Dislocation Mobility and Density in Zinc

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Dislocation Mobility and Density in Zinc Single Crystals
Citation
Adams, Kenneth Hoyt
(1965)
Dislocation Mobility and Density in Zinc Single Crystals.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/SYCE-8B03.
Abstract
Experimental measurements of dislocation mobility and density, and the strain-rate sensitivity of the flow stress have been made on 99.999 per cent pure zinc crystals. Dislocation density and the strain-rate sensitivity of the flow stress were also measured on zone refined crystals and crystals containing 0.0025 and 0.02 wt per cent aluminum. Dislocation mobilities in the 11
0 {0001} (basal), and 1
{1
12} (nonbasal) slip systems were measured by observing slip band growth produced by load pulses of controlled amplitude and duration. The results of the experimental measurements of dislocation mobility are discussed in relation to current theories. A comparison of the strain-rate sensitivity and the mobility measurements shows that a significant change in the density of roving dislocations is associated with a change in strain-rate. This change in density has generally been ignored by previous investigators. A dislocation model is proposed to explain the observed strain-rate sensitivity.
Observations were also made of the change of substructure and in particular the change of nonbasal dislocation density accompanying impurity additions of aluminum to the zinc. The effect of the aluminum on the basal stress-strain behavior is explained in terms of changes in nonbasal dislocation density which determines the separation distance of attractive and repulsive junctions between basal and nonbasal dislocations. The onset of basal slip is associated with the breaking of attractive junctions.
The change in basal dislocation density produced by plastic shear strain is shown to obey the relation Δρ = C୪
1/3
, and is independent of purity. A markedly different relation is indicated for the nonbasal dislocation density vs. strain. These results are explained by a significant difference in the average glide distance of dislocations in the basal and nonbasal slip systems.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
(Materials Science)
Degree Grantor:
California Institute of Technology
Division:
Chemistry and Chemical Engineering
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Vreeland, Thad (advisor)
Wood, David Shotwell (advisor)
Thesis Committee:
Vreeland, Thad (chair)
Buffington, Francis Stephan
Clark, Donald S.
Duwez, Pol E.
Housner, George W.
Wood, David Shotwell
Defense Date:
21 May 1965
Funders:
Funding Agency
Grant Number
Ford Foundation
UNSPECIFIED
Kaiser Aluminum and Chemical Corporation
UNSPECIFIED
Gillette-Paper Mate Company
UNSPECIFIED
U.S. Atomic Energy Commission
UNSPECIFIED
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CaltechETD:etd-09102002-095733
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DOI:
10.7907/SYCE-8B03
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DISLOCATION' MOBILITY AND DElJSITY
IN ZINC SINGLE CRYSTALS

Thesis by
Kenneth Hoyt Adams·

In Partial Fulfillmen t of the Requiremen ts
For the Degree of

Doctor of Philosophy

California Institute of Technology
Pasadena, California

196.5
(Submitted May 21,

1965)

TABLE OF CONTENTS

TITLE
ACKNOWLEDGEMENTS
ABSTRACT

LIST OF TABLES
LIST OF FIGURES

INTRO DU CTI OX

II.

ETCHING OF ZINC TO ·REVEAL DISLOCATIONS

III.

M.ATERIAL AND TEST SPECIMEN PREP.A.RATION

:i:v.

EQ,UJ:PMENT AND TEST PROCEDURES

Static Test Fixture

Dynamic Test Fixture

Pulse Tests

EXPERIMENTAL RESULTS

Static Tests

63
63

Basal Slip System

Nonbasal Slip System

Dynamic Tests

Basal Slip System

Pulse Tests

68
78

Basal Slip System

Nonbasal Slip System

8.$

Strain-Rate Sensitivity of the Flow
Stress

Basal Slip System

Nonbasal Slip System

TITLE

VI.

Influence of Impurity and Strain on
Dislocation Substructure

Dislocation Pile-Ups

102

DISCUSSION OF RESULTS

107

Basa1 S1ip System

107

Dislocation Orientations

107

Dislocation Multiplication and
Density Changes

110

Thermally Activated Dislocation
Motion

113

C.
D.

Dis1ooation Mobility in Other

Hate rials
E.

Lattice Resistance to Disloca-

tion Motion

118

Nature of Long-Range Internal
Stresses

120

Strain-Rate Sensitivity of the
..!!'low Stress

J.27

Stress-Strain Behavior

133

Nonbasal Slip System

VII.

116

136

Dislocation Orientations and
Dislocation Hul tipli ca ti on

136

Dislocation Mobility

140

Strain-Rate Sensitivity of the
Flow Stress

142

Stress-Strain Behavior as Related to
Dislocation Properties

143

SUMMARY AND CONCLUSIONS

144

REFERENCES

1.$0

ACKNOWLEDGEMENTS
The author wishes to express his thanks and appre"
ciation to Professor T. Vreeland, Jr. for his continued
interest and support during the oourse of this research.
Appreciation is expressed to Professor D.

s. Wood for

many interesting discussions on the theoretical aspects
of' this research.

Thanks·are expressed to Mr. R.

B1:i.sh a.nd. Mr • .A.. P. L. Turner !'or thei.r o.ssi.stanoo :i.n

specimen preparation and testing.
The author is indebted to the Ford Foundation,
Kaiser Aluminum and Chemical Corporation and the
Gillette-Paper Mate Company for fellowship grants.

The

teating program was conducted under a contract with the

s. Atomic Energy Commission.

Appreciation is extended

to this agency for support of' this work.

ABSTRACT
Experimental measurements of dislocation mobility
and density, and the strain-rate sensitivity of the £low
stress have been made

on 99.999 per cent pure zinc orys-

vity of the flow stress were also measured on zone refined
crystals and crystals containing 0.0025 and 0.02 wt per
cont aluminum.

Dislocation mobilities in the

(1120)

{0001} (basal), and (1'213) {i212} (nonbasal) slip systems
were measured by observing slip band growth produced by
load pulses of controlled amplitude and duration.

The

results of the experimental measurements of dislocation
mobility are discussed in relation to current theories.

A comparison of the strain-rate sensitivity and the
mobility measurements shows that a significant

chan~e

in the density of moving dislocations is associated with
a change in strain-rate.

Th.is change in density has

generally been ignored by previous investigators.

dislocation model is proposed to explain the observed
strain-rate sensitivity.
Observations were also made of' the change of sub-·
structure and in particular the change of nonbasal dis1ocation density accompanying impurity additioms o!'

aluminum to the zinc.

The effect of the aluminum on

the basal stress-strain behavior is explained in terms
of changes in nonbasal dislocation density whioh determines

the separation distance of attractive and repulsive junotions between basal and nonbasal dislocations.

The onset

of basal slip is associated w·ith the breal~ing of attraot:t.ve junctions.
'lbe change in basal dislocation density produced by
plastic shear strain is sho·wn to obey the relation

Ap.::::

..1

(;'{[fa' and is independent of purity,

A markedly dif-

ferent relation is indicated for the nonbasal dislocation
density vs, strain,

These results are explained by a

significant difference in the average glide distance

of dislocations in the basal and nonbasal slip systems.

LIST OF TABLES

TITLE

TABLE

::r::r
III
IV

Resolved Shear Stress Uncertainty
Resulting from Orientation Uncertainty

Summary of.' Tes ts

Dislocation Density Changes Produced by
Plastic Strain

of Variable Strain-Rate Data

Su'1l.lllary of Effect of Purity on Substructure
and Nonbasal Dislocation Density

101

Sum..~ary

Sui.rn:n<;u.·y o.f'

Materials

aml ')'\.. for Variouis

117

LIST OF FIGURES

FIG. NO.

TITLE

Several Crystallographic Planes and
Directions in Zinc Crystals.

Polar Stereographic Projection for Zinc
ShowJ.ng

ci~ystallographic

Dependence of:

Etch.

1.5

Crystallographic Dependence of Etch.

Etch Fi~ures on Zinc Crystal Surface
ioo to L0001] and 80° to (11'20], lOOX.

.5.

Etched Zinc Surface near [0001] , lOOX.

Pyrex Mold, a Section of a crystal and
a 1/2 in. Cube Specimen Trepanned from
a Section of the Crystal.

Crystallographic Orientation of Test
Specimens.

2.5

Kink Damage from Spark Machining, lOOX.

Test Specimen and Parallel Capacitor
Plates.

10.

Static Test Fixture.

11.

Schematic of Dynamic Test Fixture.

12.

Dynamic Test Fixture.

13.

Load Seats and Alignment Sleeve of

Dynami9 Test Fixture.

14.

Circuits Used in Dynamic System.

15.

General View of' Test Equ:ipment.

16.

Tracing of Oscillograph Record.

4.5

17.

Strain Gage Circuit.

18.

Dynamometer Strain Gage Circuit.

.50

19.

Tracing o~ Rapid Load Records.

.51

FIG. NO.

TITLE

20.

Schematic of Compression Fixture for
Rapid Load '.:\Iachine.

,52

21.

Specimen Alignment Equipment.

22.

Rapid Load Testing Fixture.

,56

2 :3.

Spherical Seats and Alignment Sleeve.

.57

24.

Air Supply System for Bearings.

,58

25.
26.

27.

28.

29.

30.

:n.

32.

)4.

Damage from Scratches and Cold Tool,

1oox.

Resolved Shear Stress vs. Resolved
Shear Strain For Basal Slip.
Specimen
17-1, Zone Refined Purity,

Compressive Stress vs. Compressive
Strain for Nonbasal Slip.
Specimen
26-6Tl, 99.999 Per Cent Purity.

Dislocation Density Resulting from
Compressive Strain of 900 x 10-5 in./in.
along c-Axis.
Specimen 26-lTl, 99.999
Por Cont Purity, $OX.

Influence of Purity on Basal StressStrain Curves.

Influence of Prior Strain on Basal

Stress-Strain Curves.

Dislocation Density Changes Resulting
from Basal Shear Strain o~ 1 Per Cent.
Specimen 22-1T2, Zn-0,002SA1 Purity,
lOOX.

Dislocation Dansity

Resul~ing

£rom Basa1

Shear Strain of 6.3 Per Cent.
Specimen
16-lTJ, 99.999 Per Cent Purity, lOOX.

7.5

Change in Dislocation Density vs. Shear
Strain for Basal Slip.

Basal Dislocations before and after a
Specimen 17-3T3,
Zone Refined Purity.
l Min Pulse
Duration, 1oox.

Pulse of 9.9 l!b/in. 2 •

TITLE

FIG. NO.

3.5.

Basal Dislocations be~ore and after a
Pulse of 15.5 lb/in.2.
Speoimen 17-4Tl,
Zone Refined Purity.
17 x 10-3 Seo
Pulse Duration, lOOX.

Basal Dislocation Velocity vs. Resolved
Shear Streaa £or 99.999 Per Oent Pur~ty
Specimens.

82
2~

"i- 7L •

37.

Rasa1 Dislocation V.c:\locity vs.

38.

Nonbasal Slip Bands Resulting from
c-i'\.xis Compressive Stress of 970 lb/in.2.
Specimen 16-4T6, 99.999 Per Cent Purity.
31.4 Sec Pulse Duration, lOOX.

Nonbasal Dislocation Velocity vs.
Resolved Shear Stress for 99.999 Per
Cent Purity Specimens.

Schematic Load-Time Curve.

J9.
40.
41.

Dislocation Substructure in Zn-0.02A1

Specimens.

42.

44.

Specimen 19-1, lOOX.

Impurity Segregation in Zn-0.02Al

Specimens.

4J.

Specimen 19-3, 25X.

Dislocation Substructure and Impurity
Segregat1on 1n zn-o.ooz~Al Spec1mens.
Specimen 22-lt 25x.

100

Nonbnsal Dislocation Density Revealed
on the Basal Plane of a Zn-0.02Al
Purity Specimen.
Density ~ 2.1 x

io.5 cm-2, 1oox.

103

Dislocation Substructure after 30 Per
Cent Shear Strain and Anneal.
Specimen

16-3, 99.999 Per Cent Purity, lOOX.

46.

104

Effect of Stress Unloading on Basal
Dis1ooation Pile-Up:s.

Shear Stre::is •

12.1 lb/in.2. Specimen 18-1, 99.999
Per Cent Purity, 1oox.
Possible

c and a Type Vectors.

106
123

FIG. NO.

48.

TITLE

Variation in Shear Stress Along a
Slip Plane.

130

49.

Cross-Slip r.Iechanism.

138

.50.

First and Second Order Pyramid Planes.

139

-1-

INTRODUCTION

Since the advent of the theory of dislocations in

the late 19JO's, a great number of mechanical and physioal properties

erysta11ine so1ids have been shown to

be dependent on dislocations and their behavior.

recent years, dislocation theory and models based upon
dislocation theory have been applied to such phenomena
as plastic

de~ormation,

work-hardening, internal fric-

tion, creep and fracture.

In general, there has been

an abundance of theories or dislocation models covering
almost all

de~ormation

processes and a conspicuous lack

of good experiments to test the validity of the theoo~

retical treatments.

This lack

has been a result

the faot that the experimental

experimental evidence

tools required for the direct study of dislocations
were not available more than ten years ago and also
the critical experiments needed to verify some theories
are sometimes tedious experiments to conduct.

The

purpose of this experimental investigation was an

attempt to bridge the gap between the theoretical and
experimental approaches and to shed some light on the
critical subject of dislocation behavior as related
to the plastic deformation and work-hardening of
orysta11~no

so1~ds.

-2A well-known result of dislocation theory is that
the plastic shear strain,

'!'p , resulting from dislo-

cation motion in a single slip system is given by

(1)
where

A = slip plane area swept over by all moving
cl.isiocations/unit vo1ume

= magnitude of the Burgers vector of glide
dislocations.

The plastic shear strain-rate is dependent on the average
velocity of the moving dislocations, 11"', and is given by

if= Ah =Nbvwhere

(2)

N is the total length of moving dislocation per

unit volume.

I£ it is assumed that all the moving dis-

location lines are straight and parallel, then

where
~- density o~ moving dis1ocations/unit area

/~,

normal to the dislocation lines

and Eq. 2 can be written as
(3)

-3Tile velocity of moving dislocations and the rate
of generation of mobile dislocations govern the dynamic
stress-strain behavior of a single crystal through Eq.

'.3.

Th.e der1.sity 0£' moving d.::i.s1ooa.tions ldl1 gonora.11y

be less than the total dislocation density of the
crystal.

Work-hardening results .from interactions

which tend to impede dislocation motion or lower the
number of mobile dislocations.
subject o.C mobili-ty of:'

Therefore the general

d:i.slooation~

which invo1vos tho

velocity of dislocations is of considerable importance
as it relates to the dynamic properties of crystalline
solids.
Equation 3 expresses the fundamental relation

between a macroscopic quantity,
scopic dislocation properties,

Of , and the micro)>M and 1f.

The

relation is equally valid for all crystalline solids
including ionic and semiconducting materials as well
as metals.

With suitable orientation :factors, Eq. J

also applies to polycrystalline material.

If the

number of moving dislocations and the velocity of
dislocation motion are known for a given material as
£unctions 0£ stress,

str~in

~nd.

tomporaturo, the

plastic stress-strain behavior of the material can be
predicted under any conditions of temperature, rate
of loading or strain-rate.

Equations 1 and

3 then

-4cor.iprise the "equatio ns of state" for the material from
which the creep, and static. and dynamic stress-s train
.behavio r of the material can be predicte d.

From an

engineer ing standpoi nt. an undArsta nding 0£ the

~actors

which control the density and velocity of moving dislocation s is necessar y before a rational design of
material s to control their plastic deformat ion properties is possible .
The ve1ocity at which a dislooa.t :ion oo.n move is

limited due to the way its kinetic energy increase s as
the velocity approach es the speed of sound waves.
a moving screw dislocat ion,

For

S parallel to the dislocat ion

line, the ldnetic energy approach es infinity as the dislocation ve1ooii:;y a.pproaohe i:ii the speed or shear waves.

The same result is true for an edge dislocat ion,

perpend icular to the dislocat ion line, in zinc single
crystals accordin g to Teutonic o

(l)*.

This result puts

an upper bound on dislocat ion velociti es equal to the
shear wave speed.

Other factors, however, may limit a

dislocat ion to speeds far below the shear wave speed.
T'ne subject of dislocat ion mobility at speeds below
the shear wave speed has been approach ed theoreti oa1ly
in several ways.

One way has been to consider the

*Numbers appearin g in parenthe ses ref er to referenc es
listed at the end of the thesis.

