Phase Behavior of Complex Superprotonic

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Phase Behavior of Complex Superprotonic Solid Acids
Citation
Panithipongwut, Chatr
(2013)
Phase Behavior of Complex Superprotonic Solid Acids.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/NXG8-TY79.
Abstract
Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb
H(SO
-RbHSO
system, Rb
H(SeO
2-Cs
H(SeO
solid solution system, and Cs
(H
SO
(H
1.5
PO
. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.
Rb
H(SO
is an atypical member of the M
H(XO
class of compounds (M = alkali metal or NH
and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb
H(SO
-RbHSO
system have revealed the disproportionation products to be Rb
SO
and the previously unknown compound Rb
(SO
. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs
(SO
[2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.
The compounds Rb
H(SeO
and Cs
H(SeO
, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.
The compound Cs
(H
SO
(H
1.5
PO
is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH
PO
) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H
O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs
(H
SO
(H
1.5
PO
undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs
(H
2-0.5x
SO
(H
1.5
1.5PO
4-x
, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.
References:
[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.
[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.
[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Solid acids, Superprotonic transition, X-ray diffraction, A.C. Impedance spectroscopy, Differential scanning calorimetry
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Haile, Sossina M.
Thesis Committee:
Haile, Sossina M. (chair)
Rossman, George Robert
Bhattacharya, Kaushik
Johnson, William Lewis
Defense Date:
17 May 2013
Non-Caltech Author Email:
chatr.p (AT) hotmail.com
Funders:
Funding Agency
Grant Number
National Science Foundation, Division of Materials Research
DMR-0906543
Army Research Office
W911NF-07-1-0410
Record Number:
CaltechTHESIS:05302013-183134007
Persistent URL:
DOI:
10.7907/NXG8-TY79
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
7778
Collection:
CaltechTHESIS
Deposited By:
Chatr Panithipongwut
Deposited On:
31 May 2013 22:42
Last Modified:
04 Oct 2019 00:01
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Phase Behavior of
Complex Superprotonic Solid Acids

Thesis by
Chatr Panithipongwut

In Partial Fulfillment of the Requirements
For the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California
2013
(Defended May 17th, 2013)

Chatr Panithipongwut

iii

Acknowledgements

Firstly and most importantly, I would like to thank Professor Sossina Haile,
Professor William Johnson, Professor George Rossman, and Professor Kaushik
Bhattacharya for reading and correcting my thesis. Professor Sossina Haile has been an
amazing and caring advisor since I joined the group. Discussions with her always
encouraged me to think about my work critically and find the connections and
explanations for the results based on theories and previously reported data. Her guidance,
patience and support were so valuable to me especially when I was clouded and could not
think clearly. Also, I would like to thank Professor Axel van de Walle who was one of
my candidacy committee members. This work was made possible by financial support
provided by the U.S. National Science Foundation (DMR-0906543) and the Army
Research Office (W911NF-07-1-0410). The Ministry of Science and Technology of
Thailand through the Royal Thai Scholarship provided additional funding in the form of
tuition and stipend.

I was fortunate to work with many exceptional collaborators and colleagues. I am
grateful to Dr. Mary Louie who helped me a lot in many ways in both life and work,
including general knowledge about solid acids, martensitic theory, measurement
techniques, operating test stations and many other things. When I had work or life
problems, she was always a good listener and gave me good suggestions. I thank
Professor William Chueh, who also was my colleague and had and still has made a lot of
contributions to the group, from some little things to some high-impact findings. My

conductivity measurements would have been more complicated without his well-written
data-collection program. For those who helped, taught me or exchanged knowledge about
how to operate, set up experimental conditions properly and perform data analysis, I
thank Dr. Yoshihiro Yamazaki and Dr. Joon-Hyung Lee for DSC; Dr. Ayako Ikeda and
Dr. Mikhail Kislitsyn for XRD; Dr. Aron Varga and Rob Usiskin for electrospray; Dr.
Chi Ma and June Wicks in GPS division for SEM and EDS; and Fenton Harvey for
general lab equipment. I thank Dr. Taesik Oh for discussions and answers to my random
questions and for giving me some ideas for my research even though it was out of his
area. Additionally, to Dr. Calum Chisholm and Dr. Lisa Cowan, for the initiation of
wonderful solid acid works that I picked up and continued, I thank both of you.

There are many other individuals to whom I owe credits for this achievement and
without whom I would not be able to complete my road to my Ph.D. I would like to thank
Nicholas Eugene Scianmarello, who was my first SURF mentee and later became a friend
and a supporter who somehow helped me through my candidacy exam. I give many
thanks to Jeffrey Adam Kowalski, another SURF mentee and a very good friend, for
helping me with some sample preparations and discussions, giving me some ideas on my
work, inspiring me to do better things in life and take better care of myself, supporting
me through the finish line of the Ph.D. program and for many other things I cannot
describe. I thank Wolfgang Gerhard Zeier, my office mate, roommate, and a good friend,
for all support and encouragements when I needed them. I also thank Stephen Wilke for
figuring out the mistake in my enthalpy calculation, discussions about many other things,
general talks about both work and life, and the support that he always provided. I was

lucky to have some others who enjoyed and fought together through the same program,
namely Dr. Nicholas Stadie, Dr. Aron Varga, Scott Robers, and Jorge Munoz. Marcel
Schreier, Carolyn Richmonds and Michael Ignatowich were friends with whom I spent
some time outside the lab for good food and relief from stress towards the end of my
residency. I thank Chirranjeevi BG for carrying the TA duty for a week when I was
finishing my thesis writing.

Lastly, I am grateful to my family and friends in Thailand and in the U.S. for love and
support, especially my parents, who encouraged and supported my decision to come to
study abroad, and my siblings who took care of everything to ease my worry about my
family and let me concentrate on my study.

Abstract
Superprotonic phase transitions and thermal behaviors of three complex solid acid
systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2
solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich
set of phase transition characteristics that set them apart from other, simpler solid acids.
A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal
analysis, as well as other characterization techniques, were employed to investigate the
phase behavior of these systems.
Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M =
alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state
involves disproportionation into two phases rather than a simple polymorphic transition
[1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed
the disproportionation products to be Rb2SO4 and the previously unknown compound
Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140
°C and is isostructural to a recently reported trigonal phase with space group P3̅m of
Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic
transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in
conductivity.
The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at
ambient temperatures, are quintessential examples of superprotonic materials. Both adopt
monoclinic structures at ambient temperatures and ultimately transform to a trigonal
(R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C,
respectively. The compounds are completely miscible above the superprotonic transition

vii

and show extensive solubility below it. Beyond a careful determination of the phase
boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in
intermediate compositions rich in Rb as compared to either end-member.
The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds
in that it has a complex cubic structure at ambient temperature and apparently transforms
to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition
temperature of 100-120 °C [3]. Here it is found that, depending on the level of
humidification, the superprotonic transition of this material is superimposed with a
decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O.
This reaction can be suppressed by application of sufficiently high humidity, in which
case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that,
under conditions of low humidity, the decomposition/dehydration reaction transforms the
compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the
temperatures of interest, but with a smaller unit cell. With increasing temperature, the
decomposition/dehydration proceeds to greater and greater extent and unit cell of the
solid phase decreases. This is identified to be the source of the apparent negative thermal
expansion behavior.

References
[1]
L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State
Ionics 179 (2008) (9-10) 305.
[2]
M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics
178 (2007) (21-22) 1262.
[3]
C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters
affecting the presence and stability of superprotonic transitions in the MHnXO4 family of
compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California
Institute of Technology, Pasadena, California (2003).

viii

Table of Contents
Acknowledgements

iii

Abstract

Chapter 1 Introduction

1.1 Solid Acids and Superprotonic Transition

1.2 Objectives

1.3 The Solid Acid Systems of Interest

1.4 References

Chapter 2 Experimental Methods

2.1 Synthesis

2.2 X-Ray Diffraction (XRD)

2.3 A.C. Impedance Spectroscopy (ACIS)

2.4 Differential Scanning Calorimetry (DSC)

2.5 Energy-Dispersive X-Ray Spectroscopy (EDS)

Chapter 3 Rb3H(SO4)2-RbHSO4 Pseudo-Binary System

3.1 Introduction: Absence of Polymorphic Transition of Rb3H(SO4)2

3.2 Synthesis and Characterizations

3.2.1

Sample preparation

3.2.2

X-ray diffraction (XRD)

3.2.3

A.C. impedance spectroscopy (ACIS)

3.2.4

Thermal analysis

3.3 Conductivity Studies

3.4 High-Temperature XRD and Rietveld Refinement of LT-Rb5H3(SO4)4

3.5 DSC Studies

3.6 Phase Diagram of Rb2SO4-H2SO4 System

3.7 Conclusions

3.8 References

Chapter 4 Phase Transition Behavior of (CsxRb1-X)3H(SeO4)2 Solid
Solutions

4.1 Introduction

4.2 Experimental Methods: Synthesis and Characterization Techniques

4.2.1

Sample preparation

4.2.2

Energy-dispersive X-ray spectroscopy (EDS)

4.2.3

X-ray diffraction (XRD)

4.2.4

A.C. impedance spectroscopy (ACIS)

4.2.5

Thermal analysis: Differential scanning calorimetry

4.3 Determination of Compositions, Solubility Limits, and Volume

Expansion at Room Temperature

4.4 High-Temperature Phase Identification

4.5 Conductivity Studies

4.6 DSC Studies: Enthalpies and Entropies of Superprotonic Phase
Transition

4.7 Phase Diagram and Variation of the Superprotonic Transition
Temperature of Rb3H(SeO4)2-Cs3H(SeO4)2 System

4.8 Conclusions

4.9 References

Chapter 5 Transition Behaviors of Cs6(H2SO4)3(H1.5PO4)4 and Apparent
Negative Thermal Expansion at High Temperature

5.1 Introduction

5.2 Experimental Methods

5.2.1

Sample preparation

5.2.2

Energy-dispersive X-ray spectroscopy (EDS)

5.2.3

X-ray diffraction (XRD)

5.2.4

Physical observations of a crystal sample

5.2.5

A.C. impedance spectroscopy (ACIS)

5.2.6

Thermal analysis: Differential scanning calorimetry (DSC) and

thermal gravimetry (TG)

5.3 Determination of Composition, Phase Identification, and Crystal
Structure at Room Temperature

5.4 High-Temperature Phase Behavior and Determinations of Lattice
Parameters

5.5 Physical Observation of a Crystal Sample

5.6 Conductivity Measurements

5.7 Determination of Heat of Transition and Study of Dehydration

5.8 Discussion: Mechanism of Transition and Origin of the Apparent
Negative Thermal Expansion in Cs6(H2SO4)3(H1.5PO4)4

5.9 Conclusions

5.10 References

Appendix A Phase Behavior of (CsxRb1-x)3H(SO4)2 Solid Solution System

A.1 Introduction

A.2 Synthesis and characterizations

A.2.1 Synthesis

A.2.2 Characterization using XRD, ACIS, and DSC/TG

A.3 Results

A.4 Conclusions

A.5 References

Appendix B Electrospray for Complex Solid Acid Syntheses

B.1 Introduction

B.2 Sample Preparation and Electrospray

B.2.1 Sample preparation

B.2.2 Electrospray

B.3 Results

B.4 Discussions, Conclusions and Suggestions

B.5 References

xii

List of Figures
Figure 1.1

Conductivity of various fuel cell electrolytes.

Figure 2.1

Schematic Nyquist plot of a material with contributions from
bulk, grain boundary, and electrode resistances.
12

Figure 2.2

Schematic Nyquist plot of solid acids (a) below and (b) above
the superprotonic transition. The dotted lines are theoretical arcs
that are not detected due to the limited frequency range of the
impedance analyzer.
13

Figure 2.3

Schematic DSC profile.

Figure 3.1

Proposed phase diagram in the Rb2SO4-H2SO4 system after
Cowan et al.; compositions within the R3H(SO4)2-RbHSO4
region examined in this work as indicated.
19

Figure 3.2

Conductivity of compositions in the Rb3H(SO4)2-RbHSO4
system upon heating under humidified nitrogen (pH2O ∼ 0.032
atm) at a ramp rate of 0.1 °C/min: (a) 0-66.67% RbHSO4; and
24
(b) 66.67-100% RbHSO4.

Figure 3.3

Equilibrium high-temperature XRD patterns of the 66.67%RbHSO4 content composition at indicated temperatures, under
25
humidified helium (pH2O ∼ 0.032 atm)

Figure 3.4

XRD patterns of the 66.67%-RbHSO4 content composition
under humidified helium (pH2O ∼ 0.032 atm) at (a) 160 °C and
(b) 190 °C. The pattern in (a) is analyzed in terms of the reported
intermediate-temperature (130 °C) structure of Cs5H3(SO4)4,
with a primitive trigonal cell, space group P3̅m, and lattice
constants a = 5.9298(2) Å and c = 14.4736(6) Å. Peaks marked
with * and v are from residual Rb3H(SO4)2 and RbHSO4,
respectively. The pattern in (b) is compared to that of a higher27
temperature form of Cs5H3(SO4)4.

Figure 3.5

DSC profiles of the 66.67% RbHSO4 sample under humidified
nitrogen (pH2O ∼ 0.032 atm) at a ramp rate of 2 °C/min. First
29
and second cycles.

Figure 3.6

Revised phase diagram for the pseudo-binary Rb2SO4-H2SO4
system, constructed on the basis of the previously proposed
31
diagram of Cowan et al. and new findings in this work.

xiii

Figure 4.1

Actual compositions of the (CsxRb1-x)3H(SeO4)2 solid solutions
determined using EDS.
40

Figure 4.2

XRD patterns of the (CsxRb1-x)3H(SeO4)2 solid solutions at room
temperature. The pattern of 97%-Cs composition indicates two
phases co-existed.
40

Figure 4.3

Volume expansion of the unit cells of the (CsxRb1-x)3H(SeO4)2
solid solutions upon increasing content of cesium.
41

Figure 4.4

Equilibrium HT-XRD patterns at indicated temperatures under
humidified helium (pH2O ~ 0.023 atm) of (a) Rb3H(SeO4)2, (b)
46%-Cs, (c) 97%-Cs, (d) 98%-Cs compositions, and (e)
Cs3H(SeO4)2. The vertical lines in (b) are meant to help notice
the small peak shifts.
42-44

Figure 4.5

Equilibrium HT-XRD patterns of all composition under
humidified helium (pH2O ~ 0.023 atm), each at a temperature
just above its superprotonic transition temperature as indicated.
46

Figure 4.6

Conductivity plots of all compositions in (CsxRb1-x)3H(SeO4)2
system upon heating (solid line) and cooling (dotted line) under
humidified nitrogen (pH2O ~ 0.023 atm) at a ramp rate of 0.5
°C/min: (a) 0-50% Cs and (b) 60-100% Cs.
48

Figure 4.7

The conductivities of all compositions in (CsxRb1-x)3H(SeO4)2
system at 200 °C.
49

Figure 4.8

DSC profiles of Rb3H(SeO4)2, 46%-Cs composition, and
Cs3H(SeO4)2 under humidified nitrogen (pH2O ~ 0.023 atm) at a
ramp rate of 10 °C/min.
50

Figure 4.9

Enthalpies of superprotonic transitions of all compositions in
(CsxRb1-x)3H(SeO4)2 system. The x-error bars of the averages
also represent those of the other points of the same
compositions.
51

Figure 4.10

Superprotonic transition temperatures of all compositions in
(CsxRb1-x)3H(SeO4)2 system from HT-XRD, ACIS, and DSC.
The x-error bars of the transition temperatures determined by
DSC also represent those of the other points of the same
compositions.
53

Figure 4.11

Phase diagram for the (CsxRb1-x)3H(SeO4)2 system.

