGraw-
Hill, New York (1939).

Walsh, J. M., and R. H. Christian, Equation of state of metals
from shock wave measurements, Phys. Rev., 97, 1544-1556 (1955).

McQueen, R. G., S. P. Marsh and J. N. Fritz, Hugoniot equation of
state of twelve rocks, J. Geophys. Res., 72, 4999-5036 (1967).

McQueen, R. G., J. N. Fritz and S. P. Marsh, On the equation of
state of stishovite, J. Geophys. Res., 68, 2319-2322 (1963).

Al'tshuler, L. V., Use of shock waves in high-pressure physics,
Sov. Phys. Usp., 8, 52-91 (1965).

Ahrens, T. J., C. F. Petersen and J. T. Rosenberg, Shock compression
of feldspars, J. Geophys. Res., 74, 2727-2746 (1969).

Kormer, S. B., M. V. Sinitsyn, G. A. Kirillov and V. D. Urlin,
Experimental determination of temperature in shock-compressed
NaCl and KCl and of their melting curves at pressures up to
700 kbar, Sov. Phys. JETP, 21, 689-700 (1965).

Kormer, S. B., Optical study of the characteristics of shock-
compressed condensed dielectrics, Sov. Phys. Usp., ll, 229-
254 (1968).

Raikes, S. A., and T. J. Ahrens, Post-shock temperatures in minerals,
Geophys. J. R. Astr. Soc., 58, 717-748 (1979).

Urtiew, P. A., and R. Grover, Temperature deposition caused by shock
interactions with material interfaces, J. Appl. Phys., 45, 140-
145 (1974).

Grover, R., and P. A. Urtiew, Thermal relaxation at interfaces
following shock compression, J. Appl. Phys., 45, 146-152 (1974).

-25-

Chapter 2

THE OPTICAL PYROMETRY TECHNIQUE IN

SHOCK COMPRESSION EXPERIMENTS

Introduction

Among the principal methods of modern physics for the study of the
equations of state and physical properties of materials at high pressure
and temperature is the technique of dynamic compression by shock waves.
Several authors [1,2] have reviewed the techniques of shock compression
of condensed matter and discussed the information which may be obtained
in experiments at pressures of 100 GPa or higher.

A major difficulty with the use of pressure-density-energy equation-
of-state data obtained from shock wave experiments on various elements
and compounds [3,4] and with understanding the thermodynamics and inter-
atomic dynamic behavior of these materials is the general lack of knowledge
of their temperatures. If the Mie-Griineisen equation of state is assumed
for a material, then its shock temperature Ty is given by the simultaneous
solution of the equations which are summarized in the preceding chapter.

As discussed there, the final temperature of the shock state along the
Hugoniot curve of a given material is controlled by the specific heat and
Griineisen parameter of that material as well as by the energetics of any
shock-induced phase transformations that may occur. An experimental
measurement of T can therefore provide constraints on Cc, and jy,

both of which are essential parameters in thermal equations of state.

-26-
Such measurements aid in an understanding of lattice anharmonicity [5],
melting [6,7], and other aspects of vibrational lattice dynamics.

The present chapter describes a fast (~5 ns) time response optical
pyrometer system which has been applied to the measurement of shock tem-
peratures in transparent materials to pressures of 175 GPa and over. the
temperature range of 4000-8000 K. The pyrometer is designed to be used
in conjunction with a two-stage light-gas gun [8], a device which is
capable of accelerating projectiles to speeds of up to ~7 km/s. Strong
shock waves are driven into sample materials upon impact of these high-
speed projectiles in vacuums of 107? Torr.

Because typical shock experiments near 100 GPa pressure are less
than 107° s in duration, the only practical means of temperature deter-
mination is a time-resolved measurement of the thermal radiation emitted
by the sample. Use of optics and solid-state detectors in the visible
wavelength range permit temperature measurements between approximately
2000 K and 10° K. These limits are determined by the lower sensitivity
limit of the silicon detectors and by the increasing insensitivity of the
slope of the visible Planck radiation spectrum to changes in temperature,
respectively. Pioneering work in the measurement of shock temperatures
by optical techniques was done by Kormer [6,7]. The present work incor-
porates substantial improvements in time resolution and spectral coverage
over previous studies and so allows a wider range of materials and pres-

sures to be studied.

Light-Gas Gun Experiments

The present series of shock wave experiments has been carried out

~27-
jointly with the collaboration and support of the Lawrence Livermore
Laboratory shock physics group, directed by W. J. Nellis, The principal
apparatus for the generation and characterization of shock waves in the
100 GPa pressure range is the Livermore two-stage light-gas gun.

The design and principles of operation of the two-stage pun are
detailed by Jones et al. [8], and the following is a general description
of the technique. Figure 2-1 is a schematic diagram of the operation of a
light-gas gun. The overall length of this device is approximately 23 meters,
and acceleration of the projectile to the desired velocity is achieved in
two stages.

In the first stage, expanding combustion products from the burning of
approximately 1 kg of gunpowder accelerate a massive (~7 kg) piston down
the length of the pump tube. The pump tube is initially filled with hydro-
gen gas at a pressure of approximately 10 bars, and as the piston moves
in the pump tube, this gas is rapidly adiabatically compressed. At a fixed
gas pressure near 1400 bars, a rupture valve opens, initiating the second
stage.

A 20 g mass projectile of 28 mm diameter is accelerated through the
length of a smooth bore launch tube (or barrel), reaching a final velocity
of up to 7 km/s, depending upon the initial explosive mass. The projectile
consists of a flat metallic impactor plate, molded into the leading face
of a lightweight plastic sabot which acts as a gas seal. The impact of
this plate with a planar target induces a flat shock front in the target
as well as the flyer plate. The lateral dimensions of the uniform one-
dimensional flow are determined by the width of the flyer plate (~25 mm)

and the duration of pressure application is limited by the finite thickness

-28-

Impact chamber
(evacuated) / Target

Breech a tube Projectile Barrel nm om

1 1

i ! '
——WY7z _
<-C. G— Piston“, gas i |
1 A LLL I
J Rupture valve !

C. G.= Combustion

Gases Flash X-ray tubes
tt
—C.G——> Pistd Ze, O+—» i
{ | Projectile
7 ———— ‘free flight
‘in vacuum

i 0

Figure 2-1. Schematic operation of two-stage light-gas gun.
Expanding gases from burning propellant drives
piston, compressing hydrogen gas. Rupture valve
opens, accelerating projectile through the barrel.
Projectile velocity is determined via timing of
flash x-ray firings.

~29—
of the plate.

The diagnostic measurements in such an experiment include measurement
of the projectile impact velocity and the shock velocities or other physical
quantities of interest which pertain to the target. Projectile velocity
is measurable to an absolute accuracy of ~0.1%, utilizing flash x-ray
radiography of the projectile in flight. The time between x-ray "snapshots"
of the flyer at positions typically a few tens of centimeters apart are
accurately measured in order to make the velocity determination.

In the course of conventional Hugoniot equation-of-state experiments,
the shock velocity is measured as the wave passes through the target. When
the Hugoniot equation of state of the impactor material is already known,

measurement of the shock velocity u, and the flyer velocity are sufficient

to determine the particle velocity Up > and thus the complete Hugoniot
P-V-E state. This is accomplished using the impedance match method described
by Al'tshuler [2].

The present set of experiments has been designed specifically to deter-
mine the temperature of the target material under shock compression, assum-
ing that the Hugoniot equation of state of the studied material is already
known from previous experiments. With the sample Hugoniot known, all that
is required to characterize the pressure state in the sample is a measure-
ment of the impactor velocity. This provides the pressure scale for each
measured Hugoniot temperature point obtained in a given shot. Additionally,
an unexpected bonus of information is often obtainable from the shock tem-
perature experiments. In many materials, the time-resolved temperature

records provide an accurate measure of the time of shock wave transit through

the sample, and thus they allow an independent check on the shock velocity

-30-
and Hugoniot of the sample. This technique is described in the discussion
of results from SiO, samples (Chapter 4), as it proved to be ‘particularly
useful in that instance.

In other experiments, investigators have undertaken measurements of
many physical properties including electrical conductivity [9], x-ray dif-
fraction [10,11], optical characteristics [7,12] and others during the
period of shock compression lasting a few hundred nanoseconds. The follow-
ing is a description of a newly developed multiwavelength pyrometry tech-
nique for the measurement of shock temperatures in light-gas gun driven

experiments.

Pyrometer Design

The pyrometer design consists of an optical subsystem for light col-
lection and spectral filtering, and a detection subsystem consisting of
the photodetectors and associated recording electronics.

As shown in Figure 2-2, the optics are located outside the impact tank,
protected by polycarbonate windows of 10 mm thickness. Six channels view
the sample in a two-by-three rectangular array, with a window center-to-
center distance of 9.2 cm. Each of the optical channels has a 5-cm-diam
achromatic objective lens of 5l-cm focal length which provides parallel
light to the filter which follows in the optical path. Each filter is a
narrow-band interference filter with approximately 50% peak intensity trans-
mission and ~9-nm half-height bandwidth. The six channels span the visible
and near infrared spectrum, with filters centered near wavelengths of 450,
500, 550, 600, 650, and 800 nm. Finally, an achromat of 19-cm focal length
in each channel provides a filtered image of the target source at the

sensitive surface of the respective photodetector.