-5motion of a dislocation through a perfect lattice and
consider the various ·ways that energy can be transferred
from the moving dislocation to the lattice,

Energy

transferred to the lattice results in a drag stress
on the dislocation which limits the velocity to a level
where the applied stress equals the drag stress.

Two

sources of drag have been considered theoretically.

Liebfried (2) has considered the interaction of phonons
w'ith a moving screw dislocation and Eshelby (3) has
considered thermoelastic damping as a source of drag.
Both treatments assume a linear dependence of dislocation velocity on applied stress or a viscous type of
drag.
A second line of approach to the problem of dislocation mobility has been to consider various interactions between dislocations and point defects as being
the primary obstacles to the moving dislocations.
Models of this type are somewhat more realistic because
crystalline solids are rarely perfect and most often
contain high densities of dislocations and impurity
atoms.

Theoretical treatments of the interaction of

dislocations with obstacles assume that the moving
dislocations spend most of their time at the obstacle
and move rapidly to another obstacle once the first
one is overcome.

The resulting dislocation velocity

-6depends on the rate at which obstacles are overoome
which is usually considered to be a thermally activated
process.

The various obstacles to dislocation motion

whioh hnvo boon oonsidorod thoorotion11y ino1ude sub-

stitutional impurity atoms (4), the Peierls barrier (5)
and £orest dislocations

(6).

Impurity atoms act as

obstacles when they are a different size than the
solvent atoms of the lattice.
produces an assooiatod stress

resistance to the motion

The size difference
~iold

which causes a

nearby dislocations.

Tile

Peierls barrier to dislocation motion is a result of·
the change in dislocation energy with position as a
dislocation moves one atom distance,

Forest disloca-

tions are disl.ocations which thread the slip plane o"f'

a glide dislocation and provide a resistance to motion
because dislocation "jogs" are produced as the glide
dislocation cuts through the forest dislocation.

The

jogs produced represent extra dislocation line energy
w'h.ich is provided by tl1e appl.i.ed stress with tl'l.e aid
of thermal energy.
trl~ich

In general, all the proposed models

depend on thermally activated motion predict an

exponential dependence

the dislocation velocity or

strain-rate on the applied stress.

The strain-rate

dependence is related to the velocity by Eq. 3.

From

theoretical considerations the possible variables which

-7might influence dislocation mobility include temperature, forest dislocation density and point defect
concentration where point defects include impurity
atoms as well as vacancies.
Various experimental tools exist for the direct
Experi-

and indirect study of dislocation mobility.

ments which have been used to deduce dislocation
mobility indirectly in single crystals include internal
f'r:i.ction measurements (7).

in:stantaneous creep rates

resulting from a rapidly applied stress (Stand strain"

rate sensit;ivity of the flow stress (9).

The first

two types of experiments depend on dislocation models
for an interpretation of the experimental results and
both su££or From an uncertainty as to the number or

density of moving dislocations taking part in the
deformation process.

In ·addition, internal friction

models such as the one of Granato and Lucke (10) assume
a linearized equation of dislocation motion where the
damping force is linearly dependent on the applied
stress.

Such an a priori asswnption may indeed be

incorrect.

Strain-rate sensitivity experiments can be

used to determine the mobility relation if assumptions
are made about the change in density of moving dislocations accompanying a strain-rate change and if the
general form for the mobility relation is assumed.

-8In general, the indirect type of experiment is relatively
easy to conduct and hence offers attractive possibilities
for a study of dislocation mobility.
ity

However, the valid-

tho various assumptions and mode1s used must

ultimately be checked against direct experimental measurements.

Many investigators have drawn conclusions

from the results of strain-rate sensitivity experiments
in \~1.ioh the asslli~ptions made about the density of
movine; dislocations were not: vor:i.f'iod.

Various experimental tools are presently available
for the direct study of dislocations.

Dislocations have

been observed directly with a field ion microscope.
The technique is limited to materials with high melting
points such as tungsten and uses sma11 specimens in the·
form of needles.

Transmission electron microscopy is

a itldely used technique :for studying dislocations in
materials with dislocation densities up to about
io 12 cm- 2 • The technique suffers from several disadvantages for experimental determinations of dislocation
mobility.

The primary disadvantages are the small

specimen size which limits observable dislocation disp1aoemants, tha raot that thin £oil specimens are not

always representative of the bulk material from which
they were prepared and the inherent dif:ficulty in
accurately controlling the stress state applied to a

-9The technique can be used

specimen in the microscope.

to determine the Burgers vector of the observed dislocations.

X-ray methods such as the Berg-Barrett tech-

nique can be used to study dislocations near the surface
of bulk material.

T'ne technique is limited to material

with dislocation densities less than about 10 cm-

2 and

offers the advantage that the Burgers vector of the
dislocations can be established.

A disadvantage of the

Berg-Barrett technique is the relatively long X-ray
~ilm

exposure times required.
Another method available for the study of disloca-

tions involves etching by chemical, electrolytic or
thermal means to reveal dislocation intersection sites
on the specimen sur£aoe

etoh pits.

Tho otoh pit

technique is limited to those materials for which a
specific technique has been developed since no one
In

method has been found to work for all materials.

addition, a technique is usually good only for certain
low index crystallographic planes o'f: a CJ:'ystal.

Dis-

advantages of this general technique include limited
resolution corresponding to densities of approximately

10 cm-

and uncertainties as to the slip plane and

character of the dislocations revealed as etch pits.
However, the etch pit technique is particularly useful
for studies on bulk material and can be used to follow

-10dislocation motion over relatively large distances for
mobility studies.

Chemical etch pit techniques have

been used to study dislocation mobility in a number of
materials.

The haRic tachn:tqne i.nvol ves sora.t:ohine to

introduce fresh or unpinned dislocations which is followed by the application of a constant stress pulse
for a specific length of time.

The etched specimen

reveals how far the dislocations have moved during the
duration of' the test.

The averae;e d:i. s1ooa t:ion ve1ooi. ty

produced by the stress level of the test is calculated
from the distance of motion and time of stress application,

Experiments of this type have been performed

on single crystal specimens of lithium fluoride (11),

silicon-iron (12), germanium (13, 14), silicon (13),
sodium chloride (15) and tungsten (16).
The purpose of this investigation was to determine
through experimental means the validity of various
theories of dislocation mobility,

\A testing program
\~

on zinc single crystals was undertaken because the
crys·tallography of' the various slip systems is known

---

and because zinc has only one system o:f easy sli.E.:_J·
The basal or easy slip system is shown in Fig. 1 along
with the twinning system and the second order pyramida1 system 'W'l"l.i.ch is one 0£ the nonbasa1 s1ip systems.