Figure 5.1

XRD pattern of Cs6(H2SO4)3(H1.5PO4)4 synthesized in this work
compared with that of the one reported by Chisholm.
62

xiv

Figure 5.2

XRD patterns of Cs6(H2SO4)3(H1.5PO4)4 collected at various
temperatures as shown in the figures. (a) under humidified
helium with pH2O ~ 0.023 atm, (b) under dry helium, (c) and (d)
under the same atmosphere as in (a) but heated up to 140 and
180 °C, respectively.
64-65

Figure 5.3

XRD patterns of Cs6(H2SO4)3(H1.5PO4)4 at 120 °C under
alternating atmosphere between humidified (pH2O ~ 0.023 atm)
and dry helium.
68

Figure 5.4

(a) Optical image of CsH2PO4 before (left) and after (right)
heating beyond the superprotonic transition. (b)-(d) Optical
images (top) and SEM micrographs (middle = 1000×, bottom =
2000×) of Cs6(H2SO4)3(H1.5PO4)4: (b) before heat treatment, (c)
after heating under humidified (pH2O ~ 0.023 atm) nitrogen, and
(d) after heating under ambient atmosphere (pH2O ~ 0.011 atm). 70-71

Figure 5.5

Conductivity of Cs6(H2SO4)3(H1.5PO4)4 measured at 2 kHz under
humidified (pH2O ~ 0.023 atm) and dry nitrogen at a ramp rate
of 0.1 °C/min.
72

Figure 5.6

DSC profiles of Cs6(H2SO4)3(H1.5PO4)4 measured under three
different humidity listed in the legend up to 122 °C at a ramp
rate of 1 °C/min.
74

Figure 5.7

DSC and TG profiles of Cs6(H2SO4)3(H1.5PO4)4 heated up to 220
°C under three different humidity listed in the legend at a ramp
rate of 1 °C/min.
75

Figure A.1

XRD patterns of (CsxRb1-x)3H(SO4)2, x = 0, 0.1, 0.2, 0.25, and
0.3 at room temperature.
80

Figure A.2

XRD patterns of Cs0.6Rb2.4H(SO4)2 at high temperature under
humidified He (pH2O ~ 0.23 atm).
81

Figure A.3

XRD pattern of Cs0.6Rb2.4H(SO4)2 at 220 °C under humidified
He (pH2O ~ 0.23 atm) compared with high temperature patterns
of Rb3H(SO4)2, Rb5H3(SO4)4, and Rb2SO4 at the temperatures as
indicated in the figure.
81

Figure A.4

Conductivity plots of Cs0.6Rb2.4H(SO4)2 upon heating (solid
lines) and cooling (dotted lines) under humidified nitrogen
(pH2O ~ 0.023 atm) at a ramp rate of 0.5 °C/min up to 210 °C.
82

Figure A.5

DSC profiles of Cs0.6Rb2.4H(SO4)2 under humidified nitrogen
(pH2O ~ 0.023 atm) at a ramp rate of 2 °C/min up to 220 °C. 83

Figure A.6

DSC/TG profile of Cs0.6Rb2.4H(SO4)2 under humidified nitrogen
(pH2O ~ 0.023 atm) at a ramp rate of 1 °C/min up to 300 °C.
84

Figure B.1

Schematic of the electrospray chamber components and
parameters. Courtesy of Rob Usiskin.
87

Figure B.2

SEM micrograph of an electrosprayed CsH2PO4 sample.

Figure B.3

XRD patterns of electrosprayed samples compared to those of
known solid acids. The desired products were (a) CsH2PO4, (b)
Cs3(HSO4)2(H2PO4), (c) Cs6(H2SO4)3(H1.5PO4)4, and (d)
Cs2(HSO4)(H2PO4).
89-90

Figure B.4

BSE micrograph of (a) Cs6(H2SO4)3(H1.5PO4)4 and (b)
Cs2(HSO4)(H2PO4).
91

Figure B.5

EDS maps of Cs2(HSO4)(H2PO4). Different colors and
intensities show distributions of different elements: Cs, S, and P. 92

xvi

List of Tables
Table 3.1

Atomic coordinates, occupancies, and isotropic displacement
parameters in Rb5H3(SO4)4 at 160 °C, refined in space group
26
P3̅m with a = 5.9298(2) Å and c = 14.4736(6) Å.

Table 5.1

Atomic percentages of the elements in Cs6(H2SO4)3(H1.5PO4)4
without H and ratios of S:P and Cs:(S+P) calculated from the
61
proposed formula and from the determination using EDS.

Table 5.2

Atomic coordinates, sites, isotropic displacement parameters,
and occupancies in Cs6(H2SO4)3(H1.5PO4)4 at 25 °C in space
group I-43d with a0 = 14.5413(4) Å, V = 3074.7(1) Å3, Z = 4,
density = 3.1919 g/cm3, Rexp = 1.817%, Rwp = 6.765%, RBragg =
63
6.679%, and GOF = 13.867.

Table 5.3

Lattice parameter of Cs6(H2SO4)3(H1.5PO4)4 at various
67
temperatures under humidified helium (pH2O ∼ 0.023 atm).

Table 5.4

Lattice parameter of Cs6(H2SO4)3(H1.5PO4)4 at 120 °C under
68
humidified (pH2O ∼ 0.023 atm) and dry helium.

Table 5.5

Onset temperatures, enthalpies, and entropies of transitions of
the samples heated up to 122 °C under three different humidity
73
levels.

Table B.1

Concentrations of desired products and methanol and Cs:P:S
87
mole ratio in solutions used in electrospray experiments.

Table B.2

Desired and identified products from electrospray determined
91
using XRD.

xvii

List of Abbreviations and Symbols
a0

Lattice constant of a cubic crystal

ACIS

A.C. impedance spectroscopy

Isotropic displacement parameter

DSC

Differential scanning calorimetry

GOF

Goodness of fit

High temperature

Low temperature

pH2O

Water partial pressure

RBragg

Bragg residual (Rietveld refinement)

Rexp

Expected profile residual (Rietveld refinement)

Rwp

Weighted profile residual (Rietveld refinement)

SEM

Scanning electron microscopy

TSP

Superprotonic transition temperature

Thermal gravimetry

Unit cell volume

XRD

X-ray diffraction

Number of formula units per unit cell

Chapter 1 Introduction
1.1 Solid Acids and Superprotonic Transition
A solid acid compound is an acid salt of a polyprotic acid that contains at least
one acidic proton. Examples of these polyprotic acids are H2SO4, H3PO4, H2SeO4, and
H3AsO4 and simple examples of solid acids are CsHSO4 and CsH2PO4, which are well
studied and can be prepared from various reactants. Sample reactions to form these
compounds are:
Cs2CO3 (base) + 2 H3PO4 (polyprotic acid)  2 CsH2PO4 (solid acid) + H2O + CO2
Cs2SO4 (salt) + H2SO4 (polyprotic acid)  2 CsHSO4 (solid acid)
Complex solid acids can be synthesized similarly using different bases, salts, acids, or
mixtures of acids. Alternatively, they can be prepared from a mixture of two solid acids.
Solid acids can be classified under four groups: MHXO4, M3H(XO4)2,
M5H3(XO4)4, and mMHXO4·MH2ZO4 where commonly M = Cs, Rb, K, NH4; X = S, Se;
Z = P. Most of the solid acids are water-soluble and insulating at room temperature. At
higher temperature, many of them are considered to be proton conductors as they exhibit
dramatic changes in conductivity in the temperature range between ~ 100 and 300 °C.
This characteristic becomes more of interest because the transition temperatures fall into
the moderate temperature range of fuel cells where fuel flexibility, efficiency, and
easiness of thermal cycling are optimal.
The transition giving this sudden increase in conductivity is called a superprotonic
transition and the proton conductivity due to this transition usually increases by 3-4
orders of magnitude, as seen in Figure 1.1. These phenomena originate from the
crystallographic transitions of solid acids from their low-symmetry, low-temperature

phases to high-symmetry, high-temperature phases, which change the arrangements of
hydrogen bonds from ordered to disordered. This allows oxyanion reorientations
followed by proton transfers, which are the mechanism of proton conductivity, to occur
much faster which consequently increases the conductivity [1].

Figure 1.1. Conductivity of various fuel cell electrolytes, reproduced from [2].

1.2 Objectives
The main objectives of this study are to explore the properties of three complex
solid acid systems, to understand the process of the superprotonic transitions, and to
establish the phase diagrams. The challenge of this work is that many solid acids have
similar physical, measurable properties, such as the increase in conductivity, and

sometimes mislead the researcher to jump to the same conclusion due to these
similarities.

1.3 The Solid Acid Systems of Interest
In the following chapters, the results presented here will reveal that among these
similarities, there is a unique behavior happens in each system. Also, some results that
were mistakenly interpreted in the past are now re-evaluated taking into account new
evidence. It is also shown that the solid acid systems are not less complicated than other
types of materials and while general trends were established, it may not apply to another
system even though they seem to be close to each other.
The solid acid systems investigated in this thesis are:
1) Rb3H(SO4)2-RbHSO4 mixtures
2) Rb3H(SeO4)2-Cs3H(SeO4)2 solid solutions – (CsxRb1-x)3H(SeO4)2
3) Cs6(H2SO4)3(H1.5PO4)4
The compounds listed in the titles of the three systems here are
thermodynamically stable at room temperature and some of which will definitely change;
either react, transform, disproportionate, or decompose; to other compounds at higher
temperature.
Rb3H(SO4)2, like many other solid acids in the family, shows a sharp rise in
conductivity at ~ 205 °C with a hysteresis of about 30 °C on cooling. This observation
was quickly conceived as a polymorphic superprotonic transition by various researchers
[3-6]. Cowan et al. [7] discovered that although the compound is isostructural to others in
the family at room temperature, the reaction happening here was not a polymorphic

transition, but a disproportionation of Rb3H(SO4)2 to Rb2SO4 and another solid acid that
must have a stoichiometry between Rb3H(SO4)2 and RbHSO4 and that is superprotonic
phase in nature. In Chapter 3, further investigation of this case is presented. Starting from
Rb3H(SO4)2 and RbHSO4, it is found that the two solid acids react and form a new
compound Rb5H3(SO4)4 at a temperature as low as 140 °C and it adopts the same
structure as the intermediate-temperature Cs5H3(SO4)4 [8]. At 185 °C, this compound
undergoes a polymorphic superprotonic transition to its high-temperature, highconductivity phase which gives an X-ray diffraction pattern similar to that of the hightemperature Cs5H3(SO4)4 [8]. This phase is stable beyond the temperature that
Rb3H(SO4)2 disproportionates and is confirmed that it is the other product of the
disproportionation.
Chapter 4 discusses about the properties of solid solutions between Rb3H(SeO4)2
and Cs3H(SeO4)2. The system demonstrates noteworthy findings. The most significant is
40-fold increase in the superprotonic conductivity in the Rb-rich compositions as
compared to either end member, while previously found in doped CsH2PO4 systems, the
superprotonic conductivities of those solid solutions decreased with the doping level [9].
Another interesting result is the trend of the superprotonic transition temperature. In other
solid solution systems, the trend of transition temperature shows one direction, i.e. either
increasing or decreasing, with the content of the dopant. For example, in the
Cs1-xRbxH2PO4 system, the transition temperature increases with the rubidium content [9,
10]. (CsxRb1-x)3H(SeO4)2 system, on the other hand, shows a minimum in transition
temperature near the middle composition. Chisholm [11] attempted to find the driving
force of superprotonic transitions of solid acids when line compounds in CsHSO4-

CsH2PO4 family were chosen to represent solid acids with different transition
temperatures and configurations of the oxyanions in the structures. The conclusion from
this CsHSO4-CsH2PO4 family was that the configurational entropy of the superprotonic
transition provides the driving force. For (CsxRb1-x)3H(SeO4)2 system, the configurational
entropy is approximately constant across the compositions since all of them have the
same high-temperature and low-temperature phases. The variation in the superprotonic
transition temperature is set by the variation of the enthalpy, which could reflect
differences in H-bond across the compositions.
Cs6(H2SO4)3(H1.5PO4)4 is the only system here that starts with a single compound.
It should be noted that the material, however, is composed of many more ions compared
to other solid acids discovered to date. This compound was also studied along with the
others in CsHSO4-CsH2PO4 family [11] and found that it was the only one that did not
have Cs:(S+P) mole ratio equals to 1, was a cubic at room temperature, and seemed to
have negative thermal expansion in the high-temperature phase. However, other
properties seemed similar to those of the other compounds in the family. Chapter 5 of this
thesis will show that the transition of Cs6(H2SO4)3(H1.5PO4)4 is not as simple as it
seemed. In a small window of temperature near the transition, at least three reactions
could happen at the same time, depending on humidity level. In other solid acids, if there
is a dehydration involved, it will be that of the solid acid itself and the compound will
transform to a liquid [7, 12-14]. If there is a decomposition or a disproportionation, the
products will be salts or other solid acids as in the Rb3H(SO4)2 system [7, 13]. This
Cs6(H2SO4)3(H1.5PO4)4 compound illustrates the case that neither of the two statements
above

true.

The

experimental

results

Chapter

will

show

that

Cs6(H2SO4)3(H1.5PO4)4 can transform to its superprotonic phase and decompose to H3PO4
and another solid acid with a smaller unit cell, and H3PO4 can dehydrate all in a small
temperature range.

1.4 References
[1]

W. Munch, K.D. Kreuer, U. Traub, J. Maier, Solid State Ionics 77 (1995) 10.

[2]
D.A. Boysen, Superprotonic Solid Acids: Structure, Properties. and Applications,
Materials Science, California Institute of Technology, Pasadena, California (2004).
[3]
A.I. Baranov, V.V. Dolbinina, E.D. Yakushkin, V.Y. Vinnichenko, V.H. Schmidt,
S. Lanceros-Mendez, Ferroelectrics 217 (1998) (1-4) 285.
[4]

V.V. Sinitsyn, A. Baranov, E.G. Ponyatovsky, Solid State Ionics 136 (2000) 167.

[5]

K. Suzuki, S. Hayashi, Phys. Rev. B 74 (2006) (13) 10.

[6]
M. Polomska, L.F. Kirpichnikova, T. Pawlowski, B. Hilczer, Ferroelectrics 290
(2003) 51.
[7]
L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State
Ionics 179 (2008) (9-10) 305.
[8]
M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics
178 (2007) (21-22) 1262.
[9]
A. Ikeda, Superprotonic solid acids : thermochemistry, structure, and
conductivity, Materials Science, California Institute of Technology, Pasadena, California
(2013).
[10] M.W. Louie, M. Kislitsyn, K. Bhattacharya, S.M. Haile, Solid State Ionics 181
(2010) (3-4) 173.
[11] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters
affecting the presence and stability of superprotonic transitions in the MHnXO4 family of
compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California
Institute of Technology, Pasadena, California (2003).
[12]

A. Ikeda, S.M. Haile, Solid State Ionics 213 (2012) 63.

[13]

C. Panithipongwut, S.M. Haile, Solid State Ionics 213 (2012) 53.

[14] Y.K. Taninouchi, T. Uda, Y. Awakura, A. Ikeda, S.M. Haile, J. Mater. Chem. 17
(2007) (30) 3182.

Chapter 2 Experimental Methods
2.1 Synthesis
Polycrystalline and single crystal samples of the solid acids studied were
synthesized by various aqueous-solution-based methods including solvent-induced
precipitation, also known as rapid precipitation and forced precipitation; thermal-induced
precipitation, also called agitated evaporation; and crystallization, so-called slow
evaporation. Each solution contained carbonate or sulfate compounds of the metal studied
and acids of interest with a specific ratio.
Polycrystalline samples were vacuum-filtered and rinsed with an appropriate
organic solvent, usually methanol or acetone, to remove residual solutions containing
ions and acids. These samples were then let dry in a drying oven or at ambient air before
further measurements were taken.
Single crystal samples were individually removed from their mother liquors and
rinsed very quickly with deionized water to remove residual liquid without forming fine
particles of other solid acids on the surface of the crystals. To be able to do this without
losing the crystals, the crystals must be large enough and the rinsing must be very quick.
The crystals were then patted dry with Kimwipe.
In general, the crystallization method is suitable for samples that require high
purity, while precipitation method is more suitable for incorporation of another ions into
a structure. Anyway, for simple solid acids such as CsHSO4, CsH2PO4, or Rb3H(SO4)2,
that are likely to be both thermodynamically and kinetically stable, the forcedprecipitation method will be the first choice to try as it is fast and the product is still a
pure phase. However, this is not always true, for example, RbHSO4 cannot be obtained as

a pure phase from the solvent-induced precipitation method in which case it is necessary
to let single crystals of RbHSO4 grow from the solution. For larger solid acids which
requires many ions in the solution to form the correct stoichiometry, the crystallization
method is the better choice since forced-precipitations will make other kinetically stable
compounds to form with the desired product due to the differences in local concentrations
of multiple ions. Specific details and appropriate methods for each solid acid system are
described in the respective chapter.