~31-

Impact
7] chamber
Lens /interference
filter

assemblies

Output to — Polycarbonate
amplifiers & op _
oscilloscopes “HY. _

~~~ & Target
assembl
— i y
HP 5082-4207 Projectile
Photodiodes flight

AD [le

Figure 2-2. Schematic design of pyrometer. Optical components
exterior to evacuated impact chamber deliver filtered
images of the target to photodetectors.

-32-

The basic detector consists of a Hewlett-Packard 5082-4207 PIN silicon
photodiode, which is reverse biased at 10 V. The diode has an active area
approximately 1 mm in diameter and produces a nominal photocurrent of
0.5 mA/mW for radiation of wavelength 770 nm. In the experimental con-
figuration, the detector has a rated speed of response of about 1 ns. The
detector is sensitive to light of wavelengths between about 400 and 1000 nm.
Since the optical system produces an image of the sample which is several
millimeters wide at the detector, the photodiode output current is propor-
tional to the power per unit area radiated by the sample. It is assumed
that each detector views the same region of the sample and that the radia-
tion flux is constant across the detected region. The validity of this
latter assumption has been checked in the case of crystalline quartz
(Si0,) as the investigated sample. The details of this work are discussed
in Chapter 4.

As shown in the schematic diagram of Figure 2-3, the photodiodes in
each channel act as current sources driving 50 2 impedance low-loss trans-
mission lines. The signals are recorded on high-speed oscilloscopes, in
this case Tektronix 585 and 7903 models. In experiments with small
expected signals (less than a few mV), intermediate stages of amplifica-
tion are employed. The Hewlett-Packard 8447 A wide-band amplifier has
been used for this purpose. The recording oscilloscopes are triggered
at signal onset by the impact-generated shock wave closing self-shorting
electrical contacts [8].

Figure 2-4 illustrates the layout of a typical target in a shock
pyrometry experiment. An expendable aluminized front-surface mirror

mounted behind the sample and base plate reflects radiation to the optical

-33-

External .
+l0V. r---> Amplifier- —5 Oscilloscope
1 (Optional) @)
ore |
Photodiode O.l_F d
= - 4) (Foo
502 transmission line 2

tkQ Foe

Figure 2-3. Detector circuit for typical pyrometer channel. Remote
recording oscilloscopes receive signals via 50 2 cable
with ~200 ns delay.

Expendable
mirror

To

Figure 2-4.

—34-

Transparent sample

or anvil
Metallic
base plate
Edge mask
——)
Ai
wer Fa
Torr ttcrrs cass -- <—
! (4 Direction
! _ §_4 of flight
e =
v Self-shorting Projectile
detector trigger pin
array
Configuration of target in shock pyrometry experiment.

Radiation from shock compressed material emerges from
rear surface and enters pyrometer optics.

-35-

channels. In the case that the investigated sample is a liquid, the
target is modified to include a containment chamber and a radiation
window. Alignment and focusing of the optical and detector systems
prior to an experiment is achieved with the target in place. A compact
light source is affixed to the target rear surface and focusing is
accomplished with the interference filters removed. Positioning of the
detectors within ~1 mm of the focal plane provides a detected flux
reproducible to a few tenths of a percent.

Calibration of the pyrometer requires a determination of the sensi-
tivity of each channel in its actual geometric configuration. A calibrated
tungsten ribbon spectral radiance source is used in place of the target.
The voltage output in this de calibration is then used to find the voltage
response for a given sample spectral radiance in power per unit area and
solid angle per unit spectral bandwidth. Assuming that the detector effi-
ciency is the same for transient and static illumination and that its
intensity response is linear, the voltages measured during a shot may be
interpreted directly in terms of radiation output. The calibration lamp
used is a General Electric commercial type having a tungsten SR-8A filament.
The lamp is calibrated by the Eppley Laboratory, Inc., Newport, RI, against
National Bureau of Standards calibrated standard sources. Figure 2-5 shows
the signals expected for a blackbody source as a function of temperature,
as measured for two of the actual pyrometer channels. The uncertainty in
radiance calibration by the tungsten ribbon standard technique is approxi-
mately 2%. More detailed descriptions of the calibration equipment and
procedures as well as a documentation of the operational details of the

present system appear in Appendix I.

-36-

1 T T T T T

Predicted Blackbody
Detector Response Curves
Signal
(VOLTS)

107!

1072

io?

i 1 ! ! ! n
4000 6000 8000 10000

Temperature (K)

1074

Figure 2-5. Pyrometer predicted response to ideal blackbody source.
Wavelength channels 450 nm and 800 nm are illustrated.

-37-

Experimental Results and Data Treatment

The pyrometer has been primarily used to determine shock temperatures
in initially transparent materials. This is because radiation from the
heated material behind the shock front can escape through the unshocked
transparent material, allowing the light to be detected during shock transit
through the sample, rather than only at the instant of shock arrival at
the free surface.

The materials which have been studied to date by this technique
include NaCl, H,0, Si05, and Mg,Si0,. NaCl is a material whose shock
temperature has been the subject of earlier work by Kormer [6,7] and it
provides a point reference from which to extend these studies. SiO, and
Mg SiO, (quartz and forsterite) are minerals whose geophysical importance
makes the characterization of their thermal equations of state significant.

Figure 2-6 shows a typical experimental oscilloscope record from an
experiment with quartz. The recorded light intensity rises abruptly as
the shock front enters the sample, and subsequently rises more gradually,
approaching an asymptotic value. Upon arrival of the shock front at the
sample free surface, the recorded intensity immediately relaxes to a value
characteristic of the residual zero-pressure state of the sample. Figure
2-6 presents a typical experimental record; however, different materials
at various Hugoniot pressures have shown different detailed behavior.

Some materials do not show the gradual intensity rise, but rather exhibit
constant brightness throughout the shock transit. Im many experiments,
an initial brief flash is observed as an overshoot in the records and

is believed to be an effect of interfacial gaps between the sample and

base plate.

-38-

O.| pesec

Figure 2-6. Typical oscilloscope record from one channel in shock
pyrometry experiment. Example is from a shot on fused
quartz at ~80 GPa pressure.

—~39-

Considerable interest centers on the origin and nature of the radia-
tion observed in these experiments, since its interpretation in terms of
the Hugoniot temperature hinges upon questions of thermal equilibrium and
emissivity. As the observations in the following discussions suggest,
the measured radiation does indeed appear to display the intensity and
spectrum of a thermal radiator with a large emissivity (i.e., nearly a
blackbody). This raises the problem of explaining how a material which
is initially a transparent insulator abruptly changes character, becoming
an opaque blackbody radiator. The solution to this problem may be related
to the very short rise and fall times observed for the shock-induced
luminescence.

Apparently, the abrupt onset and shutoff of this radiation can be
explained if the light originates in a very thin layer of material coinci-
dent with the shock front or immediately behind it. If the shock front
represents the site of copious strain-induced lattice defects, this repre-
sents a possible source of conduction band electrons and the observed
optical opacity. Theoretical arguments given in the Chapter 4 discussion
of SiO» and MgoSi0, results suggest that under most circumstances, the
time required for this defect ionization and thermal equilibration to
occur is long enough that the radiation temperature does accurately reflect
the final Hugoniot state of the compressed lattice. Exceptions to this
will occur if longer time scale changes, such as those related to a shock-
induced phase transition, take place behind the shock front. Such relaxa-
tion effects related to a phase change (fusion) have been measured in
Si02, and further discussion of this phenomenon is deferred to Chapter 4.

For the majority of cases investigated here, the assumption that the

-40-

measured radiative temperature is identical with T the Hugoniot state

temperature seems justified, at least within the accuracy of: the measurement.
Interpretation of the pyrometer signals in terms of temperature requires
comparison of the measured values of spectral radiance with a thermal radia-
tion spectrun. At a given wavelength A and temperature T, the spectral

radiance of a blackbody is given by the Planck radiation formula,

Co/AT _ 7}, (1)

Ny = C\A75e

where C, = 1.191 x 107! Wm?/sr and Cp = 1.439 x 107-2 mK. A real

source which differs from the ideal blackbody case has its spectral radi-

ance reduced by a factor e(A), the emissivity, which may depend upon

the bulk properties of the radiating material and its surface properties.
Given the measured values of Ny at six wavelengths in an experiment,

the emissivity and temperature may be simultaneously varied to obtain

the best fit of equation (1) to the data. In practice, an emissivity which

is constant or linearly varying with wavelength is used. The emissivity

is then varied to minimize the sum of the squares of deviations in tempera-

tures calculated for each channel from the mean temperature of all channels.
Figure 2-7 shows the results obtained for a SiO» crystal experiment.

The measured spectral radiance points are shown along with a Planck radia-

tion curve fit. The curve shown is for a temperature of 4625 K and a

constant emissivity of 0.68. This fit has uncertainties of approximately

24 in temperature and 7% in emissivity. Temperature determinations

above ~6000 K yield less well constrained solutions because of the relative

insensitivity of the visible spectrum shape to temperature in this region.

In summary, this pyrometry technique which has been applied to shock

compression experiments represents a potentially valuable new tool for

-41-

= 60+ ; : 7
. — i _~
> 5.57 YS 7
vo | 4 a — Quartz ;
Qo Pressure 75.5 GPa 7
x ; T=4625t80 K

4.5 4
2 Best fit curve €=0.68+0.05 i

40 pot op pp a tt

440. 500 600 700 800

A, nm

Figure 2-7. Experimental spectral radiance data for a shot on
crystalline Si0,. Blackbody fit shown with best
fit temperature and emissivity.

-42-
the exploration of high pressure shock wave equations of state. The
succeeding chapters describe and discuss the results to date which have
come from this work and are illustrative of results that can be expected

in the future as this technique finds more widespread application.

10.

-43-

REFERENCES

Ahrens, T. J., Dynamic compression of earth materials, Science,
207, 1035-1041 (1980).

Al'tshuler, L. V., Use of shock waves in high-pressure physics,
Sov. Phys. Usp., 8, 52-91 (1965).

Walsh, J. M., M. H. Rice, R. G. McQueen and F. L. Yarger,
Shock-wave compressions of twenty-seven metals. Equations
of state of metals, Phys. Rev., 108, 196-216 (1957).

McQueen, R. G., S. P. Marsh and J. N. Fritz, Hugoniot equation
of state of twelve rocks, J. Geophys. Res., 72, 4999-5036
(1967).

Barron, T. H. K., in Lattice Dynamics, edited by R. F. Wallis
(Pergamon, New York, 1965), p. 247.

Kormer, S. B., M. V. Sinitsyn, G. A. Kirillov and V. D. Urlin,
Experimental determination of temperature in shock-compressed
NaCl and KCl and of their melting curves at pressures up to
700 kbar, Sov. Phys. JETP, 21, 689-700 (1965).

Kormer, S. B., Optical study of the characteristics of shock-
compressed condensed dielectrics, Sov. Phys. Usp., 1l,
229-254 (1968).

Jones, A. H., W. M. Isbell and C. J. Maiden, Measurement of the
very high pressure properties of materials using a light-gas
gun, J. Appl. Phys., 37, 3493-3499 (1966).

Mitchell, A. C., M. I. Kovel, W. J. Nellis and R. N. Keeler,
Electrical conductivity of shocked water and ammonia,
preprint UCRL-82126, Lawrence Livermore Laboratory (1979).

Johnson, Q., A. Mitchell, R. N. Keeler and L. Evans, X-ray
diffraction during shock-wave compression, Phys. Rev. Lett.,
25, 1099-1101 (1970).

-44~

11. Johnson, Q., and A. Mitchell, First x-ray diffraction evidence
for a phase transition during shock-wave compression,
Phys. Rev. Lett., 29, 1369-1371 (1972).

12. Urtiew, P. A., Effect of shock loading on transparency of sapphire
crystals, J. Appl. Phys., 45, 3490-3493 (1974).

-45-

Chapter 3

RESULTS AND APPLICABILITY OF

SHOCK PYROMETRY EXPERIMENTS

Introduction

During the course of this research in experimental shock temperatures,
several different materials were examined, both to learn about the thermal
equations of state of a wide range of solids and liquids and to investigate
the range of applicability of the pyrometry technique. The current chapter
presents the results from a selection of these experiments. The initial
trials of the shock pyrometer were performed using NaCl (sodium chloride)
crystal samples, building upon the groundwork provided by the earlier work
of Kormer et al. [1,2].

Simultaneously with this effort to measure Hugoniot temperatures in a
simple ionic solid, experiments were considered to make such measurements
in silicate and oxide minerals of importance in problems of solid-earth
geophysics. The phenomenology of these experiments is surveyed in this
chapter; however, the detailed interpretation of the measured shock tem-
peratures in SiO, and Mg,Si0, is the subject of a separate chapter (Chapter 4).

Finally, a limited amount of experimental work has been done toward
the goal of shock temperature measurements in metals. This problem offers
considerable challenge to the optical pyrometry technique, and the current

progress toward its solution is discussed here.

-46-

NaCl Shock Temperatures

Shock pyrometry experiments were carried out on NaCl samples using
the Lawrence Livermore Laboratory light-gas gun in the experimental con-
figuration described in Chapter 2. The sample material consisted of syn-
thetic sodium chloride single crystals, cut and polished as discs 4 mm
in thickness and 19 mm in diameter. These infrared-grade crystals were
supplied by the Harshaw Chemical Co., Solon, Ohio. In all the experiments,
the crystal sample was mounted on a tantalum standard base plate 2 mm in
thickness, and this target assembly was impacted by a 2 mm thick tantalum
flyer plate.

Table 3-1 presents the results of five pyrometry shots carried out on
NaCl between shock pressures of approximately 70 and 105 GPa. The reported
shock pressures were obtained via the impedance match method (Al'tshuler
[3]). The Hugoniot equations of state of NaCl and the tantalum standard
were assumed known, so that a measurement of impactor velocity determined
the pressure in each experiment. As determined by Mitchell et al. [4], the
Ta Hugoniot (initial density 16.66 g/cm) is described between 30 and
430 GPa by the shock velocity-particle velocity relation,

us = (1.298 + .012) 4 + 3.313 + .025 km/s. (1)
The reference for Hugoniot data on NaCl was the Livermore shock wave data
compilation [5]. Table 3-1 also contains the best fit temperature and
emissivity solutions obtained from the pyrometer spectral radiance measure-
ments. Here and in the cases of other Hugoniot temperatures reported in
this thesis, only the reduced temperature and emissivity values are given.
For completeness, a collection of the unreduced spectral radiance data

appears in Appendix II, cataloged by material.

-47-

Table 3-1

NaCl Hugoniot Temperature Data

Ta Impactor Shock Pressure Shock Temperature Effective

Velocity (km/s) (GPa) (K) Emissivity
4.80 + .01 72.5 + 1.0 4440 + 150 -67 + .07
4.90 + .01 74.5 + 1.0 4650 + 150 -85 + .08
5.5 + 0.3 87 +5 5750 + 2002 ~l
5.80 + .01 95.0 1.5 6850 + 300 .73 4 14
6.18 + .0O1 104.5 + 1.0 7850 + 250 -91 + .08

*B1lackbody temperature based upon three wavelength intensity measurements.

~48-
Figure 3-1 gives a pressure-temperature plot of the NaCl Hugoniot
data, along with the reported experiments and interpolation of Kormer [1].
It is evident that the data from the present work are largely consistent
with the results of Kormer, joining smoothly with it in the pressure region
of overlap near 70-80 GPa. At relatively high pressures, Kormer'’s implicit
assumption of blackbody emissivity for the sample seems fairly reasonable,
although at the lower end of investigated pressures, the emissivity indi-
cated by this work is significantly less than unity. This decline in
emissivity accounts for the somewhat lower temperatures obtained by Kormer
through the blackbody assumption compared with the present work near 70 GPa.
Kormer's temperature points were obtained from light intensity record-
ings at two visible wavelengths (instead of six in the present experiments).
These intensity values, measured remotely by photomultipliers in high-
explosive-driven shock experiments, were converted into blackbody tempera-
tures assuming the emissivity of an opaque layer equal to unity. Separate
temperature determinations were obtained from the red (625 nm) and blue
(478 nm) temperatures, and vertical bars are used to indicate the range
between these two values in Figure 3-1. The agreement between these
values was taken by Kormer as evidence that the blackbody assumption was
justified, although it may be noted in retrospect that the fact that the
blue temperatures are always several hundred degrees higher than the red
temperatures reported indicates a systematic overestimate of the emissivity.
A second but related issue in the comparison of the current work with
that of Kormer pertains to the time dependence of the measured light.
Figure 3-2a shows an oscilloscope record of detected light intensity from

an NaCl shot in the current series, at a pressure of 72.5 GPa. This

4000 t- _
L I 4
2000 F- —
¢ Present work
I Kormer et al
0 | | | |

-49-

- NaCl { a

_ Shock Temperatures

O 20 40 60 80 100 I20

Figure 3-1.

Pressure (GPa)

Experimental Hugoniot temperatures versus pressure
in single crystal NaCl. Solid points from present
investigation. Vertical bars are measurements by
Kormer [1], with upper value at A = 478 nm (blue)
and lower value at A = 625 nm (red). Solid line
shows Kormer's calculation, with melting assumed.

+» Intensity

-50-

72.9
GPa

Figure 3-2.

Oscilloscope records of thermal radiation intensity
(vertical dimension) in NaCl experiments.

(a), Hugoniot pressure 72.5 GPa. (b), Hugoniot
pressure 104.5 GPa. Horizontal time scale, 100 ns
per division both records. Note increased time
dependence at higher pressure. Both records from
650 nm wavelength channel.

-51-
overlaps the pressure range investigated by Kormer, and the recorded
intensity history is quite similar in its time dependence to that recorded
for other materials, as illustrated in the previous and succeeding chapters.
This result is in apparent contradiction with the reported results of
Kormer in the same range. While the present studies indicate that the

rise of shock-induced luminescence occurs in a time comparable or shorter
than the instrumental rise time of ~5 ns, Kormer's earlier work indicated
that the radiation required as long as a few hundred nanoseconds to reach
full intensity. Kormer interpreted this long rise time as the period
required for an opaque layer of shocked material to accumulate behind the
shock front. In all of the NaCl experiments reported by Kormer, the light

intensity did not reach a "plateau"

value during the duration of shock
propagation, and a correction in the temperature for this apparent emissivity
effect was applied.

The present work strongly suggests that Kormer's observed rise times
were either instrumental or due to peculiarities of the shock driving
system, at least at the pressures overlapping those investigated here. The
suggestion is strong that in the present experiments an effectively opaque
radiating layer is achieved near the shock front, within a layer probably
no thicker than about 30 um, and possibly much thinner. In any case, it
appears that the Kormer shock temperature points reported at lower pressures
may underestimate the true shock temperatures. This possibility has a
bearing on Kormer's proposed identification of the NaCl melting line.

The indicated region of slower temperature increase between approxi-

mately 55 and 70 GPa along the Hugoniot was taken by Kormer as an indica-

tion of shock-induced melting. In this picture, the region of shallow

-52-
temperature slope represents the region of mixed phases in which solid and
liquid coexist and therefore defines the phase coexistence line in the P-T
plane. While the current experiments do not confirm this result, a defini-
tive answer to the problem should await further experiments utilizing the
improved pyrometry technique. It is interesting to note that in addition
to this apparent melting behavior in NaCl, Kormer reports the same results
in experiments on KCl, KBr, and CsBr, with the apparent melting occurring
at much the same temperature, near 4000 K in each of these materials. In
addition, Kormer finds evidence for a change in slope of the usu, Hugoniot
data for NaCl and KCl which correlates with the inferred transition.

While the details of the NaCl temperature Hugoniot influence the
inferred melting temperature of that particular material, the issue of
shock radiation rise times and emissivities has importance for the inter-
pretation of all shock temperature experiments. Kormer [2] discusses the
problem of equilibrium between free electrons and the crystal lattice in
the vicinity of the shock front. Very high pressure experiments discussed
by Kormer show that at large shock amplitudes corresponding to Hugoniot
temperatures higher than ~7000 K, the observed brightness temperature of
the shock front reaches a "saturation level," failing to rise further with
increasing shock pressure as expected. This behavior in ionic crystals
is attributed to screening of the lattice equilibrium temperature by a
superimposed layer of shock-ionized free electrons which have insufficient
time to reach equilibrium with the lattice.

In Kormer's view, while phonon-phonon relaxation times and the times
for lattice thermal equilibrium are as short as 10712-10713 seconds, free

electrons ionized from the valence band by shock passage require a longer

-53-
time to acquire the lattice temperature in appreciable concentrations.

In this model, at sufficiently high pressures an opaque layet of electrons
at a low temperature not characteristic of the lattice may lag a few
nanoseconds behind the shock front, screening radiation from layers in
thermal equilibrium immediately behind. Since it is expected that the
electron temperature of a fixed population of ionized electrons should
reach thermal equilibrium within 1079 s or so, this screening mechanism
depends upon the ability of the shock to produce rapidly a dense concen-
tration of free electrons, a process which it is reasonable to suggest
depends upon large shock amplitudes. It is therefore important to view
shock temperature measurements at high pressures with caution, and a
criterion would be useful for judging whether the measured temperature is
indeed characteristic of the lattice phonon value.

Figure 3-2a indicates that at lower pressures, the observed light
intensity and temperature in NaCl rise abruptly to a level that remains
nearly constant throughout the shock transit. As the shock amplitude is
increased to ever higher pressures, however, an increasingly noticeable
time dependence appears in the records. The light intensity is observed
to rise slowly during shock propagation, apparently approaching an
asymptotic value. Figure 3-2b illustrates the outcome of an experiment
at 104.5 GPa pressure, just below the onset of temperature "saturation"
reported by Kormer. The time dependence is becoming more pronounced at
this high pressure and may be taken as a Signal of the beginning of electron
screening at the shock front.

It is interesting to note that an exactly analogous result has been

obtained in the present work on H20 and Si02, with the effect most

-54-

pronounced in the highest temperature shots on fused quartz (Ty approaching
7000 K). This coincides with a pressure region in which an anomalously
high heat capacity is apparently otherwise required to explain the
observed S10, shock temperatures (Chapter 4). The present six-wavelength
pyrometry method has verified that in such cases, the observed intensity
rise represents a rise in the effective temperature, and not simply an
increase in the emissivity of a source of constant temperature. Such
observations may be taken as support of the view that temperature signals
with strong time dependence signal the departure of observed temperatures
from the true Hugoniot values, while the constant intensities recorded

at more modest pressures faithfully reflect the lattice temperature.

In summary of the present work on NaCl, it is evident that the general
agreement with the results of Kormer shows that pyrometric measurement of
shock temperatures to moderately high pressures is practical. The dis-
agreement with Kormer's conclusions regarding the opacity and absorption
length in material behind the shock front remains unresolved, as does
unequivocal confirmation of the melting observation. Future investiga-
tions should clarify these points by extending the range of pressures
investigated with the new six-wavelength high-speed method to lower values.
In the case of NaCl, it may be practical to use the present technique at
pressures as low as 50 GPa, thus confirming or refuting the melting observa-—
tion. Also, extension of this work to other alkali halides such as KC1
would be extremely useful. From a standpoint of work completed to date,
the conclusions drawn from the NaCl work allow us to proceed with inter-

pretation of similar experiments in other materials of interest.

-55-

Observations in Other Dielectric Solids

Among the solids whose thermal equations of state at high pressures
are of interest are silicate and oxide minerals which in general display
larger incompressibilities than the ionic solids whose study is described
above. As a result of this incompressibility, these solids character-
istically reach lower temperatures at a given Hugoniot pressure than the
alkali halides. For this reason, the radiation screening associated with
high temperatures is apparently not a factor, but limitations on the shock
pyrometry technique become apparent when temperatures are too low.

Three such minerals whose radiative behaviors at high shock pressure
have been studied are Mg:Si0, (forsterite), MgO (periclase) and Al203
(sapphire). In the case of forsterite, shock pressures between ~128 and
175 GPa have been investigated, with two types of results obtained. For
three shots at the highest pressures (between 150 and 175 GPa), the
expected shock radiation history with constant intensity characteristic
of the Hugoniot temperature is obtained. As illustrated in Figure 3-3a,
the recorded temperature is quite constant without indication of relaxation
effects, but as detailed in the next chapter, the effective emissivity
at these temperatures (near 4500 K) is comparatively low, and decreasing
with decreasing pressure.

At pressures lower than this, quite a different behavior is observed.
As shown in Figure 3-3b, forsterite shocked to approximately 140 GPa shows
a rapid light intensity rise and a subsequent signal decay which persists
throughout the entire shock transit time without stabilizing at any well-
defined value. It is believed that at pressures below about 150 GPa,

the shock front emissivity becomes so small that the shock-compressed

oO

> Intensity

-56-

175
GPa

Figure 3-3.

+ Time

Forsterite (Mg2Si0,) light intensity records.

(a), Shock pressure 175 GPa, 500 nm wavelength.
(b), Pressure ~140 GPa, 600 nm wavelength.

Record (a) shows normal constant shock luminescence
throughout transit. Record (b) shows loss of
emissivity in forsterite sample. Horizontal time
scales 100 ns per division.

-57-

material is essentially transparent, and the recorded light originates in
the metal base plate lying behind the sample. With this interpretation,
the decaying radiation signature is well explained by the diffusion of
heat from the metal/insulator interface. As discussed below, unless
great pains are taken to eliminate interfacial gaps and roughness, an
initial temperature "spike" will occur at the interface, which decays
with a characteristic time dependent upon the thermal diffusivities of
the target materials.

Al5,03 (sapphire) has displayed such transparency under shock com-
pression over the entire investigated pressure range. While this poses
problems for determining the sapphire Hugoniot temperature, it also means
that sapphire crystal is a good optical window material in shock experi-
ments in this range. Urtiew [6] has independently shown that A103
erystals retain their transparency to shock pressures in excess of 130
GPa. This property has been exploited in the current research program,