Rosenbaum (17) has sho1m, from observations of slip

-11-

___ (0001)
~~~2~;:--z
~,.....,_...~~::'l'I-'~ (T2Ta1

BASAL

(IT02)

Difia
r-

SLIP

PLANE
DIRECTION

(i2iO)

'\. /\;. 1 ,::-

TWIN

PLANE

TWINNING SHEAR
DIRECTION

5e::o IJ.t> l) f2..C> (Qi2.

~lvtsr

(I 2°12)

6P-{>g2.

Q(i'a}

(1213]

PYRAMIDAL

PLANE

PYRAMIDAL SLIP
DIRECTION

~~M.IV)ft-L
QtA6-4 ~

Fig. 1

Several Crystallographic Planes and Directions
in Zinc Crystals.

-12-

line markings on crystals deformed at room temperature
by nonbasal slip, that the

<121J) {12'121slip system is

the nonbasal slip system whioh confirms the results of
Bell and Oahn (18).

An experimental program involving the etch pit
method for determining dislocation positions was chosen
for the direct measurement of basal and nonbasal dislocation mobility in zinc single crystals.

Previously

reported etchants for zinc included one for cadmium•

doped zinc crystals which requires an aging treatment
to precipitate cadmium at dislocation sites (19) and
one whioh reveals nonbasal dislocation intersections
. with the basal plane (20).

Since neither etchant was

suitable for a study of the mobility of basal dislocations in high purity material, a technique for_revealing
dislocation sites on prism planes (see Fig. l) was
developed as part of the experimental progr~.

This

technique has been reported elsewhere (21, 22).

Addi-

tional observations on the etching procedure are included
in Part I I of this thesis.
Single crystals of several purities of zinc were
grown and teat specimens were prepared by teohniquea

described in Part III.

Purity was chosen as a variable

in the direct study of dislocation mobility.

Compres-

sion tests were conducted to determine the stress-strain

-13behavior for basal and nonbasal slip, compression pulse
tests were conducted to determine dislocation mobility
and compression tests were conducted at variable strainratas to re1ate the strain-rate sensitivity of the

stress to the direct mobility data.

~1ow

The orientation of

the test specimens which varied between the tests on
the basal and nonbasal slip system is described in Part
III.

TI.1.e experimental methods used to determine dis-

location mobility, stress-strain beha~ior and strain-

rate sensitivity are described in Part IV.

The results of the testing program are presented
in Part V along with observations on the dislocation
density of deformed specimens and the effect of purity
on dis1ocation density.

In Part v:I the experimental

results are related to various theories of dislocation
mobility, the fundamental mechanism governing the initiation of plastic flow and the process of work-

hardening in zinc single crystals.

-14II.

ETCHING OF ZINC TO REVEAL DISLOCATIONS

An etching procedure which reveals etch figures
corresponding to dislocation intersections with {io1o}
p1anes

zino sins1o orysta1s has been reported else-

where by Brandt, Adams and Vreeland (21, 22).

The

etching procedure involves the introduction of a very
small amount of mercury onto the surface of a zinc
crystal by etching in a weak acid solution of mercuric
nitrate.

Subsequent po1ishinc wi~h a ohromio aoid

solution results in the formation of etch figures or
"etch pits"* at dislocation intersections with the
crystal surface.
Additional observations have been made on the
dependence

the etch on the crystallographic orienta-

tion of the specimen surface by etching a 2 in. diameter hemispherical crystal of 99.999 per cent purity.

A new crystal surface orientation has been found where
etch pits are revealed.

The new surface orientation

is located between J 0 and 12. 2° to the (ooo~] and is
..Li t

axially sym..'11etric about this axis.

Figure ·z. shows on

a polar stereographic projection all the regions of
good etching as we11 as those regions ldlere the etched
surface is of marginal and poor quality.

Figure 3

11 etch pits" although
they actually are "etch pips" or hillocks.

*The figures will be referred to as

-1.5-

0001

1012

0110

1011

Good ·Etch

Marginal ·Etch

Poor ·Etch

Fig. 2

Polar Stereographic Projection for Zino Showing
Cry5tallographic Dependence o~ Etch.

-16[0001)

[10To]

r-:

Good Etch

D Marginal and
Poor Etch

Fig. 3

Crystallographio Dependence of Btch.

-17shows the same regions on a perspective drawing.

Attempts

to etch the (0001) surface were generally unsuccessful
although it was found that by using a much lower mercury
oonoentration on £rosh1y oloavod surfaces some etoh pits

were revealed that were obviously associated with twinning damage.

A fresh surface was produced by quenching

the specimen in methanol after cleaving in liquid nitrogen.

further attempts were made to etch (0001)

planes because it is generally undesirable to subject
large specimens to the thermal strains involved in the
quenching process.
_1/J'

Figure~~

shows etch pits produced on a crystal

surface whose normal is oriented io 0 from the

[oool]

and 80° from the (112'0] axes as a result of heavy razor

blade scratches.

The arrows indicate the basal plane

trace on this surface and etch pits can be seen linedup in the general direction of ~he {i212} second order

pyramidal slip plane traces as indicated by the dashed
lines.

Nonbasal {1212} type dislocations are there-

fore asswned to be revealed on planes within 3° to
12. 2° to the

(oool] .

The dark lines emanating f'rom
:.u:. ,.

the scratches in Fig. "1.f: are twins that were produced

by the razor blade scratches.
Experiments were conducted to establish whether
basal dislocations are revealed in the region between

-18-

. ···~

... ~

\<• :

·....

... ..
!.

."'(.;;,. .···, . .
'·-

•,

·'

... "

Razor
Scratch

Basal
Plano
Traco

'..

...

---~~--
/ \

{1212} Traces

Fig. 4

Etoh Figures on Zinc Crystal Surface 10° to

[ooo:iJ

and so 0 to [112'0] •

ioox.

-193° and 12. 2° to the (0001J •

Several 1/2 in. cube com-

pression specimens oriented for basal slip and containing
a .pair of' surfaces oriented 10° to the

(ooolJ as wel.1

as a pair of (10l0} surfaces were etched. deformed and
re-etched to reveal changes in .the dislocation configuration.

Basal deformation on io 0 surfaces was not

indicated even though extensive basal deformation was

indicated on {10lO) surfaces.
of the re-etched ·10

The general cona1t1on

surfaces was usually rather poor.

Areas of general background pitting resulted wil.ich
oaused d.i££icu1ty in determining whether changes in

the dislocation density and configuration had actually

ocourred,as a result of the basal deformation.

additional experiment was conducted on the 2 in. diameter hemispherical crystal previously mentioned.
1/4 in. diameter £1a:t area wa.s expo.sed at tihe

pole by cleaving the crystal.

[oool]

A brass rod was glued

to the surface with Eastman 910 adhesive.

The crystal

was held stationary while the rod was twisted 10° about
the

(0001] thus causing basal slip.

'llle etohed speci-

men revealed pile-ups of dislocations along the oircular basal plane traces near the
t":/J-! " :~M

in Fig.~"

pole as shown

The exact orientation of the region showing

dislocation pile-ups is not known.

The observations

lead to the conclusion that at least for some surface

- 20-

Fi.g. 5

Etched Zinc Surf'aco near

(0001] , 100X.

-21orientations near the [0001] axis, basal dislocations
can be revealed as etch figures.

However, the quality

of the re-etched surfaces was too poor to be useful for
the study

dislocation mobility.

The investieation

lras therefore limited to observations made on specimen
surfaces with a {lOlO) orientation since these surfaces
can be re-etched with minor changes in surface quality.

-22J::C::t.

MATERIAL AN'D TEST SFEO:t:MEN PnEPAnAT:CON

Compression test specimens of four different purities of zino were prepared to investigate the influence
of purity on dislocation mobility and the mechanical
A quantity of

c. P.

propert~es

of zinc single crystals.

grade zinc

or 99.999 per cen~ purity was obtained £rom
An analysis of this mate-

the New Jersey Zinc Company.

rial furnished by the supplier indicated the following
impurities in weight per cent:

Lead

0.0002

Iron

0,0002

Cadmium

0,00005

Other

< 0. 0001.5

A quantity of' material o:f this era.de was :further purified

by zone refining.

Zone refining was carried out under a

helium atmosphere by passing a double zone furnace over
a 6 ft long charge at the rate of 2 in./hr.

A total of

10 double zone passes were made before the oha.rge was

removed from the furnace.

The first 1/3 of each charge

was used to grow single crystals.

Q.uantities of two

additional purities of zino were made by doping 99.999
per cent purity zino with 0.02 and 0.0025 weight per
cent aluminum.
Sing1e orysta1s 0£ each of the four different pur-

ities were grown by the Bridgeman technique in graphite

-23coated Pyrex molds.

........_

The preparation o~ the molds and

the details of the growing procedure have been described
by Stofel {23).

Cylindrical single crystals 7/8 in. in

diameter and 8 in. long were grown.

Figure 6 shows a

Pyrex mold and the single crystal grown in the mold.
The orientation of a crystal was found by cleaving an
end section that had be.en acid sawed from the crystal

with SN II.N03 on a stainless steel wire 0.005 in. in
diameter.

The cleaving was done in liquid nitrogen

with a needle struck by a light hammer,

Crystals were

ooo1ed and heated at rates less than 5°F/min to prevent
damage due to thermal stresses.

The cleavage surface

established the orientation of the (0001} basal slip
plane and the direction of large cleavage steps on the

surface which correspond to the twin traces determined
the [1120] slip direotion in the basal plane.
Compression test specimens in the :Corm of 1/2 in.
cubes were machined with three different orientations
of the basal slip plane with respect to the load axis.
Figure 7 shows the orientations of the three different
specimen types all of which have a set of {lOlO) surfaces.

The 45° and 80° type specimens were oriented

for experiments on the basal slip system and the c-axis
specimens were oriented ror experiments on the nonbasal

slip system.

The 80° type specimens were used only in

Fig. 6

Pyrex Mold, a Section of a Crystal and a 1/2 in.
Cube Specimon Tropanned from a Seotion of the
Crystal .

Fig.

(b) 80° Specimen

[i2io]

t[0001]

Laad Axis

(c} c-Axis Specimen

~ [oool]"" -

[fa'-?]

7 Crystallographic Orientation o~ Test Specimens.

(a) 4.5° Specimen

[i2io]

~60o

. I.___ 45v° ,, [ooo 1]

Load Axis

1Load Axis

(\)

\J\

dislocation mobility experiments 'Whereas the 45

and

o-axis specimens were used in both stress-strain tests
and mobility experiments.
Test specimens were machined from aoid sawed and
cleaved sections of the single crystals with the use of
a servomet El.eotric Spark Discharge Machine.

Th.e spark

machining consisted of trepanning and planing operations
at minimum spark energy settings.

All spark discharge

machining operations were done in oil at 200°-210°F to
prevent cleavage cracks.

Spark machining at temperatures

less than 190°F produced surfaces With Visible cleavage
cracks.

Figure 6 shows a 1/2 in. cube specimen trepan-

ned from a section of a crystal.

The machining operations

resulted in specimen surfaces which were para11e1 to
within 0.1°.

The surface f'inish achieved by spark

planing was of' the_ order of 10 )'- in. r .m. s.
Uncertainty in the crystallographic orientation
of' the test specimens with respect to the surfaces
resulted

~rom

machining operations.

Table I gives the

resulting uncertainty in the basal resolved shear stress
from uncertainties in the orientation of the basal slip

plane and slip direction with respect to the specimen
surfaces on which compressive forces were to be applied.
These sur£acos wi1l be designated as loading sur£aoes.

-27TABLE I
Resolved Shear Stress Unoertaint y Resulting
from Orientatio n Uncertaint y
Axis Unoertaint

000

Resolved Shear Stress

1210

Uncortaint

±0.01 per cent

to.1°

±1 per cent

a-a.xis

0.2 per oent of the
normal stress (basal
shear stress nominally
zero)

Damage to the specimens resulting from the spark
machining operations was removed chemically by polishing
off approxima tely 0,005 in. of material and annealing
.at 700°F in a purified hydr,ogen atmosphere for 4 to 8
hr.

The loading surfaces were masked with tape during

the polishing to retain a flat surface,/r In the .45 0
specimens the depth of spark damage was found to extend
as far as 1/8 in. below the sur£aoe.

This damage

occurred near only one edge of the spark planed surface.
An example of the damage is shown in Fig. B.

The fan-

like array of sub-bound aries indicates that kink bands
consisting of edge oriented basal dislocatio ns have
~ormed

a1ong an unsupporte d edse

the Gpeoimen.

Blocks of zinc of the same orientatio n as the specimen
were cemented to most of the 45° speoimens during
planing operations to prevent this type .of damage.

-28-

Specimen Edge,
Spark Planed Surraoo

•·

••

.._....._~_ I !. .__

~ ••······
:N.g. 8

(lOlO)
Ed go

Kink Damage :f'rom Spark Maohining, lOOX.

-29IV.

EQUIPMENT AND TEST PROCEDURES

In this part of the thesis a detailed description
of the various mechanical tests conducted on zinc single
crystal test specimens is presented together with the
procedures used in each type of test.

Table I I gives

a summary of the tests conducted on specimens oriented

for basal and nonbasal slip.

n~e

details of each type

of test are presented in Table II.

This part of the

thesis is divided in sections which describe the static

test fixture. dynamic test fixture and pulse load tests.
Static Test Fixture
Stress-strain tests on specimens oriented for basal
slip were conducted in an Instron testing machine.

crosshead speed of 2 x io- 4 in./min and a load sensitivity of' 10 lb :f'u11 scale on a Speedoma.x recorder were

used.

Shear strain resulting from basal slip was meas-

ured with a Robertshaw Proximity Meter and parallel plate
capacitors coupled to the specimen.

Figure 9 illustrates

the relation between the specimen and parallel plate
capacitors which form one leg of a capacitance bridge.
Til.e relation between the capacitance and the plate separation of a parallel plate capacitor is given by

c::: 0.225 dKA

-30TABLE II
Summary of Tests
Slip
Slstem

Testing
Machine

Test
Fixture

Strain
Measurement

stress-strain

basal

Instr on

static

capacitor
plates

load pulselong time

basal

Instr on

static

none

stress-strain

nonbasal

Instr on

dynamio

strain
gages

variable

ba:sa.l

:tnstron

dynamio

Test

strain-rate
variable
strain-rate

nonbasal

Instr on

load pulseshort time

basal

rapid
load

load pulse-

non basal

long and

short time

oa.pac:i.tor

plates

rapid
1oad

dynamic

strain
gages
none

none

/I.: '

..!
y1''-'--

l"I /

d -Y"

~-------~--

Fig.

SLIP

I'
I ,,1,(.

- I.

/..

I PROXIMITY
METER INPUT

SHIELDED
CONNECTI ON

DIRECTION IN BASAL PLANE

Test Specimen and Par-allel Capacito r Plates.

, PRISM SURFACE

/;Ir

A-L· .. i \_ •

/x.

' ' )-~·--·~~

LOAD AXIS

',/,. 1'.. r I'

\..J
!-'

where

C "" capacitance, ~./"' f
K = dielectric constant

A= total plate area, in. 2
d = plate separation, in.
For changes in p1ate separation where

l1 d/d ~<

the

change in capacitance is given by

i.ld

L1C =-Cd ·
The proximity meter output is proportional to the change
1n capacitance.

Full scale sensitiVity of the capaci-

tanoe system is a function of the plate spacing, and
the instrument sensitivity setting for a given scale
range of the meter and plate area.
The instrument was calibrated for two different
plate spacings.

The initial plate spacing was controlled

by two micrometer barrels which position the capacitor
plates with respect. to the specimen.

For a plate spacing

of 0.05 in.
and a total capacitor plate area of 0.22 in. 2 ,
the :full scale meter reading was found to correspond to
a change in plate spacing of 0.0005 in. on the most
sensitive scale of the meter.

A second· calibration point

was achieved for a plate spacing of 0.009 in. by measuring
the :Po;L5son expansion of' a brass compression specimen.
For this case, a change in plate spacing of 13 x 10- 6 in.
produced the full scale meter deflection.

-33Figura 10
ture.

is a photograph of the static test fix-

Two micrometer heads are used to control the

initial spacing of the parallel plate capacitors and
to permit accurate location
to the loading axis.

the RpecimAn with respect

The cylindrica l rod above the test

specimen is attached to the crosshead of the Instron
testing machine.

The specimen is supported on a cylin-

drical rod which passes through a guide hole in the bottom
plate

tho £ixturo to allow the load on the specimen

to be transmitte d to the load cell of the testing machine.
In this :fashion, any interactio n between the loaded portions of the system and the plate whioh holds the strain
measuring probes is avoided.

The cylindrica l rod is

guided in the fixture plate in such a way as to permit
the specimen to be rotated about the load axis since
the axis of the rod is accurately aligned with the load
axis.

'111.e specimen is initially centered to 1ocate the

load axis along the center line

the specimen.

The

micromete r heads which position the plates are used for
the centering operation.

The specimen is rotated 90°

after beine centered in one direction in order to center
the spec1men in the transverse diraotion,

Tho specimen

alignment procedure is capable of limiting the error
in the applied stress due to bending to less than S
per cent

the average stress.

The load is transmitte d

- J4-

F~s.

Static Test Fixturo.

-35through a spherical seat above the specimen to insure
that specimens with slightly nonparallel ends are uni-

:formly loaded.
The speoim<:m, after being centered, was given a
slight preload by manual control of the Instron crosshead.

The required plate-to-speci men spacing was set

after the position of the probe corresponding to zero
plate separation had been found.

An electrical con-

tact gage was used in this operation to prevent s.urface

damage to the specimen.

An initial plate spacing of

0.01 :i.n. x-esu1te•d ;Ln a f'ull scale sensitivity oorres-

ponding to a change in spacing of 6 0.5 .:x: 10-6 in. at

33 per cent of t;he maximum meter sensitivity,

The

change in plate spacing is related to the elastic and