2.2 X-Ray Diffraction (XRD)
After the synthesis, the phase of each sample was identified using X-ray
diffraction to confirm its purity at room temperature before further examinations.
Consider Bragg’s law:
2𝑑 sin 𝜃 = 𝑛𝜆

(1)

where d is the interplanar distance or the d-spacing, θ is the angle between the normal
vector of the incident beam and the plane, λ is the X-ray wavelength, and n is the order of
reflection which is always taken as 1 since the higher order can be represented by first
order of reflections of planes with higher indices. Since every crystalline material has a
different crystal structure and lattice parameters, it will give a unique set of reflections.
By combining the diffraction data with chemical information, the sample can be easily
identify especially for the known compounds in which case, one can either simply
compare the pattern with a published one to just confirm the phase or perform Rietveld
refinement for more structural information. For a new compound, ab initio determination

can be employed using diffraction data analysis software to determine the plausible unit
cells along with related information.
For solid solution systems, XRD was used to determine the solubility limits. As
an alien ion dissolves into a structure, the lattice parameter changes due to the difference
in ionic radii of the original ion and the substituent. This will cause shifts in peak
positions, which follow the Bragg’s law until the solubility limit is reached. Beyond the
solubility limit, the peaks will no longer move and another set of peaks from another
phase will start showing up in the pattern. The raise of the other set of peaks might be
difficult to be detected and if higher accuracy is needed, one may calculate the lattice
parameters from the XRD patterns below and above the solubility limit, plot them against
the composition, extrapolate the straight lines and find the intercept which in theory will
represent the solubility limit.
In high-temperature studies, when there is no transition occurs, the shifts in peak
positions are expected because of thermal expansions of materials that change the
interplanar distance. Almost all of solid acids show regular thermal expansion behavior,
i.e. the structure expands with the temperature, except one solid acid discovered so far,
Cs6(H2SO4)3(H1.5PO4)4, that shows an apparent negative thermal expansion behavior.
Temperature dependence of lattice constants can be determined using either Rietveld
method for a known structure. For a new phase, ab initio method will give the unit cell
information such as plausible space groups as well as lattice constants associating with
the space groups. At a polymorphic phase transition, a solid acid adopts another crystal
structure, which could be a different or the same crystal system, but a different space
group, and will usually give a different XRD pattern. Hence, this technique can be used

10
to estimate the transition temperature, but, in practice, it might not give a very accurate
temperature due to operational limitations.
As mentioned above, we rely on peak positions to determine lattice parameters,
space groups, and other cell information. Thus, correctness of peak positions is crucial.
For a solid acid experiment with a regular size and thickness on an X-ray diffractometer
that is well aligned, sample displacement is the source of error that occurs easily and is
often found when a sample preparation for XRD is not done properly. The error from
sample displacement can be corrected using internal standard addition method where a
standard of known peak positions is added and mixed with the sample, then figure out the
relationship between the shift in the peak positions of the standard and the observed
positions and use the relationship to correct the peak positions of the sample. This
method works fine as long as the standard does not react with the sample and its pattern
does not interfere with the pattern of the sample. However, for a powder sample, it is
relatively very easy to prepare the sample such that it is at the correct position, leading to
the correct peak positions in the XRD pattern without the use of an internal standard and
more analysis. Plus, the internal standard may not be applicable in some situations, such
as when the peaks of the standard overlap with those of the sample. In this thesis, the
sample displacement error was avoided successfully by careful sample preparations for
the XRD experiments to ensure that the surfaces of the samples were at the right position.
Rietveld refinement is a method that is used to refine a structure using a set of
initial parameters from a known structure to calculate diffraction patterns until a set of
refined parameters giving the best fit between the calculated and the measured patterns is
found.

11
Philips X’Pert Pro diffractometer with Cu Kα radiation was utilized to obtain
X-ray diffraction data. Unless otherwise noted, the 2θ range was from 10 to 60° with a
step size of 0.0167° for a total time of about 20 minutes for each measurement at both
ambient and high temperatures.
The in situ high-temperature XRD data were collected using Anton Paar
HTK1200 high-temperature chamber equipped to the diffractometer under flowing
humidified helium (pH2O ∼ 0.023 atm) to prevent dehydration of the solid acids. Prior to
data collection, powder samples were compacted into 15-mm-diameter pellets using
∼ 194-MPa uniaxial pressure for 15 minutes to facilitate solid-state interdiffusion and
phase equilibration. The measurement temperatures were reached at a ramp rate of
5 °C/min and the samples were allowed to reach equilibrium at each temperature as no
changes in the diffraction patterns were observed.
Rietveld refinements and cell determinations were performed using X’Pert Plus
software.

2.3 A.C. Impedance Spectroscopy (ACIS)
The conductivities of the solid acids were obtained using A.C. impedance
spectroscopy. In this technique, alternating voltages, V(t) = V0·exp(iωt), at various
angular frequencies, ω, where V0 is the amplitude of the applied voltage, t is the time, and
i = −1 , are applied to the material and corresponding alternating currents,
I(t) = I0·exp(iωt+θ), where I0 is the amplitude of the current and θ is the phase difference
between V(t) and I(t), are measured. Impedances, Z(ω), are then calculated from the
equation:

𝑍 𝜔 =

𝑉(𝑡)
𝐼(𝑡)

(2)

The impedances can be written as
𝑍 𝜔 = 𝑍 cos 𝜃 − 𝑖 𝑍 sin 𝜃 = 𝑍! − 𝑖𝑍!

(3)

where |Z| is the magnitude of the impedance, ZR = |Z|cos θ is the real, and ZR = |Z|sin θ is
the imaginary parts of the impedance. A plot of -ZI against ZR is called a Nyquist plot. For
electrochemical processes with different characteristic frequencies, a separate arc along
the x-axis will represent each process and the width of the arc on the real axis will
represent the respective resistance. Figure 2.1 shows a schematic Nyquist plot for a
material with resistances from three common contributions: bulk, grain boundary, and
electrode. In this study, there are usually two arcs from the bulk and the electrode
observed at low temperatures and only a straight line representing the electrode
contribution is observed above the superprotonic transition as shown in Figure 2.2 a and
b. The dotted lines in Figure 2.2 are theoretical arcs that are not detected due to the
limited frequency range of the impedance analyzer.

Figure 2.1. Schematic Nyquist plot of a material with contributions from bulk, grain
boundary, and electrode resistances.

Figure 2.2. Schematic Nyquist plot of solid acids (a) below and (b) above the
superprotonic transition. The dotted lines are theoretical arcs that are not detected due to
the limited frequency range of the impedance analyzer.
Since the x-intercept here is the same as the width of the arc of the bulk
resistance, as seen in Figure 2.2, measuring the impedance just at the intercept is
essentially the same as fitting the arc to obtain the width. By simply selecting a frequency
that gives such data point, this mode of measurement is called single-frequency mode,
which measures the impedance of only one point instead of the full frequency range
allowing faster and continuous data collection, i.e. a few seconds as opposed to 1-2
minutes for a full-range spectrum. The single-frequency mode also reduces the
complications occurring during fittings of the spectra near the superprotonic transition

14
since the full spectra might be changing during the measurements resulting in distorted,
poorly defined arcs.
Conductivity measurements were performed on 9.3-mm-diameter pellet samples,
prepared under 15 min of uniaxial pressure (∼ 216 MPa). PELCO Colloidal silver paste
(Ted Pella, #16032) was applied to opposing sides to serve as electrodes. Data were
collected using a HP 4284 precision LCR meter.
Most of the measurements were performed under active humidification, with
pH2O ~ 0.02-0.03 atm attained by passing the inlet N2 through a room-temperature
bubbler. Only in the case of some samples, such as RbHSO4, which were found to be
particularly sensitive to dehydration, the pH2O was increased to 0.5 atm. Some
measurements were carried out under ambient and dry atmospheres to study the effect of
humidity.
The temperature ranges of measurements were from a temperature as low as
25 °C under ambient humidity or 60 °C under humidified gas to a maximum temperature
slightly above the transition temperatures of the solid acids. The samples were held at the
starting temperatures for at least 30 minutes prior to data collection, and the ramp rate
was 0.1-1 °C/min.
After a set of preliminary full spectrum measurements (20 Hz to 1 MHz), a
frequency at which the imaginary component of the impedance was at minimum was
selected as appropriate for capturing bulk phase transformation behavior in singlefrequency measurements. Because only a single frequency was examined, the data could
be recorded continuously under constant heating and cooling rates.

2.4 Differential Scanning Calorimetry (DSC)
In DSC technique, the difference in the amount of heat needed to keep the
temperatures of a sample and a reference equal is measured as a function of temperature.
At a transition, for instance, a phase transition or a disproportionation, an amount of heat
is absorbed due to the latent heat of the process, so an additional amount of heat is
required to compensate and keep the temperatures of the material and the reference equal.

Figure 2.3. Schematic DSC profile.
Figure 2.3 shows a schematic DSC profile. An integrated peak area can be
calibrated using a set of standard materials to correlate to an amount of heat and this
connection can be used to calculate the heat from a peak area of a sample.
A Netzsch STA 449 simultaneous DSC/TG instrument was employed to study
thermal behavior of the samples. Each sample was compacted to a 5.25-mm-diameter
pellet under a pressure of ∼ 226 MPa for 5 minutes to facilitate solid-state interdiffusion.
The pellet samples were examined under either dry or flowing humidified nitrogen gas

16
with various pH2O up to ∼ 0.023 atm in the temperature ranges similar to those in ACIS
experiments.

2.5 Energy-Dispersive X-Ray Spectroscopy (EDS)
When excited with certain energy, an atom can release a set of X-rays with
characteristic energies, which is unique for each element. This technique uses these
characteristic spectra to identify the elemental composition of the sample.
Energy-dispersive X-ray spectroscopy was performed on solid solution samples
and Cs6(H2SO4)3(H1.5PO4)4 to determine the actual compositions at room temperature
using Oxford X-Max SDD X-ray Energy Dispersive Spectrometer. The powder samples
were pressed into pellets and polished so that the surfaces of the samples were flat and
suitable for EDS measurements. For each sample, at least eight EDS data were collected
and the atomic percentages of the elements in the materials were used to determine the
actual compositions.

Chapter 3 Rb3H(SO4)2-RbHSO4 Pseudo-Binary System
Adapted with permission from: C. Panithipongwut, S.M. Haile. High-temperature phase
behavior in the Rb3H(SO4)2-RbHSO4 pseudo-binary system and the new compound
Rb5H3(SO4)4. Solid State Ionics 213 (2012) 53.

3.1 Introduction: Absence of Polymorphic Transition of Rb3H(SO4)2
Several solid acid compounds, materials formed of oxyanion groups linked by
hydrogen bonds, are known to undergo superprotonic phase transitions at elevated
temperatures (∼ 100 – 300 °C). At the transition, the materials transform from their
respective low-symmetry, low-conductivity phases to high-symmetry, high-conductivity
phases. The family of solid acid compounds with stoichiometry M3H(XO4)2, where
M = NH4, K, Rb, Cs; X = S, Se, typifies this behavior. Many within this family display a
transformation from a room-temperature monoclinic phase to a high-temperature trigonal
phase (symmetry R3̅m, phase I). The increase in conductivity at the transition is generally
3-4 orders of magnitude. The compound Rb3H(SO4)2 is unusual in that, despite being
isostructural at room temperature to others in the family, the increase in conductivity on
heating under ambient pressures is a result of disproportionation rather than a
polymorphic transition. [1] That is, whereas a high-temperature trigonal phase occurs for
Rb3H(SeO4)2,

Cs3H(SeO4)2,

(NH4)3H(SeO4)2

and

(NH4)3H(SO4)2,

Rb3H(SO4)2

decomposes at ∼ 210 °C into Rb2SO4 and an unknown phase of generic stoichiometry
RbmHn(SO4)p, with p=(m+n)/2 .[1] Stabilization of the trigonal phase requires pressures
in excess of 0.14 GPa and temperatures in excess of 228 °C. [2, 3] A remarkable attribute
of the two-phase mixture that results from Rb3H(SO4)2 is a sharp increase in conductivity

(by about 2 orders in magnitude) concomitant with the disproportionation reaction, giving
the impression of a polymorphic superprotonic transition. [1, 2] Indeed, the two-phase
mixture has been referred to as phase IV in the literature as a result of some
misinterpretation of the nature of the phase change. [2]
This work was carried out with the objective of fully elucidating the hightemperature behavior of Rb3H(SO4)2. Cowan et al. demonstrated that the unknown phase
RbmHn(SO4)p must be an intermediate between RbHSO4 and Rb3H(SO4)2 and suggested
the composition Rb5H3(SO4)4. [1] A preliminary evaluation of the phase behavior in the
Rb2SO4-RbHSO4 system was further provided in that study. Here, we carry out a
systematic characterization of phase behavior in the narrower composition range between
Rb3H(SO4)2 and RbHSO4 using a combination of A.C. impedance spectroscopy, hightemperature X-ray powder diffraction, and differential scanning calorimetry.

3.2 Synthesis and Characterizations
3.2.1

Sample preparation
The compositions examined are shown in Figure 3.1 as points along the abscissa

of the schematic pseudo-binary phase diagram for the Rb2SO4-H2SO4 system proposed
by Cowan et al. [1] Because the compositions of interest for the present work lie within
the range of Rb3H(SO4)2 and RbHSO4, they are hereafter referred to in terms of mole %
of RbHSO4 in the overall system. Samples of (1-x) Rb3H(SO4)2 – x RbHSO4 were
prepared simply from solid-state mixtures of the two end members, where the end
members were prepared from aqueous solutions of rubidium sulfate (Rb2SO4, Alfa Aesar
99%) and sulfuric acid (H2SO4, EMD Chemicals 95-98%).

Figure 3.1. Proposed phase diagram in the Rb2SO4-H2SO4 system after Cowan et al. [1];
compositions within the R3H(SO4)2-RbHSO4 region examined in this work as indicated.
The trirubidium compound, Rb3H(SO4)2, was obtained using a solution in which
the Rb:H molar ratio was fixed at 3:1. Introduction of methanol to the solution induced
rapid precipitation of the target compound. The product was filtered, rinsed with
methanol, and finally dried in an oven at ∼ 100 °C for 24 hours or more prior to further
experimentation. In contrast, rubidium hydrogen sulfate was synthesized in single crystal
form. In principle, the stoichiometry RbHSO4 dictates a molar ratio of Rb:H of 1:1,
however, it was found that excess sulfuric acid was necessary to obtain the target material
as the sole product. Solutions were prepared in a 1:2 molar ratio of Rb:H, and slow
evaporation of water over about 4 days under ambient conditions eventually yielded
moderately sized crystals (∼
0.3 cm × 1 cm). These were removed from the mother liquor
and quickly rinsed with deionized water to eliminate excess sulfuric acid. After an

additional rinse with acetone, they were dried overnight in a drying oven at ∼ 100 °C.
Solid mixtures of Rb3H(SO4)2 and RbHSO4 were prepared by combining and grinding in
a mortar and pestle appropriate amounts of polycrystalline Rb3H(SO4)2 and RbHSO4 for
approximately 10 minutes.

3.2.2

X-ray diffraction (XRD)
X-ray powder diffraction was performed for phase identification at both ambient

and high temperatures using a Phillips X’Pert Pro diffractometer with Cu Kα radiation.
Diffraction data were collected in the 2θ range from 10 to 60° with a step size of 0.0167°.
The dwell time for each detector position, which covers several steps, was 50.165 s for a
total measurement time for each sample or condition of 20:34 min. An Anton Paar
HTK1200 oven, supplied with humidified helium (pH2O ∼ 0.032 atm), was employed to
acquire high-temperature data.
High-temperature measurements were focused on Rb3H(SO4)2 and on 66.67%
RbHSO4, the latter corresponding to the proposed compound Rb5H3(SO4)4. To facilitate
solid-state interdiffusion and phase equilibration, samples were formed into 15-mmdiameter compacts using ∼
194 MPa uniaxial pressure for 15 min prior to data collection.
In the case of the 66.67% RbHSO4 sample, data were collected at 160, 180, 190, and
200 °C sequentially. After reaching the highest temperature, the furnace was cooled and
data collected at 160 and 150 °C and room temperature. The temperature ramp rate was
5 °C/min, and at each measurement temperature samples were equilibrated, as indicated
by the absence of changes in the diffraction patterns.

3.2.3

21
A.C. impedance spectroscopy (ACIS)
Conductivity measurements were performed using 9.3-mm-diameter pellet

samples, again prepared under 15 min of uniaxial pressure (∼
216 MPa). PELCO
Colloidal silver paste (Ted Pella, #16032) was applied to opposing sides to serve as
electrodes. Data were collected using a HP 4284 precision LCR meter. After a set of
preliminary full spectrum measurements (20 Hz to 1 MHz), a frequency of 45 kHz was
selected as appropriate for capturing bulk phase transformation behavior. Specifically, the
maximum contribution from the imaginary component to the total impedance was only
5% at 45 kHz and decreased with increasing temperature to essentially zero at the highest
temperature in the experiment. The measurements were performed under active
humidification, with pH2O = 0.032 atm attained by passing the inlet N2 through a roomtemperature bubbler. Only in the case of the end-member RbHSO4, which was found to
be particularly sensitive to dehydration, the pH2O was increased to 0.5 atm. The
temperature range of measurement was from 140 to 220 °C, except for samples with 1020% and pure RbHSO4, for which the range was 160 to 212 °C. The samples were held at
the starting temperatures for at least 30 minutes prior to data collection, and the ramp rate
was 0.1-1 °C/min. Because only a single frequency was examined, the data were recorded
continuously under constant heating.