as described later in this chapter. A single temperature experiment with
a crystalline MgO sample yielded indeterminate results suggestive of this
type of behavior, but additional experiments will be necessary to verify
the nature and range of the phenomenon in this material.

It is apparent that in at least some solid insulators, below some
threshold shock temperature or pressure, the free electrons behind the
shock front which are assumed to be the source of equilibrium radiation
fail to occur. This observation places the lower practical limit on shock
temperatures that may be observed by the present technique. This lower
limit may not, however, represent so insurmountable an obstacle as the

upper temperature limit imposed by electron screening. If a sufficiently

-58-
thin metallic layer can be introduced into the investigated sample, this
layer will come to thermal equilibrium and radiate with the’ temperature
of the surrounding crystal. Estimating the thermal diffusivity of the
samples in question, it appears that a layer of good conductor such as
aluminum 0.1 um in width is sufficiently thin that thermal equilibrium
would be achieved on the time scale of the experiment. Since this thick-
ness is large compared with the optical skin depth of a good metal, it is
expected that adequate thermal radiation would result. Experiments to
investigate this possibility should assume a high priority in future
research, especially for materials of geophysical interest in which the

relevant temperature range may be below 3000-4000 K.

Shock Temperature Measurements in Metals

Considerable interest centers on the measurement of Hugoniot tempera-
tures in opaque materials such as metals, in addition to the case of
transparent insulators discussed above. Unfortunately, the above tech-
nique cannot be immediately applied to metals, since optical radiation from
the shock-compressed material cannot escape from the opaque sample. Radia-
tion from the free surface at the moment of shock arrival may be monitored,
but such measurements pertain to the residual post-shock state of the
sample.

A solution to this problem is illustrated schematically in Figure 3-4a.
If a material can be found which offers a close shock impedance match to
the studied metal and which also remains transparent under shock loading
in the pressure range of interest, this material may be used as an "anvil"
in a shock pyrometry experiment on the metal layer. When the transparent

anvil is placed in contact with the metal sample rear surface, the shock

Figure 3-4.

-59-

Fiyer Plate Meta! Transparent
Sample = Anvil

Thermal

Radiation

Temperature
Distribution

A: [ss

Msn t Deposited
/ Metal Layer

Schematic representation of metal Hugoniot
temperature measurement. (a), ideal contact
interface between sample and shock anvil provides
intermediate temperature value. (b), Interface
gaps give rise to temperature perturbation on
radiating interface.. (c), Vacuum deposited metal
layer eliminates gaps, removing temperature per-
turbation several tens of microns into metal
layer.

~60-
wave will ideally pass from the metal layer to the anvil with minimal
reflected shocks or rarefactions at the interface, thus retaining the
metal sample near its original Hugoniot state. Thermal radiation from
the hot, compressed metal is then detected by the pyrometer through the
transparent anvil.

The temperature actually measured by the pyrometer is not that of the
bulk metal sample but that of the sample/anvil interface. As indicated
by Figure 3-4a, in a typical case, the anvil is considerably cooler than
the Hugoniot temperature of the metal sample, so that this interface
temperature gives an underestimate of the true Hugoniot value. It is
easily shown (see Grover and Urtiew [7]) that for a heat flow problem
governed by the classical one-dimensional thermal diffusion equation, the
interface temperature between two semi-infinite media of different uniform

initial temperatures T,; and T) is independent of time and given by

To-Ty
T= Ti + (49) (2)
where
1/2
K2\Di

kK and D denote the thermal conductivity and thermal diffusivity,
respectively. In the limit that one material has a much higher thermal
conductivity than the other, the interface temperature approaches that
of the better conductor.

This suggests that given the proper anvil material, preferably one
of low thermal conductivity, the proposed temperature measurement in the
shock-compressed metal should be easily accomplished. However, a compli-

cation arises from the problem of material interfaces, as discussed by

-61-

Urtiew and Grover [8]. As shown in Figure 3-4b, the real interface
between a polished metal plate and anvil will include roughness and gaps
on a scale of microns. As treated quantitatively by Urtiew and Grover,
when a shock wave encounters such a gap, release to zero pressure and
immediate reshocking of the material immediately before the gap occur.
This means that twice-shocked material with an anomalously high tempera-
ture will occur in a layer near the interface whose width is of the same
order as the gap width (or roughness scale).

As shown, this temperature "spike" at the sample/anvil interface
will mask the true Hugoniot temperature. Only after sufficient time has
elapsed for this disturbance to dissipate, does the interface assume its
time-independent temperature step profile, but for practical purposes,
this time is longer than the duration of the experiment.

This problem of interface gaps can be eliminated by careful sample
preparation. If the metal layer is prepared in intimate contact with the
anvil surface, such as by vacuum deposition or melting, the problem of
interface heating can be reduced by orders of magnitude. Since the latter
method presents problems for most materials because of differential thermal
expansion, vacuum deposition offers the most promise for ideal interface
preparation. Since, however, only relatively thin layers can be prepared
by this technique, the arrangement shown in Figure 3-4c is used.

A layer of the studied material is vacuum deposited onto the anvil,
providing an ideal radiating interface. This thin layer is then backed
by a thick plate of the same metal, serving as the impact target. The
deposited metal film must be thick enough so that the temperature spike

induced in the metal plate at the imperfect interface between the base

-62-
plate and film does not have time to diffuse through the film and affect
the measured temperature during the length of the experiment.

The set of experiments conducted in the present investigation used
silver (Ag) as the investigated metal and single crystal sapphire (A1,03)
‘as the transparent shock anvil. Urtiew [6] pointed out that A1,0, pro-
vides a good shock impedance match to many incompressible metals and
that furthermore it retains its qualities as a transparent window at high
shock pressures where many metals will become hot enough to radiate.
Silver was chosen to study because of its shock impedance match to
sapphire, its known Hugoniot. equation of state, and its ease of evapora-
tion in a vacuum furnace. For the current set of experiments, single
crystal sapphire anvils (density 3.98 g/cm*) were supplied by Adolf
Meller Co., cut to ~3 mm thickness and prepared with a surface finish
smooth to one microinch. With an evaporated Ag coating on this surface,
an effective interface roughness improvement of nearly two orders of
magnitude is realized over mechanically joining the two surfaces, which
may otherwise depart from uniform contact over the whole surface by microns.

The silver base plates and films were prepared from high purity
(99.99%) stock. Early in the pursuit of this study, the technique of
sputtering in a low density argon atmosphere was tried to achieve a silver
layer of the required thickness. While a thick deposited layer was
obtained, examination of the resulting film showed that sputtering yielded
a metal layer of high porosity and unsuitable for the present study.
Eventually, direct Ag evaporation in high vacuum yielded a good metal
film of the required thickness. In order to achieve good adhesion of

the film to the anvil, care was required in cleaning the deposition

-63-
interface and in cooling the anvil during plating.

A set of experiments was devised to check the validity of the above
methods and hopefully to provide a first shock temperature determination
in Ag. Using the shock wave data from the Livermore compendium [5] for
Ag and Al,0O,, it was determined that a shock of approximately 200 GPa
amplitude in the silver base plate would be transmitted into the A1,0,
anvil as a shock of ~150 GPa pressure, with only a modest rarefaction
reflected back into the metal. As long as the amount of release occurring
due to impedance mismatch is relatively small, a small correction may be
applied to the measured (released) temperature to give the temperature
of the first shocked state.

Figure 3-5 summarizes the experimental records obtained from this
series of shots. Record a) shows the result of a "control" experiment
in which a sapphire crystal was simply wrung onto the Ag base plate with
no special interface preparation. The contact surfaces were lapped
smooth and when assembled, several white-light interference fringes were
visible at the interface, indicating a gap size of a few microns. As
seen in the oscilloscope trace a), the recorded light intensity reached
a peak value immediately upon shock arrival at the anvil and steadily
decayed thereafter. This is just the behavior predicted above for the
imperfect interface illustrated in Figure 3-4b.

Figure 3-5b gives the oscilloscope record for an Ag shot with a
vacuum deposited interface layer. Considering the high thermal diffusi-
vity of a metal like Ag, it was anticipated that a layer thickness of a
few tens of microns (ym) would be required to isolate the optical inter-

face from anomalous heat spikes for the several hundred nanosecond

—bhe

Figure 3-5. Oscilloscope records from Ag temperature experi-
ments using Al503 anvil. (a), Ag metal base plate
in contact with sapphire anvil. Ag shock pressure
222 GPa. (b), 51 um thick vacuum deposited Ag
coating on anvil interface. Ag shock pressure
185 GPa. Note improved temperature constancy.
(c), Ag flyer plate direct impact on A103
crystal. Shock pressure 120 GPa.

~65~

duration of the experiment. In the illustrated experiment, a 51 um

Ag coating was used. The record shows that following a relatively small
interface "flash," the radiation settles down to the desired time-
independent behavior, apparently giving the ideal interface temperature.
The abrupt cutoff of light intensity upon shock arrival at the anvil free
surface is apparently due to the breakup and spallation of that surface,
resulting in an immediate loss of transparency.

While the experiment b) apparently gave successful results, an addi-
tional shot was conducted to explore an alternative solution. In the
shot of Figure 3-5c, a silver flyer plate projectile was launched by the
light-gas gun for direct impact upon a sapphire crystal with no base
plate. The reasoning behind this experiment was that the direct Ag-Al,0,
impact would eliminate the problem of multiple-shocking near a gap between
the two. While this problem is eliminated, examination of record c) shows
that objectionable interface heating occurs regardless. Apparently, the
collision process between flyer and target is accompanied by significant
micro-jetting and local strong heating due to surface roughness and non-
coplanarity, thus completely overwhelming the desired temperature signal.
These results indicate that the vacuum plating approach of the experiment
in Figure 3-5b is the most promising method. Assuming that this result
does reflect the true Ag temperature, we may further examine these data
in order to characterize the Ag thermal equation of state.

The parameters of this single successful Ag temperature shot are
summarized in Table 3-2. P, is the shock pressure in the Ag base plate,
while P, gives the pressure of the partially released Ag state seen at

the metal/anvil interface. The interface temperature T, was determined

-66-

Table 3-2

Ag Shock Temperature Experiment Parameters

Ta impactor velocity, W = 4.375 km/s + .005

Ag shock pressure, Py 185.0 GPa

Ag particle velocity, 4, = 2.46 km/s

Al,03 anvil pressure (Ag released state), P, = 134.7 GPa
Al,03 particle velocity, u_ = 2.87 km/s

Measured interface temperature, Ty = 5030 K + 150
Effective emissivity, e¢€ = 0.68 + .05

Estimated anvil temperature,” = 1250 K

T A150,

“Walsh and Christian calculation; y = 1.60 (V/V,), @p = 905K

-67-
as usual by solution of the six wavelength radiance measurements for
temperature and emissivity.

In order to derive the Ag Hugoniot temperature from the measured
interface value of 5030 K, two corrections must be applied. These cor-
rections are for the cooling effect of the relatively cold anvil in con-
tact with the sample and for the adiabatic cooling experienced by the
metal in its partial release from Hugoniot pressure Py to P,. The
first of these corrections comes from consideration of equations (2) and
(3). a is found by using the standard condition values for the thermal
conductivities and diffusivities of Ag and Alj03 as guides along with a
general knowledge of how these quantities vary with increasing temperature
and density. A general assessment of these quantities allows the
parameter a to be estimated conservatively in the range ~3-10. Using
a= 7 in (3), we obtain the bulk Ag temperature of approximately 5570 K
with an uncertainty of roughly 300 K.

In order to obtain the second temperature correction, giving the
temperature in the initial state P,, the amount of volume dilatation
the metal has undergone in partial release must be estimated. Assuming
that the release process is adiabatic and isentropic, the variation in
temperature under isentropic compression (or rarefaction) for a Mie~
Griineisen solid was derived in Chapter 1. For isentropic release from
volume V, to volume V», the temperature change is given by

Vo
T= tyexp[-| (y/v)av). (4)
Vy

For the case of Ag, y will be assumed to be given by y(V) = 2.45(v/V,)7°8

-68-
(see Grover [9]). Volume V, is obtained directly from the Hugoniot
shock state, but the released volume V, is off the Hugoniot curve and
must be estimated in some way.
Lyzenga and Ahrens [10] consider the flow in an isentropic rarefac-
tion wave. In such a flow, which takes the material from pressure Py
to Py, the additional particle velocity imparted to the material,

uu, is related to the P-V release path through the Riemann integral,

(-

a 1/2
= | - Xe. (5)

Here, 4, is the particle velocity in the shocked state, while ul is
the released state particle velocity. In [10] it is shown that an
extremum of (5) is obtained if the release path V(P) is a linear function.
In particular, this gives a maximum for the velocity jump in (5), and for
a given value of up-U,» it provides a lower limit for the released

volume Vj. It is shown in [10] that

_ 2
sy, + erp (6)

Vv
i (Pj-Po)

for any isentropic release path between P, and Po.

This gives a lower limit for Vo, and for a sufficiently short
release path, the linear release adiabat cannot be a bad approximation
of the actual path. We therefore assume for the current problem that V5
is given by the equality in (6). The Ag particle velocity at shock
pressure P, = 185 GPa is 4, = 2.46 km/s. The released velocity, which

is equal to the Alj03 particle velocity at Pp» = 134.7 GPa is

= 2.87 km/s. With V1 = 6.265 x 1075 m3/kg, we obtain

6.60 x 1075 m3/kg.

IN)

-69-

With these values, we may now evaluate the integral of equation (4).
The exponential term is ~0.94, so that the corrected Hugoniot temperature
of Ag at 185 GPa is approximately 5950 K. This temperature may now be
compared with the calculated Hugoniot temperature. When the temperature
Hugoniot is computed by the Walsh and Christian method (Chapter 1), using
the above y(V) and C. given by the Debye model with @p = 225 K, the
calculated value of Ty at 185 GPa pressure is ~7200 K. The calculated
temperature appears to be well above experimental value, and an explana-
tion of this discrepancy is desired.

If the estimated Ag equation of state is not grossly incorrect, then
a mechanism or transition is sought which will account for a shock tem-
perature over 1000 K lower than predicted. The melting transition is a
good candidate for this solution, especially since no evidence for a solid
state transition with a large volume change is apparent in the existing
Hugoniot data. An estimate of the melting behavior of Ag at high pressures
may be obtained by appealing to a theory of melting, such as the semi-
empirical Lindemann melting criterion.

As shown by Grover [9], Lindemann's law, which relates the volume
dependence of the melting temperature to the average amplitude of atomic
lattice vibrations, may be cast in a form involving the Griineisen param-
eter y. Grover shows that

d {n Tm _ _ V dim _ _
dinv "Ta ay - 2/3, (7)
which holds well for metals, and in the case of Ag, Yo = 2.86 gives
the best fit for low pressures.

Figure 3-6 shows the T-V melting curve for Ag computed from (7),

-70-

1! 1 | T T l
8000 |;-* ~
T Calculated Ag Hugoniot
(K) | ~
Experimental Point
6000 F- ~—
— _
Ag Lindemann
a Melting Curve _
#000 (Solid Phase)
2000 - Vo"
= —
0 l | 4 | l | ee

v (Io? m°>/kg)

Figure 3-6. Calculated Ag Hugoniot and melting line in
temperature-volume plane. Melting line is
calculated from Lindemann law applied to solid
phase and represents the solid-mixed phase
boundary. Experimental point is corrected for
release and heat diffusion effects.

-71-
assuming a zero-pressure melting temperature of 1234 K. As seen in this
plot, the Lindemann melting line crosses the computed solid phase Hugoniot
at a temperature near 4600 K, corresponding to a shock pressure of 137 GPa.
This estimate is consistent with the occurrence of shock-induced melting
in the present example at 185 GPa pressure. It will be useful to consider
the slope of the estimated Lindemann melting line translated into the
pressure-temperature plane. The total derivative dT/dP taken along the
melting line is given by

; -1
aw Gp) + Gy Ge | (8)
Now the total derivative dP/dV for the solid phase along the melting

line is given by

dT T 2) _ fat OT) dP
av 7 ~ y2r-3) = Gy) * GP) av’ (9)
using (7) for dT/dV. This gives for dT/dP in (8),
-1
dt oT Tov 2
ap = Gp) {2 - Hes (2y - 3) + 1| }. (10)
v P
. oe . aT av .
In the Mie-Griineisen assumption, Gp) y and Gr» are obtainable from

the equation of state parameters y, Cos and Ke (Chapter 1). The above
melting line slope is evaluated where the computed Hugoniot crosses the
Lindemann line, at V = 6.54 x 1075 m3/kg, T= 4575 K and P = 136.7 GPa.
The result obtained is dT, /dP = 12.3 K/GPa.

Figure 3-7 shows the P-T Hugoniot along with the derived Lindemann
law melting line. As illustrated in this plot, the temperature Hugoniot
curve coincides with the phase coexistence line throughout the mixed phase
region and moves up into the liquid field as the transition is complete.
To a first approximation, the liquid Hugoniot should lie below the calculated

solid Hugoniot by a temperature difference roughly equal to the latent

-72-

8000 I : 1
ToL Estimated Liquid —
(K) Hugoniot /
6000 F- _
Lindemann Melting Curve —
Experimental
4000 |- Hugoniot Point |
= a —
2000 4
Ag Solid Hugoniot
O | | | |
0 50° 100 150 200
Pressure (GPa)
Figure 3-7. Ag in pressure-temperature plane. Calculated

Hugoniot shown for solid phase and estimated for
liquid phase (dashed) above Lindemann melting
curve. Corrected experimental Ag shock tempera-
ture point is believed to fall on the liquid phase
Hugoniot.

-~73-
heat divided by the specific heat.

Knowing the slope of the melting line allows an estimate of the
latent heat of fusion, Li Stishov [11] has examined the systematics of
melting at high pressures and finds a high-pressure limit for the relative
volume change AV/V upon melting of simple metals of roughly 1%. Using

this in the Clausius-Clapeyron relation,

dT. TAV
fm. ht
dP Ln (11)

we find Lo = 0.24 MJ/kg. This corresponds to an entropy of melting
AS = 0.7 R per mole of atoms, which agrees with Stishov's systematics for
the high-pressure limit to AS.

Using this latent heat to estimate the position of the liquid tem-
perature Hugoniot, it should lie below the solid Hugoniot by approximately
1040 K, as illustrated in Figure 3-7. Interestingly, the experimental
Hugoniot temperature point at 185 GPa falls almost squarely on the calcu-
lated melt Hugoniot. Apparently, the observed temperature is well-explained
by invoking shock-induced melting, with a pressure-volume dependence given
by the Lindemann criterion. Of course, verification of this conclusion
will require additional experiments, spanning the pressure range which
includes the assumed melting transition.

While the possibility of detecting and characterizing the melting of
silver at very high pressures is an interesting prospect in itself, it
also raises the possibility of making similar measurements in other more
important metals. Urtiew and Grover [12] have discussed the melting of
magnesium under shock loading using similar techniques, but their work

primarily explored states off the Hugoniot curve.

-74-

Fortuitously, the geophysically very important metal iron (Fe) also
displays a good shock impedance match with A1,0,, so that the same tem-
perature measurement technique described above is applicable. Assuming
that the problems of vacuum deposition and sample preparation are solved
for Fe, this technique should allow detection of the iron melting -point
in the pressure range 100-200 GPa. This measurement has far-reaching
importance for the physics of the earth's core, since the liquid outer
core and solid inner core are most probably alloys of iron, and a knowledge
of the iron melting curve would serve to constrain the earth's internal
temperature distribution. The hypothetical melting of iron under shock
loading has been the subject of much investigation already, for example,
Hopson et al. [13], and the present technique may well offer a most power-
ful tool for the solution of this problem.

In summary, shock temperatures in metals may be measured by the shock
anvil technique, subject to the solution of two problems. These problems
are the elimination of interfacial gap heating and the proper correction
of interface temperature for heat diffusion into the anvil. The current
results for silver suggest that these problems can be solved and, further-

more, that the technique offers great promise for other interesting metals.

10.

ll.

12.

13.

-~75-

REFERENCES

Kormer, S. B., M. V. Sinitsyn, G. A. Kirillov and V. D. Urlin,
Experimental determination of temperature in shock-compressed

NaCl and KCl and of their melting curves at pressures up to
700 kbar, Sov. Phys. JETP, 21, 689-700 (1965). :

Kormer, S. B., Optical study of the characteristics of shock-

compressed condensed dielectrics, Sov. Phys. Usp., 11, 229-254
(1968).

Al'tshuler, L. V., Use of shock waves in high-pressure physics,
Sov. Phys. Usp., 8, 52-91 (1965).

Mitchell, A. C., W. J. Nellis and B. L. Hord, Tantalum Hugoniot
Measurements to 430 GPa (4.3 Mbar) (abstract), Bull. Am. Phys.
Soc., 24, 719 (1979).

Van Thiel, M., editor, Compendium of Shock Wave Data, Report UCRL-

50108, Lawrence Livermore Laboratory, University of California,
Livermore, CA (1977).

Urtiew, P. A., Effect of shock loading on transparency of sapphire
crystals, J. Appl. Phys., 45, 3490-3493 (1974).

Grover, R., and P. A. Urtiew, Thermal relaxation at interfaces
following shock compression, J. Appl. Phys., 45, 146-152 (1974).

Urtiew, P. A., and R. Grover, Temperature deposition caused by
shock interactions with material interfaces, J. Appl. Phys.,
45, 140-145 (1974).

Grover, R., Liquid metal equation of state based on scaling,
J. Chem. Phys., 55, 3435-3441 (1971).

Lyzenga, G. A., and T. J. Ahrens, The relation between the shock-
induced free-surface velocity and the postshock specific volume
of solids, J. Appl. Phys., 49, 201-204 (1978).

Stishov, S. M., The thermodynamics of melting of simple substances,
Sov. Phys. Usp., 17, 625-643 (1975).

Urtiew, P. A., and R. Grover, The melting temperature of magnesium
under shock loading, J. Appl. Phys., 48, 1122-1126 (1977).

Hopson, J. W., R. G. McQueen and J. M. Brown, The velocity of sound
behind shocked iron (abstract), Trans. Am. Geophys. U., 60,
951 (1979).

-76-

Chapter 4

SHOCK TEMPERATURES OF SiO» AND MgoSi0.:

EXPERIMENTAL RESULTS AND

GEOPHYSICAL IMPLICATIONS

Introduction

The properties of silica and its high-pressure polymorphs have long
been of interest because of their bearing on-problems of the physical and
compositional states of planetary interiors. Models of the high-pressure
equation of state and phase diagram of SiO» may provide direct information
about candidate mantle mineral assemblages, because SiO, readily trans-
forms to a rutile-like phase (stishovite) above 14 GPa (McQueen et al.,
[1]) in which sit" has octahedral oxygen coordination. It would therefore
appear to be a good model of other lower mantle octahedrally coordinated
silicates (Liu, [2]). Similarly, the study of forsterite (Mg Si0,)
and its high-pressure phases can provide valuable information about what
may be the dominant lower mantle mineral assemblage (Jackson and Ahrens,
[3])}. Modern techniques for the dynamic compression of minerals (Ahrens,
[4]) are providing such data at pressures near 100 GPa, which are appro-
priate to the state of the earth's lower mantle and core.

Shock wave compression of solids depends upon the generation and
propagation of a planar, steady pressure step in the material of interest.
As described previously, the time-independent profile of this pressure

discontinuity or shock front in one-dimensional flow allows application

~77-
of the Rankine-Hugoniot conservation equations, which relate pressure,
density, and energy of the compressed state to the shock and mass veloci-
ties of the flow. The Hugoniot curve or locus of (P, V, E) states acces-
sible to a given material when shocked is thus measurable through observa-
tions of shock wave propagation. One technique for producing and charac-
terizing such shocks is the method of flying plate impact, through the use
of a two-stage gas gun (Chapter 2). This apparatus accelerates projectiles
bearing metallic flyer plates to speeds of up to 7 km/sec, which upon
impact induce shock pressures in silicate specimens in excess of 150 GPa.
For silicates and oxides of geophysical interest, data for the Hugo-
niot shock state are of considerable interest. It is demonstrated below
that Hugoniot temperature measurements can provide an important source of
data specifying the thermal pressure component of the equation of state,
which is not explicitly obtainable from the R-H conservation equations.
The present optical pyrometry method for shock temperature measurement,
developed jointly with Lawrence Livermore Laboratory, is applicable to
transparent materials and has been used to demonstrate how the thermal
behavior and energy associated with phase changes in forsterite and silica
may be constrained. The new data and analysis of measured shock tempera-
tures in Si0,, when taken with the independent work of McQueen et al. [6]
provide important new information about the high-pressure phases of Si0,,
which may be applied directly in placing an absolute upper limit on the
temperature in the earth's mantle, and indirectly, in providing the basis
for estimation of the melting point of the lower mantle, and thus its
viscosity. Furthermore, evidence in the present work for shock-induced

transformation of forsterite to a high-pressure polymorph contributes to

-78-

an understanding of the behavior of this mineral at depth in the earth.

$i05 Experimental

Samples of single crystal and fused quartz were driven to shock
pressures in the range from 60 to 140 GPa via impact of 2 mm thick flyer
plates accelerated to speeds of from 4.5 to 6.7 km/sec using the two-stage
light gas gun facility at Lawrence Livermore Laboratory. Thermal radiation
emitted by the shocked samples during the period (approximately 300 to
400 ns) of shock wave transit were measured by the pyrometer, at each of
six visible wavelengths simultaneously. Briefly, the technique utilizes
the thermal radiation emitted from the high-pressure shocked portion of
the sample, viewed through the unshocked sample. The intensity is
detected via six similar optical paths and detected by an array of PIN
silicon photodiodes whose output is recorded by an oscilloscope, with a
time resolution of typically 5 ns.

The emitted light radiation (Figure 4-1) rises to nearly full inten-
sity very rapidly (within ~5 ns) upon the shock arrival in the sample.

The recorded signal then remains nearly constant approaching what appears
to be an asymptotic value until shock arrival at the free surface, when
the light is immediately extinguished, presumably by free-surface break-up.
It is apparent from data presented below that the radiation detected
originates in the shock front or a very narrow region near the front, in
order to account for the very rapid rise times, which are less than or
equal to the instrumental rise time.

As has been described previously (Chapter 2), a given experiment

yields six values of the spectral radiance of the sample at different