plastic strain ci1:f' the specimen by

L lrp ,e o-{
Ll d = T + 8 S44-Z.S13-S!>a-S11 )
(4)

= 1 {JP+ J.4" 10- er)

where

IJd = change in pla. te to specimen spacing, in.

i. • ·width of the specimen between capacitor
pla·l;.es, in.

Ip= plas:tic basal shear strain of the specimen
CT= compressi~e ~tress applied to specimen
ends:, lb/in.

-36-

s 33 , 544• s13 , s 11 • coefficients of elastic
compliance, in. 2 /lb.
Dznamic Test

Fi~ture

variable strain-rate tests were conducted in the

Instron testing machine to determine the strain-rate
sensitivity of the flow stress for the basal and nonbasa1 s1ip systems.

The 1oad

~ixture

for these tests

and the methods of measuring strain in the specimens
was different from that used for basal stress-strain tests.
'Figur-e--1-1- i-sJ~, schematic dratrlng of the dynamic test

fixture along with the capacitor plates used to measure
strain in 45° specimens oriented for basal sli~/~

The

bottom plate of the fixture ·was initially fixed to the
Instron load cell table and the load cell was then
leveled so that the plate was perpendicular to the lead
screws of the machine.

The top ball seat was then

attached to the orosshead ~rlth Eastman 910 cement after
it had been located on center with the centering pin in

the bottom plate.

The alignment procedure established

the load axis to within 0.001 in. of the center axis
of the bottom load seat.

The lower ball assured that

the :force app11ed to the specimen was uniformly distr1buted even when the loading surfaces were not parallel.
The top ball prevented small lateral translations of

-:n-

Cross head
Ball Seat

40 TPI

Grounded Capacitor
Plate

Positive Capacitor
Plate , 5 in~ Area

Ball Seat
Alignment
Sleeve

~~"

Specimen
0.001 in. Tef Ion, Top
..,.....,__,.....,...,~~~~,....,....,r-'7 and Bottom of
Specimen

Load Cell

Fig, 11·

Base on · Centerino
Pin

Schematic of DYriamio Test Fixture,

-38the crosshead from being transmitted to the specimen.
The line between ball centers defined the load axis.
The specimen was aligned with the axis of the botton
seat of the fixture with the aid of a cathatometer,

This

was done by rotating the seat and aligning the specimen
so that each of the four corners coincided with a crosshair in the focal plane of the oathatometer.

The

remaining parts of the fixture were then assembled
without disturbing the specimen.

Errors in the stress

state resulting from alignment errors and the uncertai.nty 0£ tho loa.d a.xis location were ei:stimatedto be

less than 4 per cent of the resolved shear stress.

The capacitor plates <~h.ow~~ -~n Fig, 11 were used
in connection with the proximity meter to measure the

compressive strain resulting from basal shear strain
:in the

4.:s 0 specimens.

n .. e grounded capacitor plate is

threaded onto the connecting rod so that the capacitor
system can be calibrated before each test.

The threaded

connection permits adjustment of the plate spacing.

The

initial plate spacing used for strain-rate tests was 0.1

1n, 'W'l.J.ich together With a plate area of 5 in.~ resulted
in a full scale sensitivity of 0.0004 in. on the maximum sensitivity_ range of the proximity meter.

~ ~

-,-

Figure ~2

,_ . c.~ .:~ "'. . . .

is a photograph of the a~ic test fixture and Fig.
shows details of' the load seats and alienment sleeve.

·r·;..

1'3'. ·.~

- 39-

Fia . 12

Dyna.tni.o Tost Fixture .

-40-

Fig. 1)

Load Seats and A1ignmont Sloovo of oynrunic
't'e,;t Fixturo.

-41The Instron load cell and proximity meter outputs
were recorded on a Consolidated Electrodynamics osoilloThe auxiliary circuits required to match the

graph.

load cell strain gage amplifier and proximity meter output impedences to the osoillograph galvanometers and to
filter out 60 cycle noise are shown in Fig. ·1-4. along
with the circuit used to provide timing marks on the
oscillograph recording paper.

A Consolidated Electro•

dynamics Strain Gage Amplifier type 1-ll)B was used

li'i th the Instron load cell.

The maximum load sensi-

t1Vity or 10 1b full scale (7 in. of oscillograph paper)
was maintained throughout the basal strain-rate tests
by successively shifting the load zero point by 10 lb
by means of a decade switch which shunted various resistances across one leg of the load cell bridge.

A ten

position decade switch effectively increased the osoillograph paper width from 7 in. to approximately 70 in.

:F'

••. , " i i

Figure ~ is a general view of the equipment.
Calibration of the load cell was accomplished with
dead weights after the compression fixture had been
assembled.

The capacitor plate system was calibrated

over all sensitivity scales of the proximity meter to
be used during each test.

The scales used depended on

the final value of strain desired in a given test and
the length of the specimen in the direction of the load

-42330.n.

6.8.n.

Consol idote d

I nstron
Load ceir

16.n.

600"

Gahonometer

Type 7- 215

Consoli doted
Amplifier iype 1... 113 B

(a) Load· Cell Circui·t
324.0.

200..0.
Proximi\ty.:
Meter Output

26.tl

Type 7-2l5

(b) Proximity Meter Circuit

19 v Gate Out

533 Tektroni"

1700.tl.

Scope

Type 7 ... zz3

(·o) Tl'l111ng Circuit

Fig. 14

Circuits Used in Dy~o System.

- 4J-

li'i.g.

l:i

Genera1 V.ielf of Test Bqu:lt->1uont .

-44axis.

The total sensitivity of the strain measuring

system was governed by the initial plate spacing, the
plate area of the capacitance gage and the sensitivity
scale of the proximity meter.
Strain-rate changes were made during the tests by
changing the crosshead speed Of the Instron in the
ratio of l/~/{af o.
mUiil

Full speed corresponded to the maxi-

crosshead speed of the Instron and this speed varied

betwAerl 0.001 in./min and 0.005 in./min depending on

the final value of strain of a test.

Figure 16 is a

tracing of the oscillograph record obtained with a complete sequence of crosshead speed changes.

The load

relaxation which occurs when the crosshead is stopped
is due primarily to a characteristic of the machine as

demonstrated by using a brass specimen which exhibits
only elastic strain at the test loads.
The capacitance gage

reading~

due to elastic

strain in the fixture were determined using a brass
spooimon in pl.a.co of' a. zino orysta.1 .specimen.

The

elastic spring constant of the fixture was calculated
from the measured capacitance gage readings and the
loads applied to the brass

spe~imen.

The measured

spring constant and the spring constant of the load
cell were used to estimate the

erroi~.s

i.nvol ved in

assuming that the crosshead speed ratios were equal

Off ~

~l/10

1/3 _ _ /

Full

Time

__/

· Crosshead Speed

-11-5.4

sec

Load. Zero

Fig. 16

Tracing of Osoillog raph Reoord.

-46to the corresponding plastic strain-rate ratios in
tests on zinc single crystals.

This was a more accu-

rate means of estimating the errors than measuring
strain-rates directly because the lo.ad sensitivity of
the system was relatively much greater than the strain
sensitivity.

The relation between the plastic strain-

rate ratio and the crosshead speeds is given by

':11 - l, I K-r

( .5)

'ia -L~IKr
,,,

C.p= plastic strain rate
':J = crosshead speed

L = load ra-te
/( = total spring constant of the system

including both ball seats, the load cell
and the specimen.

For basal strain rate tests, the maximum error in
assuming
,.

';/,

=-~
:J;...
was found to be less than 5 per cent, so no correction
for elastic strain of the system was made in the analysis
of the records.

Variab1e strain-rate tesii.s on o-axis specimens

oriented for nonbasal slip were conducted using the
same test procedure and dynamic system as used for ·
basal strain-rate tests except for strain measurement.
Specimens deformed in nonbasal slip work-harden at
suoh a high ra."te th.at the correc'bion term re1a:ting

Cr,

as given in Eq. 5 becomes large.

'j,

To eliminate

the correction term, strain gages were used to measure
compressive strain directly.

Type c4o foil strain

gages obtained from the Budd Instrument Company were
bonded to the (l2l0) surfaces of the specimens with
Duco cement and wired in the circuit shown in Fig. 17
so as to cancel bending strains.

Two dummy gages were

mounted on another specimen for temperature compensation.

The bridge curcuit output was amplified and recorded on
the osci11ograph a1ong wii;h the load.

circuit is shown in Fig. 17.

The associated

A shunt resistor was used

,to calibrate the strain gage circuit.

A full scale

strain sensitivity of 160 x 10-6 in.fin. was maintained
throughout the tests by the use of a series of shunting
resistors connected in one 1eg 0£ the strain gage bridge

measuring strain.

'lb.e load sensitivity for the nonbasal

tests was 100 lb full scale whioh was als.o maintained
throughout the tests.

-48-

2201l.

Rc =
200K:t

lo/o

Consolidated
______ Amplifier Type 1-1138

6.81l
600;-tf
ISJl.

330Jl
Galvanometer
Type 7-341

Fig. 17 Strain Gage Circuit,

-49?u1se Tests

The static loading system used for basal strGssstrain experiments was used to apply long duration pulses
to specimens oriented for basal slip (45° specimens).
The pulses were applied by manually controlling the
crosshead mot1on or the Instron testing machine.

pulse of 3 sec rise t.ime was easily achieved with this
system.

Such a rise time limited the minimum pulse

duration to about

JO sec because a good approximation

to a square wave was desired.
Short and long duration pulses were applied to
specimens oriented for basal and nonbasal slip in a
rapid load testing machine (24).

This machine is

capable of applying pulse loads ldth a rise time of
2 x io-3 sec and minimum duration of 17 x 10-3 sec,
Loads were measured with a Consolidated Electrodynamics
oscillograph using a four leg dynamometer bridge of
high output silicon filament gages obtained from Micro
Systcmo. :tno., Po.sadenfl.,

the gage circuitry.

Oa1if'ornia.

Figura 18 show.s

Examples of load pulse records

are given in Fig. 19 for loads

13.1 lb and 491 lb.

The rapid load machine was converted from a tensile

testing machine to a compression machine by means of a
~pec:l.e:i.J.

.C'i.x ture.

Tl:1e compress:Lon !"1.xture, as sho1m

schematically in Fig. 20 is a self-aligning system of

-.50-

1•.;.
Ar.ip11:aer

Fig. 18

Dynamomete r St~~in G~ge Circuit.

-.51-

~,__------~---------,

491 lb

tLo~
Time·

/-0.01 sec

13.1 lb

Time

Prelood

Fig. 19

i..--0.01 sec

Traoing 0£ Rapid Load RecQrds .

-52-

.., Load

l'O.~

-Yoke

Seat

Fig. 20

Schematic of Cocpression Fixture for Rapid Load

J:.Iachine.

-531.:>phei~J.cal

::;eats

;;;upport~tl

ail~

prel:)SUre.

n.1.e ai.t•

bearing feature minimizes alignment errors due to friotion between the bearing surfaces and hence reduces the
erl"'Or produced when the load a.:o;;is is off the centroid

of the specimen.

The system is stable because the

splJ.erical bearing surface centers are rrcrossed."

specimen 1 in. in length can be accommodated before the

centers become uncrossed leading to instability.
The spherical seat end pieces were ::nade :from a 2 in.
diameter chrome steel ball bearing by spark machining
operations with a Servomet Electric Spark Discharge
Machine.

Th.e cylindrical surl'ace which is a reference

surface for specimen alignment was finished ground in

a lathe using a tool post grinder.

The

axis is kno'tm to be within ±0. 0002 in.

cylindric~l

from the

spherical surface radius passing normal to the plane
specimen loading surface.
The specimen is aligned in the load fixture outside
}J , I
the Jces'b:i..ng mo.chine.

Figure 21 sho1ms the sys tam used to

align the specimen us~ng the cylinder surf ace
seats as a reference surface.

the

The bottom seat is placed

inside the alignment sleeve which is in an inverted
position on a mandrel.

The seat is rotated and the

.specimen centered with. the use o:f a cat11atometer.

Th.e

sleeve is then removed, inverted and: lowered past the

Fig. 21

Specimen Alignmnnt 2quipmont .

-5.5specimen 'and around the 1ower seat.

Nylon set screws

are tightened against the bottom seat to keep the sleeve
in place as the top seat is inserted into the sleeve.
Extreme care is taken so as not to move the specimen
during these operations.
Th.e specimen-seat a..ssemoly i1S placed in the com-

pression fixture of the rapid load testing machine and
a preload of l or 2 lb is applied depending on the level
of the final desired load.

For a final load of less

than S lb, a preload of 1 lb is used and for greater
than S lb, a preload of 2 lb is used.

nie air supply

for the seats is adjusted so as to float the specimen
assembly after the alignment sleeve has been lowered
to a position where the top of the sleeve is clear of
the top seat.

Set screws hold the alignment tube in

this position during the test.

Figure ~2 shows the

assembly in the rapid load testing machine ready for
testing,

Figure 23 shows details of the air bearing

assembly.

Figure 24 is a sohematio drawing of the air

supply system for the load bearing.

To float the

assembly while under preload, a supply pressure of 20
lb/in. 2 was maintained and the needle valves were
adjusted to establish a :flow rate of 0.08 :rt:3/hr of
air.

'Iho ca1cu1atod gap in the air bearinge under these

conditions and a load of' 2 lb is 0.0004 in.

For final

Rapid Lnad Tosting F:i.xturo .

- S7 -

~ig.

Spherical Seats and Align~ont Sleeve.

-.58-

Air Bearings

fl -o-o.os u7hr
lJ
Ball Flow Meters
...__Needle Valves

.......__Pressure Gauge ,
0- 30 lb/in~
Dust Filter

Regulated Air Supply

Fig. 24

Air Supply System for Bearings.

-59load levels less t11an lO lb tl1e air suppl.y was shut o:r:r
before loading to insure that the seat surfaces ·would
contact under the final load,

Specimen alignment errors

and er1.. ors oa.used by f'riction in the load haarin&s were

estimated to give less than a

5 per cent error in the

applied stress due to bending stresses and rotation of
the specimen axis with respect to the loading axis,
Both long and short duration pulsas wer0 applied

rapid load machine was used exclusively for pulse loadings
o:f c-axis specimens.

A range of loading times f'rom

17 x io- 3 sec to 45 sec and loads from 100 lb to 500 lb
were used in these tests,

The specimens were etched prior ·to a pulse test and
replicas of the etched sur:faces were made prior to testing
to record the initial dislocation density and configuration on (lOlO) surfaces of the specimens.

_Tho replica-

tion technique used a solution obtained from Ladd
Industries and 0.005 in, thick cellulose acetate film.
Several drops of solution are applied to the specimen

surface with a

~rush

and the acetate film is placed on

the liquid film and pressed against the specimen,

The

fil:r.i. is allowed to dry for about 5 min and then a piece
of' :'.'I;rlal., backing- t'i1m

o. 01;1 in.

t:hiok tdth double-sided

Scotch Brand tape is placed on the acetate film and the
:f'ilm i:s .stripped f'rom the specimttn.

-60Jli'tcr pulse testing, the specimens werA re-etched

and again replicated.

Th.e elapsed time between test

and i~e-etch was usually limited to less than 3 min to
minimize dislocation rearrangement .

The mercury intro-

duced during the initial etch was sufficient to cause
etoh pits to 'f'orm during the second etch.

The number

of pulse tests that could be conducted before the
specimen had to be annealed was determined by the

o.mount o:f deformation or increase in dislocation density produced in a series of tests and by the conditions
o'f' the (101'0) speu:!.men surfaces after several re-etcl1.ing

operations.

In several cases, as many as twenty pulse

tests were conducted on a specimen before high temperature annealing was required because the dislocation
density had reached too high a level.

The re}?licas of' the etched sur:faces were transparent and hence not suitable for optical examination.
To make them ref'lecti ve, a layer of' al uminu.>n ·was vapor
deposited on the replicas at vacuum pressu~es

than 5 x io-S mm of Hg.

l0ss

Optically opaque films of

alun1inu..·11 were sufficiently roflecti ve for optical
examination i:·li th a metallurgical microscope and were
not so thick as to obscure details on the replicas at
magni£ication s 1ess

th~n

5oox.

-61-

Before annealing specimens which had been previously
etched, a vacuum treatment was required to remove the
mercury from the surfaces.
vacuum of 10 -6 to 10

Specimens were placed in a

-s mm of Hg for 8 hr for this purpose.

Subsequent annealing was carried out in a purified hydrogen atmosphere at 700°F for 4 to 8 hr.

This annealing

procedure was also used after all stress-strain tests
and strain-rate tests to return the specimen to as near
its original pretest condition as possible.

Tests were conducted wherein "fresh" dislocations
were in\._Q'Jfduoed into a specimen by intentional damage
prior to pulse load testing.

In all such cases the

specimens were etched after the introduction of the
:f'resh dis1oca.tions in order to record the e:icact nature

and extent of the damage.

After replication of the

surface, the pulse test was conducted.

Various means

were used to introduce damage such as scratching with
a diamond phonograph stylus, razor blade, small cleavage
:f"ractures produced by spark planing bolow 190°F and

thermal expansion damage induced with a piece of copper
sheet cooled to liquid nitrogen temperature.

Figure 25

shows examples of the damage produced on (lOlO) planes
as a result of scratches and thermal damage.

- 62'-

.•

,. '.
-.·•

(1010)

(a) Scratch Damage

( b) Cold Tool Drunag a

Fie. 2S

D~mneo ~rom Sornto~os

and Cold Tool ,

1oox.

-63-

EXPERIMENTAL RESULTS

The results of the experimental investigation are
desoribed in this part of the thesis,

The results are

divided into sections covering the static tests, dynamic
tests, pulse tests, strain-rate sensitivity of the flow
stress, influence of purity and strain on dislocation
substructure and d.is1ocation pi1e-ups.

Static Tests
A.

Basal Slip System
nie shear stress-shear strain behavior for basal

slip of 99.999 per cent purity and zone refined purity
test specimens was measured in the Instron static test
system at a constant orosshead

spe~d of 2 x 10- 4 in./min.

Tile results of two tests on a zone refined specimen are
shown in Fig. 26.

The shear strain was taken as

!'=

+ 1. 4 x 10 -8 CT' from Eq. 4 and the resolved

shear stress as

0-/"'..a

The first test was conducted