3.2.4

Thermal analysis
Thermal behavior of the 66.67% RbHSO4 material was examined using a Netzsch

STA 449. A compact 61.141 mg in mass, 5.25 mm in diameter was formed, using 226MPa pressure for 5 minutes, in order again to facilitate solid-state reaction. The

measurement was carried out under humidified nitrogen (pH2O ∼ 0.032 atm). Prior to
data collection, the sample was held at 150 °C for 6 hours (in the STA). Data were then
collected on heating to 210 °C, and then over three additional thermal cycles in the
temperature range from 30 to 210 °C, in all cases using a ramp rate of 2 °C/min.

3.3 Conductivity Studies
The conductivities so measured of Rb3H(SO4)2, RbHSO4, and selected mixed
compositions are shown in Figure 3.2. The most striking feature of these results is the
occurrence of multiple, sharp increases in conductivity at various temperatures, with the
specific behavior strongly dependent on composition. In the case of Rb3H(SO4)2, in
agreement with the results reported earlier by Cowan et al. [1], Sinitsyn et al. [2], and
Baranov et al. [4], a single, dramatic increase in conductivity, from 3.6 × 10-5 to
2.0 × 10-3 S/cm, occurs at ~ 201 °C. On cooling, the high-conductivity state is maintained
to a temperature of ~ 180 °C.
Upon introduction of up to 66.67% RbHSO4 into mixtures with Rb3H(SO4)2, three
features are observed: a new conductivity anomaly appears at 185 °C; with increasing
RbHSO4 content the magnitude of the conductivity change at 205 °C decreases; and the
low-temperature conductivity generally increases. At compositions beyond 66.67%
RbHSO4, as exemplified by the composition with 70% RbHSO4, the anomaly at 185 °C
is retained, and, in addition, a new anomaly at 168 °C appears. In the case of 100%
RbHSO4, a small, broad anomaly occurs at 168 °C, followed by what appears to be a very
broad solid to liquid transformation at 205 °C. Upon removal from the test station, unlike
any of the other compositions, the sample of neat RbHSO4 was mechanically deformed

and displayed a glossy sheen. These characteristics are indicative of the presence of a
liquid phase at the highest temperatures examined. It is known that in the case of
CsH2PO4, for example, partial dehydration can yield a liquid phase [5, 6] and it appears
that RbHSO4 may display similar behavior. For this reason, the high RbHSO4 region of
the phase diagram has not been fully studied here.
The most significant aspect of the results depicted in Figure 3.2 is the absence of a
conductivity anomaly at 205 °C for the 66.67% RbHSO4 composition. The conductivity
of this composition at temperatures below 205 °C is moreover much higher than that of
either of the end members Rb3H(SO4)2 and RbHSO4. This combination of factors
suggests that the unknown product of the disproportionation of Rb3H(SO4)2 at 205 °C
indeed has composition 66.67% RbHSO4 as originally speculated [1] and, furthermore,
that the stability of this compound extends to temperatures below 140 °C. That is, the
conductivity data suggest that the new compound Rb5H3(SO4)2, corresponding to 66.67%
RbHSO4, is both thermodynamically stable and kinetically accessible at temperatures as
low as 140 °C.

24
(a)

(b)

Figure 3.2. Conductivity of compositions in the Rb3H(SO4)2-RbHSO4 system upon
heating under humidified nitrogen (pH2O ∼ 0.032 atm) at a ramp rate of 0.1 °C/min: (a)
0-66.67% RbHSO4; and (b) 66.67-100% RbHSO4.

3.4 High-Temperature

XRD

and

Rietveld

Refinement

LT-

Rb5H3(SO4)4
The circumstantial evidence for the existence of Rb5H3(SO4)4 as a new, stable
compound provided by the conductivity measurements is supported unequivocally by the
diffraction (Figures 3.3 and 3.4).

Figure 3.3. Equilibrium high-temperature XRD patterns of the 66.67%-RbHSO4 content
composition at indicated temperatures, under humidified helium (pH2O ∼ 0.032 atm).
At room temperature the 66.67% RbHSO4 composition displays the diffraction
pattern of a mixture of the two end-member compounds Rb3H(SO4)2 and RbHSO4,
indicating the absence of reactions under ambient conditions. At 160 °C, however, as
shown clearly in Figure 3.4a, an entirely different pattern emerges. These diffraction data
can be described according to a structure recently reported for a high-temperature form of
Cs5H3(SO4)4 with space group P3̅m [7], along with minor peaks due to residual

Rb3H(SO4)2 and RHSO4. Specifically, Rietveld refinement using as an initial starting
model the atomic coordinates of Cs5H3(SO4)4 and ab initio determined cell constants
yielded the following: a = 5.9298(2) Å, c = 14.4736(6) Å, cell volume V = 440.74(3) Å3,
and the atomic parameters listed in Table 3.1. With Z =1, the computed density is
3.0691(2) Mg/m3. The asymmetric unit contains three crystallographically distinct Rb
atoms and two distinct sulfate groups. The oxygen atoms about S(2) have low occupancy,
as reported by [7], and the coordinates listed in Table 3.1 for these oxygen species have
not been refined from their initial values. Likewise, the isotropic displacement parameters
(for all species) have not been refined. The final refinement parameters are Rwp = 7.64%,
RBragg = 2.97%, and GOF = 9.35. The rotational disorder associated with the S(2) sulfate
group appears responsible for the high conductivity of this phase (Figure 3.2).

Table 3.1. Atomic coordinates, occupancies, and isotropic displacement parameters in
Rb5H3(SO4)4 at 160 °C, refined in space group P3̅m with a = 5.9298(2) Å and c =
14.4736(6) Å.
Atom
Rb(1)
Rb(2)
Rb(3)
S(1)
O(1)
O(2)
S(2)
O(3)
O(4)
O(5)

Site
1b
2d
2d
2c
2c
6i
2d
6i
6i
12j

Occupancy
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.3333
0.5000
0.2500

0.0000
0.6667
0.3333
0.0000
0.0000
0.134(1)
0.6667
0.5532
0.5408
0.7385

0.0000
0.3333
0.6667
0.0000
0.0000
0.866(1)
0.3333
0.2766
0.4592
0.1561

0.5000
0.0621(3)
0.2613(4)
0.1373(7)
0.249(1)
0.1065(7)
0.3686(6)
0.2785
0.4162
0.3658

B (104 pm2)
0.0900
0.0552
0.0751
0.0507
0.0633
0.0633
0.0760
0.0887
0.2533
0.2533

27
(a)

(b)

Figure 3.4. XRD patterns of the 66.67%-RbHSO4 content composition under humidified
helium (pH2O ∼ 0.032 atm) at (a) 160 °C and (b) 190 °C. The pattern in (a) is analyzed in
terms of the reported intermediate-temperature (130 °C) structure of Cs5H3(SO4)4 [7],
with a primitive trigonal cell, space group P3̅m, and lattice constants a = 5.9298(2) Å and
c = 14.4736(6) Å. Peaks marked with * and v are from residual Rb3H(SO4)2 and RbHSO4,
respectively. The pattern in (b) is compared to that of a higher-temperature form of
Cs5H3(SO4)4 [7].

28
At temperatures beyond 185 °C (specifically 190 and 200 °C), at which a

conductivity anomaly is observed for almost all compositions (Figure 3.2), the diffraction
pattern of the 66.67% RbHSO4 composition changes yet again, Figures 3.3 and 3.4b. In a
manner almost identical to the high-temperature behavior of Cs5H3(SO4)4 [7], heating, in
this case, causes the pattern complexity to increase, suggesting either a reduction in
symmetry or a further disproportionation. As possible disproportionation products,
Rb2SO4 and RbHSO4 are ruled out simply by the features of diffraction patterns (though
not shown, major peaks due to the phases are absent). An overall composition change due
to dehydration is unlikely due to the reversibility of the transformation. Specifically, on
cooling, the trigonal pattern is recovered, as shown, for example, by the pattern at 160
°C. Even at room temperature, the material eventually returns to being a mixture of
RbHSO4 and Rb3H(SO4)2, as shown in the final diffraction pattern collected after several
days at ambient conditions. Dehydration is further ruled out because the transition
temperature was found to be independent of water partial pressure (data not shown). As
shown in Figure 3.2, the transformation is associated with a moderate but clear (about 3
times) increase in conductivity. This behavior, along with the general features of the
inferred phase diagram (discussed further below), suggests a polymorphic transformation
rather than disproportionation. Accordingly, Rb5H3(SO4)4 is tentatively assigned two
phases, a lower-temperature trigonal form, LT-Rb5H3(SO4)4 (below 185 °C) and an
unindexed, higher-temperature form, HT-Rb5H3(SO4)4 (above 185 °C). The overall
similarity to the behavior of Cs5H3(SO4)4 [7] is noteworthy.

3.5 DSC Studies
The thermal behavior of the 66.67% RbHSO4 composition is shown in Figure 3.5.
Based on the diffraction data, the 6-hour anneal at 150 °C (prior to the first cycle) was
implemented with the objective of generating single phase Rb5H3(SO4)4.

Figure 3.5. DSC profiles of the 66.67% RbHSO4 sample under humidified nitrogen
(pH2O ∼ 0.032 atm) at a ramp rate of 2 °C/min. First and second cycles.
On heating after this treatment, a large endothermic event with a heat of
transformation of 23.8 kJ/mol and an onset temperature of 185 °C is evident, clearly
corresponding to the transformation between the LT and HT forms of Rb5H3(SO4)4,
already diagnosed by conductivity and X-ray powder diffraction. This transformation
enthalpy is smaller, but still close to that reported for the apparently analogous transition
in Cs5H3(SO4)4 (26.4 – 29.9 kJ/mol). [8] Given the somewhat preliminary evaluation of
both materials, it would be premature to attribute this discrepancy to distinct phase

behaviors. Both values can be considered typical of superprotonic transitions heat of
transformation. Specifically, compounds in the MHSO4 family display heats of
transformation of ~ 5.5-10.5 kJ/mol [9-11], whereas those in the M3H(SO4)2 family, for
which the structural difference between the two phases is small, have values of ~ 4
kJ/mol. [12, 13] The simple molar weighted sum is then ~ 15-25 kJ/mol for a compound
in the M5H3(SO4)4 family. On cooling, the reverse transformation occurs by a two-step
process, with exothermic peaks centered at approximately 170 and 155 °C. The reasons
for the two-step behavior are unknown. On further cooling, a very weak, broad thermal
event is observed at ~ 100 °C, which may be associated with the partial
disproportionation of Rb5H3(SO4)4 back into Rb3H(SO4)2 and RbHSO4, or possibly water
condensation. The subsequent thermal cycle shows on heating a weak endothermic event
at 100 °C, and a new, but also weak, exothermic event at 170 °C. Based on the
conductivity data, no transformation is expected for the 66.67% RbHSO4 composition at
this latter temperature. However, for RbHSO4-rich compositions, a conductivity anomaly
is clearly observed at 168 °C. Thus, the occurrence of a DSC peak at 170 °C for the
66.67% RbHSO4 composition may reflect the presence of RbHSO4 that is formed on
cooling to ambient temperatures (and is not fully consumed to form single phase
Rb5H3(SO4)4 on the subsequent heating). The slight decrease in the magnitude of the
thermal event at 185 °C from the first to subsequent cycle is consistent with this
interpretation.

3.6 Phase Diagram of Rb2SO4-H2SO4 System
The combination of conductivity, diffraction and thermal data collected here
enable construction of the modified phase diagram for the Rb2SO4-rich end of the
Rb2SO4-H2SO4 system presented in Figure 3.6.

Figure 3.6. Revised phase diagram for the pseudo-binary Rb2SO4-H2SO4 system,
constructed on the basis of the previously proposed diagram of Cowan et al. [1] and new
findings in this work.
Here, the conductivity anomaly occurring at 205 °C for all compositions in the
Rb3H(SO4)2-RbHSO4 mixtures with RbHSO4 content less than 66.67 % is attributed to
the disproportionation of Rb3H(SO4)2 into Rb2SO4 and the new phase identified as
Rb5H3(SO4)4. At the high temperature of the disproportionation reaction, Rb5H3(SO4)4
adopts what appears to be a high-temperature structure with a surprisingly complex
diffraction pattern. The new compound Rb5H3(SO4)4 forms at temperatures at least as low

as 140 °C. Between 140 and 185 °C it adopts a trigonal structure, isomorphous to a
known trigonal phase of Cs5H3(SO4)4 [7], and displays a relatively high conductivity. The
conductivity anomaly observed at 185 °C for all compositions examined, with the
exception of the two end members and the 10% RbHSO4 content sample, is tentatively
attributed to the polymorphic transformation of Rb5H3(SO4)4 from its lower temperature,
trigonal form to a higher temperature, higher conductivity form.
The possibility that Rb5H3(SO4)4 itself undergoes a disproportionation reaction at
185 °C cannot be entirely ruled out; however, such behavior would appear to be
contradictory to the results obtained. Specifically, disproportionation would require the
formation of a Rb3H(SO4)2-rich and a RbHSO4-rich phase relative to Rb5H3(SO4)4. The
Rb3H(SO4)2-rich phase, existing somewhere between Rb3H(SO4)2 and Rb5H3(SO4)4
would be required to undergo some sort of transition at 205 °C, coinciding with the
confirmed disproportionation of Rb3H(SO4)2. On the other hand, this transformation
would simultaneously be required to be absent at compositions with RbHSO4 content
greater than 66.67% although such compositions would be expected to contain the new
phase. This contradiction leads us to propose the polymorphic transformation. The fact
that the 185 °C anomaly is absent for the 10% RbHSO4 content sample is attributed to the
small amount of Rb5H3(SO4)4 that would have formed at this composition (5.56 mol%).
Turning to the compositions rich in RbHSO4 relative to Rb5H3(SO4)4, Figure 3.2b, the
conductivity anomaly occurring at 170 °C for all compositions with RbHSO4 content
greater than 66.67 % is tentatively attributed to a polymorphic transition in RbHSO4. [14,
15] A surprising feature of this transition is its sharp appearance in the 70% RbHSO4
content sample, which constitutes a mixture of 75 mol% Rb5H3(SO4)4 and only 25 mol%

RbHSO4. The reason for this behavior is unclear. As noted above, measurements in the
RbHSO4-rich portion of the Rb3H(SO4)2-RbHSO4 system were limited due to the poor
thermal stability of these compositions.

3.7 Conclusions
In combination, the results from conductivity measurements, high-temperature
XRD, and DSC reveal the occurrence of a new phase in the Rb2SO4-H2SO4 system,
specifically, Rb5H3(SO4)4. The compound is not stable at room temperature but can be
formed from direct solid state reaction between Rb3H(SO4)2 and RbHSO4 at temperatures
as low as 140 °C. At 160 °C, it adopts a structure with primitive trigonal lattice, space
group P3̅m, and lattice parameters a = 5.9298(2) Å and c = 14.4736(6) Å. At 185 °C,
Rb5H3(SO4)4 undergoes what is proposed to be a polymorphic transition to a phase of
somewhat higher conductivity but lower symmetry with a heat of transformation of 23.8
kJ/mol. The reverse transition occurs at ~170 °C, depending on the cooling rate. Under
ambient temperatures, Rb5H3(SO4)4 slowly disproportionates over the course of several
days to the two original compounds, Rb3H(SO4)2 and RbHSO4. The low and high
temperature phases of Rb5H3(SO4)4 are isostructural with the intermediate and high
temperature phases of Cs5H3(SO4)4 reported by Sakashita et al.[7], respectively.

3.8 References
[1]
L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State
Ionics 179 (2008) (9-10) 305.
[2]

V.V. Sinitsyn, A. Baranov, E.G. Ponyatovsky, Solid State Ionics 136 (2000) 167.

[3]
H. Yamawaki, H. Fujihisa, M. Sakashita, K. Honda, Y. Gotoh, Physica B 405
(2010) (1) 291.
[4]
A.I. Baranov, V.V. Dolbinina, E.D. Yakushkin, V.Y. Vinnichenko, V.H. Schmidt,
S. Lanceros-Mendez, Ferroelectrics 217 (1998) (1-4) 285.
[5]

Y. Taninouchi, T. Uda, Y. Awakura, Solid State Ionics 178 (2008) (31-32) 1648.

[6]
Y.K. Taninouchi, T. Uda, Y. Awakura, A. Ikeda, S.M. Haile, J. Mater. Chem. 17
(2007) (30) 3182.
[7]
M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics
178 (2007) (21-22) 1262.
[8]

K.-i. Suzuki, S. Hayashi, Phys. Rev. B 73 (2006) (2) 024305.

[9]

C.R.I. Chisholm, S.M. Haile, Chemistry of Materials 19 (2007) (2) 270.