> Light intensity

~79-

Shock Transit
| K in sample >|

Figure 4-1.

5 > 100
Time ~ AS

Oscilloscope record of shock-induced light intensity
versus time. Record is taken through 650 nm wavelength
interference filter from a fused quartz shot at

68.5 GPa pressure. Each shot results in six such
records at wavelengths of 450, 500, 550, 600, 650, and
800 nm. The spectral radiance calibration for this
channel is approximately 3.9 x 109 W/m2/sr/nm per
division.

~80-

wavelengths, which may be inverted to determine the temperature and emis-
sivity of the sample during the flat "plateau" region of the record. In
all results reported here, the data have been inverted under the assumption
that the measured radiation spectrum is given by a Planck blackbody profile,
modified by an emissivity factor independent of wavelength. Thus, -each
shot inversion represents a two-parameter fit to the data. In addition to
obtaining temperature information from the oscilloscope records, conventional
Hugoniot pressure measurements may be obtained from the sample shock velocity
and flyer plate speed using the impedance match technique from Al'tshuler
[7]. The shock velocity measurement depends upon the very abrupt onset
and the decline of shock-induced radiance. Shock-transit times and shock
velocities can with this technique be determined with a precision of about
1%. Factors limiting the precision of this technique appear to be the
electronics rise time, and the degree of "tilt" of the shock front from
ideal coplanarity with the sample interfaces.

The results of nine shots on single crystal o-quartz are summarized
in Table 4-1. The samples used in this series of experiments were synthetic
quartz crystals with an initial density of 2.648 g/cm°>, supplied by the
Adolf Meller Co. The prepared samples were discs approximately 3 mm in
thickness by 17 mm in diameter, polished to optical smoothness. Shots
were carried out on crystals oriented with the (0001) axis oriented both
parallel and perpendicular to the direction of shock propagation, as noted
in Table 4-1. The o-quartz experiments were carried out at pressures
between approximately 75 and 140 GPa, in a range where stishovite is
assumed to be the stable solid phase of SiO, (McQueen, et al. [1]). As

is discussed below, the shock temperature data show that a temperature

~81-

Table 4-1

a-quartz Hugoniot Temperatures

Shock Pressure (GPa) _ Temperature (K) Emissivity
75.9 + 0.8% 4600 + 150 .70 + .05
85.9 + 1.0° 4860 + 150 .90 + .07
92.5 + 1.0° 5400 + 150 | .87 + .07
99.3 + 1.0° 5470 + 150 .97 + .07

107.8 + 1.0° 5820 + 150 .97 + .07
109.7 + 1.07 5700 + 150° .96 + .07
116.5 + 1.0° 4880 + 150 .88 + .07
126.6 + 1.07 5390 + 150 .80 + .07
137.0 + 1.0? 5990 + 200 72 + .07

* Shock propagation perpendicular to (0001) axis.
b : .
Shock propagation parallel to (0001) axis.

c Temperature based upon only two wavelength radiance measurements
instead of six.

~82-
decline in excess of 1000 K occurs between pressures of 107 and 117 GPa.
This temperature drop is illustrated graphically in Figure 4-2 and is

taken as evidence of a shock-induced phase transition in stishovite.

Table 4-2 summarizes the results of seven shots carried out with
samples of fused silica. The polished discs had an initial density of
2.204 g/em> and were supplied by Amersil Corp. The pressure range studied
was 58 to 108 GPa. As in the case of a-quartz, the fused quartz tempera-
ture data show evidence for a phase change in stishovite. A similar
temperature drop is observed to occur, although at a lower pressure than
in the a-quartz experiments.

As seen in the plot of Figure 4-3, the behavior in the region of
temperature decline in fused quartz near 65-70 GPa pressure appears similar
to that in o-quartz. The two anomalous temperature segments, however, do
not connect to form a continuous curve as would be expected if they
delineate an equilibrium phase boundary. In such a case, the Hugoniot
would coincide with the phase line through the region of mixed phases,
moving into the high-pressure phase region at higher shock pressures
(Duvall and Graham, [8]). In any case, it is assumed here that all differ-
ences between the Hugoniot curves for o-quartz and fused silica result
from the different initial densities and consequently different internal
energies of SiO, shocked from the two different starting phases. Also
plotted in Figures 4-2 and 4-3 are the calculated Hugoniot temperature
curves for SiO, in the crystalline stishovite phase. The details of
this calculation have been discussed earlier (Chapter 1). The calculated
curves are sensitive to the assumed values of Ey for stishovite from the

initial phases. The values assumed here are 0.822 MJ/kg and 0.697 MI/kg

-83-

— ] T | | | |
Ty (K) a — Quartz Calculated

: Liquid
6000+t Calculated

5000

Stishovite

l | l | |

4000
70

Figure 4-2.

HO
Pressure (GPa)

130 I50

Measured shock temperatures versus pressure from
experiments on single crystal a-quartz. Heavy
solid and dashed lines are calculated Hugoniot
temperatures assuming 510, in solid stishovite
phase, and in a liquid phase. Curve labelled A
is calculated assuming a monatomic metal specific
heat and 3.4 MJ/kg transition energy at standard
conditions. Fit B assumes a large specific heat
of ~4.2 R per mole of atoms, and a metastable
standard state energy 0.5 MJ/kg above fused silica
reference state.

-84-

Table 4-2

Fused Quartz Hugoniot Temperatures

Shock Pressure (GPa) Temperature (K) Emissivity
58.9 + 1.0 4980 + 150 -85 + .05
68.5 + 1.0 5130 + 150 -85 + .05
73.3 + 1.0 4700 + 150 79 + .05
81.2 + 1.0 5360 + 150 .75 + .05
93.2 + 1.5 5800 + 200 -84 + .05
104.2 + 2.0 6500 + 300 -90 + .10
109.9 + 2.0 6800 + 300 ~1.0

-85-

7 | | T a
Tu(K
HK) Fused Quartz A ig
7000 Conculated y -
Calculated
Stishovite
6000 K _
Ot
5000 4 _
yf
4000+ _
| | | | | | |
40 60 80 100 i20

Pressure (GPa)

Figure 4-3. Measured shock temperatures as a function of pressure
in experiments with fused quartz. Calculated stishovite
and liquid Hugoniot temperatures are shown as in
Figure 4-2.

—86-

for a-quartz and fused silica respectively, as measured calorimetrically
(Robie, et al. [9]). The Griineisen parameter y(V) was estimated prior
to this work using the results of Jeanloz and Richter [5], and stishovite
calculations were made for a constant y = 0.9. It is notable that in
both materials, the measured Hugoniot temperature curves show reasonable
agreement with the stishovite calculations at pressures below the observed
transitions, and that above the transitions, both Hugoniots lie well below
the predicted temperatures. These observations lend support to the view
that the peculiar temperature behavior seen in both materials signals

the same phase transition from stishovite to a new phase, even though the
transition is apparently not accomplished under equilibrium conditions.

As is discussed extensively in McQueen et al. [6], a shock wave which
decreases in amplitude with time may be used to investigate the anomalous
region of decreasing temperature. Those investigators have observed the
radiation from a decaying shock front in fused quartz and have noted the
expected temperature reversal, among other interesting results. Their
results are confirmed by a single experiment from this work, in which a
thin flying impactor plate was employed to generate a decaying shock front
(Fowles, [10]) in the fused quartz sample. As seen in Figure 4-4(a), the
radiation intensity from the sample initially falls and then rises before
extinguishing as the shock pressure falls in amplitude. The thermodynamic
path traced out by the radiating shock front is along the Hugoniot rather
than along a release adiabat, since at a given instant the material being
viewed by the pyrometer is new material which is immediately behind the
front and has been just shocked up to the amplitude of the decaying wave

at that instant. In the illustrated experiment, the initial shock pressure

Intensity

~87-

Begin SiQs Begin shock

Temperature
shock

attenuation reversal

Intensity

Figure 4-4.

Time

“Hi00 k-

(a) Light intensity versus time record for fused
quartz experiment with decaying shock amplitude.

Peak shock pressure is 97.5 GPa. Temperature increase
is observed as shock pressure decreases. Wavelength
500 nm. (b) Intensity record for fused quartz shot
at 73.3 GPa pressure. Light intensity fluctuations
are observed at this pressure near the shock tempera-
ture minimum. Calibration for this 650 nm wavelength
record is ~2.2 x 10° W/m2/sr/nm per division.

~88-
is 97.5 GPa, and as the pressure falls, the material passes continuously
through states on the Hugoniot including the phase transition.

According to the data in Figure 4-3 the temperature reversal is
expected at a pressure of ~73 GPa. Figure 4-4(b) shows the intensity
record from another fused quartz shot, in this case with constant shock
amplitude. At the pressure of this shot, ~73 GPa, the material is evi-
dently at or near the temperature minimum which signals the switch from
the anomalous transition region to the higher pressure phase. Unusual
quasi-periodic small jumps in intensity are observed during the shock-
wave transit. This behavior was not observed in identical experimental
configurations at different pressures and could not be otherwise reproduced
with the electronics and cabling of the experiment, thus apparently ruling
it out as an instrumental effect other than random noise. This behavior
is analogous to the oscillating optical signal reported by McQueen et al.
[6] in the same pressure range and may be related to rate effects and
lower phase metastability near the phase transition pressure.

The existence of such a shock-induced phase transition immediately
suggests the possibility of finding evidence for it in other shock wave
data. oa-quartz is the best candidate for such a study, since its higher
initial density makes the shock heating and masking effect of thermal
pressure less than in the case of fused silica. The previously published
Hugoniot data for a-quartz consist of points obtained at pressures below
approximately 100 GPa (Wackerle [11] and McQueen et al. [6], Podurets
et al. [12]), and a few high-pressure points obtained near 200 GPa and
above (Trunin et al. [13]). These data do not overlap the region of the

inferred phase change, so in the present study we have used shock transit

-89-
times from temperature experiments in addition to more conventional streak
camera experiments to obtain additional points between 90 and 140 GPa.
These data are listed in Table 4-3, and a summary of all a-quartz data
above the stishovite transition (~40 GPa) is presented in a plot of shock
velocity versus particle velocity in Figure 4-5. The improved Hugoniot
data obtained for both a-quartz and fused silica have resulted in small
corrections to the pressures in the temperature experiments, thus account-
ing for differences between the pressures reported here and those in
Lyzenga and Ahrens [14].

The data for experiments below the 117 GPa completion pressure of the
transition seen in the temperature data are well fitted by a linear us-u
relation, with a least squares best fit given by

us = 1.822 4, + 1.370 km/s. (1)

This agrees with the fit assigned by McQueen et al. [6] of

us = 1.850 (+ .045) uy + 1.241 (+ .16) km/s. (2)

In contrast, the Hugoniot points from experiments at pressures higher than
the new transition do not fall on this extrapolated linear fit. While the
limited data available do not absolutely exclude the possibility of fitting
the Hugoniot data with a single smooth curve, the higher pressure points
have here been fit with another linear segment of shallower slope. The

fit line shown in Figure 4-5 is given by

us = 1.619 4, + 2.049 km/s . (3)

Besides the shallower slope on the high-pressure branch, this two-
segment fit evidently requires a discontinuity between the two branches

rather than a smooth joining of the two where the break in slope occurs.

-90-

Table 4-3

Supplemental SiO, Hugoniot Data

Tantalum Sample Shock Sample Particle Pressure
Studied Impactor Velocity Velocity (calculated)
Sample Velocity (measured) (calculated) P (GPa)
W (km/s) US (km/s) U5 (km/s)
O®=-quartz 5.172 £ .007 8.64 + .06 4.02 + .01 92.0 i 0.7
o-quartz* 5.62 + .01 9.27 + .16 4.34 + .02 106.5 + 1.9
a-quartz® 5.871 = .010 9.73 + .06 4.51 7 .01 116.0 + 1.4
a-quartz 5.926 + .O11 9.70 = .12 4.55 + .01 116.9 + 1.4
a—quartz 6.297 + .012 9.82 + .10 4.84 + .01 126.0 $1.5
a—quartz 6.600 + .012 10.30 = .10 5.05 + .01 137.7 + 1.5
fused 5.134 + .007 7.98 = .14 4.17 = .01 73.3 $1.3
fused 5.445 + .009 8.42 + 11 4.3974 .012 81.6 + 1.1
fused 5.888 + .011 9.08 + .10 4.7162 .013 94.4 + 1.0
fused 6.285 + .007 9.40 t+ .10 5.023 .008 104.1 = 1.1
fused 6.499 + .010 9.73 + .09 5.175 + .011 111.0 + 1.0

a : :
Data obtained from streak camera records. All others obtained from
duration of shock-induced luminescence in temperature shots.

U; — SHOCK VELOCITY (km/sec)

~91-

Up - PARTICLE VELOCITY (km /sec)

Figure 4-5. Summary of a-quartz Hugoniot data plotted in the

particle velocity-shock velocity plane. Solid

t T T T
| | Us=1.370 + 1.822U
=1370 +1. 2
I2+ | i°s PY ard
a-SiO. summary | | 7
ie © present study | | |
° L |
lo 0 | | :
6 |
9 a —_
7h | :
6 nz —
5 | 1 t \
2.0 3.0 - 4.0 5.0 60

points are results from the present investigation.

Separate linear fits are given for SiO, in the
stishovite regime and for points above newly
observed phase transition. Sources of data are
{liJa, [6]b, [13]e, amd [12]d.

-92-
This break corresponds to an approximately 2% discontinuous increase in
density if it is real. It is of interest to note that if extrapolated back
into the low-pressure region, the high-pressure fit would intersect the
steeper low-pressure fit in the neighborhood of 4 = 3.5 km/s, corres-
ponding to a shock pressure of about 70 GPa. This will be of interest

later in considering the apparent nonequilibrium nature of the phase

transition reported here.

MgoSi0, Experimental

Shock temperature experiments were carried out in the same manner as
described above, using crystalline forsterite (Mg,5i0,,) samples. Forsterite
samples were cut from a single crystal boule grown by the Czochralski tech-
nique, and this material was the same as that used by Jackson and Ahrens
[3]. Sample densities were measured by the Archimedean method to be
3.222 g/em?.

In the experiments carried out on Mg)Si0, (Table 4-4), the samples
used were approximately 3 mm in thickness and the shock was propagated
along the (001) direction (parallel to the C-axis). The temperature uncer-
tainties reflect the errors of measurement and errors in the least-squares
fitting of the six spectral radiance values to mean values of emissivity
and temperature, just as in the case of Si0,. The pressure and temperature
range of the data for forsterite (Figure 4-6), although relatively narrow,
is in general agreement with the expected Hugoniot temperature on the basis
of calculations (Ahrens et al. [15]).

As discussed in the following section, these temperature data, when

compared with theoretical calculations, provide evidence that transformation

~93-

Table 4-4

MgoSi0, Shock Temperatures

Pressure (GPa) Temperature (K) Emissivity
153 + 3 4490 + 100 -66 + .08
166 + 3 4690 + 100 .60 + .06
175 +4 4950 + 100. -53 + .03

a interpolated value

-94-

5000F

2000

Mo SIOg
Shock
Temperatu res

2.0
Olivine Calculation

(Ahrens et al. [969a)

SO

Figure 4-6.

lOO I50

COO
Pressure (GPa)

Measured and calculated shock temperatures versus
pressure for forsterite. Calculations for three

assumed values of the transition energy, Fer are
shown.

~95-
to a dense polymorph or mineral assemblage does occur during the exceedingly

short duration of the shock-wave experiment.

Interpretations

The present set of experiments suggest that the high-pressure phase
of Si0,, presumably stishovite, undergoes a shock-induced phase transition
which is apparent in shock temperature data for both a-quartz and fused
quartz Hugoniot states. Both sets of data display steep temperature
declines with increasing pressure. Since the two negative sloping segments
do not form a continuous curve, they probably do not represent an equilib-
rium phase boundary with a negative Clapeyron slope. The preferred inter-
pretation is that the abrupt temperature drop is observed because the
stishovite phase is metastable, at least on the time scale of the shock
rise time, throughout what would otherwise be the mixed phase region of the
Hugoniot curve. Finally, at the pressure of completion of the phase change,
the material abruptly absorbs the latent heat of transition, entering the
high-pressure phase all at once. This interpretation allows the phase
line to be drawn by connecting the temperature minima in the two data sets,
as has been shown in Figure 4-7. This phase boundary appears to have a
small but positive slope, and this, taken with a positive entropy change
estimated from the temperature drops to be of order R per mole of atoms,
implies that the transition is accompanied by a modest volume increase.

This observation is not inconsistent with the apparent volume decrease
seen in the Hugoniot pressure-volume data above 117 GPa. This is because
the volume decrease corresponds to the sudden change from the relatively

incompressible metastable stishovite to the more compressible stable phase.

-96-

t ! | l l | q
7OO00r 7
fused
quartz
6000 4
T (K) /
Davies /
\i
4000F / 7
/ 7 Hypothetical Fusion Curve
[-7
3000 Hi _
Stishovite
2000 F _
Coesite
1000 ! l l | ! l 1
20 40 60 80 1ee) 120 l40

PRESSURE (GPa)

Figure 4-7. Si0> Hugoniot temperatures and pressures and the
SiO» phase diagram. Proposed phase boundary between
stishovite and liquid phase is drawn through tempera-
ture minima, assuming that superheating of the solid
occurs in the shock wave. The coesite-stishovite-
liquid triple point is estimated from Jackson [33].
Stishovite melting line of Davies [32] also shown.

-97-
Indeed, as pointed out earlier, if the transition were not overdriven,

but occurred in equilibrium at all pressures, the extrapolated upper
branch of the us - 4 Hugoniot in Figure 4-5 would join the stishovite
branch continuously at about 70 GPa pressure, which is approximately the
pressure at which the observed Hugoniot temperatures first cross the pro-
posed phase boundary.

To summarize the characteristics of the transition seen here, it is
apparently accompanied by a small decrease in density, a fairly large
positive latent heat, and an apparent increase in the compressibility
along the Hugoniot upon completion of the transition. These results are
all consistent with the identification of the transition with melting.
Stishov [16] has shown that, for simple solids, the entropy of fusion is
expected to be of order R per mole of atoms in the limit of high tempera-
ture and pressure. Furthermore, it has been well established, for example
by Duvall and Graham [8], that equilibrium shock-induced melting should
appear in the Hugoniot data only as a change in slope similar to that seen
in the SiO) data interpolated for equilibrium transition conditions. The
parameters of the melting transition may be estimated by computing theo-
retical Hugoniot temperature curves for the liquid phase and comparing them
to the experimental results for o-quartz and fused silica.

The calculations of Hugoniot temperatures in this work were performed
using the following method. The adiabat of isentropic compression Po™

of the phase of interest is obtained through numerical solution of the

equation,
dP!
dP dP! H
—S§. HH ,yd Mop _ -y | (V,-v) == - PI - oP i. (4)
wo a tyva Qey-? taf °° WR” s

~98-
Here, Pa and V) refer to the "metastable Hugoniot" of the phase in
question (solid or liquid stishovite) centered at S.T.P. conditions. This
metastable Hugoniot is derivable from the principal Hugoniot as described
by McQueen et al. [17] and depends upon the magnitude of the transition
energy Ee at standard conditions.

In the present work, an interpolation formula was fit to the metastable
Hugoniot, and (4) was solved for Po), the isentrope. Given Pv),
the shock temperature T, was found at various values of V_ through

solution of T

| C aT (P= PS) : (5)

~\<

where now Pu is the principal Hugoniot pressure, and T, is the tempera-
ture on the isentrope at specific volume V.

Unfortunately, the computed shock temperatures of the liquid (stisho-

vite) prove to be insensitive to the assumed value of the Griineisen
“parameter, y = V (aP/9E) | because of the lack of a constraint for a
liquid isotherm. For the liquid state, a nominal value of y = 0.6 was
used.

The computed temperatures are sensitive to the assumed model for the
specific heat, Cy. In the case of the solid phase calculations shown in
Figures 4-2 and 4-3, the results were obtained using a specific heat model
which has the classical 3R value at low temperatures and rises due to
anharmonicity as the melting temperature is approached. The 3R value is
exceeded by 10% at the melting temperature of 4800 K in this model.
Specifically, the solid heat capacity, adapted from the data collected

by Grover [18] is

~99-
C= 3r[1 + 0.1(T/T,)*1, (6)
where Th is the melting temperature.

Figures 4-2 and 4-3 also include calculated Hugoniot temperatures
for the liquid phase regions. The heavy curves labeled "A" employ a liquid
specific heat model of the type also formulated by Grover for monatomic
liquid metals. The specific heat formula used for curve "A" is

C, = 3R{1 - -083(T/T - 1], (7)
and this curve fit requires a larger enthalpy for the metastable liquid
than stishovite at standard conditions by an amount ~2.7 MJ/kg.

For both a-quartz and fused quartz, the slopes of the "A" Hugoniot
temperature curves are not an optimum fit to the data. The calculated
slopes are strongly influenced by the value of Cy: A larger value of
Cy with a smaller energy difference at standard conditions gives a better
fit. It must be noted, however, that the lower-than-expected temperature
rise observed in the liquid may not be real. Kormer [19] showed that in
ionic materials, as shock temperatures exceed 7000-8000 K, the measured
brightness temperature of the shock front saturates, presumably due to
shielding by electrons not in thermal equilibrium. Such problems are dis-
cussed below in connection with the time-dependence of these temperature
records obtained at high pressure and should be kept in mind in the inter-
pretation of these data.

The curves labeled "B" in Figures 4-2 and 4-3 were calculated using
Cc, = 4.2 R, and the standard energy of metastable 6-fold coordinated liquid
was 0.5 MJ/kg higher than that of 4-coordinated amorphous silica. This
value is much more in line with the energy difference between o-quartz and

stishovite (0.8 MJ/kg), but the anomalously high specific heat is difficult

-100-
to explain on physical grounds. In the discussions that follow, models A
and B will be referred to in calculations assuming these two possible
behaviors of the liquid stishovite phase.

The Lindemann melting criterion is a semi-empirical theory of melting
which predicts the volume dependence of the melting temperature on. the
basis of the amplitudes of atomic lattice vibrations. It can be used, with
some qualifications, to estimate the trajectory of the melting line of a
solid if the volume dependence of its vibrational spectrum is known.
Grover [18] has shown that, for metals, the Grumeisen parameter y for
the solid phase adequately describes this dependence, and the Lindemann
law in this formulation becomes

- (d in Tid In V) = 2y - 2/3. (8)

This equation has been integrated for 3 values of y, assuming the
melting temperature Th is known to be 4800 K at the volume corresponding
to 117 GPa pressure in a-quartz. These computed melting curves are shown
in Figure 4-8, along with the observed Hugoniot temperatures translated into
the V-T plane. The o-quartz curve was obtained through the two-segment
Hugoniot described above, and the density jump encountered in going from
metastable solid to liquid accounts for the observed gap in the V-T plot.
The fused quartz data, when viewed in such a plot, are much more compressed
along the volume axis, presumably because of the greater thermal energy
and the smaller contrast between the compressibilities of the liquid and
solid phases in silica shocked from the low initial density of fused quartz.
A fused quartz Hugoniot fit was derived from the work of McQueen et al.

[6], Wackerle [11], Jones et al. [20] and the new points obtained from

this study, given in Table 4-3. A two-segment linear fit was again used,

7000
T (kK)

5000

3000,

-101-

! | L | | | q

a -Quartz Fused Quartz _

¥ 20.4

> 0.6
Lindemann Melting 0.9

Curves
i | i | l |
Re) 2.0 2.1 2.2 2.3

Specific volume (10 * m*7kg)

Figure 4-8. SiO, shock temperatures as a function of specific

volume and theoretical melting curves calculated
from the Lindemann criterion (Eq. 8). Hugoniot
temperatures are transformed into the V-T plane
using experimental P-V Hugoniot data. Disconti-
nuities in the P-V data give rise to breaks in the
temperature plot. Melting line calculations are
based on assumed value of T,, = 4800 K along
o-quartz Hugoniot.

-102-

but the quality of the data and the magnitude of the observed kink was
not sufficient to make any definitive statement about density jumps or
discontinuities due to transition overdriving. In the present work,
McQueen's fit of

| us 1.861 u, + 0.211 km/s — (9)
has been adopted below 86 GPa pressure, joining smoothly with a fit of

us = 1.568 u, + 1.538 km/s (10)

at high pressures.

It is apparent from Figure 4-8 that calculated Lindemann melting
curves are in fairly good agreement with the observations, for values
of y in the expected range. The slope of the V-T melting line can be
translated into the Clapeyron slope of the P-T phase line if we know the
compressibility of the material along the equilibrium phase line. The
equilibrium Hugoniot should coincide with the phase line in the mixed
phase region, so that (dP/dv),, along the Hugoniot should approximate
(dP/dV) along the melting line in the equilibrium case.

We can approximate this equilibrium Hugoniot in the case of a-quartz,
by using the linear extrapolation of the liquid ust 4, Hugoniot branch
as discussed earlier. If the us - 4, relation is given by

us=s u, + Cy, (11)

then the pressure-volume Hugoniot is

(Vo - V)
(Vo - S(Vp - VD)“ *

Differentiating this gives approximately the compressibility of o-quartz

P = ci (12)
along the equilibrium melting line. Using y = 0.6 in the Lindemann law,
this gives a melting line slope of aT /dP x 10 K/GPa. If y= 0.9 for

solid stishovite, the slope is ~20 K/GPa. This result is in good agreement

-103-
with the estimated phase line in Figure 4-7.

Both the volume change and the latent heat of melting of stishovite
at high pressures may be estimated using the present data. Figure 4-9 is
a pressure-volume plot of the Hugoniot fits for a-quartz and fused silica,
with their relations to the solid and liquid phase fields. In the case of
a-quartz, the region of superheated solid is graphically illustrated
adjacent to the dashed equilibrium Hugoniot, which spans the region of
mixed phases. The mixed phase "band" is constructed by connecting the
corresponding pressures of melting onset and completion along the two
Hugoniot curves, as inferred from the shock temperature data. At 70 GPa
pressure on the fused quartz Hugoniot where the melting point is first
reached, the labeled quantity AV is the high-pressure volume change upon
melting at constant T and P. The volume jump estimated in this way is
approximately 0.08 x 107* m?/Kg or 3.9%.

Next, the latent heat of melting may be estimated by comparing the
energies of the solid on the melting line and liquid on the fused quartz
Hugoniot at a pressure higher by amount AP. The latent heat is given by
the difference between the Hugoniot energies Ey on the two curves, less
the thermal energy corresponding to the pressure offset AP, and plus the
PAV work done by the sample in melting at constant pressure. The latent
heat is Te

AH = (Ene - En - | C, dT + PAV, (13)
Ty
where subscripts f and a denote states on the fused quartz and o-quartz

Hugoniots respectively. The results obtained here are AH = 3.8 MJ/kg

and 3.3 MJ/kg, assuming the above liquid models A and B_ respectively.

Figure 4-9.

-104-

| |
— a-Quortz Fused Quartz >
Hugoniot Hugoniot
ISO}— =
Equilibrium
<= 100t—- Hugoniot ™~
® 9 \ |
oO = 4
5 = _
a = Liquid _
50 | Mixed Phase _|
- \ Solid 7
eal \ —
= Stishovite Isotherm _
(Liu et al., 1974)
| |
L8 1.9 2.0 2. 2.2 2.3

Specific volume (107* m°/kg)

Pressure-volume Hugoniot curves for a-quartz and
fused silica. Relation to liquid and solid stisho-
vite phases is indicated by the heavy lines. AP is
pressure offset between SiO, melted from o-quartz
Hugoniot and fused quartz at same density. Liquid
Griineisen parameter y is determined from this
offset. Stishovite static compression data (Liu

et al. [24]) are also plotted.

~105-
The calculated Clapeyron slopes are (dT/dP) = 9 K/GPa and 11 K/GPa, in
agreement with the predictions of the Lindemann law as well as the experi-
mental data. This latent heat corresponds to an entropy change of
1.8-2.0 R in general agreement with the systematics of Stishov [16].

While the Griineisen parameter y is not strongly constrained by the
shock temperature data alone, an analysis of other available equation of