on the specimen after it was machined and annealed.

The second test was oonducted after annealing the speoimen at 700 0 F for 2 hr following the first test.

The

critical resolved shear stress was taken as the stress
corresponding to the first detectable deviation from
linear stress-strain behavior when the strain sensitivity of the system was 1 x 10- 6 in.fin. The critical

cc:

-0 4

"'C
CD

CJ)

.c. 8

CJ)

~12
+-

fl)

..Q

N.
'IG

(;

Fig. 26

20 I

Resolved

100

Shear Strain ,

150

200
250
10-6·1n. ;·tn.

Test I

Test 2

Resolved Shear Stress vs. Resolved Shear Strain £or Basal Slip.
Specimen 17-1, Zone Re£ined Purity.

~-------

300

resolved shear stress was approximately the same for
both tests.

At strains greater than 200 x 10 -6 in. I in.

the slope of the stress-strain curves was approximately
the same for both tests with the curve for the second
test being above the initial curve.

The dashed, straight

line represents the calculated elastic curve for both
tests.

'Ihe initial portion of the stress-strain curves

did not correspond to the elastic curve.

This was prob-

ably the result of translation or rotation of the compression specimen proportional to the load.
lation

approximately 0,001 in.

A trans-

or a rotation about

the specimen base of 0.3° at 10 lb/in. 2 would give the
slope observed in Test 2.

A critical resolved shear

stress of about 9 lb/in. 2 was observed for the zone
refined specimen.

A static test on a specimen of 99.999

per cent purity indicated a critical resolved shear

stress of 12 lb/in. 2 •
One static test was conducted to determine the
change in dislocation density with a given amount of
plastic deformation.

A specimen of 99.999 per cent

purity was etched and replicated prior to the test to

record the initial dislocation density as revealed on
the (lOlO) surfaces of the test specimen.

nie specimen

was re-etched tdthin one minute after the test to deter•
mine the final density.

An increase in density from

-661 x io5 cm- 2 to 5 ±o.8 x io5 cm-2 was found for a strain

of 3.6 x 10-4 in./in.

Dislocation densities were deter-

mined by counting the number of etoh pits per unit area

on photomicrographs of the replicas taken at lOOX,
B.

Nonbasal Slip System
The stress-strain curve for nonbasal slip was

obtained on a 99.999 per cent purity c-axis specimen.
The results on specimen 26-6Tl are shown in Fig. 27
where compressive stress on basal planes is plotted

against compressive strain along the o-axis of the test
specimen.

Tl in the specimen desi~nation means the

first test on this specimen.

The test was conducted

in the Instron testing machine at a constant crosshead
speed of o.ooi in./min.

The dynamic test fixture seen

in Fig. 12 was used together with a strain gage circuit
to measure compressive strain along the c-axis,

Type

040 strain gages were cemented to the (l2l0) sur:faces
of the speoime.n and the gage circuit output and load

were recorded on the Instron X-Y chart recorder.

strain sensitivity of 5 x 10- 6 in./in. was achieved
lrlth this system.

The stress-strain curve shows that

plastic do£orma~ion £irst ooours at about 1'00 1b/in.2

which is taken as the point where the curve deviates
from a linear stress-strain relation.

The work-hardening

"' c. 25
.......

..0

... 20
(fJ

(;')

....
s...

(/)

(J)

·->
( f)
(f)

(D
\.....

a. 10

(.)

aoo
1200
1600
Compressive Strain , 10-· in.fin.
400

Fig. 27

Compressive Stress vs. Compressive Strain ror
Nonbasal Slip. 'Specimen 26·6Tl, 99.999 Per Cent

Purity.

-68rate in the plastic region is high relative to that in
the basal slip system.
The c-axis test specimen was etched before and after
the strain-rate test to determine changes in dislocation
density.

Figure 28 shows the dislocation density after

900 x 10- 6 in./in. of permanent strain along the c-axis.

The dislocation density as revealed on a (lOlO) surface
+ x 10 6 cm -2 as
increased
from about 1 x 10 !) cm-2 to 3 -1
a result of nonbasal deformation.

Only the center region

in Fig. 28 is representative of the dislocation density
on a (lO'i°O) surface because the test was conducted on

3/8 in. diameter cylindrical test specimen.

Dynamic Tests

Basal Slip System
Results of variable strain-rate tests eonducted in

the Instron dynamic test system.on specimens oriented
~or

basal slip were analyzed to give shear stress-shear

strain behavior to strain levels of about 1 per cent.
'Ule load and strain corresponding to the zero strain-

rate part of the variab1e strain-rate oyc1e were used
to plot the stress-strain curves shown in Fig.

29 •

.Test results from specimens of four different purity
levels are shown.

'Ille four tests were conducted at a

ful1. Instron orosshead speed o-ro.001 in./min ·rith speed
changes in the ratios of i/§li_~o.

••

Compression
Axis

,,
.....
..

·.

(lOlO)

Fig. 28

Dislocation Density Resulting from Compressive
Strain of 900 x i o- 6 in./in. along c-Axis,
Specimen 26-lTl. 99.999 Per Cent Purity, SOX.

•70-

·-c:

..0

(/) 60

,.._

(/)

0"""'
Q)

..c:
(/) 40
Al
0.0025

- i.-

99.999 Zn

Zone Refined-

l.2

Resolved Shear Strain , per. cent
Fig. 29

Influence 0£ Purity on Basal Stress-Strain CurYes.

<., :

-71Figure '29 shows that with increasing impurity additions the stress-strain curve is, shifted to higher stress
levels.

Work-hardening.rates are relatively unchanged

although some variation in work-hardening rate oan be
seen.

This may have been due to the faot that the.strain-

rate cycles were not conducted at the same frequency from
one test to another.

The results shown in Fig. 29 are

from specimens in the annealed state that had not been
previously deformed·.

The influence of prior strain on the stress-strain
curve for two different purities is shown in Fig. JO.
Test 2 results were obtained on the previously deformed
specimens after an annealing treatment.

The effect of

prior deformation is to shift the stress-strain curve
to higher stresses without appreciably changing the
work-hardening rate.
Several. specimens tested under variable strainrate conditions were etched before and after testing to
determine dislocation density changes and the general
nature of the dislocat~~n array~ resulting from plastic
deforµiation.

Figure :;1 shows similar areas on a speci-

men before and,after l per cent shear strain.

Both

photographs are of random areas on a Zn-0.0025Al specimen and are generally representative of the entire
specimen in terms of dislocation density and substructure.

80
N.

..0

I-

0.0025 Al

.s::.
40
CJ)

,___.

- Test I

(J)

Test 2

-----

a::
20

Test 2
• Test I

99.999 Zn

Resolved

1.2

Shear Strain, per cent

Fig. 30 Influence of Prior Strain on Basal Stress-Strain
Curves.

- 73 Sub-Boundaries

~.J;:'·· ..-

.·

): .

(a) Random Area Before

.._'......

(10To >

·-

(b) Random Area After
Fi g . 31

Dislocation DShoar Strain of l Per Cent. Specimen 22-1T2 ,
Zn-0.0025Al Purity, lOOX.

An increase in dislocation density from 6.4 x 104 cm- 2
to 1.1 ±0.2 x 10 6 cm· resulted from a shear strain of

The result on a 99 •. 999 per cent purity

per cent.

specimen strained to 6.3 per cent is shown in Fig. 32.
The initial dislocation density was approximately 105 cm· 2
which increased to 2,7 :0.3 x 10 6 cm-

·A distinct

feature of the deformed specimens is that, in addition
to a~ increase in density of randomly distributed dislocations. pile-ups of dislocations against substructure
'>
occur as can be seen in both Fig. '.ll and )2. No significant difference in density increase for a given strain
l.IJ 0. '.!.

level -"~ noted between the various purities of zinc
tested.
The resu1ts of measurements of changes in dislooa-

tion density produced by plastic strain are summarized

in Table III.

Figure '':33 shows the basal slip system

results plotted as the log of the dislocation density
change against the log of the shear strain.

'Ihe slope

of the line drawn through the points is about 1/3
indicating a relation of the form

where

C • constant
Ll_}'.) = total change in density o~ dislocations
~ •

plastic shear strain.

- 75-

...-,

(10l0)

Fig, J2

T .

·-

[1210)

Dislocation Density Resulting from Basal Shear
Strain of 6,J Per Cent, Specimen 16-lTJ, 99.999
P•r Cont Purity, 1oox.

TABLE III

Dislocation Density Changes Produced by Plastic Strain
Purity
Specimen

I?er cent

Change in Dislocation

Final Strain

Density, cm... 2

in, /in.

Basal

3.6 x 10-4

16-1T2

99.999

4 :!:o. a x 10.5

22-lT2

0,002.$Al

1.0 :to.2 x 10

16-4T3

99,999

2.6 :t.o. 3 :x: 106

1 x 10-2

6.3 x io- 2

Nonbasal
26-6Tl

99.999

3 :1 x 10 6

9.0 x io· 4

·-

(!)

o ....

-·-en

0 c:
:;: 0
0 ..c

c en

(!)

C\J

106

Fig. 33

Resolved

Sh~ar

Strain,

10 in.fin.

100 -4

r---~

Change in Dislocation Density vs. Shear Strain for Basal Slip.

.~--

__,.,.. ~

.... ~

__,.,.. v

1000

--I
--I

Pulse Tests
A.

Basal Slip System
Several test specimens of

99.999 per cent and zone

refined purities were pulse loaded to determine basal
dislocation mobility.

The specimens were etched prior

to testing to reveal the initial dislocation arrangement.
Pulse load durations from 4.5 sec to 1 min were applied
in the Instron static test system.

The results on a

zone refined specimen loaded to 9.9 lb/in. 2 resolved
shear stress for l min are shown in Fig.

34.

The scratch

was made with a diamond phonograph sty1u.s under 1.2, gm

of contact force prior to etching and testing to introduce fresh dislocations.

The dark spots are caused by

bubbles in the replicas.

As seen in Fig.

34. disloca-

tions appear to have moved away from the scratched
region and from the sub-boundary.

A general increase

in background dislocation density is seen as well as a
number of long pile-ups of dislocations parallel to
basal slip plane traces.

These pile-ups are not asso-

ciated with the deformation introduced by sQratching.
Several pile-ups were found to extend entirely across
the prism surface of the test specimen.

Mobility data

could not be obtained from this test as dislocations
moved too far to establish the location of the sources.

- 79/Sub-boundary

...

.. .•

., . ..

.. , .
•;'It.\.

·•

*' :·

!·

-..£'l -- ~
,•

...,,.

.. ·-

,-.. -·

. .-J
: ·:: ·-· -

-~:-

.. '

•:· i. -

... .

·- -

. ~·

! .:

• :r .

.....

....

--.
..

. .. i

. .,

(a) Boforo

-·

.·

...•

(lOlO)

.. - ... -·-. . -.....__:,.,,., ..
..~~-.

...

~-.:-

&\".::" :._- .·

\9 .-~

.......
(b) Af'ter
'Fig.

Basal Dislocations before and af'ter a Pulse of
9.9 lb/in,2 , Specimen 17-JTJ, Zono Refined
Purity. 1 Hin Pulse Duration, lOOX.

...

-80Pulse tests on 99.999 per cent purity specimens were
made at stresses o:f 7.7, 12.0, 15.4 and 20.J lb/in.
-:for Li.me durations of:

4; sec.

7.7 lb/in. 2 ,

The test at

which is lower than the initial :flow stress f'or 99.999

per cent purity material, indicated some local rearrange-

ment of dislocations but no increase in dislocation
density or formation of pile-ups.

At progressively

h:1.gl"l.er stresses, greater i.ncreases l.n dislocation den-

sity and numbers of pile-ups were observed.

Mobility

data was not obtained from the pulse tests on 99.999
per cent purity material because dislocation sources
could not be established and because pile-ups were
observed to extend across the entire specimen surface
in all tests except the test at 7,7 lb/in. •

In other

words, the distance moved by an individual dislocation
dnrine the t:tme duration of' the applied stress could

not be determined.
Pulse tests on specimens

99.999 per cent and

zone refined purities oriented 'for basal slip were conducted in the rapid load testing system.

'nle.specimens

wore scratched and etched bo£oro testing and re-etohod

within about three minutes after the pulse test.

Tests

were performed at resolved shear stresses from 7 to 19
lb/in.

and for times of 17, 34 or 51 x

same general result was

~ound

io- 3 sec.

'Ihe

in these tests as in the

-81pulse tests conducted in the Instron system. \ Dislocation
sources within the specimen or at the surfaces where the
load was applied appeared to operate and cause dislocation pile-ups at the same stress levels that influenced
the £resh dislocations produced by scratching or by
thermal strain damage,

This, in effect, prevented any

one-to-one correspondence of before and after dislocation
positions from being made.

Long, extended pile-ups along

basal slip plane traces were observed within the shear
stress range of 7 to 19 lb/in. 2
Figure 3.5 shows the

same regl.un on a

z.une r(;).c'ined speci.men

be:C'o1~e

and a..c'ter

a pulse test of 1.5 • .5 lb/in. 2 for 17 x io-3 seo.

Pile-

ups of dislocations against dislocation substructure
can be seen.

The longest pile-up found on either prism

face is shovm in Fig. 35 and is indicated by an arrow.
The total length of this one pile-up was 0.78 cm with
one end extending to the edge of the specimen oorres-

ponding to the surface of load application.

By assuming

that the dislocation source was located at the load
surface and that the leading dislocation in the pileup traversed the entire distance, a maximum dislocation
velocity of 4S.8 cm/sec was calculated for a shear stress
of lS.5 lb/in. 2 • A minimum velocity of 22.9 cm/sec
would be obtained by assuming that the dis1ooation souroe

was located at the center of the pile-up.

In several

- .- •

·~

.!. .·.
(..

(a) Before

•·
·- ....
. Mr

-....•.. _

·:

(lOlO)

[1210)

. .t_,

.,,.. ·t-.

f.
~ --.

·,,L""',-

_ J-

.. . . . .

.:''.

1A·
.·'f .
,,.j. '·

--r ., .·:
,.

.1 "..

~1:
..

,...

\t ·...,..,-._
. ' ..

1-..

··~

..7

.) ..r-.. <

. . ·: ."'
.::;

;;,

"'»

(b) After
Fig. 35

Basal Dislo~ations before and after a Pulse of
Spocimen 17-4Tl, Zone Refined
Purity. 17 x lo-3 Sec Pulse Duration, 1oox.

15.5 lb/in. •

-83-

tests, dislocation pile-ups were observed on both (lOlO)
sur£aces of' the test specimen that appeared to be associated with the same basal slip plane.
The results of' a series of' tests on 99.999 per cent

purity specimens are shown in Fig. 36.

Log velocity has

been plotted against log resolved shear stress.

Points

labelled with a caret { A ) are measurements on pile-up
lengths that extended across the entire specimen face
and hence are to be regarded as lower limits for the
velocity at the corresponding stress level.

The points

in Fig. )6 without a caret represent pile-up lengths
that extended from a load surface into the specimen.
Each point represents the maximum velocity calculated
for a given test and hence involves the maximum length
of' all the observed dislocation pile-ups.
Figure )6 shows a considerable scatter in the
experimental data.

A straight line has been drawn through

the points representing the maximum observed velocity for
a given stress level.

Tile straight line indicates that

the data can be represented by an emperioal relation of
the form

v=(~f
where

(7)

80 !·

3'3$ ""

......

0 .20

........

·.;: (/)

(.) 10

OJ> 8

Fig·. 36

Edgo to Edge Measurement

a 10
15
20
Resolved Shear Stress, lb/in~

Basal Dislocation Velocity vs. Resolved Shear
Stres::i .for.99:-999 Per Cent.Purity Specimens.

-8.5/' • applied shear stress

i1 ... 5

10 = the shear stress whi-~~~es a velocity
of l om/sec and is 5 lb/in. •

Several sources of error existed that may explain the
scatter observed.

One of the uncertainties was the

location of the source o~ the dislocation pile-up and
another was introduced in the process of' maasurine the

pile-up lengths because the location of the end point

of a pile-up was not always clear •
./.,.

The data plotted in Fig. )6 is shown plotted as

log velocity against 7- ll

6 lb/in. 2 -was taken for

in Fig.

·"'

37.

A value of

re· which is the lowest stress

at which any dislocation motion was observed.

A straight

line has been drawn through the maximum velocity points
which represents a function of the form
1""-7,'

v- : : Ce -a
where

C • constant

o. 1.is.s 1b/1n. 2 •
B.

Nonbasal Slip System
Pulse load tests were conducted in the rapid load

testing system on several 99.999 per cent purity speci-

mens oriented for nonbasal slip to determine the

Cl)

·-

...

o(I) (!)

-0

c .!:::

· - ;>,.

(i')

(.)

(l)

.,._,

c: 0

too

200

Fig. 37

o.,..

lb I in.2

'r-1"L

""0

Measur omont

11= 6 lb/ln 2

""C.

"" Edge to Edoo

Basal Disloca tion Velocit y vs. 't'-1"'\.

/ "'

°'

CX>

mob111 ty o:f nonbasal dis1oca·Uons ln the (1213'] ( 12'12)
slip system.

A uniaxial stress parallel to the c-axis

of the test specimens ranging from 390 to 2010 lb/in. 2
was applied for times ranging f'rom Sl .x: 10-:3 to 33 sec,
The specimens were etched before and re-etched within
three minutes arter testing to estab11sh any changes
in background dislocation density as well as changes in
regions where the specimen had been scratched to produce
fresh dislocations.

No significant generation of dis-

locations occurred near scratches in any of the tests
conducted.

Deformation bands occurred at compressive

stresses in excess of 790 lb/in. 2 whereas none were
found between 390 and 690 lb/in. 2 in load durations from

6.2 to 33 sec.

Figure JS is a photograph of the slip
bands produced at a compressive stress of 970 lb/in. 2
or 40~ lb/in.

resolved in .the [1213] (1212) system.

The load duration was 31.4 sec.

The slip bands seen

in Fig. 38 are oriented along traces of the {1212} slip

planes on the prism sur~ace of the test specimen.

significant increase in background density was noted,
other than the formation of slip bands containing high
densities of dislocations.
The mobility of nonbasal dislocations was calculated
from the longest length of new slip band produced at a

given stress by assuming that the dislocations with the

-88-

Traces

or {1212}

Compression
A.xis

(lOlO)

Nonbasal Slip Bands Resultine from a-A.xis
Compressive Stress of 970 lb/in,2,
Specimen
16-41'6, 99,999 Per Cent Purity.
Jl . 4 Seo Pulse
Duration, 100X.

maximum velocity moved one-half the total length of the
slip band during the duration of the test.

This is

equivalent to assuming that the dislocation sources are
located at the center of the bands.

The experimental

data is sho1. m in Fig. .39 plotted as log velocity against
log stress resolved in the [1213'].(1"212) nonbasal slip
system.

The straight line dra1m through the points

corresponds to a power law relation of' the form
(0)

where

i'l. = 9.S

Ta = the resolved shear stress which produces