[10]

M. Friesel, B. Baranowski, A. Lunden, Solid State Ionics 35 (1989) (1-2) 85.

[11]

S. Yokota, J. Phys. Soc. Jpn. 51 (1982) (6) 1884.

[12] A. Pawlowski, M. Polomska, B. Hilczer, L. Szczesniak, A. Pietraszko, Journal of
Power Sources 173 (2007) (2) 781.
[13] A. Pawlowski, L. Szczesniak, M. Polomska, B. Hilczer, L. Kirpichnikova, Solid
State Ionics 157 (2003) (1-4) 203.
[14]

H. Feki, H. Khemakhem, Y. Abid, J. Phys.-Condes. Matter 13 (2001) (37) 8509.

[15]

V.G. Ponomareva, G.V. Lavrova, Solid State Ionics 145 (2001) (1-4) 197.

Chapter 4 Phase Transition Behavior of (CsxRb1-X)3H(SeO4)2
Solid Solutions
4.1 Introduction
Trirubidium hydrogen diselenate, Rb3H(SeO4)2, and tricesium hydrogen
diselenate, Cs3H(SeO4)2, are solid acids in the M3H(XO4)2 family where M=NH4, K, Rb,
Cs and X=S, Se. Many of the solid acids are monoclinic at room temperature and are
known to undergo superprotonic phase transitions at elevated temperatures, ranging from
~ 100 to 300 °C, to high-symmetry, high-conductivity phases. These two materials have
the same behavior with an additional phase transition at a lower temperature for each of
them. Specifically, Rb3H(SeO4)2 transforms from its monoclinic A2/a phase to another
monoclinic C2/m phase at 175 °C before its superprotonic transition occurs at 178 °C
giving the high-temperature trigonal R-3m phase [1]. Cs3H(SeO4)2, on the other hand, is
C2/m at room temperature and transforms to A2/a at 96 °C before further transforming to
the same R-3m phase at 183 °C [2-7].
Properties and behaviors of solid solutions of other solid acids have been studied
to explore the nature and to understand the reasons behind such behaviors, for example,
what affects the transition temperatures or what the driving force of the transition is.
Louie et al. [8] studied solid solutions of CsH2PO4 and RbH2PO4 to try to find the
correlation between the magnitude of the hysteresis and the crystallographic
compatibility between the high- and the low-temperature phases. Also observed in the
same work was the change in the superprotonic transition temperature with increasing
rubidium content. Ikeda [9] also studied the same solid solution system and
Cs1-xKxH2PO4 system to investigate the effects of dopants on the transition temperatures,

the dehydration temperatures, and the conductivities of the materials. Chisholm [10],
even though the materials he studied were not solid solutions but line compounds
between CsHSO4 and CsH2PO4, demonstrated that the transition temperatures varied with
the ratios of CsHSO4:CsH2PO4 and the driving force of the transitions was the
configurational entropies change at the transition of each compound.
This current work was carried out to explore the transition behavior, the phase
diagram, and the conductivity of Rb3H(SeO4)2-Cs3H(SeO4)2 solid solutions using a
combination of high-temperature X-ray diffraction, A.C. impedance spectroscopy, and
differential scanning calorimetry.

4.2 Experimental Methods: Synthesis and Characterization Techniques
4.2.1

Sample preparation
The compositions of (CsxRb1-x)3H(SeO4)2, x = 0–1 with 0.1 increment and x =

0.15, 0.95, 0.98, were examined in this work and were prepared from aqueous solutions
of cesium carbonate (Cs2CO3, Alfa Aesar 99.99%), rubidium carbonate (Rb2CO3, Alfa
Aesar 99.8%) and selenic acid (H2SeO4, Alfa Aesar 40%) at specific molar ratios of
Cs:Rb. Despite the stoichiometric ratio of (Cs+Rb):H = 3:4, the actual ratio used to
obtain the pure phase of each composition was fixed to 3:5, except for the pure
Rb3H(SeO4)2 where the ratio was 3:6. An ice bath and slow addition of selenic acid into
carbonate solution were used to prevent excessive heat released from the reaction that can
cause decomposition of selenic acid. The solution was then gently heated (below 70 °C)
on a hot plate to accelerate water evaporation until the precipitate of the product formed
and eventually the whole solution turned into slurry. After the slurry was vacuum-filtered

for a long time to remove residual liquid, the remaining solid was rinsed several times
with methanol until it became non-sticky to ensure complete removal of the residual acid.
The product was dried in a drying oven at ∼ 100 °C overnight before further examination.

4.2.2

Energy-dispersive X-ray spectroscopy (EDS)
Energy-dispersive X-ray spectroscopy was performed on the samples to

determine the actual compositions at room temperature using Oxford X-Max SDD X-ray
Energy Dispersive Spectrometer. The powder samples were pressed into pellets and
polished so that the surfaces of the samples were flat and suitable for EDS measurements.
For each sample, at least eight EDS data were collected and the average molar ratio of
cesium-to-rubidium was taken.

4.2.3

X-ray diffraction (XRD)
For phase identification of each sample, X-ray diffraction data were obtained

using Philips X’Pert Pro diffractometer with Cu Kα radiation at both ambient and high
temperatures from 10 to 60° of 2θ with a step size of 0.0167° for a total time of 20:34
minutes for each measurement.
The in situ high-temperature X-ray diffraction data of the samples were collected
with Anton Paar HTK1200 high-temperature chamber equipped to the diffractometer
under flowing humidified helium (pH2O ∼ 0.023 atm) to prevent dehydration of the solid
acids. Prior to data collection, powder samples were compacted into 15-mm-diameter
pellets using ∼ 194-MPa uniaxial pressure for 15 minutes to facilitate solid-state
interdiffusion and phase equilibration. The measurement temperatures were reached at a

ramp rate of 5 °C/min and the samples were allowed to reach equilibrium at each
temperature as no changes in the diffraction patterns were observed.

4.2.4

A.C. impedance spectroscopy (ACIS)
9.3-mm-diameter pellet samples were also prepared under 216-MPa uniaxial

pressure for 15 minutes for conductivity measurements with PELCO Colloidal silver
paste (Ted Pella, #16032) applied on both sides to serve as electrodes. An HP 4284
precision LCR meter was used to obtain A.C. impedance data. The measurements were
carried out in the temperature range from 140 to 200 °C, except for Cs3H(SeO4)2 to 210
°C, under flowing humidified nitrogen gas with pH2O ∼ 0.023 atm. Every sample was
held at 140 °C for at least 30 minutes prior to data collection and the temperature ramp
rate was 0.5 °C/min. A set of full spectra (20 Hz to 1 MHz) was collected in the
temperature range in order to determine an appropriate frequency to follow the transition
behavior for each sample which were 1.6 kHz for Rb3H(SeO4)2, 1 kHz for Cs3H(SeO4)2,
and 2.5 kHz for all of the solid solutions. These frequencies were selected from the
frequency giving the intercept on the real axis of the Nyquist plot of the full spectra of
each sample. At these frequencies, the real component dominates and the contribution of
the imaginary component to the total impedance was minimal, specifically, only 0.041.84% for most the samples and 5% for only one sample, Rb3H(SeO4)2.

4.2.5

Thermal analysis: Differential scanning calorimetry
A Netzsch STA 449 simultaneous DSC/TG instrument was employed to study

thermal behavior of the samples. An amount of 120-180 mg of each sample was used to

prepare a 5.25-mm-diameter pellet under a pressure of ∼ 226 MPa for 5 minutes to
facilitate solid-state interdiffusion. The pellet samples were examined under flowing
humidified nitrogen gas with pH2O ∼ 0.023 atm in the temperature range from 30 to 223
°C for three consecutive thermal cycles at a ramp rate of 10 °C/min, the highest ramp rate
among the three methods to improve the DSC signals.

4.3 Determination of Compositions, Solubility Limits, and Volume
Expansion at Room Temperature
The actual compositions of the solid solutions determined using EDS are shown
in Figure 4.1 and were found to be different from the nominal cesium compositions. This
is not unusual for solid acids consisted of multiple ions, especially for those with more
than one metal cations, due to different solubility of each compound which allows each
compound to form at a different moment. The room-temperature XRD patterns of these
compositions (Figure 4.2), nonetheless, showed that every solid solution remained a
single phase and retained the structure of Rb3H(SeO4)2 with the space group A2/a up to
93% Cs, while the composition from 98% Cs and above adopted the structure of
Cs3H(SeO4)2 with the space group C2/m. This indicates that the missing cations did not
form solid products and were filtered out during the synthesis or the amounts of other
compounds that might form were so small that XRD could not detect. The two-phase
region of A2/a and C2/m was found to be small, between 93 and 98% Cs as the XRD
pattern of 97%-Cs sample depicted.

Figure 4.1. Actual compositions of the (CsxRb1-x)3H(SeO4)2 solid solutions determined
using EDS.

Figure 4.2. XRD patterns of the (CsxRb1-x)3H(SeO4)2 solid solutions at room temperature.
The pattern of 97%-Cs composition indicates two phases co-existed.

41
Rietveld refinements were performed on all diffraction data to determine the

lattice parameters (not shown here) and the cell volumes (shown in Figure 4.3) of the
solid solutions. The unit cells of both phases (A2/a and C2/m) expand monotonically with
cesium content as expected since the ionic radius of cesium is larger than that of
rubidium.

Figure 4.3. Volume expansion of the unit cells of the (CsxRb1-x)3H(SeO4)2 solid solutions
upon increasing content of cesium.

4.4 High-Temperature Phase Identification
High-temperature X-ray diffraction (HT-XRD) data were used to determine the
phase diagram of the system. Five out of thirteen studied data sets were shown in Figure
4.4 a to e as representatives of the three regions observed at room temperature mentioned
above and the two end members.

Figure 4.4 (See caption on next page)

Figure 4.4. Equilibrium HT-XRD patterns at indicated temperatures under humidified
helium (pH2O ~ 0.023 atm) of (a) Rb3H(SeO4)2, (b) 46%-Cs, (c) 97%-Cs, (d) 98%-Cs
compositions, and (e) Cs3H(SeO4)2. The vertical lines in (b) are meant to help notice the
small peak shifts.
The HT-XRD patterns of Rb3H(SeO4)2, Figure 4.4a, shows very minimal changes
in peak shape and peak positions as the low-temperature and the high-temperature phases
are highly compatible, i.e. the crystallographic planes barely move to transform from one
to the other phase. However, two small changes could be observed in the peak at ~ 35.8°
of 2θ at 168 and 180 °C indicating the transition temperatures which are close to reported
values [11-14]. The low-temperature phase (T < 168 °C) again is the monoclinic A2/a
and the high-temperature phase (T > 180 °C) is the trigonal R-3m. The intermediate phase
(168 < T < 180 °C), even though could not be recognized clearly here, is another
monoclinic C2/m, according to the literatures [1].

45
The changes in HT-XRD patterns of the 46% Cs composition, Figure 4.4b, were

even harder to be noticed, but still distinguishable as follows: The peak at 35.2° moved to
lower 2θ as the sample was heated from 25 to 155 °C because of thermal expansion of
the lattice. The same peak, though, started to shift upward to higher angle at 157 °C,
indicating the phase transformation, and eventually settled at 159 °C before moving
downward again at higher temperatures due to thermal expansion as usual. Both the lowand the high-temperature phases in this case are still A2/a and R-3m, respectively, as
found in Rb3H(SeO4)2. The two-phase region is small (157-159 °C) and the phase
boundaries are considered ‘converged’ at this composition. Other compositions, which
have A2/a structure at room temperature, on the other hand, gave larger temperature
range of the two-phase region (data not shown).
The patterns of the 97% Cs composition, which represents the compositions in the
two-phase region at room temperature, are presented in Figure 4.4c. The two phases
became a single phase of A2/a after the sample was heated to 100 °C and transformed to
R-3m at 185 °C.
The 98% Cs composition, although started off with a single C2/m phase, passed
through a two-phase region of A2/a and C2/m, as can be seen in Figure 4.4d, as the pellet
sample was heated to 100 °C. Nevertheless, this two-phase region was small since the
pattern at 125 °C shows that the sample turned into another single phase of A2/a before
further transformed to R-3m at 185 °C.
The patterns of Cs3H(SeO4)2 in Figure 4.4e shows similar results as previously
reported by other authors [3-7]. The room-temperature phase of the monoclinic C2/m

transformed to another monoclinic phase, A2/a, at a temperature between 80 and 120 °C
and then to the trigonal R-3m at 190 °C.
The high-temperature phases of all composition examined in this work are
confirmed to be the same phase with different lattice parameters because the peak
positions of the HT-XRD patterns shown in Figure 4.5 shift to lower 2θ as the cesium
percentage increases and no new peaks from phase separation were observed. In other
words, this system has full-range solubility at high temperature.

Figure 4.5. Equilibrium HT-XRD patterns of all composition under humidified helium
(pH2O ~ 0.023 atm), each at a temperature just above its superprotonic transition
temperature as indicated.

4.5 Conductivity Studies
Figure 4.6 a and b show the results from the conductivity measurements of
Rb3H(SeO4)2, Cs3H(SeO4)2, and their solid solutions. A sharp increase in conductivity,
indicating the phase transition from a low-temperature, low-conductivity phase, A2/a, to a
high-temperature, high-conductivity phase, R-3m, i.e. the superprotonic transition,
occurred in the plot of each composition at a different temperature. The superprotonic
transition temperature (TSP) decreased from 180 °C of the pure Rb3H(SeO4)2 to ∼ 159 °C
at 46% Cs, then increased again to 188 °C of the pure Cs3H(SeO4)2. The transition
temperatures of Rb3H(SeO4)2 and Cs3H(SeO4)2 quite agreed with previously reported
temperatures from ACIS of 178-182 [11, 13] and 193 °C [11], respectively.
The hysteresis of the solid solutions became larger around 50% Cs and got
smaller as the compositions approach either end members of the system. Nevertheless,
the overall magnitude of the hysteresis of this system is still very small, ranging from
0.75 to 4.23 °C, compared to other solid acids.
The high-temperature conductivities of the solid solutions including those of the
two end members at 200 °C are shown in Figure 4.7. The most outstanding feature of this
system is that the superprotonic conductivities of all intermediate compositions are
significantly higher than those of the two end members, especially those of the
compositions rich in Rb (5 – 20% Cs) that are 30 – 40 times higher. (CsxRb1-x)3H(SeO4)2
is the first solid solution system amongst other solid acids to show this improved
conductivities; those of the others decrease with dopant contents [9].

Figure 4.6. Conductivity plots of all compositions in (CsxRb1-x)3H(SeO4)2 system upon
heating (solid line) and cooling (dotted line) under humidified nitrogen (pH2O ~ 0.023
atm) at a ramp rate of 0.5 °C/min: (a) 0-50% Cs and (b) 60-100% Cs.

Figure 4.7. The conductivities of all compositions in (CsxRb1-x)3H(SeO4)2 system at 200
°C.

4.6 DSC Studies: Enthalpies and Entropies of Superprotonic Phase
Transition
Thermal behaviors of the samples were studied using DSC and three data sets are
selected and shown in Figure 4.8 as examples. As can be seen in the examples, the DSC
profiles of the compositions adopting the Rb3H(SeO4)2 structure showed only one
endothermic peak on heating with one corresponding exothermic peak on cooling, while
those of the compositions with the Cs3H(SeO4)2 structure revealed two endothermic
peaks. These behaviors were expected as both Cs3H(SeO4)2 and Rb3H(SeO4)2 have two
phase transitions reported previously in the temperature range examined: For
Cs3H(SeO4)2, at 96 and 183 °C [2] and for Rb3H(SeO4)2, at 175 and 178 °C [1] which
obviously are very close to each other and often cannot be separately detected in many

experiments and it was the case here where these two signal peaks overlapped and
formed one peak. The transition of interest, however, is still the one at the higher
temperature as the conductivity results showed earlier that it was where the superprotonic
transition occurred. The TSP observed by DSC showed the same behavior as the one by
A.C. impedance spectroscopy. Again, the TSP decreased from 167 °C of Rb3H(SeO4)2 to a
minimum temperature, 159 °C of the 46% Cs composition, then went back up to 185 °C
of Cs3H(SeO4)2.

Figure 4.8. DSC profiles of Rb3H(SeO4)2, 46%-Cs composition, and Cs3H(SeO4)2 under
humidified nitrogen (pH2O ~ 0.023 atm) at a ramp rate of 10 °C/min.

Figure 4.9. Enthalpies of superprotonic transitions of all compositions in
(CsxRb1-x)3H(SeO4)2 system. The x-error bars of the averages also represent those of the
other points of the same compositions.
Figure 4.9 shows the enthalpy (ΔH) of the superprotonic transformation of every
composition. The enthalpy of the transition of Rb3H(SeO4)2 was 3.27 kJ/mol which
agreed well with the values reported in the literatures (3.0-3.8 kJ/mol) [12-14], while that
of Cs3H(SeO4)2 was 3.44 kJ/mol, somewhat lower than 4.3 kJ/mol reported by
Kirpichnikova et al. [12]. The heats of the solid solutions generally decreased from 3.39
kJ/mol of the 7%-Cs composition to 3.03 kJ/mol of the 46%-Cs composition, where once
again the minimum occurred, then increased to 3.73 kJ/mol of the 98%-Cs composition.
The entropy of Rb3H(SeO4)2 was 7.43 J/(mol·K) which fell in the range of the published
values, 6.7-8.2 J/(mol·K) [12-14], and that of Cs3H(SeO4)2 was 7.48 J/(mol·K), again
lower than the published value of 9.3 J/(mol·K) [12].