state data yields considerable information about the thermal EOS dependence.
y is obtained by determining the finite difference approximation, V(AP/AV)
to the definition of y = V(dP/dE) between states in the same solid or
liquid phase. Unfortunately, the regions of pure liquid or pure solid
phase along the measured Hugoniot curves for a-quartz and fused silica do
not overlap in volume, with the fused quartz Hugoniot lying everywhere at
lower densities than the corresponding phase a-quartz Hugoniot. This
makes it impossible to determine y immediately from a comparison of the
two Hugoniots, since as shown in Figure 4-9, in the region where they
overlap, the fused quartz Hugoniot is in the liquid field, while the
ad-quartz Hugoniot at the same volume is in the solid stishovite field.

The Griineisen y for the liquid phase can be determined, however,
from the magnitude of the pressure offset AP between the fused silica
Hugoniot and the liquid state obtained by melting from the o-quartz
Hugoniot, assuming AV is known. At a liquid specific volume of
2.155 x 1074 m3/kg, we find AP = 17.8 GPa while the internal energy
difference given by [oar is 1.4 MJ/kg for model A and 1.9 MJ/kg for

model B. Substituting into the Mie-Griineisen equation, this gives
AP
yY=ryv TE 2.0 (model B) - 2.8 (model A) (14)

for the liquid SiO, phase. This determination of y is very strongly

-106-
dependent upon the assumed value of AV, and so has a large uncertainty
(+ 25% or more).

An independent check of this value for y of the liquid phase may be
obtained from an analysis of the decaying shock fused quartz experiment
illustrated in Figure 4-4(a). As stated by McQueen et al. [17], the sound
speed in states on the Hugoniot is

vf?

HOV . (15)

=v (2 -yt-
c, =v A [vw -v a-1] +P

The subscript H denotes quantities evaluated on the Hugoniot at volume V.
Since Cy is the velocity with which a rarefaction wave propagates with
respect to the shocked material, knowledge of the time required for an
overtaking rarefaction to reach the shock front allows a calculation of

Cy and y for the shocked state.

Figure 4-10 is an X-t diagram in which time increases vertically down-
ward, and the horizontal direction represents the positions of target and
impactor during the collision process. The trajectories of the shock waves
and overtaking release waves may be seen schematically, and for the present
case, the shock attenuation in the Si0) layer begins at a time dependent
upon the Si0, rarefaction speed. The experimentally observed time of this
event is approximately 250 ns after the shock enters the SiO, , which
requires the rarefaction to propagate at 19.2 km/s, or 14.4 km/s with
respect to the material which is moving with particle velocity 4.8 km/s.

. Applying equation (15) to this result, y ~ 1.6 + 0.2 for liquid Sid, at
97.5 GPa on the fused quartz Hugoniot. This general agreement with the

previous determination of y at a similar volume is reassuring for con-

sidering both the y measurement, and the melting interpretation used above.

-107-

300 — ketal 2-H 6 mm ——>}
S Sy -------+--- l«— —277 ns impact

N Ta flyer

NI 6.02 km/s

NWN
- 200 - NN

Pk [| ------------- <— -|38 ns shock ot rear
\ \ surface, begin release
-100— N L—Ta shock wave
\ 7.22 km/s
2 O- NN A. Vannnnnnnneneneneie <— Ons begin Si02
i \ ‘
N SiOz shock
+100 — NN 9.18 km/s
NN
SN SiO, rore-
+200 — faction
SN \\ 19.2 km/s
RQ ------- +«— +250 ns rarefaction
NN Decaying overtakes shock,
AN shock begin shock

attenuation

Figure 4-10. Graphical position-time representation of the decaying
shock experiment shown in Figure 4~4(a). Determination
of rarefaction wave velocity allows calculation of the
Griineisen parameter y. Heavy lines are trajectories
of shock waves in the tantalum driver and fused quartz

sample. Dashed lines are release waves propagating at
longitudinal sound speed.

-108-
The above calculations depend upon knowledge of the equation-of-state
parameters of the tantalum flyer plate and base plate. Tantalum (density

16.66 g/cm®) shock and sound velocities used here were calculated from the

fit to the Hugoniot data

us = (1.298 + 0.012)u, + (3.13 + 0.025) km/s _ (16)
of Mitchell et al. [21], and assuming that the Griineisen y varies in
direct proportion to V/Vo> with a zero-pressure value of 1.69 (Walsh
et al. [22]). Uncertainties in these quantities affect the calculated
value of y for Si0,.

The situation concerning the Griineisen. y for solid stishovite is

somewhat more difficult. The zero pressure thermodynamic Griineisen

parameter, given by thermodynamic identities as

Yen = OK, /PC (17)

has been measured by Ito et al. [23] to be ~1.5. Above, a, Ks> and C,
are the volume coefficient of thermal expansion, adiabatic bulk modulus,
and specific heat at constant pressure respectively. Liu et al. [24] have
measured the isothermal compression of stishovite up to pressures of 23 GPa.
While this range of compressions does not quite overlap the densities on
the o-quartz Hugoniot in the stishovite regime, as seen in Figure 4-9,
these data may be extrapolated a short distance (dashed curve) to obtain
overlap with the a-quartz data near 40-50 GPa. The second-order Birch-
Murnaghan fit obtained by Liu has been used for the fit, with bulk modulus
and its pressure derivative equal to K, = 335 GPa and Ky = 5.7 respec-
tively. Using the pressure-energy offset between the Hugoniot and

extrapolated static compression data, we find y * 0.9 + 0.1 for stishovite

-109-
near a relative compression of 0.92. This value is in fairly good agree-
ment with previous estimates of y for stishovite, but difficulty is
encountered in trying to check this against the a-quartz versus fused
quartz offset, as done above for the liquid phase. This method is not
applicable because uncertainties in the density on the fused quartz Hugo-
niot and the extreme steepness of the Hugoniot at lower pressures make
estimates of pressure and energy offsets highly uncertain. Also, as noted
for Figure 4-8, the melting transition along the fused quartz Hugoniot in
this region may be less well defined than along the a-quartz curve. The
calculation of y for the liquid phase is not so adversely affected, since
it makes use of the o-quartz and fused quartz Hugoniot curves where they
are in well-defined single phases of relatively shallow slope, and where
the magnitude of the measured offsets are large compared with their
uncertainties.

The properties of the newly observed liquid phase of Si0,, which pre-
sumably preserves approximately the six-fold coordinated nearest neighbor
distribution of stishovite, can be summarized in order to characterize its
complete equation of state. If the liquid y and zero pressure volume Vo
are assumed known, the Hugoniot curve of "liquid stishovite" shocked from a
hypothetical metastable S.T.P. state may be calculated after the manner of
McQueen et al. [17]. By drawing analogy with the density difference between
4-coordinated and 6-coordinated crystalline Si0,, we estimate the six-fold
coordinated glass to have a zero-pressure density ~60% greater than fused
quartz, corresponding to a specific volume of 2.8 x 1074 m3/kg. Performing
the metastable Hugoniot calculations, a considerable volume dependence for

y is apparently required to obtain physically reasonable results. Using

~110-
a value of y proportional to the square of relative compression or
y x 3.0 (W/V)? yields a metastable Hugoniot with an extrapolated zero-
pressure bulk sound speed of roughly 3-4 km/s and a bulk modulus of
6-coordinated glass in the neighborhood of 50 GPa. These values are
clearly dependent upon the assumed zero-pressure specific volume and
therefore are considerably uncertain.

These results characterize the properties of the high-pressure Si0,
liquid phase and the melting of stishovite to this six-fold coordinated
phase. It is interesting to note that studies of coordination in the
silica analog systen, GeO, (Sharma et al. [25]), indicate that the liquid
in equilibrium with the 6-coordinated rutile phase is in four-fold coordi-
nation up to pressures of at least 1.8 GPa, well into the rutile stability
field. While we find no clear evidence here for persistence of 4-coordina-
tion in liquid S5i0, at stishovite pressures, this should be considered a
possibility. It is interesting to note that the difficulty in recovering
erystalline stishovite from shock compression of fused quartz is explained
by the fact that the Hugoniot curve chiefly occupies the liquid field. The
observed permanent densification of fused silica in such experiments
(Wackerle [11]) may be related to a coordination increase in the liquid,
although densification has not been seen at pressures higher than ~50 GPa.

Table 4-5 summarizes the results which have been obtained or which are
consistent with the present data pertaining to stishovite and its six-fold
coordinated liquid analog. It should be noted that the properties of the
liquid phase at metastable S.T.P. conditions are rough estimates, intended to
give agreement with the experiments, but are by no means uniquely determined.

It is appropriate at this point to discuss some of the limitations of

-111-

Table 4-5

5i02 High-Pressure Properties

Solid Stishovite

a@-quartz centered Hugoniot: u

s 1.822 wD + 1.370 km/s (+2%)

Metastable zero-pressure volume: Vp) = 2.333 x 107" m?/kg
Bulk modulus: Ky = 335 GPa
Griineisen parameter: y 2 0.9

Liquid Phase (6-coordinated)

a-quartz centered Hugoniot: u 1.619 u, + 2.049 km/s (41.5%)

Metastable volume: Vo ~ 2.8 x 107+ m3/kg

Bulk modulus: Ky * 50 GPa

Griineisen parameter: y ~% 3.0 (v/V,)?

Specific heat: ‘ C. < 3R (model A) (eqn. 7)
C= 4.2 R (model B)

Melting Transition (at 70 GPa pressure)

Melting temperature Th = 4400 K + 5%
Melting line slope: aT /dP = 10 K/GPa + 5
Volume change on fusion: Av/V = 0.04

Latent heat of fusion: An = 3.5 MJ/kg +15%

-112-
the current experimental technique and the assumptions which are implicit
in the interpretations discussed here. Perhaps the most crucial issue in
this regard is the question of the source of the observed blackbody radia-
tion and whether that source is truly representative of the Hugoniot state
as claimed. Experimental evidence suggests that the light observed in
these experiments originates in a thin layer near or coincident with the
shock front. The chief evidence for this is the extremely rapid (<5 ns)
rise and fall times observed for the radiation, which would not be observed
if the light source were distributed throughout a larger volume of the
sample. These observations are in apparent conflict with those of Kormer
[19] in which substantially longer rise times were seen in shocked alkali
halides. Those earlier observations were done, however, at lower pressures
and with less time resolution than the current studies, so that the dis-
agreement may not be significant. Subsequent experiments using the present
apparatus with NaCl samples have produced signals qualitatively identical
with the Si0, results reported here (Chapter 3).

In addition to the very shallow (<50 um) depth of the light-emitting
region, the mechanism for light emission is unusual as well. Shock tempera-
ture measurements in forsterite indicate that below a sharp threshold
pressure or temperature (in that case T ~ 4000 K) the efficiency of the
radiating mechanism decreases sharply and the material behaves as a
transparent dielectric with insignificant emissivity. This suggests that
the source of radiation may have a thermal activation threshold. The
source may be in the region of intense lattice deformation and defect
generation within the shock front, and the high metal-like emissivity

would be ascribable only to this narrow zone of material with disturbed

-113-
electronic states, while material some distance behind the front relaxes
to a "normal" electronic state.

If the radiation originates in the shock front, immediate doubt is
raised concerning the degree of thermal equilibrium between the light
source and the bulk material of interest behind the shock. Electronic
temperature equilibrium in the presence of defect states is expected to be
achieved on a quite short time scale (10°? s). As long as the thermal
equilibrium between the material in the final compressed state and the
radiating region is maintained, the observed radiation temperatures are
reliable. Since the rise time of pressures and lattice deformation on the
shock front is probably a few orders of magnitude shorter than the 1 ns
temperature equilibration time, we may infer that the observed temperatures
correspond to lattice temperature for the final states achieved in times
shorter than 1 ns. If the final state takes longer than this to equili-
brate, the observed temperature may not follow the final Hugoniot state.
This may be the explanation for the observed superheating of SiO, above
the melting temperature. . It is reasonable to conclude that shock com-
pressed silica required longer than 1 ns to form a mixed phase assemblage
of solid and partial melt.

The foregoing discussion assumes that the properties of the radiating
shock front are constant in time. While this is nearly true in most
experiments, some notable exceptions occur. Figure 4-4(b) and the results
of McQueen et al. [6] illustrate that near the pressure of transition from
solid temperatures to liquid temperatures, the radiation region may
“oscillate” between the two phases, and a complicated transition between

purely solid temperatures and purely liquid temperatures may occur,

-114-
Furthermore, at the highest pressures (and temperatures) observed in fused
quartz and to some degree in a-quartz, the nearly constant intensity during
shock transit is replaced by signals, which still begin abruptly but then
rise more slowly, apparently approaching an asymptotic value several per-
cent higher, on a time scale of a few hundred nanoseconds. This time-
dependent evolution of the shock structure suggests that care must be
taken in using those temperatures, and while an effort has been made to
determine the final asymptotic temperature, large uncertainties for the
high-pressure fused quartz data have been quoted to reflect this problem.
Kormer [19] pointed out in his study of shock temperatures in alkali
halides that at the highest investigated pressures, corresponding to
Hugoniot temperatures 2 7000 K, the measured brightness temperatures fail
to rise as rapidly as expected with increasing pressure, eventually
"saturating" at some value. Kormer ascribed this behavior to high con-
centrations of shock-produced free electrons which form an opaque screen-
ing layer in a time shorter than that required for thermal equilibration
with the fons. Subsequent experiments on NaCl using the present pyrometer
(Chapter 3) suggest an association between this screening effect and the
onset of the time-dependent “ramp" effect in the luminescence records.
This may indicate that the observed small rate of shock temperature increase
with pressure, which is particularly evident in the liquid data at the
highest temperatures, may be an effect of radiation screening, rather than
the true Hugoniot temperature. If this is the case, liquid model A
should more accurately describe the true behavior than model B with its
large specific heat, required to explain the low temperature slopes.

One final issue regarding the source of the shock-induced radiation

-115-
has to do with the question of heterogeneous yielding and temperature
deposition in quartz. Several investigators (e.g., Neilson et al. [26];
Grady [27]) have discussed the localized heating and luminescence which
occurs in narrow "shear bands" when a-quartz is shock loaded at relatively
low pressures. This behavior is observed at pressures well below the
stishovite pressure regime, but not in the presently investigated range.
If heterogeneous heating occurs in a sample, optical pyrometry will gener-
ally yield an erroneous temperature, characteristic only of the localized
"hot spots" and not the bulk sample.

While this behavior is not expected to persist through the extremely
high pressures and phase transitions of these experiments, an effort has
been made to search for this effect. Figure 4-11 is a reproduction of a
Streak camera record from an o-quartz equation-of-state experiment at
106.5 GPa pressure. The record presents a time history of the light
emerging (or reflected) from a strip across the back surface of the target.
As the image of this slit is swept down across the cathode ray tube record-
ing screen, the onset and termination of shock luminescence is clearly seen
during shock wave transit through the Si0, sample. The inclination of the
observed shock arrivals is due to tilt of the impacting flyer plate with
respect to the target. Within the resolution of the photographic record,
the light intensity is spatially uniform and constant throughout the record.
The faint dark vertical lines are scan line artifacts from the image con-
verter tube face. If temperature inhomogeneities exist at all, they must
be on a scale of microns or smaller.

Discussion of the shock temperature results from Mg,Si0, experiments

centers on the apparent transformation under dynamic compression to a

-116-

Time increasing

; k<— fe) mm ——>|

Begin SiO,
shock

Shock
luminescence

End SiO,
shock

SiO, Arrival mirrors
sample

Figure 4-11.

Image converter streak camera record of shock lumines-
cence in o-quartz shock to 106.5 GPa pressure. Hori-
zontal dimension is lateral distance across the sample
face. In addition to determining shock velocity in
sample, this photograph was intended to record any
spatial or time variation in light intensity arising
from local temperature inhomogeneities. No evidence
of heterogeneous thermal distribution is detected.

-117-

denser polymorph, with an accompanying absorption of energy. The effect
of this transition energy should be evident in the Hugoniot ‘temperatures.

Shock experiments on single crystal forsterite carried out by Jackson
and Ahrens [3] support the existence of shock-induced transformation to a
high-pressure assemblage with a zero-pressure density of approximately
3.9 g/cm*. Jackson and Ahrens could fit their data by assuming the olivine
crystal structure changed to MgSi03 (perovskite) and Mg0 (periclase)
or alternatively, mixed oxides, 2Mg0 + Si05. They made estimates of
Ee, 7 1040.5 MJ/kg and y = (1.5 0.5) ot°5 + °5 where o = V/VynPP
is the compression relative to the hpp volume. Those values were used as
starting models in fitting the forsterite data. The measured temperatures
are consistent with theoretical calculations using Ever = 1.5 + 0.3 MJ/kg.
As in the case of Si09, the data do not constrain y, but the above range
of values are consistent with the measured temperatures, with the central
value of the range y = 1.5 o1-5 giving the best agreement. Varying the
volume dependence of y through the volume exponent weakly varies the
pressure-temperature slope, but does not strongly change the fit to the
data. There appears to be some problem in exactly fitting the observed
temperature-pressure slope, and further data will be required to determine
whether this discrepancy is real. The slope centered on a pressure of

170 GPa is (dT/dP),, = 23 K/GPa + 7. In contrast, the range of values

calculated by varying the volume exponent between zero and 2.0 is

+12

34 K/GPa |".

Conclusions and Implications

The observation of melting in stishovite at pressures near 1 megabar

~118-

(100 GPa), and the estimation of the latent heat of fusion have significant
implications for the state of this mineral under conditions éxisting in the
earth's lower mantle. Knowledge of the melting temperatures of candidate
constituents of the mantle allow constraints to be placed on the geotherm
in the solid mantle and further allow the estimation of such quantities
as creep viscosity which may have a temperature dependence which scales
with the melting point.

Kennedy and Higgins [28] have made arguments concerning the melting
temperature of mantle material using a simplified model of this material
as a binary eutectic system with MgO and Si02 as end members. If the
melting temperature of the pure substances is known at the pressure of
interest, the liquidus temperature of the idealized mantle material should
lie at lower temperatures. Kennedy and Higgins further argue that the
depth of the eutectic minimum at low pressures should be a lower limit to
the depth of the trough at high pressures. Applying this reasoning to
SiO,, with a melting temperature of 4800 K, the solidus temperature of the
hypothetical binary system should be no higher than about 3500 K. This
estimate is based upon the 1305 K difference between the lowest observed
melting temperature in the SiO» (quartz)-MgO(periclase) system (1820 K) and
that of periclase (3125 K) the estimated low-pressure melting point of
stishovite, following the reasoning of Weertman [29].

Another estimate of the mantle melting temperature may be made using
the Si05 high-pressure latent heat of fusion in an elementary melting
point depression calculation (Slater, [30]). In the approximation that
mole fractions X of MgO solute in SiO» form an ideal noninteracting

dilute liquid solution, then the depression of the $10) melting temperature

-119-
is given by

RTS (0)

T 60) - T OX) = Tt x (18)

for small values of X. Ls is the latent heat. The coefficient of X
in the case of high-pressure SiO, is approximately 3500 K. This defines
the initial slope of the liquidus curve and independently suggests that
the depth of the eutectic trough should be at least ~1600 K, again placing
a limit to the solidus temperature in the neighborhood of 3000 K to 3500 K.

These results indicate that in order for a silica-bearing mantle to
be solid at pressures near the core-mantle boundary, the temperature must
be at or below ~3500 K. .A final issue in the discussion of these Sid,
results and their geophysical importance pertains to the creep viscosity
of mantle minerals. A separate paper [31] discusses the impact the present
Si0, melting curve estimate has upon estimates of creep viscosity, based
upon melting point systematics. In general, the melting temperatures
obtained in the present work imply that this viscosity is probably not a
barrier to thermal convection in silica-bearing mineral assemblages,
under the conditions of pressure, temperature, and strain rate prevailing
in the earth's mantle.

Finally, the new Mg,Si0, shock temperature data are in good agreement
with previous calculations which assume a shock-produced phase with a zero
pressure density of ~3.9 g/cm? and a heat of transformation of
1.5 + 0.3 MJ/kg at standard conditions. This result indicates that such
polymorphic transitions can occur in silicates on the time scale of shock
experiments, although the possibility exists that the shock-synthesized
high-pressure phase may retain only short-range order in a crystalline

lattice.

10.

ll.

12.

13.

-120-

REFERENCES

McQueen, R. G., J. N. Fritz and S. P. Marsh, On the equation of state
of stishovite, J. Geophys. Res., 68, 2319-2322 (1963).

Liu, L., A fluorite isotype of SnO, and a new modification of TiO):
Implications for the earth’s lower mantle, Science, 199, 422-425
(1978).

Jackson, I., and T. J. Ahrens, Shock-wave compression of single-crystal
forsterite, J. Geophys. Res., 84, 3039-3048 (1979).

Ahrens, T. J., Dynamic compression of earth materials, Science, 207,
1035-1041 (1980).

Jeanloz, R., and F. M. Richter, Convection, composition and thermal
state of the lower mantle, J. Geophys. Res., 84, 5497-5504 (1979).

McQueen, R. G., J. N. Fritz and J. W. Hopson, High-pressure equation
of state of SiO, (to be published) (1980).

Al'tshuler, L. V., Use of shock waves in high-pressure physics,
Sov. Phys. Usp., 8, 52-91 (1965).

Duvall, G. E., and R. A. Graham, Phase transitions under shock-wave
loading, Rev. Mod. Phys., 49, 523-579 (1977).

Robie, R. A., B. S. Hemingway and J. R. Fisher, Thermodynamic Properties
of Minerals and Related Substances at 298.15 K and 1 Bar (10° Pas-
cals) Pressure and at Higher Temperatures, 216-221, Government
Printing Office, Washington, D.C. (1978).

Fowles, G. R., Attenuation of the shock wave produced in a solid by
a flying plate, J. Appl. Phys., 31, 655-661 (1960).

Wackerle, J., Shock-wave compression of quartz, J. Appl. Phys., 33,
922-937 (1962).

Podurets, M. A., L. V. Popov, A. G. Sevast'yanova, G. V. Simakov and
R. F. Trunin, On the relation between the size of studied specimens
and the position of the silica shock adiabat, Izv. Acad. Sci. USSR
Phys. Solid Earth, No. 11, 59-60 (1976).

Trunin, R. F., G. V. Simakov, M. A. Podurets, B, N. Moiseyev and
L. V. Popov, Dynamic compressibility of quartz and quartzite at
high pressure, Izv. Acad. Sci. USSR Phys. Solid Earth, No. i,
13-20 (1971).

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24,

25.

26.

-121-

Lyzenga, G. A., and T. J. Ahrens, Shock temperature measurements in
Mg,5i0, and Si0, at high pressures, Geophys. Res. Lett., 7, 141
(1980). ;

Ahrens, T. J., D. L. Anderson and A. E. Ringwood, Equations of state
and crystal structures of high-pressure phases of shocked silicates
and oxides, Rev. Geophys., 7, 667-707 (1969).

Stishov, S. M., The thermodynamics of melting of simple substances,
Sov. Phys. Usp., 17, 625-643 (1975).

McQueen, R. G., S. P. Marsh and J. N. Fritz, Hugoniot equation of state
of twelve rocks, J. Geophys. Res., 72, 4999-5036 (1967).

Grover, R., Liquid metal equation of state based on scaling, J. Chem.
Phys., 55, 3435-3441 (1971).

Kormer, S. B., Optical study of the characteristics of shock-compressed
condensed dielectrics, Sov. Phys. Usp., 11, 229-254 (1968).

Jones, A. H., W. M. Isbell, F. H. Shipman, R. D. Perkins, S. J. Green
and C. J. Maiden, Material property measurements for selected
materials, Report NAS 2-3427, 56 pp., General Motors Material and
Structures Laboratory, Warren, Michigan (1968).

Mitchell, A. C., W. J. Nellis and B. L. Hord, Tantalum Hugoniot
measurements to 430 GPa (4.3 Mbar) (abstract), Bull. Am. Phys.
Soc., 24, 719 (1979).

Walsh, J. M., M. H. Rice, R. G. McQueen and F. L. Yarger, Shock-wave
compressions of twenty-seven metals. Equations of state of metals,
Phys. Rev., 108, 196-216 (1957).

Ito, H., K. Kawada, and S. Akimoto, Thermal expansion of stishovite,
Phys. Earth Plan. Int., 8, 277-281 (1974).

Liu, L., W. A. Basset and T. Takahashi, Effect of pressure on the
lattice parameters of stishovite, J. Geophys. Res., 79, 1160-1164
(1974).

Sharma, S. K., D. Virgo and I. Kushiro, The coordination of Ge in
crystals and melt of GeO, composition at low and high pressures
by Raman spectroscopy, Annual Report of the Director, Geophysical
Laboratory 1977-1978, 665-672, Carnegie Institution, Washington,
D.C. (1978).

Neilson, F. W., W. B. Benedick, W. P. Brooks, R. A. Graham and G. W.
Anderson, Les Ondes de Detonation, edited by G. Ribaud, Editions
du Centre National de la Recherche Scientifique, Paris (1962).

27.

28.

29.

30.

31.

32.

33.

-122-

Grady, D. E., High Pressure Research: Applications to Geophysics,
edited by M. Manghnani and S. Akimoto, 389-438, Academic Press,
New York (1977).

Kennedy, G. C. and G. H. Higgins, Melting temperatures in the earth's
mantle, Tectonophysics, 13, 221-232 (1972).

Weertman, J., The creep strength of the earth's mantle, Rev. Geophys.
8, 145-168 (1970).

Slater, J. C., Introduction to Chemical Physics, p. 289, McGraw-Hill,
New York (1939).

Lyzenga, G. A., and T. J. Ahrens, Shock temperatures in SiO, and
high-pressure equations of state (unpublished manuscript) (1980).

Davies, G. F., Equations of state and phase equilibria of stishovite
and a coesitelike phase from shock-wave and other data, J. Geophys.
Res., 77, 4920-4933 (1972).

Jackson, I., Melting of the silica isotypes Si0,, BeFy and GeO0o
at elevated pressures, Phys. Earth Plan. Int., 13, 218-231 (1976).

~123-

Chapter 5

SHOCK. TEMPERATURE MEASUREMENTS IN H,0

Introduction

Water (H20) has been the subject of various dynamic compression
Studies extending continuously to pressures over 100 GPa, and in a few
experiments (Podurets et al. [1]) to pressures of ~1.4 TPa. The equation
of state of water at high pressures and temperatures is of interest in a
wide variety of technological applications, in addition to its importance
to geophysical problems such as the interiors of the major planets and
satellites. Shock wave studies of various molecular fluids including H,0
have been undertaken at Lawrence Livermore Laboratory [2] in an effort to
characterize the thermal equation of state and its dependence upon the
microscopic states of the constituent molecules. That work on H,0
enlarged upon earlier results [3,4] obtained in high-explosives experi-
ments at different pressures.

In the current investigation, the newly developed six-wavelength
shock pyrometry technique has been employed to determine Hugoniot tem-
peratures in water in the range of pressures accessible to light-gas gun
experiments. Shock temperature experiments carried out jointly with
Lawrence Livermore Laboratory have explored pressures between approxi-
mately 50 and 80 GPa. The results presented here allow an evaluation of
the Mie-Griineisen equation of state for liquid H,0, consistent with the

results of previous experiments in H,0 states off the Hugoniot. As with

-124-
experimental results presented elsewhere in this thesis, a more detailed