a velocity of l cm/sec and is 790 lb/in.2.

Strain-Rate Sensitivity of the Flow Stress
A.
./·

Basal Slip System
The indirect method of' determining the mobility

relation involves the inverse strain-rate sensitivity
of the flow stress.

Two different functional relations

between the plastic strain rate,

!'p , and the applied

shear stress were employed in analyzing the variable
strain-rate data.

The :first relation assumes a power

law dependence of' the form

t, = c '!""

(9}

-90-

0.5

~''

0.2

.~ 0

.:-0
0 (1'
(,)

.......

()

·-0 ...

10..2

....

10-3

()

lOO

200

400

800 1000 2000 3000

Resolved Shear Strass, lb/inf
Fig.

Nonbasal Dislocation Velocity vs. Resolved Shear
Stress for 99,999 Per Cent Purity Specimens.

where C is a constant.

The inverse strain-rate sensi-

tivity from Eq. 9 is given by

ak ip

n'=

(10)

d .tn 'r

f?71;

;t;

n I:::

rt..

L1.,...
,,.....

in terms of the strain-rate after the change,
and thai; imposed prior to the change'

df2

.,d'/""i5

the jmjp in stress accompanying the change and is much
,..,._,

less than the shear stress, /
calculated f'rom the

~xperimental

Tiie values for

1A I
,~

data are given in

,;!

Table IV f'or speoime'i1s of' f'our different purities ranging

from zone re:fined to 0.02 wt per cent aluminum.
each test, the mean value f'or

For

n' has been listed along

'td th the standard deViation from the mean. \ Specimen

17-2Tl sho·wed a somewhat linear increase in

·w'i. th

strain ( j1. = .50 to lOlJ.) but no such variation was
found :for the other tests

conducted~:

No sign1t"icant

difference ·was found bet·ween the values of '11..

calcu-

lated from increasine changes and decreasing changes
in strain-rate and between the various purities of' zinc

tested.

-92TABLE rv

Summary of Variable Strain-Rate Data
Synchro-

S;eecimen

Purit;t

nous
Speed,
10-'.hn./

Final
Strain

min

;eer cent

?t 'j:

m'-:!: tr

Basal
1.7-ZTl

zone
Re:Cined

1.2

.50-10!.t-*

l. 71.:t.0. 28

16-4T2

99.999

77±..17

1.91.t0.46

16-4T3

99.999

6.3

90.:t.20

2. 04.tO• '.30

22-lTl

o.002.5Al

1.1

90.±,2.5

1. .56.t.0 .10

22-1T2

. o. 0025Al

136.:t,20

l.6.5.:t,0;30

19 ... JT2

0.02Al

1.2

78.t20

1. 06t,.O• 23

Nonbasal

2.)-lTl

99.999

*Linear Cunction of strain.

800 x 10- 6 720±,10

in. /in.

-9'.3The seoond relation used in analyzing the strainrate sensitivity data assumes that the strain-rate is
related to the difference between the applied stress
and the flow stress at zero strain-rate,

1°'/

, or

Ht./

01'
The exponent

c cr-0.·) .

(11)

m is given as

1i1. ;;

( 1'2)

,tn.. orz./f ,,
J$1..' ·--· -·- - - - -

- ,,t,.._(?i.-7")
1i - r;,·

where

7.t. is the stress immediately after the strain-

rate change and

?J is the stress immediately prior to

the strain-rate change.

Measurements of the load imme-

diately before the "machine on" part and after the
"machine off" part of the strain-rate cycles were used
to determine the values of

1;,·

for a given set of
r·~

strain-rate ohanges.

Figure '2}0 shows schematically a

typical load-time curve obtained experimentally.

The

load jumps resulting from increasing changes in crosshead speed,

If• , are shown as do , ~ and J; . The

stress difference ratios are then given as

y=O

Load
Time

Fig. 40

Schematic Load-Time Curve.

-9.5-

12. - Tt'
r; -rt·

Jo +J',
- Jo

and

The values of in

calculated from the experimental data

are given in Table IV as mean values and standard deviat.ions

:fi~om

the mean.

No :si.gni£icant di:f:f'erences uorc

found in the Values of )yt

calculated for four different

purities of zinc except for the test on a specimen of'
Zn-0. 02Al purity. /
_J

Nonbasal Slip System

A variable strain-rate test on a c-axis specimen
was conducted at crosshead speeds in the ratio oi' l~~/O
and a maximum crosshead speed of'·0.002 in./min.

The

strain-rate sensitivity of' the flow stress for nonbasal
slip was found to be considerably less than that for
basal slip.

The value for

Pt I calculated from the

experimenta1 da·t-a is given in Tab1e :CV.

stress at zero strain-rate,

The :f'low

7(.' , could not be determined

because of a large uncertainty in the value of

t5 which

resulted from the very small strain-rate sensitivity.

-96In:fluence of Impurity and Strain on Dislocation Substructure
In the course of etching and examining single
crystal specimens of four different purities of zinc,
several observations were made regarding the influence
of alrnninum impurity on the type 0£ dislocation substructure and degree of impurity segregation found in·
single crystals.

Figure 31 illustra·!;es the generai' type

and density of substructure found in single

cryst~ls

of zone refined, 99.999 per cent and Zn-0.0025Al purities.

The substructure is for the most part perpendj.-

oular to the basal plane trace on the etched prism
surface of the specimen.

Upon closer examination, the

substructure is found to consist of closely spaced dislocations 1·,rhich are most likely basal dislocations 0£

pure edge character as sholm by Brandt, Adams and Vreeland
(22).

Such substructure would then be characterized as

small angle tilt boundaries.

The general type of sub-

structure found in specimens of Zn-0.02A1 purity differed
:from that found for the other purities.

Figure 41 shows

an etched prism surf'ace where the substructure oan be
seen to be oriented more or less parallel to the basal
plane trace.
Examples of' macroscopic impurity segregation were
found in specimens of Zn-0.02Al and Zn-0.0025Al purities.

-97-

--~-~·-

----- . "'\.

(1010)

Filj:. 41

Dislocation Substructure in Zn- 0.02Al Specimens ,
Specimon 19-1, lOOX.

The segregat;ion ::id;;ruc-ture as revl;;)a1ed on a i:ioli1Shed and

'etched prisr.a,,ai;;d transverse faces of a 4.5° compression
1: 7

: ,,, ~ C;>. D:J.,4J

test speci:r:ien,;is shoi:m in Fig. lfa.
for tho specimen sho'tm in Fig.

The growth direction

42 was almost parallel to

the prism surface and within about

io 0 to the basal plane

trace. 'Impurities have segregated to rorm the elongated
cellular structure 1tlth the cell axes oriented along the
growth direction.

Comparison of' Figs. 41 and 42 illus-

tra.tes the re1a·l::i.an bett-ref.ln ir_J_purity segregation and

dislocation substructure as observed in specimens of
Zn-0.02A1 purity.

The dislocation substructure can be

seen to correspond to the cellular boundaries formed by
the impurity segregation.
Figure !J-.3 shows -i:;he sagre5atio1"l substructure as

revealed on a prism face of a Zn-0.0025Al

specimen.

A cellular structure oriented along the crystal growth
direction was observed as in the case of Zn-0.02Al
specimens.

However, no correlation between impurity

segregation and dislocation substructure was found in
/(:;!

the Zn-0.002,5Al crystal.

Figure 4'.3 shows the charac-

teristic tilt boundary substructure ·with no apparent
relation to the impurity segrega·tion substructure.
Table 'V summarizes the observations made on impurity
segregation and dis1ocat;:l.on substructure.

- 99-

( a ) Prism Surface

(b) Transverse Surf::.oe of 45° Spooioien
Fi;:.

1~2

Impurity Soe;regation in Zn- 0 . 02Al Spooimons .
Spooimon 19- J, zsx .

- 100-

.,..

::.

Gro1rth

Direction

Impurity
Scgi·ogation
Substructure

Dislocation
Substructure

{10Io)
[I2Io]

Fig. 4J

Dislocation Substructure and Impurity Secrocation
in Zn- 0 . 002,!)A1 Spooimons.

Specimen. 22 - 1, 2,:)X .

-101 ...

TABLE V
Summary of Effect of Purity on Substructure and
Nonbasa1 Dislocation Density

Impurity
Segregation
into Ce11s

Nonbasal
Dislocation
Density

Purity
l2er cent

Substructure
Character

Zone
Ret'ined

Perpendicular
to basal
planes

99.999

Perpendicular

- ~~ ~~~-~~ ~3.

to basa1

cm-2

planes
Zn-0.002.$Al

Perpendicular
to basal
planes

Yes

89 x 103

Zn-0.02Al

Parallel to
basal planes

Yes

210 x 103

-102Several specimens of each purity were cleaved and
etched with Rosenbaum's Etch (20) to reveal nonbasal
dislocation intersections with the basal plane.

example of the etch pit density on a Zn-0.02Al specimen
is shown in Fig.

44.

The results of nonbasal etch pit

counts are tabulated in Table "Y,.

An increase 1n nonbasal

was observe4 to have

an effect on

the density of substructure in ~)eoimens which had been
strained and annealed.

Figure

45 illustrates the tilt

boundary density in a specimen after 30 per cent basal
shear strain followed by annealing at 700°F for

The tilt boundary density seen in Fig.

4 hr.

is about three

to four times that found in undeformed specimens of the
same purity.

Dislocation Pile-Ups
An experiment was conducted to establish whether

the dislocation pile-up configurations observed on
specimens deformed in basai slip were truly representative of the deformed structure of the specimen before
the stress was removed.

A 99.999 per cent purity speci-

men was etohed and replicated prior to the application
of a load corresponding to a resolved shear stress of
12.1 1b/in. 2 •

The load was held constant while the

- 103-

(0001)

Fig. 44

[12To]

Nonbasal Dislocation Donsity nevealed on the
Basal Plano ox a Zn- 0 . 02Al Purity Specimen.
D~nsity ~ 2.1 x io5 om- 2 , lOOX.

- 104 -

r•

~~-~:~."".....~-....

. ··.~

t _. _

: .

..... ·.·

-· · .. :
-:.:-... . .

Ift·.:.•.: .. ..·.:. .· ..
~-

·.

...-:-··.- : . .

(lO'iO)

Fig, 45

[r2roJ

Dislocation Substruoturo after JO Per Cent Shear
Strain and Anneal, Specimen 16- J , 99,999 Per
Cont Purity , lOOX,

-105-

specimen was re-etched and then the load was removed.
Prism sur:f'aoes were replicated and aeain the specimen

was re-etched and replicated.

r•

Figure ·46 shows the dis-

location distribution in identical regions of the specimen be:f'ore application of stress, under stress and after
the stress was removed.

A J.arge number of' pile-ups

against a tilt boundary can, be seen but :f'ew changes in
either the number o:f' pile-ups or their length have
occurred between the stressed and unstressed states.

-106-

.·
(a) Bei'ore

(lOlO)

[r2ro]
(b) Under Stress

-·

•.·.

1;7~

.tz-.. ·-:·. .

.,..-

·..;.·

..: ..._ -.- • •.......
. -.
,........

Ei'i'ect of Stress Unloading on Basal D~slocation
Pile-Ups. Shear Stross • 12 . 1 lb/in • •
Spooimon 18- 1. 99.999 Per Cent Purity. lOOX.

-107-

VI.

DISCUSSION OF RESULTS

The stress-strain behavior of zinc single crystals
has been found· to be drastically different depending on
whether the crystal deforms in basal or nonbasal slip.

A low critical resolved shear stress and work-hardening
rate are characteristic of basal slip as compared to nonbasal slip which confirms the work of Stofel (23).

The

differences between basal and nonbasal slip can be understood in terms o:f thA basic relat:ton given by Eq.

3 if'

the dislocation mobility relation ·and rate of' dislocation
multiplication with strain are known for each mode of
deformation.

Etch pit observations can be used to

establish the most likely dislocation mechanisms responsible £or the observed v~lues 0£ £1ow stress and

work:-hardening rate.
Basal Slip System
A.

Dislocation Orientations
The dislocations observed after pulse tests on

specimens oriented for basal slip are most likely close
to the edge orientation.

The specimen orientation is

such that dislocations with a Burgers vector in the
[1210] direction w'i.11 experience a force per unit length

equal to 1'a

where

a is a lattice parameter and r is

the applied shear stress.

the dislocation line.

'lllis force acts normal to

Dislocations with Burgers vectors

-108at

60° to the [1210] w1ll experience a force per unit

length equal to

I ,.,..a. • Etch pi ts were observed on the

(lOlO) surfaces of the test specimens parallel to the

[r2Io].

Ther~fora, edge dislocations with a [12ro]

Burgers vector make a perpendicular intersection lrlth
etched surfaces and screw dislocations ~~th the same
Burgers vector lie parallel to the etched surfaces.
The mobility of basal screw dislocations is of

the same order of magnitude as that of basal edge
dislocations for the same stress lave.ls at very low
strains.

This is deduced from the observation that

in several pulse tests, pile-ups observed on one of
the (lOlO) surfaces of the test specimen were located

on the same slip plane as pile-ups observed on the
other (10l0) surface with.in the limit of measurement
accuracy.

This observation suggests that dislocation

loops expand in a slip plane with' the edge and screw
dislocation components of the loop traveling at about
the same rate.

This result is different from that

found for lithium fluoride (11) and silicon-iron (2~)
where edge dislocation velocities are much greater
than screw velocities at the same stress level.
The results of the variable strain rate tests
undoubtably involve both edge and screw dislocations
'with (1210] Burgers vectors.

If this is taken into

-109-

account, Eq. 3 should be written as

(13)
where ~ and Vj are the velocities of edge and screw
dislocations respectively.
The effect on strain-rate of di~ferent edge and
screw velocities at relatively large strains may be
tal~en

into account by the following model.

Assume that

an infinitesimally small square dislocation loop is
formed by some means and that in time

i it expands to

the size shown be1ow

--r

-.Po2.
__________ _l
--1~

f e. = total length of edge dislocation
J!.s= total length of screw dislocation.
The lengths of edge and screw dislocation formed in

time

t are

is :;: 4 vet
~e = 4 vst

-110which gives the relation

-~fe vs

A ::. -ve •

..Pe

Equation 13 may now be written as

ir =.J>e bve +/>s b rA ve)
2_,;:>eb ve.
This result shows that the strain-rate can be related
o.lono ovon if'

.?s :J ~e.

TI1.erefore the indirect method may be used to determine
the mobility relation for edge dislocations when both
edge and screw dislocations are contributing to the

strain.
B.

Dislocation Multiplication and Density Changes
The results of the pulse tests indicate that basal

dislocations moved long distances and. in some cases,
out of the specimen at stress levels near the macro-

scopic flow stress as determined by stress ... strain tests.
;.

,''

"",,;/'·~.,,,

Each dislocation pile-up I sh'o1m
on a single slip plane.

to be

These individual pile-ups

appear to be associated with other pile-ups on the same
slip plane.

These observations imply that one very

active dislocation source was responsible for an entire

-111-

slip line involving hundreds of individual dislocations.
Dislocation multiplication of this type would be characteristic of a Frank-Read source located at the surface
or within the crystal.

In almost all cases the pile-ups

were observed to extend from a loaded surface of the
specimen which indicates that surface sources are probably more important than volume sources.

This may be

due to stress concentrations on the surface where the
load is applied.

given length are

:In addition. sur:f'aoe sources 0£ a
abl~

to generate dislocations at half

the stress level of volume sources of the same length.
This is a result o'f: ffimage forces" on a dislocation
near a free surface.
Figure 33 gives the resu1ts 0£ severa1 determinations of the change in total dislocation density acoom1

panying shear strain.

The relation

L.'.f

J' :: C Op 3

for zinc differs from the experimentally determined
relations

Ll,IJ =C lf'p

Lip= 8 + C.fo3 E.?

:for copper (26) and

for stage I deformation of silver {27),

and lithimn :fluoride (11).

The relation found for zinc

is less dependent on shear strain than the relation
reported for

silver~

This indicates a relatively high

probability that a glide dislocation in zinc will reach
the surface and therefore contribute to the strain but
not to the etch pit density.

The mean travel distance

-112-

of glide dislocations in zinc can be of the order of
1/4 in. as determined by the pulse load tests.

This

is in agreemen~ with a speculation made by Mott (28)
that large numbers of basal dislocations in hexagonal
close-packed crystals might be able to leave a specimen
and thus would not be able to influence the flow stress
by interaction with other dislocations.
'Iha experimentally determined basal dislocation
.l

density changes given in Table III.are numerically
equal to the total etoh pit density counts observed on
the (10l0) pri.sm surf'a.ces of' the te.s t specimens.

i.f.·-·""

-explained in the derivati.on -0t: ~. ~ ihe number of
dislocations per unit area is equal to the total length
of dislocation line per unit volume if all basal dis locations are straight and perpendicular to ti+e area of
observation.

A better approximation may be

tha~

that

the basal dislocations are randomly oriented with respect
to the observation surface.

The relation between ob-

served etch pit density and total line length of basal
dislocation per unit volume,~: is then

.fl=

o.61-A

from equations developed by Sohoeok (29).

-113-

Thermally Activated Dislocation Motion
Figure 37 shows the dislocation mobility data plotted

where 7;:. was taken as
as log velocity against T- T'j
6 lb/in. 2 or the lowest stress at which dislocations
were observed to mo~e in 99.999 per cent purity crystals.

The slope from Fig.

)~ gives B • 1.45 lb/in. 2 where B

is defined by

(l4)
Th.is form for the mobility relation wpuld be expeoted i£ the rate determining mechanism "Was the thermal

activation for a glide dislocation to pass some obstacle
in the glide.plane.

Seeger, Mader and Kronmuller (30)

and Friedel (31) have considered this problem and·botb.
believe that the flow stress for basal glide in hexagonal
close-packed crystals is determined by the stress required
to overcome the "long-range internal stresses" produced
by parallel glide dislocations and by the thermal activation of jogs as basal dislocations glide past forest
dislocations thre.ading the glide plane.

The strain•

rate resulting from thermal activation of jogs is given
by Friedel as

... 114-

where

i'Jl/. energy required to produce the jog
"',- • applied shear stress

7/.,' • long-range internal shear stress

cf a separation of extended basal dislocatio ns
~ • forest spacing
of slip plane swept over by dislocatio n
A • area
after jog is formed

J) • Debye frequency.
The velocity of a dislocatio n is then given by

. t1U
- 'E-

V (-b)2A e

where.

(i"ii)

k.T

The forest spaoingJ. for the crystals used in this
investigat ion can be estimated from the etch pit density

observed on basal planes. and gi:ven in Table- V-. - Wi:th-.a