4.7 Phase Diagram and Variation of the Superprotonic Transition
Temperature of Rb3H(SeO4)2-Cs3H(SeO4)2 System
The superprotonic transition temperatures of the system from all three methods,
summarized in Figure 4.10, were consistent with one another with some deviations due to
the limitations of the methods. Once again, every method detected a minimum of TSP at
46% Cs and it is noteworthy that this solid solution system is the first to show this
behavior among the other systems of solid acids. With the results from the three methods
combined, the schematic phase boundaries could be determined, as also shown in Figure
4.10, and the two-phase region upon heating of each composition was small, ranging
from 0 to 5 °C, and converged at the minimum temperature. The boundaries on the left
side of the diagram are a little more complicated than the other part and were not studied
in detailed; however, they were estimated from some results in this work and the
presence of the intermediate phase of Rb3H(SeO4)2 at 176 °C [1].
Further combination of Figure 4.10 and the results from room- and hightemperature XRD below the superprotonic transition allows construction of the phase
diagram of the Rb3H(SeO4)2-Cs3H(SeO4)2 system proposed in Figure 4.11.

Figure 4.10. Superprotonic transition temperatures of all compositions in
(CsxRb1-x)3H(SeO4)2 system from HT-XRD, ACIS, and DSC. The x-error bars of the
transition temperatures determined by DSC also represent those of the other points of the
same compositions.

Figure 4.11. Phase diagram for the (CsxRb1-x)3H(SeO4)2 system.

54
The entropies of the transitions of all of the compositions are taken to be a

constant, R·ln 3 J/(mol·K), for the following reason: The entropy of the transition
consists of (1) the change in the mixing entropy, ΔSmix, of Cs and Rb ions from the lowto the high-temperature phase and (2) the change in the configurational entropy, ΔSconfig,
from the low- to the high-temperature phase. The ΔSmix is zero because the composition
does not change upon transition. The ΔSconfig = R·ln (Ω), where Ω is the number of
equivalent, distinguishable ways of hydrogen-bond formation. For the transition of this
system from A2/a to R-3m, Ω = 3 [15]. Thus, ΔS = ΔSmix + ΔSconfig = 0 + R·ln 3 = 9.13
J/(mol·K).
From the trends of ΔH in Figure 4.9 and TSP in Figure 4.10, it can be concluded
that the superprotonic transition temperature of this solid solution system varies with the
enthalpy of transformation which can be explained as follows: At the transition, the
chemical potentials of the two phases are equal, hence the Gibb’s free energy is zero and
ΔH equals TSP·ΔS. ΔS of these solid solutions are constant as described above. Therefore,
TSP varies with the heat of transformation.

4.8 Conclusions
With the results from XRD, A.C. impedance spectroscopy, and DSC, the phase
diagram at room temperature of the Rb3H(SeO4)2-Cs3H(SeO4)2 system is divided into
three regions: A2/a phase of Rb3H(SeO4)2 below 93% Cs, two-phase region of
A2/a+C2/m between 93 – 98% Cs, and C2/m phase of Cs3H(SeO4)2 above 98% Cs. All
compositions, however, became a single phase of A2/a above 100 °C before underwent
the superprotonic transition at various temperatures through a small two-phase region,

depending on the composition, to the same trigonal phase, R-3m. The transition
temperature has a minimum at 46% Cs as opposed to either an increasing or a decreasing
trend with the increasing dopant and varies with the enthalpy of the superprotonic
transition. The superprotonic conductivities of the intermediate compositions increased
tremendously. At 5 – 20% Cs content, they increased ~ 40-fold.

4.9 References
[1]

B.V. Merinov, S.M. Haile, U. Bismayer, Solid State Ionics 146 (2002) (3-4) 355.

[2]
Y. Matsuo, Y. Tanaka, J. Hatori, S. Ikehata, Solid State Communications 134
(2005) (5) 361.
[3]

B.V. Merinov, A.I. Baranov, L.A. Shuvalov, Kristallografiya 35 (1990) (2) 355.

[4]
B.V. Merinov, N.B. Bolotina, A.I. Baranov, L.A. Shuvalov, Kristallografiya 33
(1988) (6) 1387.
[5]
B.V. Merinov, N.B. Bolotina, A.I. Baranov, L.A. Shuvalov, Kristallografiya 36
(1991) (5) 1131.
[6]
R. Sonntag, R. Melzer, T. Wessels, P.G. Radaelli, Acta Crystallographica Section
C-Crystal Structure Communications 53 (1997) 1529.
[7]
M. Komukae, K. Sakata, T. Osaka, Y. Makita, J. Phys. Soc. Jpn. 63 (1994) (3)
1009.
[8]
M.W. Louie, M. Kislitsyn, K. Bhattacharya, S.M. Haile, Solid State Ionics 181
(2010) (3-4) 173.
[9]
A. Ikeda, Superprotonic solid acids : thermochemistry, structure, and
conductivity, Materials Science, California Institute of Technology, Pasadena, California
(2013).
[10] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters
affecting the presence and stability of superprotonic transitions in the MHnXO4 family of
compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California
Institute of Technology, Pasadena, California (2003).
[11]

A. Pawlowski, C. Pawlaczyk, B. Hilczer, Solid State Ionics 44 (1990) (1-2) 17.

[12] L. Kirpichnikova, B. Hilczer, M. Polomska, L. Szczesniak, A. Pawlowski, Solid
State Ionics 145 (2001) (1-4) 191.
[13] A. Pawlowski, L. Szczesniak, M. Polomska, B. Hilczer, L. Kirpichnikova, Solid
State Ionics 157 (2003) (1-4) 203.
[14] A. Pawlowski, M. Polomska, B. Hilczer, L. Szczesniak, A. Pietraszko, Journal of
Power Sources 173 (2007) (2) 781.
[15]

A.I. Baranov, Crystallogr Rep+ 48 (2003) (6) 1012.

Chapter 5 Transition Behaviors of Cs6(H2SO4)3(H1.5PO4)4 and
Apparent Negative Thermal Expansion at High
Temperature
5.1 Introduction
Solid acids are chemical intermediates between oxy acids and its salts. Many solid
acids are found to undergo superprotonic phase transition at elevated temperatures (~ 100
– 300 °C) where their conductivities usually suddenly increases by 3 – 4 orders of
magnitude due to the changes of their structures from low-symmetry phases to their
respective high-symmetry phases. Most of the compounds in CsHSO4-CsH2PO4 family
exhibit the same way. Specifically, they are monoclinic, such as C2/c and P21/m, at room
temperature and transform to tetragonal I41/amd or cubic Pm-3m phases [1-9]. Even
though in this family, Cs6(H2SO4)3(H1.5PO4)4 becomes of interest due to the fact that it is
already a cubic structure with I-43d space group, but still transforms to another cubic
Pm-3m phase and exhibits the superprotonic behavior [9]. The driving force of the
transitions in CsHSO4-CsH2PO4 system was determined by Chisholm to be the entropies
of the transitions [9]. Another interesting property of Cs6(H2SO4)3(H1.5PO4)4, also
previously observed by Chisholm [9], is the negative thermal expansion in the hightemperature phase which has never been found in any other solid acid compounds before.
The objectives of this work are to explore the physical properties and to
understand the transition behavior and the origin of the negative thermal expansion
observed in Cs6(H2SO4)3(H1.5PO4)4.

5.2 Experimental Methods
5.2.1

Sample preparation
Crystals of Cs6(H2SO4)3(H1.5PO4)4 were prepared by slow evaporation of water

from an aqueous solution consisted of cesium carbonate (Cs2CO3, Alfa Aesar 99.99%),
sulfuric acid (H2SO4, EMD Chemicals 95-98%), and phosphoric acid (H3PO4, Fisher
Scientific 85%) in the stoichiometric ratio. Some large crystals (larger than ~ 2 mm × 4
mm × 5 mm) were carefully extracted from the mother liquor and rinsed quickly with a
few drops of water to remove the remaining solution on the their surfaces. Even though
rinsing with water dissolved the exterior of the crystals, it was the best way to obtain the
pure phase since using an organic solvent such as methanol or acetone would cause other
compounds to precipitate on the crystals. The rinsing water was combined with the
mother liquor to ensure that the stoichiometry of the solution remained the same. This
solution was then allowed to evaporate further until completely dried. The dry chunk of
the

product

was

ground

mortar

and

pestle

form

polycrystalline

Cs6(H2SO4)3(H1.5PO4)4.

5.2.2

Energy-dispersive X-ray spectroscopy (EDS)
The composition of the sample at room temperature was determined using Oxford

X-Max SDD X-ray Energy Dispersive Spectrometer. The powder sample was pressed
into pellets and polished so that its surface was flat and suitable for EDS measurements.
Eight EDS data were collected and the atomic percentages of cesium, sulfur, phosphorus,
and oxygen were taken.

5.2.3

59
X-ray diffraction (XRD)
Philips X’Pert Pro diffractometer with Cu Kα radiation was utilized at room and

elevated temperatures for phase identification. Diffraction data of the samples were
collected over the 2θ range from 10 to 60° with a step size of 0.0167° resulting in a total
time of 20:34 minutes for each measurement.
The XRD patterns at high temperatures were obtained in situ using a hightemperature chamber HTK1200 from Anton Paar. The powder sample was pressed using
∼ 194-MPa uniaxial pressure for 15 minutes to form 15-mm-diameter compacts before
the measurements to promote interdiffusion and phase equilibration in the solid. The
high-temperature experiments were conducted for two purposes: 1) study the transition
behaviors and determine the lattice parameters; and 2) study the effect of humidity level
on dehydration of the compound at a fixed temperature.
To study the transition behaviors and determine the lattice parameters, the
measurements were carried out both under stagnant ambient atmosphere (pH2O ∼ 0.011
atm) and under flowing humidified helium (pH2O ∼ 0.023 atm). The temperature ramp
rate was 5 °C/min and the pellet samples were hold at each temperature until reaching
equilibrium, i.e. until the diffraction patterns were stable.
To study the effect of humidity level, the sample was heated up and held at 120
°C under flowing humidified helium (pH2O ∼ 0.023 atm) until the equilibrium was
reached before the diffraction pattern was taken. The atmosphere was then changed to
flowing dry helium and the sample was allowed to reach the new equilibrium before its
diffraction pattern was collected. The atmosphere was switched between humidified and
dry helium three times and a diffraction pattern was collected each time.

5.2.4

Physical observations of a crystal sample
The crystal sample was heated up to 130 °C both under stagnant ambient

atmosphere of which pH2O measured using a humidity sensor was about 0.011 atm and
under flowing humidified nitrogen gas with pH2O ∼ 0.023 atm to study physical changes
due to the phase transition. Magnified images of the crystal were taken using an optical
microscope and the microstructures were examined using ZEISS 1550VP field emission
scanning electron microscope.

5.2.5

A.C. impedance spectroscopy (ACIS)
The impedances of the polycrystalline sample were measured using an HP 4284

precision LCR meter. The polycrystalline sample was also compacted into 9.3-mmdiameter pellets under 15 minutes of ~ 216-MPa uniaxial pressure. PELCO Colloidal
silver paste (Ted Pella, #16032) was applied onto opposing sides of the pellets to be
electrodes. The measurements of the samples were performed under two atmosphere, dry
and humidified (pH2O ∼ 0.023 atm) nitrogen, in the temperature range from 60 to 122 °C
with a ramp rate of 0.1 °C/min for both cases. Single-frequency mode, which allowed for
continuous recordings, was employed to capture the transition behavior. After full
spectrum scans (20 Hz to 1 MHz), an appropriate frequency of 2 kHz was selected. At
this frequency, the imaginary part contributed to the total impedance only at most 0.42%
for the pellet.

5.2.6

Thermal analysis: Differential scanning calorimetry (DSC) and thermal

gravimetry (TG)

61
5.25-mm-diameter pellets were prepared from the powder sample using ~ 226

MPa pressure for 5 minutes, again to facilitate the diffusion. The samples were examined
in a Netzsch STA 449 simultaneous DSC/TG system. The atmospheres were controlled
to have three levels of water partial pressure: < 0.001, 0.011, and 0.023 atm. The
temperature range was from 30 to 122 °C with a ramp rate of 1 °C/min for the study of
the transformation below 122 °C and the samples were heated up to 220 °C to study the
dehydration.

5.3 Determination of Composition, Phase Identification, and Crystal
Structure at Room Temperature
The composition of the synthesis product determined using EDS is shown in
Table 5.1 in comparison to the expected normalized atomic percentages and ratios of S:P
and Cs:(S+P) in the proposed formula, Cs6(H2SO4)3(H1.5PO4)4. The measured values and
ratios were very close to the ideal values. The XRD pattern of the sample collected at
room temperature, shown in Figure 5.1, matched very well with that presented by
Chisholm [9] and no reflections from other phases were observed. The combination of
the results from EDS and XRD confirmed that the product was a pure phase of the new
compound Cs6(H2SO4)3(H1.5PO4)4.
Table 5.1. Atomic percentages of the elements in Cs6(H2SO4)3(H1.5PO4)4 without H and
ratios of S:P and Cs:(S+P) calculated from the proposed formula and from the
determination using EDS.
Cs
S:P
Cs:(S+P)
Normalized atomic
percentage in
68.3
14.6
7.3
9.8
75.0
85.7
formula
Average atomic
71.1(11) 12.9(8)
6.8(2)
9.2(4)
74.0(32) 81.0(41)
percentage by EDS

Figure 5.1. XRD pattern of Cs6(H2SO4)3(H1.5PO4)4 synthesized in this work compared
with that of the one reported by Chisholm [9].
The diffraction data were further refined via Rietveld method using the atomic
coordinates also reported by Chisholm [9] as the initial values. At room temperature, the
material is cubic with space group I-43d and refinement yielded a0 = 14.5413(4) Å, V =
3074.7(1) Å3, and the atomic parameters listed in Table 5.2. It was also determined that
the number of formula unit per unit cell, Z, was 4. Consequently, the calculated density is
3.1919 g/cm3. The occupancy and the isotropic displacement parameters for all elements
have not been refined. The final refinement parameters are Rwp = 6.765%, RBragg =
6.679%, and GOF = 13.867.

Table 5.2. Atomic coordinates, sites, isotropic displacement parameters, and occupancies
in Cs6(H2SO4)3(H1.5PO4)4 at 25 °C in space group I-43d with a0 = 14.5413(4) Å, V =
3074.7(1) Å3, Z = 4, density = 3.1919 g/cm3, Rexp = 1.817%, Rwp = 6.765%, RBragg =
6.679%, and GOF = 13.867.
B (Å2)
Atom Site Occupancy
0.50
48e
1.0000
0.69(2)
0.84(2)
0.84(1)
0.50
Cs
24d
1.0000
0.7500
0.8483(2)
1.0000
0.50
16c
1.0000
0.7443(8)
0.7443(8)
0.7443(8)
0.50
12a
1.0000
0.7500
0.1250
1.0000
0.50
O(1)
48e
1.0000
0.696(1)
0.859(2)
0.794(1)
0.50
O(2)
48e
1.0000
0.684(1)
0.187(2)
0.020(2)
O(3)
16c
1.0000
0.706(2)
0.706(2)
0.706(2)
0.50

5.4 High-Temperature Phase Behavior and Determinations of Lattice
Parameters
A set of high-temperature X-ray diffraction experiments, illustrated in Figure 5.2
a-d, was performed to study the transition behaviors of the sample under different
humidity levels and maximum temperatures.
Firstly, as being heated up to 120 °C under flowing humidified helium, the
material underwent a phase transition upon heating between 112 and 116 °C, as can be
seen in Figure 5.2a, to a high-temperature phase that gave XRD patterns similar to those
of the high-temperature, cubic Pm-3m phases of other compounds in the CsHSO4CsH2PO4 family [8-11]. On cooling, the reverse transition occurred at a lower
temperature between 82 and 78 °C (data not shown). The reflections of the sample after
cooling measured immediately at 25 °C appeared at the same 2θ positions as those of the
original phase which indicates that the material had transformed back to its lowtemperature phase.

Figure 5.2. (See caption on next page)

Figure 5.2. XRD patterns of Cs6(H2SO4)3(H1.5PO4)4 collected at various temperatures as
shown in the figures. (a) under humidified helium with pH2O ~ 0.023 atm, (b) under dry
helium, (c) and (d) under the same atmosphere as in (a) but heated up to 140 and 180 °C,
respectively.