compilation of measured spectral radiance data appear in Appendix II.

Experiments

The present series of H,0 shock temperature experiments was carried
out through the incorporation of a few modifications of the technique
described in Chapter 2. Most of these modifications were those required
to accommodate and contain a liquid sample. Figure 5-1 shows the liquid
target assembly. A transparent rear window of single crystal sapphire
(Al203) allowed thermal radiation to escape from the shocked water sample,
while the remaining optical path was identical to the other experiments.
The metallic base plate in each shot was composed of high purity aluminum
(alloy 1100), with a thickness of 2 mm. The water sample chamber, incor-
porating a 3-4 mm shock propagation distance, was filled with high purity
deionized water through the indicated fill tubing. A bubble-free sample
was obtained by evacuating and repeatedly flushing the chamber with pure
water. The target assemblies were impacted by gun-launched tantalum
flyer plates at impact velocities between 4.9 and 6.7 km/s. A copper-
constantan thermocouple was attached to the aluminum body of each shot
target, in order to provide a measurement of the water sample temperature
and thus, an accurate determination of the initial state density.

Figure 5-2 illustrates a typical experimental record of emitted
thermal radiation, as shown previously for other sample materials. The
initial portion of the intensity record is qualitatively similar to the
results obtained with solid samples, with a nearly constant "plateau" of
sample radiance during the period of shock wave transit. Unique to this

experimental configuration is the terminal portion of the record, as the

~125-

Al base plate

Ta impactor

H5O0 sample
chamber

. H20 fill tube

_IN SL N radiation

to pyrometer

AloOz window

self-shorting
trigger pin

Figure 5-1.

Schematic cross section of the liquid water
target assembly. Impact driven shock is trans-
mitted to water sample through aluminum base
plate. Sapphire (Al 03) crystal radiation window
forms rear wall of H,O chamber. Shorting pins
provide trigger pulses for pyrometer diagnostics
upon shock arrival in H,0 layer. Shock travel

in water is 3-4 mm during ~400 ns.

-126-

Shock enters Shock reflection
H,O layer at Al,03 window

Alles lel

” i theggpes ae seomet cetiobas alee nals arian spa elie eatin alate ty

——__—_— Intensity

~ Time

Figure 5-2. Typical light intensity record from H,0 shock
temperature experiment. Shock transit through
water layer displays constant thermal radiation
output. Shock reflection from Al203 window is
accompanied by abrupt brightness increase.

Record is for H,0 shock pressure of 61 GPa.
Horizontal time base scale is 100 ns per division.

-127-
shock wave encounters the Alj03 window. Since Al,03 is a material with a
higher shock impedance than water, a second shock of higher amplitude is
reflected back into the sample, so that an increase in light intensity
rather than a decrease is observed at the end of shock transit in the
water. The reported values of shock temperature are obtained from- the
plateau intensity. The measured intensities in the doubly shocked state
are not, however, constant in time; therefore, no attempt is made here
to derive temperatures for the second shock. This time-dependent behavior
may be due to heat diffusion at the sample/window interface, rarefaction
wave interactions, relaxation in the H20 emissivity, or a combination of
these. While double shock temperatures have not been obtained, these
records can provide a supplementary measurement of shock velocity in the
sapphire anvil and thus, as described below, an approximate determination
of pressure and density in the doubly shocked state.

Table 5-1 summarizes the results of four successful shock temperature
shots in H,0, listing the temperatures and emissivities for each value of
Hugoniot pressure. As in the investigations of other materials, the
Hugoniot pressure-volume states were determined from a measurement of the
impactor velocity and previous knowledge of the Hugoniot curves of the
target and projectile materials. For the present investigation, linear
fits to the shock velocity~particle velocity Hugoniots for these materials
were used, as computed from the Livermore data by W. J. Nellis [private
communication]. The Hugoniot for H)0 is given by

u, = 1.332 u, + 2.396 km/s; py = 0.998 g/em>, (1)
This description is assumed valid for 2.5 km/s $ 4, < 7.0 km/s. In

calculations for states with 4, < 2.5 km/s, a second linear fit was

~128-

Table 5-1

H»O0 Experimental Results

H20 reflected
shock state

H20 shock Shock density Temperature Emissivity Pressure Density

pressure(GPa) (g/cm3) Ty (RX) e (+.07) (GPa) (e/em3)
49.0 2.262 + .012 3510 + 150 0.44 59 + 6 3.4041.0
61.0 2.354 + .015 4190 + 150 0.67 127 + 8 3.70+.26
7041 2.38 + .05 4780 + 150 0.52 --- ---
78.5 2.462 + .019 5390 + 150 0.71 172 + 8 3.474.15

-129-
used, joining continuously with (1) at u, = 2.5 km/s, and with a zero-
intercept equal to the sound speed in H20 of u, (0) = 1.483 km/s.

Similarly, the aluminum Hugoniot is assumed given by

u, = 1.300 uy + 5.530 km/s; 9, = 2.715 g/em?, (2)

Here, the linear fit is valid for 1.9 s u, < 5.0 km/s. Finally the

tantalum Hugoniot describing the impactor shock state is that of Mitchell

u, = 1.298 u, + 3.313 km/s; pg = 16.66 g/cm’. . (3)
Each of the above Hugoniot fits is based upon measurements with approxi-
mately 0.5% absolute uncertainty in u,-

Figure 5-3 illustrates graphically the impedance match method which
has been employed to determine the water Hugoniot states. Since pressure
and particle velocity are continuous across material interfaces in a
shocked configuration, the Pou, plane gives a convenient representation
of shock wave interactions, with the common states between material layers
in contact given by the intersection points of their Pru, adiabats. As
illustrated schematically, the Hugoniot locus of a tantalum flyer moving
with initial velocity W crosses the Hugoniot of the aluminum base plate
(at rest) at a common pressure and particle velocity of P, and u,. As
the aluminum shock reaches the HO layer, which is of lower impedance, the
aluminum undergoes partial release along the path shown, reaching a pres-
sure and velocity (P, and u,) corresponding to the transmitted shock on the
Hj0 Hugoniot. A common approximation, which in the present case of alumi-
num has been justified to an accuracy of a few tenths of one percent [2],
is the representation of the release adiabat in the Pru, plane by the

mirror-reflection of the Hugoniot curve through the line 4, =u ,- Under

Pressure,

-130-

Aluminum
Hugoniot

Tantalum

HzO Hugoniot

Figure 5-3.

Particle velocity, up

The shock impedance match construction in the
pressure-particle velocity plane. The locus of
P-u. shock states in a tantalum flyer decelerated
from initial velocity W is shown intersecting

the aluminum Hugoniot (at rest) in the state
(u,>P,)- The aluminum release curve is constructed
by reflecting the Hugoniot in =u,- The
aluminum release curve intersects the water
Hugoniot in the H,0 shock state (uy ,Po)-

-131-
this assumption, it is seen from Figure 5-3 that knowledge of the three
pertinent Hugoniot curves allows P, and ug to be calculated from a
measurement of W alone. Density and the other parameters of the shock-
compressed H0 state are then directly obtainable from the Rankine-
Hugoniot equations (Chapter 1).

Similarly, the reported double shock states in Table 5-1 have been
obtained from an impedance match solution with the Al,0, anvil. The Pou,
state of the second shocked state is identical with the single shock state
of the sapphire. This state is obtained from the known sapphire Hugoniot,

us = 0.934 u, + 9.075 km/s; Pq = 3.98 g/cm’, (4)
fitted to the Livermore data compilation [6], and from the experimental
measurement of u, in the sapphire. Since errors in the determinations
of density and particle velocity accumulate from the first shock state
in the second shock state determination, the reported uncertainties are
necessarily much larger in the latter.

As described elsewhere in this thesis, the reported values of

Hugoniot temperature, T,,

H and emissivity have been calculated from the

six independent spectral radiance measurements at different visible wave-
lengths for each shot. The relatively constant time history of radiation
emitted from the sample is taken as evidence of its equilibrium character,
in addition to the Planck distribution of its wavelength dependence. Table
5-1 shows monotonically increasing temperature with increasing shock pres-
sure and, taking these values as the true shock temperatures, comparison

may be made with the predictions of H20 equation of state models.

-132-

Interpretations

Figure 5-4 shows the measured HO shock temperatures as a function of
pressure, along with the results and calculations of earlier investigations.
As indicated, a few lower pressure points were reported by Kormer [7],
using the two-wavelength method described in the discussion of NaCl results
(Chapter 3). A theoretical calculation of Ty was given by Rice and
Walsh [3], based upon an assumed constant specific heat and a thermal
equation of state derived from double shock experiments.

It is apparent that the results of the current investigation are in
generally good agreement with the expectations for shock~compressed water,
with no sign of the temperature anomalies which have been associated in
shocked solids with first-order phase transitions to the liquid or denser
solid phases. In detail, however, it is apparent that the measured values
fall slightly below the trend of earlier calculations, based upon equation-
of-state estimates made at substantially lower pressures.

The dashed curves of Figure 5-4 indicate the results of temperature
calculations performed in the current investigation. The calculations
followed the method outlined in Chapter 1 by computing the liquid water

compression isentrope and then finding T, from the pressure (and energy)

offset between the isentrope and observed P-V Hugoniot. The input param-
eters for this calculation are the principal Hugoniot, the Griineisen
parameter y(V), and the specific heat at constant volume Ci. The
Hugoniot used was the two-segment linear uu, fit discussed above. It
should be mentioned that the actual isentropic compression process carried

out on HoO from $.T.P. conditions eventually carries it into one or more

of the high-pressure solid ice polymorphs (see, for example, Kamb [8])

-133-

6000

foes
i Cy=2.35R / a
5000 / rf |

Th H,0 / y
(K) | Shock temperatures ft =
$¢ = This work y, A

4000 |— 1 Kormer a

3000 f-

2000 f-

100 a .
° Rice and Walsh calculation

oeeti tits ta tat py ft gt
6) 20 40 60 80

Pressure (GPa)

Figure 5-4. H,0 shock temperature data plotted as a function
of pressure. Results of the current investigation
are shown with those of Kormer [7]. Calculated
Hugoniot temperatures are indicated for different
specific heat models.

-134-
and that in fact the solid phase, ice VII has been observed upon doubly
shocking liquid H20 (Kormer [7]). Therefore, the liquid isentrope referred
to here in theoretical calculations is a metastable curve, characteristic
of the same liquid phase as seen along the principal Hugoniot, compressed
in a hypothetical supercooled condition.

Another input parameter which has been taken from earlier work is
y(V). The combined results of Gurtman et al. [9], Rice and Walsh [3], and
Mitchell and Nellis [2] have been used to formulate a working Griineisen y.
Where double-shock and other non-Hugoniot pressure~volume measurements
exist at densities overlapping the measured Hugoniot, the pressure-energy
offsets between these two data sets have been used to calculate y from
the Mie-Griineisen definition,

aP AP
y= VGR) -Vag- (5)
Vv

where the second equality holds when the Mie-Griineisen equation is valid.
These results show y to increase from a zero-pressure value of 0.5,
passing through a maximum of ~1.5 near a compression (V/V)) = 0.6. There-
after, Y is observed to decrease rapidly with increasing density, drop-
ping below 0.5 again at (V/V,) =~ .45. The present calculations have used
the approximate fit,

y = 0.5(1 + 21.0n - 37.9n*), (6)
where n= (1- V/V5)-

As discussed in Chapter 4 in the cases of Si0, and MgoSi0,, when
the isentrope is not independently constrained in the theoretical tempera-
ture calculation, large variations in the assumed y have very little
effect on the computed temperatures. In the present case, temperature

calculations using a constant y = 0.9 yielded shock temperatures

~135-

essentially indistinguishable from the case of equation (6). While shock
temperature measurements alone do not constrain y effectively, experi-
mental measurements can determine whether the Mie-Gruneisen model is
generally a valid description of the material. Mitchell et al. [10] have
observed the electrical conductivity of shock compressed water and- have
detected a plateau in the rapidly increasing trend of conductivity with
rising shock pressure. This "saturation" of the electrical conductivity
is coincident with the observed decrease in y. In [10] speculation is
raised that the ionization mechanism presumed responsible for the conduc-
tivity increase may also act as a sink of thermal energy, thus reducing
available thermal pressure and the inferred value of y. Such behavior
would be expected to introduce a strong non-Gruneisen dependence (tempera-
ture dependent y) in the thermal equation of state, in addition to a
relative "softening" of the P-V Hugoniot. As shown below, evidence for
these effects are lacking in the present data.

In Figure 5-4, the uppermost dashed curve is computed, assuming the
Same constant specific heat used in [9]. In that work, a value of
C. x 3300 J/kg-K was derived for liquid Hj20 near a pressure of 2.5 GPa
and assumed valid throughout the investigated range. This calculation
gives excellent agreement with the calculation of Rice and Walsh, but
gives temperatures everywhere several hundred degrees higher than the
measured values. Several explanations for this deviation may be offered.

The first possible conclusion is that the specific heat Cc, is
underestimated in the calculation. At the temperatures considered here,
electrons cannot play an important role in the heat capacity, so it is

difficult to admit a specific heat larger than ~3R, the classical solid

-136-
value. Some value between this and the monatomic ideal gas value of 1.5R
is more likely. The above assumed Cc, is equivalent to ~2.35R, so that
some room for increase in c, is admissible. The lower dashed curve in
Figure 5-4 shows that a very good agreement with experiment is obtained
by simply assuming a constant C, = 2.8R (per mole of atoms). Such a
modest change in the value of the specific heat of liquid water at high
pressure appears quite reasonable and is presently favored as the simplest
hypothesis required to explain all the present data.

Alternatively, the observation of shock temperatures somewhat lower
than a priori calculations may be an indication of departure from ideal
Mie-Grineisen thermal behavior, in which thermal pressure at a fixed volume
varies linearly with internal energy. This departure would presumably
coincide with the hypothesized “ionization softening" proposed in [10].

In the case that y is a function only of volume, the temperature
difference AT between the Hugoniot and the isentrope at volume V is

given by Mie-Griineisen as
(7)

where AP is the pressure difference between these states. If the Mie-
Grineisen assumption is not valid, this fact may be expressed by allowing
a temperature dependence in y. If this is the case, then (7) must be

replaced by the equation

Ty
| y(V,T)dT = ——. (8)

Temperature variations along the isentrope are, in general, small compared
with those along the Hugoniot so that we may assume the hypothetical

temperature dependence of y to take the forn,

-137-

y(V,T) = y,(V) + ¥,(V,T), (9)
where y, describes the temperature independent behavior along the isen-
trope and Y2 is zero on the isentrope and increasing in absolute value
with distance from the isentrope as T increases.

In this case, (8) becomes

Ty
y.AT + | y,dT = VAP (10)
1 2 C.
Vv
Ts
or equivalently,
Ty
VAP _ 1 _ - .

Ts

Here, Yo is the average value of the temperature dependent component
of yY, over the temperature interval between Ts on the isentrope and
Ty on the Hugoniot. It is interesting to note that if the temperature
dependence of y is completely separable from the volume dependence, as
in

yV,T) = y,@)[1 + ¥,(7)], (12)
then the effect of Yo in the temperatures predicted from (11) would be
indistinguishable from a simple increase in C, as proposed above.

This model of the observed shock temperatures in H,0 is not favored
for a few reasons. First, the observed excursions in y through the sus-
pected range suggest that lyo/y,| should be large, of the order of unity.
Since changes in the product ye, of only ~20% are required to obtain
agreement with experiment, invoking this effect may be unwarranted. Fur-
thermore, the sign of the change in y with increasing temperature that
is required in (11) to explain the low temperatures is the opposite of

that indicated by the drop in y estimated from double shock experiments.

-138-
These observations, combined with the lack of evidence of any anomalous
change in compressibility along the Hugoniot in the region of interest
argue against the importance of temperature variations in y. Of course,
more complicated or subtle departures from the Mie-Griineisen assumption
cannot be precluded, but in light of the present data, invoking such
behavior is evidently not required.

Finally, the possibility exists that temperature "saturation" analo-
gous to the high-pressure effect seen by Kormer [7] in NaCl (Chapter 3)
accounts for the slightly low observed temperatures and gradients. This
explanation may be largely discounted on two grounds. First, the work
done in the present research program on NaCl and SiO, has indicated that
this radiation screening effect due to copious free electrons on the shock
front is accompanied by a considerable time dependence in the observed
radiation. The current H,0 experimental records, such as that reproduced
in Figure 5-2, have displayed rather constant intensity during each experi-
ment in the investigated pressure range, indicating that this effect has
not yet become important. Secondly, in both the observations of Kormer
and the present study, it appears that for a wide range of materials,
the temperature threshold for onset of this screening effect is 7000-8000 K,
well above the investigated range for H,0.

In conclusion, the present experimental shock temperature measurements
in liquid H,0 have provided a check on the thermal equation of state models
determined for this material in previous dynamic compression experiments.
The current results are consistent with the Mie-Griineisen equation of state,
requiring only modest changes in the specific heat of water from that

observed at lower pressures, in the regime of static compression experiments.

-139-
These Hugoniot temperature data could provide even more rigorous constraints
on y and other parameters of thermal pressure variation in the presence
of independent measurements of the water isentrope (or isotherm) at large
compressions. While such measurements often present formidable problems
for the presently available techniques of static compression, progress
is currently being made in the development of dynamic methods to achieve
isentropic compressions in low-density condensed materials like water, to
pressures comparable with those achieved in Hugoniot experiments. The
final chapter describes the results of an ongoing study of the feasibility

of one such technique for isentropic compression.

-140-

REFERENCES

1. Podurets, M. A., G. V. Simakov, R. F. Trunin, L. V. Popov, and B. N.
Moiseev, Compression of water by strong shock waves, Sov. Phys.
JETP, 35, 375-376 (1972).

2. Mitchell, A. C., and W. J. Nellis, Water Hugoniot measurements in the
range of 30 to 220 GPa, in High-Pressure Science and Technology,
1, 428-434, edited by K. D. Timmerhaus and M. S. Barber, Plenum,
New York (1979).

3. Rice, M. H., and J. M. Walsh, Equation of state of water to 250
kilobars, J. Chem. Phys., 26, 824-830 (1957).

4. Skidmore, I. C., and E. Morris, in Thermodynamics of Nuclear Materials,
p. 173, Intern. Atomic Energy Agency, Vienna, Austria (1962).

5. Mitchell, A. C., W. J. Nellis and B. L. Hord, Tantalum Hugoniot
measurements to 430 GPa (4.3 Mbar) (abstract), Bull. Am. Phys. Soc.,
24, 719 (1979).

6. Van Thiel, M., editor, Compendium of Shock Wave Data, Report UCRL-
50108, Lawrence Livermore Laboratory, Livermore, California (1977).

7. Kormer, S. B., Optical study of the characteristics of shock-
compressed condensed dielectrics, Sov. Phys. Usp., ll, 229-254
(1968).

8. Kamb, B., Structure of ice VI, Science, 150, 205-209 (1965).

9. Gurtman, G. A., J. W. Kirsch and C. R. Hastings, Analytical equation
of state for water compressed to 300 kbar, J. Appl. Phys., 42,
851-857 (1971).

10. Mitchell, A. C., M. I. Kovel, W. J. Nellis and R. N. Keeler,
Electrical conductivity of shocked water and ammonia, preprint

UCRL-82126, Lawrence Livermore Laboratory, Livermore, California
(1979).

-141-

Chapter 6

ISENTROPIC COMPRESSION FROM SHOCKS

IN CONDENSED MATTER

Introduction

The earlier chapters have discussed the high-pressure equations of
state of solids and liquids, focusing in particular upon those states on
or near the Hugoniot, the locus of P-V-E states achieved through a single
shock transition from standard conditions. While the examination of
Hugoniot shock states offers considerable advantages in experimental
measurements and in the range of accessible pressures (in some experi-
ments, such as those of Ragan [1], as high as several tens of megabars),
restriction of experiments to only these states neglects regions of
potentially great interest in high-pressure research.

Shock waves of sufficiently large amplitude are expected finally to
carry the investigated material into the region of high temperature and
pressure in which the material is a high-density plasma, well described
by the Thomas-Fermi statistical model (see, for example [2]). Such
calculations become valid as the electronic shell structure of atoms
becomes "smeared out" and the mean field description of T-F theory
becomes accurate. Along the Hugoniot of most condensed materials,
these conditions are satisfied when the pressure reaches ~50 Mbar and
T > 10 eV. While equation-of-state information in this high-temperature

regime finds direct application in astrophysical problems, as well as in

-142-

those natural and man-made processes which generate shocks of very large
amplitude, the condensed phases of matter undoubtedly display a rich
variety of phase relations and interesting properties at large compressions
but low temperatures. While Hugoniot experiments are capable of producing
extreme pressures, the accompanying strong irreversible shock heating
effect prevents the desired high densities from being achieved.

This effect of shock-generated thermal pressure is most pronounced
in materials of low initial density, since the degree of shock heating

manifested in the Hugoniot internal energy, E, is greater as the initial

volume V, is larger. An extreme illustration of this fact is afforded
by Hugoniot measurements on initially porous media. As discussed in the
review of Al'tshuler [3], in such cases the density in shocked states
on the Hugoniot can actually decrease with increasing pressure.
Unfortunately, many of the materials whose behavior in dense high-
pressure phases are of most interest are those molecular crystals and
fluids whose low densities at standard conditions make these interesting
regions inaccessible to shock experiments. Liquid hydrogen is an example
of such a substance. While shock compression data for H, exist [4],
they provide only indirect information concerning the transition to denser
phases such as the hypothesized metallic state transition. Hydrogen in
solid or liquid metallic phases occurs along the compression isotherm
and isentrope in the pressure range of several megabars, so that these
phases assume great importance in the interior of Jupiter and the major
planets. Additionally, such high-pressure transitions potentially have
importance in technological applications. While the ultimate fate of

all elements and compounds compressed at low temperature may be

~143-

metallization due to the pressure-induced closure of electron band gaps,
the approach and accomplishment of this transition is an important aspect
of solid state physics, whose observation at high pressure largely eludes
present experimental techniques. While some observations may have
recorded such transitions [5], refinement and development of new tech-
niques to achieve large compressions at moderate temperatures are desired.

Experimental techniques which afford compression of specimens along
their isentropes or isotherms generally require a longer time to achieve
the final state than the quasi-discontinuous pressure jump of the shock
front. Static isothermal compression experiments, employing diamond anvil
presses have recently succeeded in reaching pressures in the range near
100 GPa (1 megabar), but accurate determinations of pressure and density
are difficult to obtain. Pressure calibration standards for use in the
rather small sample volume of uniform pressure present a significant
problem, and density determinations via x-ray diffraction are generally
restricted to high-Z materials with strong x-ray scattering ability.

Isentropic compression to megabar pressures has been the goal of
investigations [6,7] using magnetic implosion apparatus. In these experi-
ments, the magnetohydrodynamic pressure of an intense pulsed magnetic
field is transmitted by a conducting shield to the investigated sample
in a cylindrical geometry. The rise time of the pressure in a sample
of a few centimeters dimension is many microseconds. This is a suffi-
ciently long time that shock steepening does not occur within the sample,
and the adiabatic compression is essentially isentropic. In an example
of the application of this technique, Pavlovskii et al. [7] have reported

on the compression of quartz (Si0,) to over 100 GPa. That work suggests

~144-
the occurrence of a major volume collapse in SiO, near 125 GPa pressure
to a presumably new high-pressure phase of density ~10 g/em>.

This observation is of particular interest in light of suggestions
of the metallization of $id, in isothermal compression [5] in the same
general pressure range. While such observations generate much interest in
the high-pressure behavior of silica, considerable uncertainty remains
with the interpretation of pressure, density, and even electrical con-
ductivity measurements in these experiments. Indeed, double shock experi-
ments on 5i0, performed in the course of the present research (Lyzenga
and Ahrens, unpublished data) have failed to detect any major density
changes in the indicated pressure range. Clearly, the large compressions
achieved in isentropic experiments are necessary for the solution of this
and similar problems, but improved techniques for the characterization
of the high-pressure, high-density state are desirable.

Many of the experimental advantages of shock wave experiments result
from their simple one-dimensional geometry. For this reason, the possi-
bility of the conversion ‘from plane-wave shock compression to isentropic
compression is attractive. In principle, this conversion may be accom-
plished by one of two experimental strategies. As discussed in some
theoretical treatments [8,9], in a medium whose initial density and
acoustic properties vary continuously along the longitudinal direction,
the shock wave amplitude may be observed to vanish, to be replaced by
a more gradual (reversible) rise in pressure as the disturbance propagates
along the gradient in material properties. Alternatively, isentropic
compression may be approximated by the successive passage of multiple

low-amplitude shocks through the sample. This technique may be thought

~145-
of as a generalization of the double shock experiment in which states
of higher density than those on the Hugoniot are achieved by reflecting
a first shock from a high impedance anvil. Multiple shock pressures at
a given density approach the pressure on the isentrope as a limit when
the final state is reached through an ever larger number of smaller indi-
vidual shocks. Proof of this principle is straightforward, considering
the graphical illustration of Figure 6-1.

As discussed in Chapter 1, the internal energy jump upon shock

transition from a state (P,,V,) to (P,,V,) is given by
1 in

This is just the area of the trapezoid in the P-V plane which is between
the V-axis and the straight line segment connecting state 1 and state 2.
As seen in Figure 6-1, the internal energy rise in a material which under-
goes a series of successive shocks is given by the sum of the areas of
the shaded trapezoids. In the limit of a large number of intermediate
shocks, this sum approaches the integral, fray. Since the internal
energy of states on that locus is given by the external work integral,