forest d-ensity oJ:~,.ahont.(10 cm- )_~--£-epes-t -spaci·ng,J ,
.,,

is 10
then

_j .;;~

om fo'?' ~9.-999 p.er oen-t purity material-. B is
is taken as 7
equal to 2. S x io- 3 lb/in. 2 if

-2

·- .

This value o:f B is considerab ly lower than the
directly determined value of 1.45 lb/in. • This lack
( 32).

of agreement shows that a model based on the thermal

-11,_
activation of jogs is incapable of explaining the observed
dislocation mobility.
One reason the above model is not correct can be
seen by comparing the terms Lf t.J and (f':.. T1:) hdl in the
14

exponential term of.' Eq. ':t:;!).

For an applie<:'f. shear stress

of 16 lb/in. 2 , (~~·} bJ.f % 120eV f'or the forest
spacing observed and a long-range internal stress of
about 6 lb/in. 2 which is the lowest stress at which
basal dislocations were observed to move long distances.

IJ{J has been estimated by Friedel ()2) to be

A l.J is then about

leV

for basal dislocations in zinc.

This result means that the applied stress is more than
sufficient to supply the jog energy required and thus
no assistance from the thermal energy of the lattice is
required.
I r-

Eq ua ti on 1-6 predicts that in the limit as ('1!-7;·) be:/f.
approaches LJ(.j , the velocity of a dislocation will
A which is approximately equal to
approach JI {

JI b2 •
J/ b'2.. ;:;: ;

For basal dislocations in zinc single crystals
'1 :x: io-

cm/sec.

This veloc1 ty is much lower

than the velocities measured in the present work and
indicates that all thermally activated mechanisms which
predict dislocation velocities of a form similar to

-116-

Eq. 16 will not explain the present results.

The ther-

mal activation of glide dislocations past impurity atoms

(4) is one such mechanism and as such can be eliminated
as a controlling factor in the present work.

Dislocation Mobility in Other Materials
/0

Figure's % -and~ -39 show" that the direct mobility
da.-ta. f"or zino may be approprlate1y represenCied as

v-,,. (:;,) h

Were 7'0

equals the stress to move a

dislocation at 1 cm/sec.

Mobility data on other

materials has been found to fit this same form with
different values for fl. and 7(, •

A summary of

T;,

and

It for zinc as well as other materials is given in Table
VI.

The large differences between the values of

'ro

are to be expected from the differences in atomic bonding .
.· I

and crystal s.tructure.
•,,,

•<

The

materials listed in Table ·v:r

·,,.,,,

inolude 1.ionic bonding (lithium fluoride and sodium

chloride), covalent bonding with diamond cubic structure
(germanium) and metallic bonding with body-centered
cubic structure (silicon-iron and tungsten).

The present

results on zinc are the f"irst diroot mobi1ity measurements reported on a metal in the so-called "soft" group
which includes face-centered cubic and ha:x:agonal closepacked metals.

1he conspicuous difference between

basal dislocations in zino and all the other materials

-117_'ii

TABLE VI

Summary of

'To and 1\. for Various Materials
Temperature

7'"o

1bLin. 2

1\-

Silicon-Iron (12)

298

30,000

'.3.5

Tungsten (16)

298

45,000

4.8

Lithium Fluoride (11)

298

1,400

Sodium Ch1oride (1.5)

298

210

Germanium (13}

693

:Material

973

3 • .5 x io 6
24,ooo

1.5
l.$

Zinc

Basal

298

Non basal

298

790

9 • .5

-118-

listed in Table VI is the low value of

'ro which indi-

cates a much lower la~tioe resistance to dislocation
motion.

Lattice Resistance to Dislocation Motion
Two possible sources of lattice resistance to dis-

location motion in an otherliise perfect lattice have
been considered theoretioa11y.

Leib~ried

(2) was the

first to consider the drag on a screw dislocation moving
at a constant velocity caused by the scattering of phonons
or sound waves and Eshelby (3) has estimated the drag
Lothe (3J) has recently

caused by thermoelastic effects.

reViewed and extended the calculations for both effects.
Lothe concludes that for metals the thermoelastic effect
is negligible and that Leibfried 1 s result for the phonon
drag is correct and should be about the same for a edge
as well as a screw dislocation.

'lb.e drag stress due to

phonon scatter is given by

where

e = thermal energy density
'V"' • dislocation velocity

C • velocity of shear waves.
Sinoe zinc at room temperature is above the Debye tem- ·
perature (250°K)

-119-

<:=

-3/b3

and

o.3 k.Tir

'Tc1

b3C

wherG 'f'or zinc

b • 2.66 x 10-S cm
C • 2.31 x 10 5 cm/sec.
'lb.e phonon drag stress on a dislocation moving at
25 cm/sec in zinc is calculated to be about l lb/in. 2
which from the present mobility. results is a factor of
10 lower than the observed stress required to move a

dislocation at this velocity.

Seeger ()4) has indicated

that the damping constant for an edge dislocation should
be an order of magnitude greater than that for a screw
dis1ooation which wou1d resu1t in a drag stress o-r

about 10 lb/in. 2 for. a;, ,disiocat.ion moving at 2.5 cm/sec.

I:f this conclusion is

correct·~~~he

present results

suggest that the drag stress shou1d vary as the ve1oI
city to the ~

power rather than the first power.

Considering the uncertainties involved in the theoretical calculations, the possibility that the entire lattice resistance to moving dislocations may be due to
phonon scattering cannot be excluded.

.•

..-·

-120-

F.·

Nature of Long-Range Internal Stresses

..,-"

As mentioned above, in Section C, Seeger, Mader

and I\ronmuller {3.il) consider the flow stress for zinc
in basal slip to be determined by the long-range internal

stresses of parallel glide dislocations and a thermally
The athermal or

dependent term due to jog :formation.

long-range stress term at room temperature has been
sho-cm to account for the major portion of the :flow

._,,.;!

stress ( 3.5).

.A.11

obsta.o1es to dislocation motion which

involve internal stress interactions over distances where
thermal activation cannot assist in overcoming the
obstacle are classed as athermal.
The present results as shown in Fig. 29 indicate
that ohangas in orysta1 purity oan have an appreciable
·~

}'1

C'.,/

j•

(1 . ! r,. !

effect on the flow stress,w:Lth
litt.lc change in.the
,,
densitf of basal dislocations.

This L!e s ul.t- -al.ong w-i th

tho correlation of dislocation density change with shear
strain shotm in Fig. 33 and Table III f'or two different
.p.uriti.es suggests that the long-range internal shear
st;res.s which must be overcome :for glide to occur is
Ir ,

not due to interaction of parallel glide dislocations~

A possible source of long-range internal stress
results when glide dislocations form attractive and
repulsive junctions with forest dislocations (31) •
•I~·

/ ,\

Saada (36) gives the conditions required for the f'ormation

-121-

of attractive and repulsive junctions between two dis-

b1 and b2 •

locations with Burgers vectors

is negative, an attractive junction is formed by the
dislocation reaction

b, • b.a. is positive, the d.islooa tions repel one

another and constitute a repulsive junction.

I:f the

scalar product is zero, the reaction is neutral from an
energy viewpoint.

These vector conditions are equi-

Valent to a statement in terms

accompany a dislocation reaction.

energy changes which
Namely, a reaction

occurs only if t]J.e energy per unit length of
less than the sum 0£ energies o~

b3 is

b, and b~ or

2 •
Gb3 2 < G b,2 + fJ b2

Saada has calculated the stress required to overcome
attractive and repulsive junctions as

Gb
7= fiP,
where

b • Burgers vector {assumed to be the same
for both dislocations)

• distance between attractive or repulsive

junctions

... 122-

.,,15 = 2.5 (for attractive junctions)
10 (for repulsive junctions).

Nora dotai1ad ca1cu1ations have been made by Gale ('37,)

for specific dislocation reactions in FCC and BOC structures where such junction reactions are thought to have

effect on the flow stress.

The specific dislocation reactions in zinc which
are most liko1y to :f'onn a:ttra.otive and repulsive juno-

tions are reactions between basal dislocations

b, - a.

and nonbasal dislocations ·with b.J.

Reactions

. . (O' + a) •

a and 0 type dislocations are neutral because

between
(a • o) ...

A\.(o + a} dislocation is likely because

from an energy standpoint this Burgers vector is the

o type dislocation

next shortest nonbasal one after a

and because the (O' + a)dislocation has been shown by
f )

Price ()BJ to be responsib1e
/' ;·

Figure 1f.i. shows the
hexagonal

and ±.

cell.

Possible

~or nonbasa1 slip.

a and o directions in the
values of'

a are :!: al , :!: a2

a3 ·which together with ± 0 give a total of 12

!- + -r
possible\c
a,type dislocations.
sib1e reactions :tnvo1ving ";',

is then 6 x 12 = 72.

'Ihe number of pas-

and(o + 'a dis1ooo.tions

Half of these reactions form

attractive and half form repulsive junctions.
'lb.e effect of attractive and repulsive junctions
in the present investigation can be estimated.

'Ihe

density of forest dislocations, as deduced from etch

-12'.3-

., ~--.

...... --,_,

02'~

Fig. 47

Possible

o and a Type Vectors.

-124Uf

pit densities on basal planes, is given in Table -V for

the various purities of zino.

'lb.e number of these dis-

locations with(c + a)type Burgers vectors is not known,
but for the sake of a calculation, it will be assumed
that 1/2 are dislocations with this type of Burgers
vee~or. (Taking the forest density to be about 104 om·2
··-""'··-

·:'.J'

for the 99.999 per cent purity material, the density of
(-0 + a)dislooations is 5 x 103 cm- 2 and the density of
,.._,..
i.

--\

c + ai dislocations forming attractive junctions is

2.5 x 103 om- 2 •

1'herefore, the spacing between attrao-

tive junctions as well as that between repulsive ones
'rill be 2 x 10- 2 cm.

ni.e stress to overcome both

junctions is given by the stress to overcome attractive
junctions, which £rom Eq. 17 is

where

c; = s.6 x 10 6 lb/in. 2
b = 4 .13 x 10... a om (average of h/

and

h,.)

,,,t = 2 x 10-2 cm.
This gives a value of 4.6 lb/in. 2 for the internal
stress, ?;.·

, due to attractive and repulsive junctions

which is approximately the lowest stress at which basal
dislocations were observed to move long distances

-125compared to the forest spacing in 99.999 per cent purity
crystals.

This calculation indicates .that the stress

required to overcome attractive and repulsive junctions
is the correct magnitude to explain the lowest stress
at. whicl.f.-.~}sl~,,?7t~fw¥~~:-"e;~,~ ;\l'e~~ observed.
The nature of< 'ri, caused by a ttraoti ve and repulsive junctions is such as to cause a resistance to
dislocation motion in either direction of motion of the
dislocation.

This fact may explain why the dislocation

pile-ups observed in the relaxation experiment were
no!.; ob.served l;o rela..x: a:C(;er un1oading !'rom a resolved
.. , ,. . . '~ l ;'. ~1
·~

shear stress of 12.1 11:?/in. 2 •

·i ....

Assuming that each disI

location in a pile-up is held in equilibrimn under'load
by a forward applied stress of 12.1 lb/in. 2 and a
reverse stress of 6 lb/in. 2 due to attractive,and
',:'- .,:
:..;~·
'.,~
.·
repulsive junctions andr6 1b/in. from/other disio./'

cations in th~· p.ile-up~~~h'len the

__../

appli~d stress is
I.

removed the stress from junctions reverses sign and

balances
that due to the other
surrounding.. dislocations.'!\.
,.;
,,_

~, ·~

~..-~

Additional relaxation tests would have to be conducted·
at different levels of applied shear stress to confirm
this explanation. ·
Tinder

("'
("9) has recently argued in a similar way

to explain the closed hysteresis loops obtained in the
microstrain ~egion for zinc single crystals.

The

closed loops require a friction stress which acts in
both directions which would be the case for the junotion model for applied stresses below the stress level
required to break attractive and repulsive junctions.
Tinder found a closed hysteresis loop upon stressing
a crystal to 2.25 lb/in. 2 after it had been d~formed
to a shear stress level of 11.4 lb/in. 2 when the 2.25
lb/in. 2 was applied in the same direction as the preload.

\fiien a shear stress of 2.25 lb/in. 2 was applied

in the reverse direction an open loop was obtained
lnrl.ch indicates that the friction stress was overcome.
Th~s

behavior is entirely consistant ldth the picture

envisioned to explain why pile-ups did not relax upon
removal 0£ an ~ppliod shonr stross 0£ 12.l lb/in. 2 •

According to the model, in the unloaded condition the
junctions are stressed to their b.±leaking p·oints in the
reverse stress direction so that upon application of a
small reverse stress they can be overcome with ease.
The long-range internal stresses provided by
attractive and repulsive junctions does not explain
why work-hardening occurs once the internal stress is
exceeded because the forest density and therefore the
junction spacing does not increase during basal slip.
11

Seeger, Hader, ICronmuller and Trauble (4-0) have coneluded from observations of slip line lengths on the

-127-

surface of def'ormed zinc crystals that work-hardening
is caused by the long-range internal stresses of dis·~.

location pile-ups.

Figures 3i and J2 of the present

results illustrate the nature of the basal dislocation
distribution in work-hardening specimens.

A conspicuous

feature of the work-hardened state is the appearance of
large numbers of dislocation pile-ups.

It is therefore

likely that a work-hardening model based on pile-up
interactions is appropriate for zinc deformed in basal

Strain-Rate Sensitivity of: the Flow Stress
As originally suggested by Guard (9). the dislo-

cation mobilit~ exponent may be deduced from the strain•
rate sensi ti vi ty of the flow stress providing the numher of moving dislocations does not change as a result
of the change in strain-rate.

The shear·strain-rate

is re1ated to dis1ocation motion by

so that

?J.k,PM + (;£.n_ 1f ,
a.tY\ r c1s)
a rtn r
The values f'or

determined £or zinc
--·~."

,LL

crystals of diff'erent purities are given in Table X...:V.

The average value of 71,

:for,,two tests '6tt·a99.99-9 per
!1

·c~··purity

orys:tti is 83.

The mobility relation deter-

mined by the direct experiments is assumed valid, so
that

x.. - 5'·
and

for 99.999 per cent purity material.

This discrepancy

between j/L and )'\. is 1ar~ and clearly shows that the

number of moving dislocations changes as a result of a
strain-rate change.
Similar experiments have been conducted on lithium
.,., <

fluoride (41), silicon-iron ,(4J.) and. tungsten ( 16)

crystals where the inverse strain-rate sensitivity
has been found to increase with strain.

When the data

is extrapolated to zero strain, the resulting ?1very close to the mobility exponent, n....

The validity

of the strain-rate sensitivity experiment· for determining
mobility exponents has been argued from these results.
,,,. I

However, no explanation for the increase in "'· with
strain has been proposed.

The values

of~

. as given

-129 ...

in Tab1e IV were not observed to increase with strain
except for one test on a zone refined purity specimen
where the extrapolat ed value at zero strain was about 50.

An alternativ e model to explain the results found
for zinc is proposed where the density of moving dislocations, .,t°M , is a function of the difference between
the applied shear stress and the flow stress at zero
strain-rat e,

1"j or

A ( lrp ) is some unknown runcliion 0£ the plastic sh.ear
strain and

1/,' may be regarded as the long-range internal

stress produced by junction reactions and dislocatio n
pi1e-ups.
is

It would therefore be a function of

T,; = r,;{fp)

t"p , that

The velocity of a moving dislooa-

tion is still regarded as a function or

r-- because the

average stress experience d by a moving dislocatio n is
independen t of

1i:

(the internal stress

1';.• must average

to zero along a slip plane).

A qualitativ e pictura of the stress difference 1"'-i;,
as a function of distance along a slip plane is given
in Fig.

·4:8.

Glide dislocatio ns will be prevented from

moving when 1""- 1-l

is negative or equal to zero.

oondi ti on is shown f'or several ·dislocatio ns.
increase in the applied stress will shift the

'lb.is

A slight

-130-

Distance Along Slip Plane

Fig. 48

Variation in Shear Stress Along a Slip Plane.

-131curve upwards allowing some obstructed dislocations to
glide.

The specific number of dislocations released

in this manner would depend on the details of the
internal stress variation and, in particular, the distribution of points where

T-Ti

goes negative because

this stress difference governs whether a dislocation
will be released when a given stress ohange is imposed.
'Ill.a strain rate is now given as

and

J.k. ¥r

The experimentally determined values of lJ kl1'"-1'.·)
are given in Table IV.
to the ratio
There~ore

YA/x

The term

;; 1...,,..
{ 1:- ·r,;)
J hi.

::: m..'

is equal

and is determined experimentally.

11'\. is given by

Since 1'\. is much less than

11. 1 , bl:::. >ft/.

Table IV

-132-

gives the values of It\ I

determined~f'or

the v-arious

For 99.999 per cent purity

purity materials.

and is a little less for the other purities.

,,,,,,.
"~ '- 2

The reason

for the low va1ue of l.l for the Zn-0.02Al purity is not

known._..: An exponent of

m = 2 would be expected if the

number of dislocations released per unit length of
glide plane were a linear function of the stress diff erence

'!he model proposed to explain the results for zinc
may also apply to other metals of the soft metal group
such as copper.

Conrad (!.:i•2) has measured the strain-

rate sensitivity of copper single crystals at low
temperature and finds that

f! ! = 100-200 at 170°11:.

This result is clearly unreasonable for a mobility

exponent.

An alternative interpretation of the results

in terms of the newly proposed model is suggested.
More important, if the density of moving dislocations

changes during a strain-rate change, many of the conclusions that Conrad makes regarding thermally activated
mechanisms would be completely invalid.
The present model would not be expected to apply
to hard type materials such as silicon-iron and lithium
fluoride because in these materials the variation of
the internal stress

1'i

should be much less than the

levels of applied stress required to cause dislocation

-133motion at apprecia ble velociti es.

'!he large value of

7;.

in these material s is responsi ble for this conditio n.