66
Secondly, once again another pellet was heated up to 120 °C similar to the

experiment above, but under stagnant ambient atmosphere instead. The XRD patterns in
Figure 5.2b show that, on heating, the sample transformed to the high-temperature phase,
similar to what was observed previously. On cooling, however, the sample did not
transform back to its original phase, even after cooled down to 25 °C as the pattern
collected shortly after that revealed. This pattern did not match any of the known solid
acids either. The sample looked shiny and its edge looked curved after taken out from the
high-temperature chamber as if it was partially melted and solidified. About 4 days after
the pellet sample was left at room temperature under ambient atmosphere, another XRD
pattern was collected and it showed that the material slowly transformed back to the
original phase.
Thirdly, a pellet was examined under the humidified atmosphere used above, but
this time heated up to 140 °C. As shown in Figure 5.2c, upon heating, similar patterns
were observed. The pattern of the high-temperature phase remained unchanged up to 140
°C, except small shifts of the peak positions due to thermal expansion. On cooling, the
sample showed the same behavior as the one that was measured under stagnant
atmosphere. That is the reverse transition did not occur right away, but eventually several
days later (data not shown). The physical appearance of the pellet after the measurement
was also similar to that of the one under stagnant atmosphere.
These three experiments indicated that dehydration might happen around 120 –
140 °C and higher humidity level helped prevent the dehydration to occur. Additionally,
the fact that the pellets looked as if they were partially melted supports the possibility of
dehydration since many solid acids become liquid when partially dehydrated [12-14].

67
In an attempt to obtain lattice parameters at various temperatures, Figure 5.2d

shows the XRD patterns of the material up to 180 °C under humidified helium. The
results from ab initio indexing are listed in Table 5.3. In the low-temperature phase, even
though the material is cubic, unlike many other solid acids that are monoclinic, it did
behave alike, i.e. it expanded as the temperature went up. Above the transition
temperature, on the other hand, the peaks in the diffraction patterns shifted to higher
angle, which could lead one to think of “negative thermal expansion”. The same behavior
was

also

previously

observed

Chisholm

[9]

for

this

material

and

Cs6(H2SO4)3(H1.5PO4)4 is so far the only solid acid that shows this behavior.

Table 5.3. Lattice parameter of Cs6(H2SO4)3(H1.5PO4)4 at various temperatures under
humidified helium (pH2O ∼ 0.023 atm).
Phase
Space Group
Temperature (°C)
a0 (Å)
25
14.5413(3)
Body50
14.5566(3)
I-43d
centered cubic
70
14.5657(2)
90
14.5756(2)
120
4.9902(1)
140
4.9912(2)
Primitive cubic
Pm-3m
160
4.9776(2)
180
4.9641(9)
Nevertheless, Figure 5.3 demonstrates the effect of the humidity levels on the
material and hence on the peak positions. Only the peak at about 25.3° of 2θ was shown
in the figure although the full range of the diffraction data were collected. It was found
that, as the sample was held at a fixed temperature, 120 °C, and the atmosphere was
switched back and forth between humidified (pH2O ~ 0.023 atm) and dry helium, the
peak position really changed accordingly. Specifically, under humidified gas, the
reflection appeared at a lower angle, while under dry condition, it shifted to a higher

angle. It was clear that every time the sample exposed to the same level of humidity, the
peak lined up at exactly the same position. The lattice parameter of the sample under
humidified and dry conditions were determined using ab initio indexing and listed in
Table 5.4.

Figure 5.3. XRD patterns of Cs6(H2SO4)3(H1.5PO4)4 at 120 °C under alternating
atmosphere between humidified (pH2O ~ 0.023 atm) and dry helium.
Table 5.4. Lattice parameter of Cs6(H2SO4)3(H1.5PO4)4 at 120 °C under humidified (pH2O
∼ 0.023 atm) and dry helium.
Step
a0 (Å)
Humidified 1
4.9950(6)
Dry 1
4.9729(3)
Humidified 2
4.9914(3)
Dry 2
4.9715(2)
Humidified 3
4.9909(6)
Dry 3
4.970(1)
Humidified 4
4.9918(6)

69
This finding supports the hypothesis that dehydration occurs around this

temperature range and the process is reversible, i.e. the only decomposition product
leaving the sample is water vapor and the remaining product has a smaller unit cell and
once the material reabsorbs water, it can transform back to the original phase.
Furthermore, this result suggests that the cause of the shift of the peaks to higher angles
in the XRD patterns of the high-temperature phase in Figure 5.2d is related to the
dehydration. As the water partial pressure is fixed, increasing temperature will dehydrate
the material more, making more Cs6(H2SO4)3(H1.5PO4)4 decompose to the product with a
smaller unit cell and therefore, the negative-thermal-expansion-like behavior was
observed. This also implies that the decomposition product must give a very similar
diffraction pattern and even have a very similar crystal structure. The high-temperature
phases of the compounds in CsHSO4-CsH2PO4 family such as Cs2(HSO4)(H2PO4),
Cs3(HSO4)2(H2PO4), or Cs5(HSO4)3(H2PO4)2 are promising candidates for this
decomposition product since they all have the same space group, Pm-3m, and their unit
cells are about the same size among one another, but smaller than that of
Cs6(H2SO4)3(H1.5PO4)4 at high temperatures [9-11].

5.5 Physical Observation of a Crystal Sample
In many solid acids, microcracks form when their crystals are heated up beyond
the transition temperature and cooled down. The formation of these cracks makes the
crystals turn cloudy as in the case of CsH2PO4 depicted in Figure 5.4a. Nonetheless,
Cs6(H2SO4)3(H1.5PO4)4 acts differently from those solid acids. Either heat-treated under
humidified or stagnant atmospheres, the crystal remained clear. Shown in Figure 5.4 b-d,

optical images and SEM micrographs of a crystal of this compound displayed no cracks
at all, but it can be seen in the micrographs of the crystal treated under stagnant condition,
Figure 5.4d, that the surface and edges of the crystal became rougher, suggesting a sign
of dehydration.

(a)

(b)

Figure 5.4. (See caption on next page)

Figure 5.4. (a) Optical image of CsH2PO4 before (left) and after (right) heating beyond
the superprotonic transition [15]. (b)-(d) Optical images (top) and SEM micrographs
(middle = 1000×, bottom = 2000×) of Cs6(H2SO4)3(H1.5PO4)4: (b) before heat treatment,
(c) after heating under humidified (pH2O ~ 0.023 atm) nitrogen, and (d) after heating
under ambient atmosphere (pH2O ~ 0.011 atm).

5.6 Conductivity Measurements
The conductivities of Cs6(H2SO4)3(H1.5PO4)4 measured in the single-frequency
mode under humidified and dry nitrogen are shown in Figure 5.5. Like many other solid

acids, Cs6(H2SO4)3(H1.5PO4)4 showed the superprotonic behavior. A sharp increase in
conductivity arise in each case at about the same temperature, ~ 97 °C, where the
conductivity dramatically increased by 3-4 orders of magnitude, from 8.76 × 10-7 to 1.68
× 10-3 S/cm for the humidified case and from 7.05 × 10-7 to 1.84 × 10-3 S/cm for the dry.
Although the transition temperatures on heating in both cases were at a lower temperature
compared to that observed in the HT-XRD experiments, the reverse transitions were
consistent. Under the humidified condition, the reverse transition occurred at ~ 78 °C and
finished at a temperature slightly below 70 °C, while the conductivity of the sample
under the dry atmosphere remained high until 60 °C where the temperature cycle ended
and decreased very slowly down to its initial value in a period of 2-3 days.

Figure 5.5. Conductivity of Cs6(H2SO4)3(H1.5PO4)4 measured at 2 kHz under humidified
(pH2O ~ 0.023 atm) and dry nitrogen at a ramp rate of 0.1 °C/min.

5.7 Determination of Heat of Transition and Study of Dehydration
Figure 5.6 illustrates the DSC profiles of the material under the three humidity
levels listed in the legend, heated up to 122 °C. Upon heating, an endothermic peak was
detected in all cases at an onset temperature of about 113.5 °C. The enthalpies of
transitions associating with these peaks, listed in Table 5.5, were around 110 kJ per mole
Cs6(H2SO4)3(H1.5PO4)4 or 17 kJ per mole of CsHXO4 unit where 6.43 units were assigned
to Cs6(H2SO4)3(H1.5PO4)4 based on the formula weight. On cooling, only the sample in
the higher humidity transformed back to its low-temperature phase as indicated by an
exothermic peak at ~ 74 °C. The corresponding enthalpy was however lower than that of
the endothermic peak, suggesting that a part of the sample did not undergo the reverse
transition. The DSC signal from the experiment under the lower humidity was broad and
spread over a wide temperature range, 70 – 30 °C, while the signal was almost undetected
for the sample under the dry condition, indicating that the samples did not change back at
all. The outcomes were also consistent with those from conductivity and hightemperature XRD measurements.

Table 5.5. Onset temperatures, enthalpies, and entropies of transitions of the samples
heated up to 122 °C under three different humidity levels.
pH2O
Tsp-onset
ΔH
ΔS
ΔH*
ΔS*
Step
(atm)
(°C)
(kJ/mol)
(J/mol·K)
(kJ/mol)
(J/mol·K)
0.023
113.3
107.5
278.2
16.72
43.28
Heating
0.011
113.8
110.7
286.2
17.22
44.53
< 0.001
114.1
106.7
275.6
16.60
42.88
0.023
74.1
73.9
213.0
11.50
33.14
Cooling
0.011
68.0
34.0
99.7
5.29
15.51
< 0.001
69.9
22.3
65.0
3.47
10.12
* Values per CsHXO4 unit. Cs6(H2SO4)3(H1.5PO4)4 has 6.43 units based on the formula weight.

Figure 5.6. DSC profiles of Cs6(H2SO4)3(H1.5PO4)4 measured under three different
humidity listed in the legend up to 122 °C at a ramp rate of 1 °C/min.
Another set of DSC/TG measurements was conducted to study the dehydration of
the material. The DSC profiles in Figure 5.7 agreed well with the findings from other
experiments. The endothermic peaks emerged at the same temperature as in the previous
experiments. Since all three samples were intended to be dehydrated, there were no
exothermic peaks observed on cooling as expected. The TG profiles showed that the
dehydration temperature increased as the humidity increased. In other words, the water
vapor helped prevent the dehydration of the material. The data also confirmed that at a
fixed water partial pressure, the sample dehydrated more as the temperature raised.

Figure 5.7. DSC and TG profiles of Cs6(H2SO4)3(H1.5PO4)4 heated up to 220 °C under
three different humidity listed in the legend at a ramp rate of 1 °C/min.

5.8 Discussion: Mechanism of Transition and Origin of the Apparent
Negative Thermal Expansion in Cs6(H2SO4)3(H1.5PO4)4
As discussed above, the origin of the apparent negative thermal expansion relates
to the dehydration. However, this dehydration might not be the dehydration of the solid
acid. This is because partially dehydrated solid acids are usually liquid [12-14] which will
not give reflections in an X-ray diffraction pattern. Thus, the fact that the peaks did show
up in the diffraction pattern and are very likely to be from a solid acid indicates that the
dehydration must occur in another phase that is not crystalline, while the solid acid
remained a crystalline solid. This definitely implies that a phase separation is involved,
similar to what found in Rb3H(SO4)2 in which case the phase separation products are
Rb2SO4 and the high-temperature phase of Rb5H3(SO4)4 before the latter is dehydrated

and becomes a liquid at a higher temperature, while Rb2SO4 remained solid [12, 16],
except what is happening in the current study is the opposite. The plausible candidates for
the solid acid phase, as mentioned above, are likely to be in the CsHSO4-CsH2PO4 family
because of the lattice constant and space group, while the other phase could be H3PO4 for
the following reasons: 1) the stoichiometry of Cs6(H2SO4)3(H1.5PO4)4 suggests that there
is an extra oxy-anion group which could relatively easily separate to form the acid, 2)
H3PO4 can be dehydrated in the temperature of interest of this work to form fractions of
its dehydrated compounds such as pyrophosphate and triphosphate [17], and 3) H3PO4
and its dehydrated products are all liquid in this temperature range. Hence, the proposed
reactions involved in the temperature range above 100 °C are as follows:

Cs6(H2SO4)3(H1.5PO4)4 (s, LT)  Cs6(H2SO4)3(H1.5PO4)4 (s, HT)

(1)

Cs6(H2SO4)3(H1.5PO4)4 (s)  Cs6(H2-0.5xSO4)3(H1.5PO4)4-x (s, HT) + x H3PO4 (l) (2)
2 H3PO4 (l)  H4P2O7 (l) + H2O (g)

(3)

To explain the proposed reactions in words, the low-temperature (LT) phase of
Cs6(H2SO4)3(H1.5PO4)4 undergoes superprotonic transition to its high-temperature (HT)
phase at a temperature between 110 – 120 °C as described in Reaction (1). Then,
Reactions (2) and (3) occur along with the superprotonic transition under low humidity or
they can occur at a higher temperature under higher humidity. In Reaction (2), the
proposed formula for the partially decomposed product of Cs6(H2SO4)3(H1.5PO4)4 is
Cs6(H2-0.5xSO4)3(H1.5PO4)4-x where x = 0-1 indicating the degree of decomposition and
this product has a smaller unit cell. As Reaction (3) proceeds to the right, Reaction (2) is

also driven to the right. In other words, the more dehydration occurs, the more
decomposed product Cs6(H2-0.5xSO4)3(H1.5PO4)4-x is formed and the smaller lattice
parameter observed which explains the apparent negative thermal expansion behavior. It
also should be noted that at x = 1 the solid acid emerged in Reaction (2) could be any of
the solid acids in the CsHSO4-CsH2PO4 family. Cs2(HSO4)(H2PO4) is, however, more
likely than the others because it fits the stoichiometry proposed in Reaction (2) perfectly
and its superprotonic transition temperature is below 100 °C, so it is already in its hightemperature cubic phase when the decomposition occurs. Cs5(HSO4)3(H2PO4)2 is another
plausible candidate for similar reasons.

5.9 Conclusions
A new solid acid, Cs6(H2SO4)3(H1.5PO4)4, was synthesized and confirmed the
composition. At room temperature, it is a body-centered cubic in I-43d space group with
a0 = 14.5413(4) Å, V = 3074.7(1) Å3, Z = 4, and density = 3.1919 g/cm3.
According to the combination of the findings from the three techniques above, it
can be concluded that Cs6(H2SO4)3(H1.5PO4)4 transforms from its low-temperature, lowconductivity phase to its high-temperature, high-conductivity phase at a temperature
between 110 – 120 °C with a heat of transition of ~ 17 kJ per mole of CsHXO4 unit and
the dehydration process also starts about the same temperature. The dehydration observed
in this work is not that of the solid acid itself as found in other cases, but is of one of the
phase

separation

products,

H3PO4,

while

the

other,

proposed

Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, remains solid. The humidity in the gas phase controls the
degree of the dehydration, which is the cause of the apparent negative thermal expansion.

The dehydrated products eventually reabsorbs water and recombines to form
Cs6(H2SO4)3(H1.5PO4)4 under the ambient condition over the course of a few days.

5.10 References
[1]

C.R.I. Chisholm, S.M. Haile, Acta Crystallogr B 55 (1999) 937.

[2]

C.R.I. Chisholm, S.M. Haile, Mater Res Bull 35 (2000) (7) 999.

[3]

S.M. Haile, P.M. Calkins, J Solid State Chem 140 (1998) (2) 251.

[4]

S.M. Haile, P.M. Calkins, D. Boysen, J Solid State Chem 139 (1998) (2) 373.

[5]

S.M. Haile, K.D. Kreuer, J. Maier, Acta Crystallogr B 51 (1995) 680.

[6]
Z. Jirak, M. Dlouha, S. Vratislav, A.M. Balagurov, A.I. Beskrovnyi, V.I. Gordelii,
I.D. Datt, L.A. Shuvalov, Phys Status Solidi A 100 (1987) (2) K117.
[7]

H. Matsunaga, K. Itoh, E. Nakamura, J. Phys. Soc. Jpn. 48 (1980) (6) 2011.

[8]

A. Preisinger, K. Mereiter, W. Bronowska, Mater Sci Forum 166 (1994) 511.

[9]
C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters
affecting the presence and stability of superprotonic transitions in the MHnXO4 family of
compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California
Institute of Technology, Pasadena, California (2003).
[10] S. Takeya, S. Hayashi, H. Fujihisa, K. Honda, Solid State Ionics 177 (2006) (1516) 1275.
[11]

C.R.I. Chisholm, S.M. Haile, Solid State Ionics 136 (2000) 229.