Jaw alone, that curve must be the isentrope (curve of constant entropy).
The current chapter is concerned with calculations which have been
carried out to determine the degree of reversible compression that may
be obtained in practically realizable experimental configurations, util-
izing multiple shock interactions and material property gradients. These
calculations have been carried out numerically, as increasing numbers of
interacting waves rapidly make direct closed form shock propagation

solutions impractical.

Pressure, P

-146-

multiple shock
States

\)

Figure 6-1.

Specific Volume, V

Multiple shock states in the P-V plane. As the
number of successive shocks increases, the sample
State approaches the isentrope. The internal energy
increase in each shock is given graphically by the
area of the shaded trapezoid.

-147-

Numerical Calculation Results

The current set of computer “experiments" investigating shock inter-
actions and the approach to isentropic compression was carried out with
the aid of a general purpose one-dimensional wave propagation simulation
computer code. This code, WONDY IV, has been developed and documented
by the Code Application Division of Sandia Laboratories, Albuquerque,

New Mexico, and complete listings and instructions for the use of the
program are given by Lawrence and Mason [10]. This program handles large
amplitude (nonacoustic) wave propagation problems by solving the finite
difference analogs to the Lagrangian equations of motion on a mesh of up
to 1800 discrete mass elements in one spatial dimension. The steepening
of shocks is stabilized through the use of an artificial viscosity term
in the equations, which serves to spread the otherwise discontinuous
shock front over several zones and retain the validity of the overall
calculation.

While the program includes provisions for constitutive relations
describing anistropic material strength effects, rate dependent and strain
history dependent effects, as well as other specialized material proper-
ties, the current work has employed a strictly hydrodynamic description
of the flow in the experiments described below. All the pressures of
interest will be considerably above the yield strengths of the materials
considered, and in the phenomena which are of interest in this investiga-—
tion, the materials are subjected to compressive stress so that fracture
and spall effects do not assume an important role.

Kompaneets et al. [8] showed that for a particular form of the

Hugoniot equation of state, a gradient of initial density along the

-148-
propagation direction of a one-dimensional shock could effectively convert
it into a wave of continuous isentropic compression. In that work, the

density variation assumed is of the form
= 2,71

Here, m is a Lagrangian position coordinate, fixed in the moving mass
of the medium and Po0 is the reference initial density at m= 0.

The results of Kompaneets show that while shock conversion is achieved
with this gradient, full accomplishment of this desired state is not
reached until a propagation distance of ~O.7 mo. Since m= mp repre-
sents a singularity in py), as m grows to the order of m,, the
initial density becomes a rapidly varying function of position.

This result is not unexpected, since large gradients in Pg seem
necessary to counteract the tendency for pressure pulses to steepen into
shocks in materials of constant properties, after a propagation time of a
few pulse rise times. Such a requirement however places heavy demands
upon the experimental technique. Not only is it required that a sample
be fabricated with as much as an order of magnitude variation in starting
density over its width but diagnostic measurements of the state compressed
at constant entropy can only be obtained during the final few percent
of the wave propagation distance near the terminal free surface or inter-
face, where reflected waves disrupt the measured state. Furthermore,
diagnostic pressure and density measurements must be made in a region of
large gradients in these quantities.

More varied behavior in the attenuation of the discontinuous shock

front is reported by the same authors in [9]. By allowing both the initial

-149-
density Py and the sound speed Cy) to be functions of Lagrangian
position m, a wide variety of shock behaviors.is observed. By taking

the assumed variations

= Pygll + om)" (3)

DoD

and

Cy = Cy), {1 + am], (4)

where a is a positive constant, a significant decrease in the degree
of shock heating is observed after a propagation distance of approxi-
mately a ?.

This observation formed the basis for the first exploratory computer
experiments in the current program. Since the pre-existing WONDY code
is designed to calculate flows in layers of constant initial properties,
with the ability to accommodate up to 20 distinct layers or "plates,"
these calculations must approximate the continuous gradients discussed
above with a series of constant "steps" through the medium.

Figure 6-2 shows the results of a calculation carried out for a
stack of plates ~2 cm in thickness, in which the initial density of the
hypothetical material varies monotonically from 3.5 g/cm? down to 1.3,

while the sound speed C) increases from 5.0 to 13.5 km/s. The assumed

reference Hugoniot equation of state was that given by Kompaneets et al.

[8],

= (£0) (Vo-V)
"a Vo) (2V-Vo) ©)

while the thermal pressure variation was determined by a Griineisen

parameter taken to be y = 2.

-150-

Initial sound

speed

Pressure profile
history

t=O.2us |t=O.7 pus t= 1.2 pes t=|.7us
al 1 T

ae Initial density
(g/em>) 2+

Figure 6-2.

5 Ke) 15 20
Position (mm)

Shock wave conversion in a medium of variable acoustic
properties. Decreasing density (bottom) and increasing
sound speed (top) profiles are given. Wave pressure
profile is illustrated at center as a function of posi-
tion and time.

-151-

As Figure 6-2 illustrates, when a shock with an initial amplitude
of 30 GPa enters the stack, the shoulder of the shock front becomes pro-
gressively smeared, as the magnitude of the discontinuous pressure jump
drops. Toward the end of the shock travel, as the gradients in Pg and
Cy begin to die out, evidence is seen for resteepening of the front as
expected.

While in the illustrated case, scarcely a 10% reduction in the shock
amplitude was achieved with initial property variations as big as 100%,
the results are nevertheless encouraging and indicative of the direction
in which progress might be made. It is possible, as will become apparent
later in this chapter, that in many cases only a partial elimination of
the shock transition in compression of condensed material can result in
a proportionately much greater reduction in the net irreversible heating
of the sample. With results such as those of Figure 6-2 in hand, it
became apparent that additional progress might be made by considering
experiments with large density and compressibility contrasts between
layers, discarding the assumed connection with samples of smoothly vary-
ing density and of uniform composition.

Experimental precedent for this kind of approach already exists.
Adadurov et al. [11] for example, have employed multiple shock reflections
in layers surrounding an investigated sample of low shock impedance to
elevate its pressure to ~50 GPa via approximately 10 successive small
amplitude shocks, thus reducing the temperature rise upon compression
from that of a single shock by a full order of magnitude.

The principle of this method can be illustrated in the simplified

experiment of Figure 6-3. If a thin layer of investigated material is

-152-

——_—>
Velocity W
Impactor \ E nmi
Investigated sample
p A
\ f Anvil Hugoniot

Impactor Hugoniot

W Up

Figure 6-3. Shock reverberation experiment. Low-impedance investi-
gated layer is multiply shocked by surrounding high-
impedance flyer and anvil. Dashed curves indicate
states of successive reflected shocks, approaching the
intersection pressure of the high-impedance Hugoniots.

-153-
sandwiched between two thick layers of some standard substance of high
shock impedance, the shock produced by the impact of one of the thick
layers, acting as a flying impactor plate upon the intermediate layer
will be multiply reflected from the two interfaces, gradually raising
the pressure of the middle section. In the limit that the two outer
plates are much thicker than the investigated layer, the ultimate pressure
attained in the investigated region is equal to the Hugoniot pressure in
the two surrounding plates if they were impacted at the same velocity
with no intermediate layer. Furthermore, if the shock impedance of the
investigated material is very small compared with the surrounding plates,
the amplitude of the first shock in the sample is low compared with the
ultimate pressure, and the degree of irreversible heating is consequently
reduced. Even closer approximation of isentropic compression is achieved
through the use of several material layers displaying a gradation in
shock impedance properties, as in [11].

In that work, however, the ultimate goal of the experiment was the
post-shot recovery of the compressed sample, with no attempt to determine
the density state of the material at peak pressure. A set of computer
experiments was carried out in the current investigation to examine possible
experimental configurations which would be amenable to impact-driven
experiments, with density measurements made using pulsed x-ray shadow-
graph techniques.

The initial calculations were performed using water as the investi-
gated sample. While it was desired to conduct these "experiments" under
conditions which as closely as possible duplicated actual realizable

experiments, some simplifying assumptions were made concerning the material

-154-
equations of state. All materials considered in these calculations were
assumed to have their Hugoniot adiabats described by the linear ust 4,

relation,

us su, + Cy (6)

with the values of s and C, tabulated in Table 6-1. The data in this
table have been derived, except as noted, from the Livermore shock wave
data compendium [12]. Furthermore, the Griineisen parameter was assumed

given by the simple volume dependence,
Y = ¥g(V/Vo)- (7)

Assumed values of Yo are also tabulated. Throughout the discussion
that follows in this chapter, when reference is made to the behavior of
H,O or other substances under isentropic compression, it is to be under-
stood that this refers to the idealized material described above, without
consideration of phase transitions or departures from the assumed equation
of state which surely occur in the actual substance. With this in mind,
the results of the numerical calculations should be considered as indica-
tive of the general behavior of the investigated substances in actual
experiments, even if not useful for precise predictions of their true
outcomes.

Figure 6-4 shows the pressure-particle velocity Hugoniot curves of
the six layer materials used in a set of symmetric impact calculations,
in relation to that of H,0. These materials comprise a sequence of
materials whose impedances steadily increase from that of H,0. The
13-layer impact configuration illustrated in Figure 6-5 was calculated

for an impact velocity of 2.5 km/s.

-155-

Table 6-1

- Assumed Hugoniot Parameters for Impact Calculations

Material py (g/cm) C, (km/s) s Yo
W 19.30 4.005 1.268 1.20
Ta 16.66 3.423 1.214 1.69
Fe 7.86 3.768 1.655 1.30
Al 2.70 5.355 1.345. 2.13
Mg 1.78 4.650 1.200 1.46
Lexan 1.196 2.796 1.258 2.00
H,0 1.00 3.111 1.160 2.00
co, 1.56 2.160 1.470 2.86
Hy -0704 3.940 1.033 1.20

-156-

250 : |
Layered Impact
Material Hugoniots
200r- 4
(GPa)
I50- =
W, Ta Fe
100F =
Al
50 3 7
Lexan
H20
O = i ] |
fe) 1.0 2.0 3.0 40
Up ( km/s)

Figure 6-4.

Pressure-particle velocity Hugoniot curves used for

the six layer materials in symmetric impact calculations.
The progressive increase in shock impedance from water
(H20), through Lexan polycarbonate, magnesium, aluminum,
iron, tantalum, and tungsten is illustrated.

ANG

A.) E 3 aSs

Bet ng
ol1lmeé
(oes) 3
W Ww
eu OW
i OY [1]
aA
ww US
Vr wn Oo
gagé
As Aa dU
Ged
ow
oc
Pa)
is}

oe /layer

oO og

SS KE 8 Heo

vo wo

Soe o

VEN E SkREo.

1 vu wh Pp

ise) HOW

AN “geag

——

LOEN F ES

|3-layer symmetric impact experiment
8- wy symmetric impact experiment _

-158-

When H,0 is impacted by a composite flyer of the six materials,
tungsten, tantalum, iron, aluminum, magnesium and Lexan (polycarbonate
plastic) in the indicated sequence, a relatively smooth buildup of
pressure in the central H,0 layer results. Figure 6-6 shows the computed
pressure in a particular H,0 zone as a function of time from the impact.
The time scale of the pressure rise is determined by the width of the
material layers, which in this case were assumed to be 5 mm wide initially
and divided into 20 discrete zones each.

In Figure 6-6 and succeeding plots of computed results, solid curves
are used to show the theoretical Hugoniot curve and isentrope of H,0,
obtained from the assumed equation-of-state properties (Chapter 1). As
seen in this graph, the H,0 pressure rises monotonically over a period of
about 10 microseconds, tracing out a P-V path which is remarkably near
to the isentrope. In terms of pressure, the deviation from the isentrope
is negligible, although a measurable amount of shock heating is apparent
in the energy and entropy results which are discussed below.

The peak observed H;0 pressure is ~70 GPa, which while being well
below the 135 GPa limiting pressure possible with infinitely thick tung-
sten outer layers, is much higher than the 15 GPa maximum pressure attain-
able via a single shock with the same impact velocity. This result indi-
cates that the method is generally feasible for producing isentropic
compression in planar geometries. The described 13-layer impact demon-
strates this in principle, but such an experiment could prove difficult
in practice. In order to examine the validity of this approach in
similar but more simple configurations, the 8-layer experiment illus-

trated schematically in Figure 6-5 was calculated. In this run,

-159-

120 T TT
H20 Compression
a symmetric layered impact
1oo L (3 layers width Smm/layer _
velocity 2.5 km/sec
BO Hugoniot |
(GPa)
60 -
40 5
20r 7
Z aps _
0 j a | I
3.0 4.0 5.0 6.0

V_ (1074 m?/kg)

Figure 6-6. Computed results of 13-layer symmetric impact experi-
ment. Points indicate computed pressure and specific
volume within H,0 layer at the indicated times after
impact. Theoretical Hugoniot and isentrope for H20
are shown for comparison. Pressure in H20 rises
monotonically along a nearly isentropic path.

~160-
intermediate layers of tantalum and magnesium were omitted as well as
one of the Lexan plates. The spatial scale of this experiment was reduced
in order to check the invariance of the results with the sample size.
In this case, the 2 mm H,O layer was surrounded by 1 mm plates of Lexan,
aluminum and iron, with final 2 mm tungsten plates whose increased thick-
ness was intended to raise the final peak pressure.

As Figure 6-7 illustrates, even with the simplified 8-layer symmetric
impact, compression very close to the isentrope is obtained. In just
under 2 microseconds, the H,0 pressure rises to nearly 90 GPa, corres-
ponding to a density increase on the isentrope of ~3.5 times. Such
results are important since they demonstrate the possibility of achieving
large isentropic compressions with experimental scales and impact veloci-
ties applicable to currently existing apparatus. Another important
observation from these calculations is that in these cases, the pressure
distribution with the investigated H,0 layer is uniform to within a few
percent, thus suggesting the applicability of flash x-ray radiography
as a density determination diagnostic technique.

While the symmetric impact approach discussed above shows consider-
able promise, it will be useful to consider an alternative approach which
is more directly derived from the simple shock reverberation experiment
of Figure 6-3. This alternative configuration, illustrated in Figure 6-8,
offers some advantages from a standpoint of experimental simplicity. As
the schematic illustration shows, a series of alternating plates of high
and low shock impedance materials is impacted by a single thick flyer
plate. In the present case, the flyer and high impedance layers are

tungsten (W) while the investigated material comprising the low impedance

-161-

120 T T T U
H20 Compression
a symmetric layered impact
8 layers width [Imm total
100r- . _
velocity 2.5 km/sec
— _—
80 Hugoniot "]
Pp a
(GPa)
60 F- 4
a Isentrope |
40 -
20+ 7
fe) ! i { |

3.0 4.0 5.0 6.0
V (10-7 m3/kg)

Figure 6-7. Results of 8-layer symmetric impact calculations.
As in Figure 6-6, H20 pressure path approximates
isentropic compression.

-162-

Alternating W Layer Experiments

jj

2.5km/s

Yj

30 mm thick
flyer plate

constant thickness run:
increasing thickness run:

decreasing thickness run:

Figure 6-8.

20 zones/ layer

Lie

WML
SY

H20

Vox

Vs

WY

LE

i ot | | roid!
15} 5 15/5) 51515 | (mm)
Py or hp tg |
| |
M112 [3 415 [6 17 (mm)
po to ob bop boty
ne |
i716 15t(41 312+ tb i(mm

Configuration of alternating plate compression runs.

Three cases are shown, with constant, increasing, and
decreasing plate thickness along the propagation

direction.

H20 layers labelled A, B, and C are moni-
tored for pressure and density.

Tungsten impactor

velocity is 2.5 km/s.

-163-

layers is H,0.

Three cases of this experiment are presented here. The first case
considers the alternating layers to have all equal thicknesses of 5 mn.
The remaining two cases have increasing and decreasing plate thickness
along the propagation direction, as indicated in detail for each in
Figure 6-8. Figure 6-9 displays the results of the constant layer thick-
ness experiment, assuming the same 2.5 km/s impact velocity of the sym-
metric impact series. Two immediate differences from the result of the
symmetric experiments are evident. The first is the expected observation
that the pressure history in the sample is not monotonic, but oscillating
in time. The sample pressures recorded in this figure and the succeeding
alternating plate results are the pressures calculated in the second H,0
layer (labeled "B" in Figure 6-8). In addition to this fluctuating time
dependence, the second difference from the earlier set of results is the
relatively high peak pressure attained. In this case, the highest observed
pressure along the quasi-isentropic compression path is actually somewhat
higher than the 135 GPa tungsten reverberation pressure.

Figures 6-10 and 6-11 present the analogous results for layer "B"
pressures in the increasing and decreasing plate thickness geometries,
respectively. The qualitative nature of each of these calculations is
the same, displaying pressure-volume states near or on the isentrope,
corresponding to up to four-fold compression of H,0 from standard condi-
tions. In order to obtain a more objective evaluation of the symmetric
impact and alternating plate runs, a quantitative measure of the "quality"
of the achieved state is sought. In addition to providing pressure-volume

calculations during wave propagation, the WONDY program provides as a

-164-

250 T I T
H>2O Compression
Alternating W layer geometry
5Smm/layer thickness
velocity 2.5 km/sec
200 4
I50-L Hugoniot _
(GPa)
100 F- 7
Isentrope
50 [- am
O | | |
2.0 3.0 4.0 5.0

V (10°* m°/kg)

Figure 6-9. Computed results for H20 in central layer B of
alternating plate run with constant plate thickness.
Indicated times show oscillatory pressure behavior.
H)O Hugoniot and isentrope again shown for comparison.

-165-

250 T
H20 Compression
Alternating W layer geometry
increasing layer thickness
velocity 2.5 km/sec
200 |- +
150;- 7
Hugoniot
(GPa)
lOO Isentrope |
50 - =
fe) a al |
2.0 3.0 4.0 5.0

V (1074 mkq)

Figure 6-10. Results from H20 alternating plate run with increasing
plate thickness. Pressure is in central H20 layer B.

-166-

250 T | —
H2O Compression
Alternating W layer geometry
decreasing layer thickness
velocity 2.5 km/sec
200 F =
I50 Fr >
Hugoniot
Pp
(GPa)
100 f-
Isentrope
50 |- 5
SpLS @ sys
O I I
2.0 3.0 4.0 5.0

Vv (10-7 m°/kg)

Figure 6-11. Results from H20 alternating plate run with decreasing
plate thickness. Pressure is in central H,0 layer B.

-167-
matter of course, the zone-by-zone specific internal energy of the investi-
gated materials. By employing this quantity, along with some assumptions
about the material properties, the entropy generation in each experiment
may be calculated.
The entropy increase As from standard conditions in going to an
arbitrary state (P;> V5> E,) may be expressed in terms of the temperatures

in state i and on the isentrope at the same volume. This may be written

as

As =

fi Cat
| = (8)

Furthermore, the specific internal energy difference between these same

states may be written,

AE=E, -E_ = | Cc dT. (9)
s Vv

If we assume that Cy = constant, then the above integrals are immediately

evaluated and

AE
3RT

ds = CIn(T,/T,) = Clin +1). (10)

Therefore, in the present calculations, AE is obtainable directly
from the WONDY calculated state E, and the known theoretical isentrope.
T, is calculated readily from Mie-Grineisen theory (Chapter 1) and the
entropy jump As is directly obtained. In the case of ideal isentropic
compression, AE and As are both zero. Since in these computer
"experiments" the correct isentrope is implicitly assumed known in the
formulation of the computer code's equation of state, values of As cal-

culated for various computed runs accurately reflect the relative degree

~168-
of irreversible heating due to each configuration, even though the abso-
lute values of calculated entropy may not bear a strong resemblance to
the reality of actual substances.

Figures 6-12 through 6-15 show the entropies calculated in this
manner, for each of the experimental configurations. Entropy is plotted
as a function of pressure, and the theoretical entropy along the Hugoniot
is also shown for reference. Figure 6-12 illustrates the interesting
result that the entropy production in the symmetric impact is small and
relatively constant up to very high pressures. Additionally, this entropy
production is apparently not strongly influenced by the number of stacked
plates.

The magnitude of this "background" entropy level is evidently con-
trolled by the amplitude of the first shock to traverse the investigated
layer. In the symmetric impacts of Figure 6-12 (W = 2.5 km/s), the first
shock in the H,O layer is caused by the impacting Lexan layer and has an
amplitude of ~5 GPa. Interestingly, the observed entropy production is
very nearly the Hugoniot entropy at just this first shock pressure of
5 GPa. Evidently, the bulk of the entropy contribution comes from the
initial shock, with essentially negligible contribution from succeeding
disturbances which elevate the pressure to as high as 100 GPa or more.

Entropy calculations for the alternating plate experiments display
the same behavior, with the chief determining factor in the entropy of
each layer being the initial shock amplitude early in the compression
history. Several general trends are evident in a comparison of the
results in Figures 6-13, 6-14, and 6-15 for the various alternating plate

geometries. In general, the rearward layers "B" and "C" display lower

-169-

3 if J ' q | q '
- Hugoniot =
H2O Entropy production
5 Symmetric impact
© |3 Layers
e 8 Layers
AS/yt
IF 4
oO e PF 000 sal of o 4 ° i { a] 1
fe) 50 100 150 200

P (GPa)

Figure 6-12. Specific entropy rise calculated from results of
symmetric impact runs. Entropy in computed experi-
mental points and on theoretical Hugoniot is from
equation (10). Note nearly constant low entropy at
all pressures.

-170-

3 l T T 7 T T
| HO Entropy production 2
Alternate layers Hugoniot
Constant thickness
ae © Layer A 4
e Layer B
x Layer C
AS/Cy + J
Ir 4
a re) o 0 ° o 0 7
0 1 e¢ hdl ° ! ! ! “ l
0 50 100 150 200

P (GPa)

Figure 6-13. Calculated entropy production in constant thickness
alternating plate experiment. Entropy production in
all three H,0 layers (A, B, and C) is shown with
theoretical Hugoniot entropy curve.

~171-

3 q ml q qT q q
H>O Entro roduction .
, @ Py P Hugoniot <
Alternate layers
Increasing thickness
2r © Loyer A -
® Loyer B
x Layer C
AS/Cyr
Ir -
T x x *
° ‘ e ° ee ° e ° e ° e
fe) 1 1 a _L | 1
@) 50 100 150 200
P (GPa)
Figure 6-14. Calculated entropy production in increasing thickness

alternating plate experiment.

-172-

3 } J q | mi | q
HsO Entro roduction ;
- Py P Hugoniot =
Alternate layers
Decreasing thickness
abt © Layer A 4
e Layer B
x Layer C
AS/Cy a 7
IF 4
T ° oO ° ° |
0 9 1: ! 4 ball 1
0 50 100 150 200

P (GPa)

Figure 6-15. Calculated entropy production in decreasing thickness
alternating plate experiment. Note exceptionally low
entropy rise in this case.

-173-
entropy than the directly shocked layers "A." Furthermore, the configura-
tion with decreasing plate thickness along the propagation direction affords
the least entropy production, which is even smaller in plates "B" and "Cc"
than that obtained in the symmetric impact runs. Such an experimental
configuration may point the way toward the optimum geometry. One desirable
refinement would be a configuration which accurately produces the W
reverberation pressure in one or more of its layers, thus obviating an
independent pressure calibration in actual experiments.

For purposes of completeness in discussing the results of the current
research, the following is a brief summary of similar results obtained in
calculations with other candidate materials for investigation. Solid
carbon dioxide (Ty = 196 K) and liquid molecular hydrogen (Ty = 20 K) are
two low-density molecular substances whose behavior under conditions of
large isentropic compression are of considerable interest. Layered sym-
metric impact calculations have been carried out for each of these materials,
to provide comparison with the H,0 calculations and to give some indication
of the range of probable applicability of these techniques to materials of .
various properties.

The Hugoniot equations of state for liquid H, and solid co, have been
reported in [4] and [13] respectively, and the fits to the existing data
used in the present work appear in Table 6-1. Figures 6-16 and 6-17
present the pressure and entropy results for solid CO, compressed in the
13-layer symmetric layer configuration, with an impact velocity of 2.5 km/s.
It is apparent that the results obtained are qualitatively similar to
those of the H,0O experiments, with only a slightly larger specific entropy

production due to the initial shock.

-174-

200m T T T T 7
Solid COs
- |3-Layer 5
symmetric impact
Velocity 2.5 km/s
I50r 4
Pf Hugoniot
(GPa) |
}OOF
50r
1 J i] i i 1
0 25 3.0 35

Figure 6-16.

V (1074 m/kg)

Computed results obtained from 13-layer symmetric
impact with solid CO. replacing water as the investi-
gated layer. CO» isentropic compression points
plotted with theoretical Hugoniot and isentrope,

as in Figure 6-6.

-175-

3 | J q L q mi qT
COs Entropy production Hugoniot
5 13- Layer symmetric impact
AS/Cy+ 4
IF 4
fo) o Oo oO ° ° ro)
‘@) 1 J J I 4 _i ]
OQ 25 50 75 100
P (GPa)

Figure 6-17. Calculated CO, entropy production in symmetric impact
run of Figure 6-16.

~176-

Liquid hydrogen results are shown in Figures 6-18 and 6-19, with two
cases illustrated. Both cases incorporate a 6.0 km/s impact velocity.
The 8-layer symmetric impact run, analogous to the 8-layer water experi-
ment, reaches a relatively modest peak pressure of ~70 GPa, while achiev-
ing states close to the isentrope. For purposes of comparison, a calcu-
lation for the case of simple reverberation between thick tungsten plates
(as in Figure 6-3) is also shown. This experiment reaches the substan-
tially higher W reverberation pressure but accomplishes this in rela-
tively few large shock steps. The entropy plots of Figure 6-19 show that
the symmetric impact experiment produces the least irreversible heat of
these cases, but that in either case, the compression of the very low-
density hydrogen is accompanied by more specific entropy production in a

given configuration than for the relatively dense H,O and CO,.

Summary and Implications

The results of the current calculations allow a few broad conclusions
to be drawn, in addition to pointing the way toward further calculations
and actual experiments. ‘Ip general, it is apparent that a good approxima-
tion to isentropic compression may be realized experimentally through the
method of multiple shock interactions. The major obstacle to such work,
however, is devising practicable experimental designs which allow density
and pressure determinations with useful precision. In the promising cal-
culations of the alternating plate compression experiments, it appears
likely that given a sufficiently large number of plates, the tungsten
reverberation pressure can be nearly duplicated in the H,0 layers, thus

providing an unequivocal pressure determination. In the same experiments,

-177-

) q qd q 4 Tt
200 4
a Hy drogen |
® 8-Layer symmetric impact
© W reverberation
I50b | Velocity 6.0 km/s 7
p — Hugoniot |
(GPa)
lOOF
50F
1 aI a] 1 1
O| 2 3 4

V (1073 m3/kg)

Figure 6-18. Computed pressure-volume results for two runs with
liquid hydrogen (Hj) as the investigated sample.
Results for 8-layer symmetric impact and simple
tungsten reverberation are given.

-178-

ml q q Lf q ~ q q .