In such oases the change in moving dislocat ion density

would be small and have little effeot on the nominall y
high mobility exponen ts.

Stress-S train Behavior
Numerous investig ations have been made on the

in~lu-

enoe of various variable s on the basal stress-s train
behaVi.or of zinc s1ng1e crystals .

ni.ese investig ations
.....

have included the effects of temperat ure (28),
purity
'~

(28t

43), substruc ture (44) and nonbasal forest dislolu

cation density
sho~m

(2·~).

The present investig ation has

that the nonbasal forest dislocat ion density and

the characte ristics of the dislocat ion substruc ture
are signific antly influenc ed by the impurity level.
TI:le eff.'e ct of cad.mi um impurity on the degree of impurity

segregat ion and associat ed dislocat ion substruc ture in

zinc single crystals has been sho1m by Damiano and Tint

(45).

The present observat ions on segregat ion and sub-

structur e in crystals 1dth aluminum impurity are in
essentia l agreemen t 1dth the work of Da.iniano and Tint.
1famoly, at some i.mpuri t;y level5 and. under certain grot'lth

conditio ns, impuriti es may segregat e into a cellular
structur e and a dislocat ion substruc ture is associat ed
with the impurity segregat ion if the degree of segregat ion

-134is great enough.

This is probably due to impurity

pinning of the dislocations which stabilizes the dis- ·
location substructure.

In terms of the mechanical

properties 0£ zinc single crystals, the interrelation
between impurity changes and changes in dislocation
substructure as well as forest densities has not
generally been appreciated by previous investigators.
An important point is that when the impurity changes
are made. the effects on the mechanical properties may
be due to resultant changes in forest densities and
substructure as well as direct impurity effects.

'lhis

J* .,

ag!f'~i!H5' 11fi'6h: Seeger ~ . . . has e"S-timat.·&d that the

primary effect of impurity changes on the stress-strain
behavior 0£ hexagona1 close-packed crystals is through

changes inAdislooation densities•
Figure 29 shows the effect of impurity additions
on the stress-strain behavior.

The effect of the forest

dislocation density on the initial flow stress can be
estimated £rom the dis1ooation densities given in

Table V and by the use of Eq.

17 which gives the stress

required to overcome attractive and repulsive junctions.
Following the assumptions given above, in Section F,
the

~tress

required to overcome junctions in Zn-0.0025Al

and Zn-0.02Al crystals is estimated to be 14.o and 21.2
lb/in. 2 respectl. ve1y.

The initial flow stress f'or

-13.$-

crystals of these purities is 27 and 73 lb/in.

2 as shown

Thus a large share of the increase in flow

in Fig. 29.

stress over that for

99.999 per cent purity crystals can

be attributed to changes in the forest density produced
by impurity additions.
Impurity additions were noted to have an effect on
the character of dislocation substructure as shown in
Table

These changes may have an influence on the

measured stress-strain curves because certain dislocation
sub-boundaries can have long-range stress fields which
must be overcome by the applied stress if dislocations
are to glide past the boundaries.

The notable

differ~

ence between the substructure in Zn-0.02Al material as
compared to the other purities may account for the
large difference between the initial flow stress and
the stress to overcome junction reactions in the Zn-0.02Al
material.

A detailed knowledge of the dislocation char•

acter of the substructure would be required to estimate
the specific effect of' the substructure change on the
f'1ow stress.

The effect of prestraining and annealing on the
ff/
The stress'S-P.
stress-strain behavior is shotm in Fig.
strain curves are shifted to higher stresses which is
prob~bly

due to an increased dislocation substructure

density s:i.noo tho dons:i.'ty 0£ £orost dis1oco.t:i.ons 'ttt'ldoubt-

''&~ did not ohang1

Figure 4j shows the ef':f'eot ot'

-136prestraining on the substructure density.

'Ihe present

results are consistent with the results of Washburn (.44)
on the effect of tilt boundaries on the stress-strain
behavior of zinc single crystals.
Nonbasal Slip System
A.

Dislocation Orientations and Dislocation Multiplicatio n
The initial stages of nonbasal deformation occur in

isolated slip bands as shown in Fig. 38 which shows the
result of a c-axis pulse test.

This mode of slip defor-

mation is somewhat different than that found for basal
slip in that the nonbasal slip bands are broad and not
, I"

' t

limited to one slip plane. ·The appearance of the;,slip
bands is similar to those found in deformed·sing le

crys~

tals of lithium fluoride {'!>?) where dis.looa ti on multiplication has been attributed to a multiple cross-slip
mechanism.

Multiple cross-slip occurs when a screw:

dislocation segment in one slip plane glides onto another
slip plane which contains the same Burgers vector.
Cross-slip will be likely in cases where the screw dislocation is not extended into widely spaced par.tial
dislocations and when a resolved shear stress occurs
on the cross-s1ip plane.

1'lhen a screw dislocation seg-

ment glides onto the cross-slip plane. it is likely to
cross-slip once again onto another slip plane parallel
to the original slip plane.

The screw segments that

-137lie on the parallel slip plane can then act as a FrankRead source because the dislocation segments on the
cross-slip p1ane are edge dislocations wlll.ch cannot
glide in the same direction as the ·screw segment.

Figure 49 shows a bowed dislocation segment on a
,,,parallel slip plane a:fter cross-slip has occurred.

Price (38) has used electron miorosoopy to study
the nonbasal slip system in zinc.

Nonbasal Slip was

found to ooour by the glide of screw dislocations with
a ( c +·a ) or

1 (1213] Burgers vector.

The slip plane

was :tdentif'ied as the {112'2} or second order pyramidal

plane.

However

~~xtensi ve

cross ... slip was observed

which must have occurred on {1011} or first order pyramidal planes because this plane is the only other low
index, nonbasal)plane that contains the 0 +

a direction.

Figure '~·shows the first and second order pyramidal
planes.

In addition, Price observed large dipole trails

and jogs on screw dislocations and attributed these to
cross-slip.
The orientation of the load axis along the c-axis
:i.n the present l-rork causes a. re:so1ved shear stress in

the first order pyramidal plane equal to about 90 per
cent of that produced on the second order pyramidal
plane.

This produces a favorable condition for cross-

slip to occur and hence the conclusion is drawn that

-138-

'\
Cross- Slip
Plane
Priniary Slip PJane

Fig. 49

Cross-Slip Mechanism.

-139-

{1122}

(a) Second Order Pyrami dal Plane

f1oi1}

(b) First Order Pyramid al Plane

Fig. SO

First and Second Order Pyramid Planes.

-140-

multiple cross-slip is responsible

~or

the nature of the

observed slip bands.
T'ne dislocations observed in the direct mobility

experiment areAmost likely close to the
-ti on wi i{h a,
:,/ jt' .,.

ed~e

orienta-

~ , (1213) Burgers vector._ Th~/~lip band

, , ,, .- ·' .~

_. ~

trates on the specimen prism surfaces correspond to

{1tl}22} pianes which make- a normal intersection with
the observation surface.

The-refore, edge dislocations

will lie perpendicular to the observation surface and
screw dislocations will lie parallel to it;
B.

Dislocation Mobility
The mobility 0£ dislocations in the nortbasal slip

system can be expressed in the form

where

I\ = 9 • .5 and

7;, = 790 lb/in. 2 :from Fig. 39.

These parame-bers are i;abu1a-bed i.n Tab1e v.t where -they

may be compared to those of other materials.

Nonbasal

dislocations are clearly less mobile than basal dislocations so that the mobility limiting process must not
involve phonon scatter.

In addition, nonbasal dislo-

oa.iiion mobi1ity cannot be claislSed wlth tht' "harU. 11 gl"oup

o:f body-centered cubic and diamond cubic crystals in

mobility.

There:fore, the rate-limiting

process is probably not the thermal activation of

-141-

dislocation kinlcs over a strong Peierls barrier which

has been used to explain results in lithium fluoride
(.5) and germanium(48).

Models based on a Peierls

barrier predict that the mobility should depend on the
applied stress as

y oe e

- .A

(19)

£.Iobility data on silicon-iron (12), lithium fluoride
(11) and germanium (14) have been found to satisfy this
relation.

nie data on nonbasal mobility in zinc does

not fit Eq. 19 and thus a Peierls barrier mechanism
can be considered unlikely,
!-~odels

based on thermally activated events such as

jog :f'orma.tion a.nd thermally a.otiva.tod oross-slip (:'.31)

should give a mobility relation of the form
7'-~·

vcx:ea
where

?f. is the long-range internal stress.

The non-

basal mobili ·cy data does not fit this form using

7;: = 0

and a poor correlation is obtained by using values for

?"! greater than zero.

Therefore, none of the theoretical

mechanisms considered are appropriate to the present
results and additional experiments over a more extended
stress range and at different temperatures are suggested
to bettor define the physical mechanism which limits the
nonbasal dislocation mobility.

-142-

Strain-Rate Sensitivity of the Flow Stress
The dislocation mobility exponent as deduced from

the variable strain-rate test is listed in Table IV as
The fact that this value is signifioant1y

720 t10.

above the directly measured exponent of 9.5 indicates
that the assumption of a constant density of moving
dislocations during a rapid change in strain-rate is
incorrect.

This conclusion must be correct even though

the disl.ooatlon velooitleB measured directly were 0£

the leading dislocations in a slip band and thus represented the maximum velocities,

id~ereas

the variable

strain-rate test depends on average velocities in a
specimen covered by intersectinff slip bands like those
seen in ~ig. 28.

An analysis of the strain-rate data

in terms of a di~ferenoe between the applied stress and
the flow stress at zero strain-rate was not possible
because of the very low strain-rate sensitivity.

There-

fore, the model proposed to describe the change in
density of moving dislocations for the basal data could
not be applied to the nonbasal data.
is some

lil~elihood

However, there

that the same model would be appro-

priate to the nonbasa1 s1ip system and, i£ so, this wou1d

explain the high value of the inverse strain-rate sensitivity in terms of the change in density of moving
dislocations.

Stress-Strain Behavior as Related to Dislocation Properties
Basal slip in zinc single crystals occurs at low
stresses and involves tho motion of relatively small
nurabo:rs

of.' vory mob:i.lo di.slooa.tions.

The :i.ni. t i al f'low

stress appears to be determined by the stress required
to overcome attractive and repulsive junctions between
basal and nonbasal dis1ocations.

Once the initial flow

stress has been exceeded, work-hardening occurs at a
very low

i~ate

tions does

no~

because the density o"f: nonba.sal disloca-

increase and because tha mobility of

basal dislocations is high enough to allow many of them
to leave the crystal ~tltlch prevents them from contributine to work-hardening through interactions with other
para11e1 glide dislocations.

Dislocation pile-ups occur

and their interactions probably determine the observed
work-hardening rates.
As opposed to basal deformation, nonbasal slip
involves the movement of relatively large nu..'llbers of
slo1v·ly raoving dislocations.

Dislocations appear to

multiply by a multiple cross-slip mechanism which produces slip bands.
~or

The high work-hardening rates observed

nonbasa1 s1ip are caused by dis1ocation pile-up

interactions within individual slip bands and by the
interaction of slip bands on the six equivalent slip
'planes ·which results in an increase in the density of
forest dislocations i;d th increasing strain.

-144SUNJvIARY AND CONCLUSIONS

VII.

T'ne mobility of basal dislocations in zinc single
crystals of 99.999 per cent purity has been experimentall y
determined .Crom observations of.' dislooation pilo-up

lengths produced by load pulse tests.

. .'t'
the relation V::. {

t;,)

for

The results obey

'r~ 6 lb/in. 2 , where V

the dislocation velocity in cm/sec,

1L is the mobility

exponent and is equal to .5, and '/0

is !) lb/in. 2 •

Tne

maximum velociti.es observed are in the range of 7 to 80
cm/sec for shear stresses between 7 and 12 lb/inf·.

The

results are inconsistent with.the predictions using
oretical models which involve the thermally activated
motion of a glide dislocation past forest dislocations
or impurity atoms.

The drag stress on a. moving dislo-

cation caused by ·phonon scattering is ~ to be -the.
m-e-&t likely velocity limiting process.

The minimum

shear stress requi·red to cause dislocation pile-ups is
about 6 lb/in. ~nd tl~is stress is sho'tm to correspond
to the stress to break attractive junctions between
basal and nonbasal dislocations.

Tb.us plastic flow in

the basal slip system occurs when attractive junctions

The strain-rate sensitivity of the flow stress for
basal slip has been determined for'Z,one- ref'ined•' 99.999
per cent, Zn-0.002,5Al and Zn-0.02Al specimens.

A large

-14.5difference is observed between the inverse strain-rate
sensitivity and the directly determined mobility exponent.

A dislocation model is proposed which explains

the observed di£~erencAs.

ThA major part of the strain-

rate sensitivity is attributed to changes in the number
of moving dislocations which accommodate a change in
strain-rate, rather than to the change of dislocation
velocity.

The" mo9-e,l. ~.roposed ;for basal slip in zi.no
~·

may also app1y to nonbe.sa,l slip in zino a.nd to o'opper

and aluminum crystals deformed in easy glide, in which
large strain-rate changes may be made with very small
changes in stress.
The mobility of dislocations in the

nonbasai slip system has been experimentally del.;ermined
from measurements of the length of slip bands produced
by pulse load tests.

The results obey the relation

V': {.;,,) h.. where It • 9, 5 and

1-;, • 790 lb/in, 2 ,

Velocities between 2 :x: lo- 4 and 2 cm/sec were measured
in the stress range :from 300 to 800 lb/in. 2 •

The results

are inconsistent ldth theoretical models which involve
thermally activated events.

The appearance of the non-

basa1 s1ip bands suggests that dislocation multiplication takes place by a double cross-slip mechanism in
which segments of screw dislocations with

c + a Burgers

vectors glide :from second order pyramidal planes onto

-146first order pyramidal planes and then back onto another
second order pyramidal plane.
The addition of 0,0025 and 0,02 per cent aluminum
'to z:i.no produoes: a s:egregat:lon substructure• and increases

the density of nonbasal dislocations.

The raise of the

basal shear stress vs. shear strain curve, which is
observed to accompany the addition of aluminum, is
attributed primarily to this increase in the density of
nonba:.sa1 dis1ocations.

The increased density of.' nonbQ.SQ.l

dislocations produces an increase in the density of
attractive junctions between basal and nonbasal dislocations.

Hence, the stress required to move basal dis-

locations is increased.

The change in basal dislocation density,
duced by plastic shear strain,

Aj> , pro-

("f , obeys the relation

/J?:: C tfp3 where C is a constant, and is independent
of purity.

This relation is different from the relations

that have been reported for copper, silver, and lithium
fluoride single crystals.

The difference may be explained

by the long glide distances observed for basal dislocations in zinc crystals.
0£

Glide distances of the order

the specimen' size have been obsArved wh:'Loh ind:icates

that large nmnbers of dislocations may glide out of the
specimen and hence produce strain but do not contribute
to etch pit densities.

T.ae important results and conclusions of this investigation are:
1.

The mobility of dislocations in the basal and
nonbasal slip systems has been determined
experimentally and the results have been
evaluated in terms of current theories.

The

drag stress caused by phonon scattering is
shown to be the most 1ilrely velocity limiting
process for basal dislocations.

No theory

has been found which predicts the mobility
relation for nonbasal dislocations.
2.

The strain-rate sensi ti vi ty of' the· flow stress

has been determined for zinc single crystals
de£ormed in basal slip.

The inverse strain-

rate sensitivity differs ·greatly from the
mobility exponent and a dislocation model is
proposed to explain the difference.

The model

attributes the strain-rate sensitivity to

·changes in the number of moving dislocations.
The importance of changes in the density of
moving dislocations accompanying a strain-rate
change has 1_1ot generally been recognized by
previous investigators.

'llle model proposed

may also apply to nonbasal slip in zinc and

-148to copper and aluminum crystals deformed in

easy glide.

The long-range internal stress which must be
overcome for basal slip to ooour is attributed
to attractive junctions between basal and non-·
basal dislocations.

This source of internal

stress is shown to be consistent with the
follo'tdng observations:

{l) the stress

rGquired to cause dislocation pile-ups;

(2) the effect of alumintun impurity on nonbasal

dislocation densities and on the basal stressstrain behavior; and (3) dislocation pile-ups
do not relax with the removal of applied stress.
The importance 0£ attractive junctions in rola-

tion to basal slip of hexagonal close-packed
crystals has generally not been recognized by
previous investigators.

The influence of alu~inum impurity on the basal

stress-strain bahavior is due in large part to
changes in the density of nonbasal dislocations
which determine the spacing of attractive
junctions.

The change in basal dislocation density with
sh.ear strain is given by the relation
and is independent of' purity.

Llt:: c~f

This relation

-149is different from the relations that have been
reported for copper, silver and lithium fluoride
single crystals.

The d·ifference is attributed

to the long glide distances observed for basal
dislocations in zinc.

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11