[12] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State
Ionics 179 (2008) (9-10) 305.
[13]

A. Ikeda, S.M. Haile, Solid State Ionics 213 (2012) 63.

[14]

Y. Taninouchi, T. Uda, Y. Awakura, Solid State Ionics 178 (2008) (31-32) 1648.

[15] M.W. Louie, Electrocatalysis in solid acid fuel cells, Chemical Engineering,
California Institute of Technology, Pasadena, California (2011).
[16]

C. Panithipongwut, S.M. Haile, Solid State Ionics 213 (2012) 53.

[17]

C.E. Higgins, W.H. Baldwin, Anal Chem 27 (1955) (11) 1780.

Appendix A Phase Behavior of (CsxRb1-x)3H(SO4)2 Solid
Solution System
A.1 Introduction
In spite of the fact that many solid acids in the family M3H(XO4)2, where M = Cs,
Rb, K, NH4; and X = S, Se, such as Cs3H(SeO4)2, Rb3H(SeO4)2, Rb3H(SO4)2, exist and
stable at room temperature, Cs3H(SO4)2 does not. Even though there are some groups that
claimed they had synthesized Cs3H(SO4)2, they had never showed any proof that they
actually had got the correct compound. Additionally, although Rb3H(SO4)2 exists at room
temperature, it disproportionates at a high temperature and does not show its own
superprotonic phase [1, 2]. This study of (CsxRb1-x)3H(SO4)2 is an attempt to stabilize
both Cs3H(SO4)2 at room temperature and Rb3H(SO4)2 at an elevated temperature.

A.2 Synthesis and Characterizations
A.2.1 Synthesis
The solid solutions were prepared from aqueous solutions of rubidium sulfate
(Rb2SO4, Alfa Aesar 99%), cesium sulfate (Cs2SO4, Alfa Aesar 99.99%), and sulfuric
acid (H2SO4, EMD Chemicals 95-98%) with different ratios. The solutions were poured
into methanol to induce precipitation of the solid solutions. The products were then
filtered, rinsed with methanol, and dried in a drying oven at ∼ 100 °C overnight prior to
further characterizations.

A.2.2 Characterizations using XRD, ACIS, and DSC/TG
All of the measurement parameters and settings were the same as those used in
Chapter 3 for Rb3H(SO4)2-RbHSO4 system except the temperatures of the measurement
were adjusted accordingly as shown in the following figures.

A.3 Results
The solubility limit was determined by XRD measurements at room temperature
as shown in Figure A.1. It can be seen that additional peaks showed up in the patterns of
above 20% Cs, so Cs ions can dissolve into the rubidium structure up to about 20% mole
Cs and this composition was selected to represent the solid solution system in further
characterizations.

Figure A.1. XRD patterns of (CsxRb1-x)3H(SO4)2, x = 0, 0.1, 0.2, 0.25, and 0.3 at room
temperature.

Figure A.2. XRD patterns of Cs0.6Rb2.4H(SO4)2 at high temperature under humidified He
(pH2O ~ 0.23 atm).

Figure A.3. XRD pattern of Cs0.6Rb2.4H(SO4)2 at 220 °C under humidified He (pH2O ~
0.23 atm) compared with high-temperature patterns of Rb3H(SO4)2, Rb5H3(SO4)4, and
Rb2SO4 at the temperatures as indicated in the figure.

82
Upon heating to 220 °C, the low-temperature phase of the 20%-Cs composition

was stable up to at least 170 °C before a reaction occurred between 170 and 200 °C as
illustrated in Figure A.2. The resulting XRD pattern of this reaction was compared to
those of Rb3H(SO4)2 and Rb5H3(SO4)4 at 236 °C, Figure A.3, and found that the pattern
was consisted of those of Rb5H3(SO4)4 and Rb2SO4, similar to what was found in the
pattern of Rb3H(SO4)2. Therefore, this reaction of the solid solution is also a
disproportionation similar to that of Rb3H(SO4)2, but takes place at a lower temperature.
The solid solution also displayed superprotonic behavior as can be seen in Figure
A.4. The conductivity rose quickly at ~ 186 °C for about 4 orders of magnitude and on
cooling, started dropping sharply at 167 °C. Similar to Rb3H(SO4)2, the apparent
superprotonic behavior is expected to be from a high-temperature phase of the solid
solution of Rb5H3(SO4)4.

Figure A.4. Conductivity plots of Cs0.6Rb2.4H(SO4)2 upon heating (solid lines) and
cooling (dotted lines) under humidified nitrogen (pH2O ~ 0.023 atm) at a ramp rate of 0.5
°C/min up to 210 °C.

83
The DSC profiles, Figure A.5, revealed that there were two endothermic

processes upon heating to 220 °C at 165 and 180 °C. The former is still unidentified, the
latter is assigned to the disproportionation observed in the HT-XRD since it falls into the
temperature range and is close to the transition temperature in the conductivity
measurement. The enthalpy associating with this disproportionation is 15.1 kJ/mol, close
to 17.8 kJ/mol of disproportionation of Rb3H(SO4)2 [1].

Figure A.5. DSC profiles of Cs0.6Rb2.4H(SO4)2 under humidified nitrogen (pH2O ~ 0.023
atm) at a ramp rate of 2 °C/min up to 220 °C.
Figure A.6 shows that the solid solution started dehydrating at a temperature as
low as 230 °C. It is inconclusive whether the dehydration stops after 0.9% weight loss or
it could continue if the sample is heated up to a higher temperature or kept at 300 °C for
longer time.

Figure A.6. DSC/TG profile of Cs0.6Rb2.4H(SO4)2 under humidified nitrogen (pH2O ~
0.023 atm) at a ramp rate of 1 °C/min up to 300 °C.

A.4 Conclusions
The solubility limit of Cs ions into Rb3H(SO4)2 structure at room temperature is
just about 20% mole Cs and not more than 25%; thus, Cs3H(SO4)2 cannot be stabilized.
At a temperature about 180 °C, the 20%-Cs solid solution disproportionates similar to
Rb3H(SO4)2, but a lower temperature and does not undergo a polymorphic transition
either. The apparent superprotonic behavior is expected to be from another phase similar
to Rb5H3(SO4)4.

A.5 References
[1]
L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State
Ionics 179 (2008) (9-10) 305.
[2]

C. Panithipongwut, S.M. Haile, Solid State Ionics 213 (2012) 53.

Appendix B Electrospray for Complex Solid Acid Syntheses
* This work was a part of the SURF program in summer 2012. Most of the lab work in this appendix was
performed by Jeffrey Kowalski under the supervision of Chatr Panithipongwut and Rob Usiskin.

B.1 Introduction
Solid acids have been prepared via conventional methods such as precipitation,
crystallization, and hydrothermal synthesis methods. Many of the solid acids were
relatively easy to prepare, either from precipitation or crystallization. Some require
slightly different ways to get around some specific issues, for example, the
decomposition of selenic acid used in syntheses of selenate compounds. The others are
more difficult to make, especially the ones that are more complex like the compounds in
the

CsHSO4-CsH2PO4

family:

Cs2(HSO4)(H2PO4),

Cs5(HSO4)3(H2PO4)2,

Cs6(H2SO4)3(H1.5PO4)4. These complex solid acids are obviously composed of many ions
that are the same as ions in smaller compounds, which make them hard to be reproduced
as a pure phase since the simpler solid acids can co-precipitate easily. Specific ways to
reproduce these compounds were reported [1], yet reproducibility is still an issue. The
cause of this issue is conjectured to be from concentration gradients of these ions
occurring from different mobility in solutions. As the crystallization or the precipitation
proceeds, the local concentration of each ion is no longer the same as the stoichiometric
concentration. A promising idea to avoid the concentration gradients is to produce small
drops of the solutions and quickly force the droplets to precipitate by fast evaporation.
Electrospray has been utilized in fabrication of various types of materials
including solid acids. CsH2PO4 was the first solid acid successfully electrosprayed [2]

although with a different purpose, to fabricate an intricate nanostructure. This technique
meets the proposed resolution above, both producing small droplets and fast evaporation,
so it is expected that the correct composition of the complex solid acids can be obtained
using electrospray. Varga et al. [2], however, precipitated CsH2PO4 out and confirmed
the compound before dissolving it again into a solution. In the case of this study, again
the conventional methods do not give the desired products, so one of the objectives here
is to confirm that solid acids can be obtained directly from solutions of the reactants.

B.2 Sample Preparation and Electrospray
B.2.1 Sample preparation
Water-methanol solutions containing specific ratios of cesium carbonate (Cs2CO3,
Alfa Aesar 99.99%), cesium sulfate (Cs2SO4, Alfa Aesar 99.99%), sulfuric acid (H2SO4,
EMD Chemicals 95-98%), and phosphoric acid (H3PO4, Fisher Scientific 85%) were
prepared in volumetric flasks to obtain accurate concentrations. The solutions were
prepared fresh or kept in polyethylene bottles with a Parafilm seal for only a short period
of time before electrospray. The ratios of these reactants and the desired products are
listed in Table B.1.

B.2.2 Electrospray
Electrosprays of the sample solutions were performed using an in-house
electrospray chamber constructed by Rob Usiskin. The schematic components of the
chamber are shown in Figure B.1. Depending on the solutions, the voltages used were in
the range from 6.8 to 8.3 kV; solution flow rate from 0.030 to 0.075 ml/h; gas, stage, and

wall temperatures from 20 to 100 °C; and deposition time from 2 hours to 7 hours. Most
of the depositions were done on B-doped Si wafer substrate except one on carbon paper
and one on Inconel (Ni-Cr alloys).

Table B.1. Concentrations of desired products and methanol and Cs:P:S mole ratio in
solutions used in electrospray experiments.
Desired Product
CsH2PO4
CsH2PO4
CsH2PO4
CsHSO4
CsHSO4
Cs2(HSO4)(H2PO4)

% Product % MeOH
10
3.959
14
20
10
7.92
15
7.92
15

Cs3(HSO4)2(H2PO4)
Cs3(HSO4)2(H2PO4)
Cs5(HSO4)3(H2PO4)2

15
15
15

Cs6(H2SO4)3(H1.5PO4)4
Cs6(H2SO4)3(H1.5PO4)4
Cs6(H2SO4)3(H1.5PO4)4

15
15

Cs:P:S
1:1:0
1:1:0
1:1:0
1:0:1
1:0:1
2:1:1

Formation Equation
Cs2CO3 + 2 H3PO4 
2 CsH2PO4 + H2O + CO2
Cs2SO4 + H2SO4 2 CsHSO4

Cs2CO3 + H3PO4 + H2SO4
Cs2(HSO4)(H2PO4) + H2O + CO2
3:1:2
3 Cs2CO3 + 2 H3PO4 + 4 H2SO4
2 Cs3(HSO4)2(H2PO4) + 3 H2O + 3 CO2
10:3:7
29:17:15 5 Cs2CO3 + 4 H3PO4 + 6 H2SO4
2 Cs5(HSO4)3(H2PO4)2 + 5 H2O + 5 CO2
6:4:3
3 Cs2CO3 + 4 H3PO4 + 3 H2SO4
Cs6(H2SO4)3(H1.5PO4)4 + 3 H2O + 3 CO2
6:4:3
20:11:9

Figure B.1. Schematic of the electrospray chamber components and parameters. Courtesy
of Rob Usiskin.

B.3 Results
A SEM micrograph of an electrosprayed CsH2PO4 sample, shown in Figure B.2,
demonstrate a general resulting deposition of the solid acids studied. In general, there are
islets, crystallites, crystals, and large smooth areas. The size of the crystals can be
anywhere from 20 to 500 micrometers. The shape of the particles also vary, from a
sphere to a needle to a platelet.

Figure B.2. SEM micrograph of an electrosprayed CsH2PO4 sample.
Figure B.3 a to d show XRD patterns of selected samples with those of the
references. The pattern of CsH2PO4, Figure B.3a, demonstrates that the sample was
deposited with a preferred orientation. The two highest peaks were from (200) and (400),
respectively. This behavior was also observed in other samples of CsH2PO4 and CsHSO4
(data not shown).

89
(a)

(b)

(c)

Figure B.3. (See caption on next page)

90
(d)

Figure B.3. XRD patterns of electrosprayed samples compared to those of known solid
acids. The desired products were (a) CsH2PO4, (b) Cs3(HSO4)2(H2PO4), (c)
Cs6(H2SO4)3(H1.5PO4)4, and (d) Cs2(HSO4)(H2PO4).
The

XRD

patterns

Cs3(HSO4)2(H2PO4),

Cs6(H2SO4)3(H1.5PO4)4,

and

Cs2(HSO4)(H2PO4) in Figure B.3 b-d are somewhat complicated and cannot be identified
instantly due to the combination of the already-complicated patterns of the monoclinic
solid acids and the orientation effect. By visual comparisons and Rietveld refinements,
these patterns can be identified to multiple phases listed in Table B.2. Note that while
Cs3(HSO4)2(H2PO4) and Cs6(H2SO4)3(H1.5PO4)4 formed along with other solid acids from
their respective solutions, the deposition of Cs2(HSO4)(H2PO4) solution resulted in
Cs5(HSO4)3(H2PO4)2 and CsH2PO4 without Cs2(HSO4)(H2PO4) formed at all.
Backscattered electron (BSE) micrographs and EDS mapping of the selected
samples, Figure B.4 and B.5, were taken to find the distributions of the phases in each
sample. The BSE results of Cs6(H2SO4)3(H1.5PO4)4 and Cs2(HSO4)(H2PO4), shown in
Figure B.4 a and b, revealed that there were three and two phases in the samples,
respectively. The brightness of each region in BSE micrographs and the intensities in
EDS maps can be used to identify which region is which phase.

Table B.2. Desired and identified products from electrospray determined using XRD.
Desired product
Identified phases
Cs3(HSO4)2(H2PO4)
Cs3(HSO4)2(H2PO4) + CsHSO4
Cs6(H2SO4)3(H1.5PO4)4
Cs6(H2SO4)3(H1.5PO4)4 + Cs3(HSO4)2(H2PO4) + CsHSO4
Cs2(HSO4)(H2PO4)
Cs5(HSO4)3(H2PO4)2 + CsH2PO4
(a)

(b)

Figure B.4. BSE micrograph of (a) Cs6(H2SO4)3(H1.5PO4)4 and (b) Cs2(HSO4)(H2PO4).

Figure B.5. EDS maps of Cs2(HSO4)(H2PO4). Different colors and intensities show
distributions of different elements: Cs, S, and P.
In BSE technique, lighter elements backscatter electrons less than heavier
elements and therefore show darker area in micrographs. In Figure B.4a, since S is
heavier than P, the region becomes darker with P content in the compound. Thus, the
brightest region corresponds to CsHSO4, the medium grey is Cs3(HSO4)2(H2PO4), and the
darkest is Cs6(H2SO4)3(H1.5PO4)4. For the product of Cs2(HSO4)(H2PO4) solution, the
combination of BSE micrograph (Figure B.4b) and EDS maps (Figure B.5) help identify
the two phases: the bright region is Cs5(HSO4)3(H2PO4)2 and the dark region is CsH2PO4.

B.4 Discussions, Conclusions and Suggestions
Using electrospray to synthesize simple solid acids directly from water-methanol
solutions such as CsHSO4 and CsH2PO4 is proven to be successful without having to
obtain the respective compounds by conventional methods first. Nonetheless, the more
complex solid acids which this work attempted to synthesize, Cs2(HSO4)(H2PO4),
Cs3(HSO4)2(H2PO4), Cs5(HSO4)3(H2PO4)2, and Cs6(H2SO4)3(H1.5PO4)4, were not
successfully achieved as a pure phase and the phases were also intertwined in each
sample, so these phase could not be separated either. The possible causes of this are
accumulation of the droplets and difference in migrations of ions under the provided bias.
It was observed for some sprays that droplets accumulated on the substrate and
formed a larger drop with a maximum size of about 2 mm, which is large enough for
diffusions of ions to occur. To avoid this, the parameters that could be adjusted are
temperatures – to make sure that solvents evaporate quickly before droplets approach the
substrate – and methanol content – which will lower surface tension of droplets, lower
the boiling point of solutions and thus facilitate evaporation of solvents.
Another possible cause is the migration of ions under bias. Ions of different sizes
and charges migrate under an electric field with different mobility and this can cause
concentration gradients. The migration can occur in the capillary of the electrospray
apparatus and when droplets leave the tip of the capillary, the stoichiometry in the
droplets differs from the original solution. Since there are several ions involved in
formation of these complex solid acids, once the stoichiometry changes, another,
undesired solid acid could form easily.

94
In summary, it is not impossible to synthesize complex solid acids, but definitely

there are many parameters that need to be taken into account. More detailed studies of
each parameter are required to understand its effect on the synthesis of the complex solid
acids.

B.5 References
[1]
C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters
affecting the presence and stability of superprotonic transitions in the MHnXO4 family of
compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California
Institute of Technology, Pasadena, California (2003).
[2]
A. Varga, N.A. Brunelli, M.W. Louie, K.P. Giapis, S.M. Haile, J. Mater. Chem.
20 (2010) (30) 6309.