r Ho Entropy production Hugoniot
© 8-Layer symmetric impact
Cr oe Wreverb. 7
4e 4
AS/Cy L . |
e bd a
0o o 90 re)
2r 4
O _i i 1 j 1 | |
e) 50 100 150 200

P (GPa)

Figure 6-19. Calculated entropy production in liquid Hp from the
two compression runs illustrated in Figure 6-18.
8-layer impact affords less entropy production than
W reverberation impact.

-179-
density measurements via x-ray shadowgraph techniques could be obtained,
given layers of sufficient dimensions to allow satisfactory precision of
measurement.

All of the above calculations have assumed one-dimensional flow,
neglecting the edge effects which result in any real shock experiment
from the finite lateral dimensions of the shocked specimens. In the pre-
viously described shock temperature experiments, the spurious effects of
edge rarefactions propagating inward were eliminated by studying speci-
mens several times larger in their lateral dimensions than the thickness
along the direction of shock motion. In that case, masking of the rela-
tively narrow affected edge region eliminates any spurious radiation
coming from the released regions. In the presently considered isentropic
compression experiments, however, large target (and impactor) thicknesses
are evidently required in order to satisfy simultaneously the requirements
for good pressure and density determinations.

While such large thicknesses can be accommodated by devising shock
driving systems of large lateral dimensions, the difficulty and cost of
performing such experiments rises rapidly with increasing scale. For the
present consideration of impact experiments of conventional scale, atten-
tion must be focused upon finding variants of the above described isen-
tropic experiments, which can accomplish the desired compression with a
minimum thickness of surrounding layers.

Future successful experiments employing the multiple-shock principles
illustrated here should take advantage of material configurations which
minimize the initial shock amplitude and entropy production in the sample,

while subjecting it to as uniform and continuous a compression process

-180-

as possible. On the other hand, application of the density-gradient
method for conversion of shocks to isentropic waves evidently requires
variable density target materials with rather large ranges in initial
state. One solution to this problem may be the use of variable porosity
media, such as plastic foams. In such a case, variable density medium
would not constitute the investigated layer but could be used to transmit
a "broadened" shock wave into a material of interest. Clearly in such a
case, the sample wave profile would vary in time, and the state of com-
pression would vary from point to point within the medium. Such experi-
ments thus would require density and pressure measurement techniques
sensitive to spatial variations as well as to the motion of the studied
medium. Imbedded foil x-ray shadowgraph measurements could provide such
records.

The basis of such measurements rests upon the Riemann solution for
isentropic flow in an ideal fluid. As derived by Rice et al. [14], the
particle velocity in such a flow is simply related to the isentropic

compressibility through the Riemann integral,

fo)

u_= | Cdp (11)

P p

Po
Here, C is the sound speed defined by
1/2

9P
C = | . 12
(0) = Ge) (12)

Using this together with the fact that the pressure along the assumed
isentropic compression path is a function of the density p (= 1/V)

only, equation (11) may be rewritten,

~181-

1/2
u - | (-2) a. Oo (13)

These equations are applicable in compressive flow for times before
x-t characteristics of the flow cross, and the wave profile steepens into
a nonisentropic shock. Equation (13) may be applied to an experiment in
which a wave of isentropic compression is transmitted to a sample of
interest. If a series of thin foils which are opaque to x-rays are
imbedded in the sample, inclined at an angle to the plane of oncoming
waves, flash x-ray photographs of the sample can be used to characterize
the flow with minimal perturbations of the wave. Observations of changing
inclination angle and displacement of the foil layers in shadowgraphs taken
at two successive times provide measurements of density versus particle
velocity throughout the compression wave. Thus in principle, these data
could be inverted through equation (13) to obtain the isentrope P(V)
for the studied material.

The potential applications of equation-of-state measurements along
the isentrope at very high pressures are numerous. For the general sub-
ject of this research, the implications of such experiments would be
important. Direct observation of states on the isentrope would consider-
ably strengthen the interpretations of shock temperature measurements by
placing stricter limits on the Grimeisen y and its variation with volume
and temperature. Furthermore, as the isentropes of various materials are
observed to cross the boundaries of new high-pressure phases, a rich field
of condensed matter physics will be explored. This is yet another appli-

cation in which pyrometric temperature measurement could be employed to

-~182-
advantage, in characterizing the thermal processes in such transitions.
In summary, the development of techniques for achieving isentropic com-
pression in solids may prove practicable, and it promises to augment
considerably the information currently obtained from more conventional

shock wave experiments at high pressure.

10.

-183-

REFERENCES

Ragan, C. E., Hugoniot measurements near 50 Mbar, preprint no.
LA-UR-79-1992, Los Alamos Scientific Laboratory, Los Alamos,
New Mexico (1979).

Al'tshuler, L. V., N. N. Kalitkin, L. V. Kuz'mina and B. S.
Chekin, Shock adiabats at ultrahigh pressures, UCRL transla-
tion ref. 02251 (from preprint of Institute of Applied
Mathematics, USSR Academy of Sciences), Lawrence Livermore
Laboratory, Livermore, California (1976).

Al'tshuler, L. V., Use of shock waves in high-pressure physics,
Sov. Phys. Usp., 8, 52-91 (1965).

Ross, M., A theoretical analysis of the shock compression experi-
ments of the liquid hydrogen isotopes and a prediction of
their metallic transition, J. Chem. Phys., 60, 3634-3644
(1974).

Kawai, N., S. Mochizuki and H. Fuilta, Densification of vitreous
silica under static high pressures higher than two Mb, Phys.
Lett., 34A, 107 (1971).

Hawke, R. S., D. E. Duerre, J. G. Huebel, R. N. Keeler and
H. Klapper, Isentropic compression of fused quartz and liquid
hydrogen to several Mbar, Phys. Earth Planet. Int., 6, 44-47
(1972). :

Pavlovskii, A. I., N. P. Kolokol'chikov, M. I. Dolotenko and A. I.
Bykov, Isentropic compression of quartz by the pressure of a
superstrong magnetic field, JETP Lett., 27, 264-266 (1978).

Kompaneets, A. S., V. I. Romanova, P. A. Yampol'skii, Conversion
from shock to isentropic compression, ZhETF Pis. Red., 16,
259-262 (1972).

Kompaneets, A. S., V. I. Romanova, and P. A. Yampol'skii, On shock
propagation in an inhomogeneous condensed medium, Fizika
Goreniya i Vzryva, 11, 807-809 (1974).

Lawrence, R. J., and D. S. Mason, WONDY IV -— A Computer Program
for One-dimensional Wave Propagation with Rezoning, report
no. SC-RR-710284, Sandia Laboratories, Albuquerque, New
Mexico (1975).

il.

12.

13.

14.

-184-

Adadurov, G. A., V. V. Gustov, V. S. Zhuchenko, M. Yu. Kosygin
and P. A. Yampol'skii, On the transformation of shock com-
pression into isentropic compression, Fizika Goreniya i
Varyva, 9, 576-579 (1973).

Van Thiel, M., editor, Compendium of Shock Wave Data, Report
UCRL-50108, Lawrence Livermore Laboratory, University of
California, Livermore, California (1977).

Zubarev, V. N., and G. $. Telegin, The impact compressibility |
of liquid nitrogen and solid carbon dioxide, Sov. Phys. Dok.,
7, 34-36 (1962).

Rice, M. H., R. G. McQueen and J. M. Walsh, Compression of
solids by strong shock waves, Solid State Physics, 6, 1-63
(1958).

-185-

Appendix I

DESIGN AND EXECUTION OF SHOCK

PYROMETRY EXPERIMENTS

Experimental Apparatus and Layout

The experimental components which accomplish and support the shock
temperature measurements presented in this thesis are described here under
four subsystem classifications. These are the target assembly, the
pyrometer optical and mechanical unit, the electronic detection and
recording subsystem, and the support diagnostics relevant to the light-
gas gun operation and performance. The current description applies to
shock pyrometry experiments carried out with the Lawrence Livermore
Laboratory light-gas gun.

The basic target assembly design is illustrated in Figure I-l,
for the case of solid samples. The modifications incorporated for liquid
samples are straightforward and are elucidated in Chapter 5. As noted in
the illustration, the target assembly is positioned in the evacuated
impact chamber so that projectile impact occurs after a free-flight dis-
tance of roughly 30 cm. The target position is fixed by the requirement
of maintaining the sample location near the axis of symmetry of the pyrom-
eter optical array.

The target assembly is mounted with a three-point adjustable
suspension plate, which permits adjustment of the target plane to per-

pendicularity and concentricity with the projectile launch tube. The

~186-

Pin Output to
Trigger Circuit

Gas Gun
[ Target Frame

Coaxial
)) Shorting Pin
First Surface
<«— ~30cm f
to Barrel C) Cryetal Mirror
1)
«s. ——

45° Bracket

Figure I-1. Light-gas gun target assembly for shock pyrometry
experiments. Target plane is adjustable with
3-point suspension, and 45° mirror directs light
paths into pyrometer optics. Shorting pins are
mounted with contact surfaces at sample/base
plate interface plane.

~187-

target mounting plate, as illustrated, is a triangular aluminum plate
(10 mm thickness), with a central hole to accommodate the sample and with
a notch removed to prevent light path obstruction to the pyrometer optical
channels. The standard target base plate (usually 1-2 mm thick tantalum)
is attached to this plate, with the sample crystal mounted on the base
plate rear surface. While the projectile flyer plate diameter is 25 mm in
the LLL gun, the sample diameter is typically 17-19 mm in diameter. Sample
Specimens are cut to 2-4 mm thickness and polished to optical smoothness
on each face. Attachment of all target materials is accomplished using
epoxy adhesive around component edges, taking care to keep epoxy out of
the direct optical path of the pyrometer. Spurious light from edge
regions and the epoxy is eliminated by attaching an opaque circular mask
to the sample rear surface as the final step of target assembly. This
mask restricts the pyrometer view to the central ~10 mm of sample diameter.

Mounted next to the sample on the base plate rear surface are two
coaxial self-shorting trigger pins. These pins, which are positioned in
a vertical plane through ‘the target center, provide an electronic trigger
signal upon shock arrival in the sample, and additionally provide a measure-
ment of projectile "tilt" in the vertical plane. Each of these pins con-
sists of a ~1 mm diameter coaxial conductor pair, with a brass end cap
which shorts the outer and center conductors upon the passage of a pressure
pulse. These pins are biased at ~150 v. prior to impact, and the shorting
pulse is carried through conventional 50 2 coaxial cable to the appropriate
diagnostics.

Finally, an expendable first surface (aluminized) mirror is

attached to the target plate with a 45° bracket, thus reflecting light

-188-
from the target to the pyrometer optical subsystem, whose axis is perpen-
dicular to the direction of impact, in order to minimize fragment damage
to the systen.

The pyrometer proper, as shown in Figure I-2, consists of the
optical and mechanical assembly entirely outside the evacuated impact
tank. Figure I-2 is the cross section in a side view of the pyrometer, so
only two of the total of six optical paths are shown. The steel flange
plate bolts directly to the side access door of the LLL gun, and vacuum
integrity as well as shrapnel protection for the pyrometer optics is
afforded by the 10 mm-thick polycarbonate plastic windows. Transmission
spectra of commercially available polycarbonate stock (e.g., Lexan and
Tuffak brands) verify that it serves as a satisfactory window for wave-
lengths between 400 and 1100 nm. Vacuum seals are accomplished using
conventional neoprene O-rings.

Mounted rigidly to the 19 mm flange plate is the optical frame.
Each of the six optical channels consists of a pair of positive achromatic
lenses, with a narrow-band interference filter inserted between them. The
target-facing and detector-facing lenses of the pair are each 52 mm in
aperture diameter and have focal lengths of 508 mm and 193 mm respectively.
These focal lengths were selected to be approximately the distances to
the target and to the detectors, measured from the lens doublets, so that
the light rays between the elements are approximately parallel and strike
the interference filters at normal incidence.

The interference filters, which are commercial units of laminated
dielectric and glass construction, are removable from their spring clip

mountings in the lens cells. Each filter has a transmission half-height

-189-

Vocuum Interference

Enclosure Filter

Box

Detector oN,
-— —— —— Output 7 HT]

y/_Imeoc Chamber
Flange Plate

Bios Power
Supply

|_— Polycarbonate
a Window

[ MW’

~50 cm
to torget ——

ANS

Ssorernre wanes

Objective
ee Achromats

WWW

Figure I-2. Exploded view (side cross section) of pyrometer
components. Optical elements are fixed to flange
plate, while detector array is adjustable in
position. Vacuum enclosure box surrounds entire
assembly to provide backup vacuum integrity in
the event of window failure. Lens aperture is
52 mm and effective system focal length is 140 m.

-190-
wavelength bandwidth of ~9 nm, and the peak transmission of each is ~40%.
The central wavelengths of the filters have been determined with a trans-
mission spectrophotometer and are tabulated along with the integrated
equivalent bandwidth of each in Table I-1.

The detector rack is located behind the optical frame, supported
in the optical focal plane by struts attached to the flange plate (not
illustrated). The six individual detectors are mounted on mechanical
positioning fixtures, which allow precise adjustment of detector position
in all three orthogonal directions.

The entire pyrometer assembly is finally enclosed by a box of
10 mm welded aluminum construction, which provides backup vacuum integrity
in the event of a window rupture. As earlier described, the light-gas
gun pump gas is hydrogen, so that care must be taken to prevent atmospheric
oxygen from entering the hydrogen-filled impact chamber immediately follow-
ing a shot. Vacuum-secure coaxial BNC feed-through connectors are used
to transmit detector signals from the pyrometer and to supply the detectors
with external power. Removable side ports allow adjustments and connections
to be accomplished with the vacuum box in place.

The detector circuit schematic has been given in Chapter 2. The
photodetector, which is a Hewlett-Packard 5802-4207 PIN silicon photodiode,
is reverse biased at 10 volts, so that a transmitted photocurrent propor-
tional to the flux of incident photons is produced at the output terminal.
This current source drives a 50 2 effective load, in the form of a coaxial
transmission cable, terminated at the recording oscilloscope.

The photodiode active area is approximately 1 mm in diameter,

so that it intercepts only a fraction of the ~4 mm diameter area of the

-191-

Table I-1

Interference Filter Parameters

Channel Central wavelength Integrated equivalent
identification A_(nm) bandwidth (nm)
451 . 450.2 4.37
506 507.9 4.11
546 545.1 4.98
598 598.0 | 5.04
651 650.0 5.52

793 792.0 8.96

-192-

masked target image, which has been demagnified by the focal ratio of
approximately 2.6:1. Therefore, in a fixed geometric configuration, the
detector output current (or voltage across 50 %) is proportional to the
image brightness per unit area and is relatively insensitive to small
lateral misalignments of the detector and image center. Similarly,
sampling only the central portion of the image disk makes the intensity
measurement relatively insensitive to depth of focus errors. The central
"blur circle" intensity falls off from the value at perfect focus by an
amount approximately proportional to the square of the distance from the
true focal plane, and in the present case, 0.1% tolerance in detected
intensity is obtained with a positioning precision of ~l mm in focal
depth. Furthermore, the image of the shock front remains in satisfactory
focus throughout its travel through the sample, since the 3-4 mm shock
travel translates into an image shift (2.6)? times smaller, or ~.5 mm.
Since the onset of shock luminescence in the sample and shorting of
the trigger pins occur simultaneously, it is necessary to delay the
detector signals relative to the trigger pulses which initiate the oscil-
loscope sweep. This is accomplished by passing each detector signal
through a ~200 ns delay line consisting of low-loss 50 2 impedance coaxial
cable. The voltage waveform then enters the oscilloscope input, with
nominal 50 2 cable termination. The oscilloscopes used in these experi-
ments have been Tektronix models 585 and 7903, with the latter providing
superior high-frequency response and greater vertical voltage gain. The
scopes are operated with a time base rate of 100 ns per horizontal
division in the single sweep mode, and the waveforms are recorded with

a Polaroid camera and high-speed (ASA 10,000) recording film. The

~193-
photodiode detector has a manufacturer-rated speed of response of <1 ns
with a 50 2 load, and calibration tests using a pulse-modulated solid-
state laser light source have verified that the total system of detectors,
cabling, and oscilloscopes are capable of discriminating signals 5 ns
or less in duration. In a typical experiment, each of the six detector
channels has two cascaded oscilloscopes in parallel with the signal line
with different gain sensitivities in order to ensure optimal recording
of the signal waveform.

The prompt signals provided by the shorting trigger pins are ulti-
mately routed to three devices. The first of these is the triggering
network of the oscilloscope bank. The first pin to close causes the
oscilloscope sweeps to begin and fiducial time marks to be superimposed
on the beginning of the baselines. Secondly, each of the pin pulses is
recorded relative to an absolute time reference fiducial on high-speed
Tektronix 519 oscilloscopes. These records provide projectile tilt
information. Finally, the trigger pulse provides the stop signal for
electronic counters used to measure the projectile flight time.

The most important diagnostic function apart from the pyrometer
detectors is the flash x-ray velocity determination. A flash x-ray
source with a pulse duration of ~20 ns illuminates the projectile flight
path 10 cm. in front of the target face. The shadow of the passing pro-
jectile is recorded on Polaroid film, as the x-ray flash is triggered by
the projectile interruption of a preceding CW (continuous wave) x-ray
beam. The precise location of the target relative to the x-ray photograph
frame is determined in a pre-shot calibration photo. -A high-speed fre-

quency counter is employed to measure the interval (typically ~20 pS)

-194-

between x-ray firing and target pin closing. After corrections are

applied for the semi-duration of the x-ray pulse, tilt of the projectile

flyer plate and other systematic timing errors, the projectile velocity

is determined to within typically 0.2%.

Operational Procedure

The following is a procedural list of events and required operations

in the routine conduct of a single shock pyrometry experiment. This list

serves as a partial checklist of procedures in preparation for an experiment.

1.

Target is mounted in impact tank and adjusted to proper position and
orientation for projectile impact.

X-ray calibration photo is taken. Photo should show the frame center
approximately 9.0-10.0 cm from the target base plate center.

New polycarbonate windows are positioned on the door flange plate,
which is bolted to the tank door directly adjacent to the target.
Window O-rings should be clean and free of cuts. Windows are held

in place with a retaining plate finger-tight.

Optics frame is bolted to the flange plate with interference filters

removed.

Detector array is positioned on supporting struts and secured.

Small focusing lamp is attached to rear surface of sample crystal.
Focusing lamp consists of miniature clear envelope battery-powered
bulb.

Each channel detector is adjusted in position to give best focus of
filament image on detector active area. Adjustment is made for rela-

tive depth displacement between bulb filament and actual sample

10.

ll.

12.

13.

14.

15.

16.

17.

-195-
position. Horizontal positioning fixtures travel on a threaded
movement with 32 revolutions per inch of travel.
When the focusing procedure is completed, the lamp is removed and
the light path is cleared of obstructions.
Trigger pin cables within impact tank are connected and verified.
Impact tank receives final preparation, is sealed and vacuum pumping
begins.
Interference filters are inserted into proper optical channels.
Internal power supply and signal cables are connected to detector
BNC terminals.
Vacuum box is installed and cable connections completed to BNC feed-
throughs.
Vacuum box side ports are installed and box is purged with inert gas
(dry nitrogen or argon).
External cable connections to oscilloscopes are completed and con-
tinuity is verified. Optional signal preamplifiers are connected as
necessary.
Oscilloscope time bases and vertical sensitivities are calibrated
in the settings appropriate to the expected signals. Oscilloscope
triggering and cameras are adjusted and verified for single shot
exposure.
Pyrometer power supply is turned on, and the pyrometer is ready for

final gun preparation and firing.

Pyrometer Calibration Procedure

In order to translate experimental signal levels into sample spectral

radiance values, calibration must be carried out with a standard light

-196-
source of known characteristics, If the calibration is carried out in
the same geometric configuration and with the same optical components as
in the actual experiment, then a light source of known spectral radiance
provides a direct full-system calibration, without the necessity of
explicit measurements of detector area, filter bandwidth, optical losses,
or subtended solid angles. Any changes in filters or optical components
of the pyrometer necessitate recalibration. Sufficient variations (sev-
eral percent) in the transmission spectra among different lots of window
plastic material are observed that recalibration is necessary when
changing from one polycarbonate lot to another.

As described in Chapter 2, the standard light source is a tungsten
ribbon filament incandescent lamp, which is calibrated in spectral
radiance at a specified lamp current and is traceable to National Bureau
of Standards sources. The ribbon width is just great enough to illuminate
fully the detector active area in the experimental geometry. Table I-2
gives the calibration values for the lamp used in this work, at selected
appropriate wavelengths. .

The following is a procedural list of steps for the pyrometer cali-
bration. For the purposes of calibration and data reduction, the assump-
tion that the measured spectral radiance is constant across the inter-
ference filter line width (~9 nm) introduces negligible error in the
present cases.

1. Pyrometer optics and detectors are assembled in the experimental
configuration, with the tungsten filament occupying the position

of the sample.

2. Fine focusing is accomplished as in the experimental procedure, with

~197-

Table I-2

Calibration Lamp Spectral Radiance Values

LLL Standards Lab lamp no. EPT 1013 operated at 35 Amperes A.C.

A (om) Spectral Radiance
(Wo mm 2 nm? sr?)

450 11.6
500 22.9
550 39 .6
600 57.7
650 78.3
700 98.5
750 115.

800 126.

~198-
interference filters removed.
Pyrometer calibration is accomplished at essentially DC response,
with light beam interruption by a rotating chopper wheel at ~100 Hz.
With chopper rotating and lamp at full current (35 Amperes AC),
the detector signal without interference filter is measured in each
channel with an oscilloscope. 50 2 terminators from the experimental
layout are used as loads.
Since pyrometer signals for the tungsten source at ~2700 K are
expected to be prohibitively small, measurements with the narrow
band filters in place must be taken with-the 50 2 load omitted,
and the oscilloscope high impedance input appears in parallel with
the detector circuit internal impedance of ~1 kf. This affords an
effective gain of 20 in measured voltage. Signal measurements without
interference filters and without 50 2 termination are made to obtain
the gain correction for each channel.
Signal measurements are made with interference filters in place and
without 50 2 termination. Care should be taken to eliminate sources
of external noise, since millivolt-level signals are to be measured
with maximum precision (~a few percent).
The calibration factor for each channel is obtained by first obtaining

the detector voltages for a 50 2 load from

E nite 20%)

Cika) ° (1)

E (502) = Z
white

filter (1ks2)

Fedlter

Dividing the quoted lamp spectral radiance at each wavelength by the

signal voltage determined above yields the channel calibration factor,

-199-

Ky in units of watts per square millimeter, per nanometer bandwidth,

per steradian, per Volt of signal. Alternatively, this is expressed

in the units W/m?/sr/V.

For reference purposes, the calibration factors determined on
10 October 1979 are listed in Table I-3. The pyrometer calibrations
obtained in this manner assume that the photodiode quantum efficiency
of photocurrent production is constant for response times from DC to
the experimental times of 1077 - 10°8 s. Furthermore, photocurrent
response is assumed proportional to light intensity over the ~3-4 decades
of intensity variation between calibrations and experiments. This is
consistent with the manufacturer's quoted response linearity over six
decades.

The uncertainty in the standard lamp spectral radiance calibration
is quoted at ~2-3%, and this limits the precision of the pyrometer cali-
bration. The assumed impedance constancy of the 50 2 cable terminations
from DC up to 108 Hz introduces 1% or less uncertainty in the calibration.
Experiments have verified that delay cable dispersion introduces no
measurable amplitude effect in this frequency range. Therefore, the
calibrations given here and the radiance measurements in Appendix II
have associated with them a conservatively estimated uncertainty of

approximately 42.

-200-

Table I-3

Pyrometer Calibration Factors

Measured 10 October 1979 in LLL Standards Lab.

Channel A (nn) Ky
Identification (Wm73 sr7? v4)
451 450.2 8.007 x 101%
506 507.9 | 5.295 x 101"
546 545.1 5.024 x 1014
598 598.0 3.965 x 1014
651 650.0 3.913 x 1034
793 792.0 1.500 x 101"

-201-

Appendix II

EXPERIMENTAL SPECTRAL RADIANCE MEASUREMENTS USED IN

SHOCK TEMPERATURE DETERMINATIONS

The experimentally measured spectral radiance values for studied
samples in the shock pyrometry investigations are tabulated here. The
reported intensity values have been obtained from measurements of
detector voltage amplitude on oscilloscope records. The calibration
factors used for conversion of these voltage measurements into spectral
radiance values were obtained by the procedure outlined in Appendix I.
In all cases, the intensity measurements refer to the terminal value
recorded at the end of shock transit in the sample. As discussed in
Appendix I and Chapter 2, the estimated uncertainty in spectral radi-
ance measurements is approximately 4%, although isolated examples of
larger systematic deviations occur.

Tables II-1 through II-6 contain the unreduced data for shock
pyrometry experiments on NaCl, H,0, a-quartz, fused silica, forsterite
(Mg,Si0, ) and silver (Ag). Each of these tables contains the identifi-
cation number, tantalum impactor velocity, and calculated pressure for
each shot. The spectral radiance measurements are reported in units
of 1013 W/m3/sr, and each of the six measurements at different wave-
lengths is identified in the column headings by the channel wavelength

numbers given in Appendix I.

-202-

The temperature and emissivity determinations reported in this
thesis have been obtained through a least squares fit of the spectral
radiance data to a Planck spectrum. The spectral radiance for emission
normal to the surface of the radiating region is assumed to be given
by

N, = €C€\-*[exp(C,/AT) ~ iy (1)

where in SI units, C, = 1.191066 x 10716 Wm2/sr and

C, = 1.43883 x 107? mK. If the angular dependence of the radiated
flux obeys the blackbody cosine law, then the cancelling effect of area
foreshortening as seen by the fixed area detectors causes (1) to be
measured with equal validity at all viewing angles. The temperature T
and emissivity ¢€ are derived from this fit with uncertainties which
reflect the approximate range of solutions consistent within the

radiance values and uncertainties.

-203-

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