Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of c

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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)
Thesis by
Calum Ronald Inneas Chisholm
In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
California Institute of Technology
Pasadena, California
2003
(Defended December 13th, 2002)
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 2003
Calum Ronald Inneas Chisholm
All Rights Reserved
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Acknowledgements
I must first say that I have had a truly wonderful time here at Caltech. I can only
hope that the carefree lifestyle and true intellectual forum Caltech offers to its graduate
students remain available to future generations. I count myself doubly blessed to have
been accepted at this most distinguished institution.
I owe, of course, the greater part of my success and happiness at Caltech to my
professor and mentor, Sossina Haile, without whose care and guidance I might never
have discovered my love of research. I feel my critical thinking and ability to express
ideas has been incalculably increased by our interactions. It has truly been a pleasure and
honor to have worked with Professor Haile, and I am overjoyed to have the opportunity
to collaborate with her for post-doctoral research.
Needless to say (but I certainly must), I thank my mother, who, after all, typed up
my graduate applications and kept me from sending them in late. She has been a constant
source of comfort and encouragement. Thanks, Momma. To my father, I am ever grateful
to him for being my hero and role model, not just in the sciences, but in all of life’s
pursuits. His love for his work and his words of wisdom regarding a career in science
convinced me long ago that my life would be fuller following the path I now tread.
Cheers, Dad.
This work would not be possible without the efforts of other co-researchers. First
and foremost, Dane Boysen, without whose efforts, assistance, and collaboration I might
never have stepped into the lab, much less have arrived at the conclusions of this study. I
must also single out Ryan Merle, who helped me immensely by doing all the “dirty
work” and who has been a constant sounding board for new ideas. For the simulations
work, I owe a huge debt of gratitude to Yun Hee Jang. Without her ever thoughtful
assistance I could not have begun or finished that study.
There are a whole host of others that I have to thank for their time and effort,
including: Sonjong Hwang, Dr. Ma Chi, Dr. Chuck Strouse, Lisa Cowen, Liz Miura,
Prof. Rossman, Prof. Goddard, Lan Yang, Prof. Grubbs, and Prof. Fultz. To Dr. Chuck
Witham, who was my first friend at work and always helped me both on and off campus,
I wish you were here laughing at my defense, buddy. I must also thank my friends all
over the states that have always supported me in my endeavors.
Financial support was provided by The National Science Foundation and various
Caltech fellowships, making my life very easy here.
And finally, I must thank Erica, with whom I have shared this entire experience.
You make me a better person who looks to the future while still enjoying the present.
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Abstract
The present work attempted to uncover the structural and chemical parameters
that favor superprotonic phase transitions over melting or decomposition in the MHXO4,
MH2ZO4, and mixed MHXO4-MH2ZO4 classes of compounds (X=S, Se; Z=P, As; M=Li,
Na, K, NH4, Rb, Cs) and to thereby gain some ability to “engineer” the properties of solid
acids for applications. Three approaches are described. First, the general observation that
larger cations enable superprotonic transitions was investigated in both the isostructural
M2(HSO4)(H2PO4) and non-isostructural MHSO4 family of compounds. The results of
these studies confirmed and explained such a cation size effect, and also supplied a
crystal-chemical measure for determining the likelihood of a compound undergoing a
phase transition. Second, the entropic driving force behind the transitions was explored in
the mixed CsHSO4-CsH2PO4 system of compounds. From these investigations, a general
set of rules for calculating the entropy change of a superprotonic transition was
established and the role of entropy in the transitions illuminated. Finally, the
superprotonic phase transition of CsHSO4 was simulated by molecular dynamics, with
which means the transition was probed in ways not possible through experimental
methods. A sufficiently general approach was utilized so as to be applicable to other (as
yet un-synthesized) compounds, thereby speeding up the process of discovering novel
superprotonic solid acids. All three approaches increase the fundamental understanding
of which chemical/structural features facilitate superprotonic transitions and should aid
attempts to create new solid acids with properties ideal for application.
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Contents
Acknowledgements
iii
Abstract
iv
1 Introduction
1
1.1 Overview ………………………………………………………………….. 1
1.2 Ionic Conductivity ………………………………………………………… 3
1.3 Structural Features of Solid Acids ………………………………………...
14
1.3.1 Characterization of hydrogen bonds ……………………………….
14
1.3.2 Hydrogen-bonded networks in solid acids ………………………… 18
1.3.3 Common structures found in the low temperature phases of
solid acids …………………………………………………………. 20
1.4 Protonic Conduction ……………………………………………………… 22
1.4.1 Mechanisms of proton transport …………………………………... 22
1.4.2 Room temperature proton conduction in solid acids ……………… 28
1.4.3 High temperature proton conduction in solid acids ……………….
32
2 Experimental Methods
36
2.1 Synthesis ………………………………………………………………….. 36
2.2 X-Ray Diffraction ………………………………………………………… 37
2.3 Neutron Diffraction ………………………………………………………. 38
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2.4 Thermal Analysis …………………………………………………………… 39
2.5 Chemical Analysis ………………………………………………………….. 40
2.6 Optical Spectroscopy / Microscopy ………………………………………… 41
2.7 NMR Spectroscopy …………………………………………………………. 42
2.8 Impedance Spectroscopy …………………………………………………...
43
2.8.1 Complex impedance ………………………………………………...
44
3 Cation Size Effect on the Superprotonic Transitions of MHnXO4
Compounds (M = Cs, Rb, NH4; X = S, Se, P, As; n = 1-2)
50
3.1 Introduction ………………………………………………………………...
50
3.2 Mixed Cation Sulfate Systems……………………………………………… 52
3.2.1 Synthesis and characterization techniques ………………………….
55
3.2.2 Resulting phases of the mixed system investigations ………………. 56
3.2.3 Conclusions from mixed system investigations …………………….
64
3.3 M2(HSO4)(H2PO4) Compounds …………………………………………….. 70
3.3.1 Structures of the M2(HSO4)(H2PO4) compounds …………………… 71
3.3.2 Synthesis of the M2(HSO4)(H2PO4) compounds ……………………. 74
3.3.3 Characterization of the M2(HSO4)(H2PO4) compounds …………….. 75
3.3.4 What exactly is the effect of the cation size? ……………………….. 82
3.3.5 Conclusions and interpretations of the cation/anion effect ………….. 88
4 Mixed Cesium Sulfate-Phosphates: Driving Force for the
Superprotonic Transitions of MHnXO4 compounds (M = Cs, Rb,
NH4; X = S, Se, P, As)
95
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4.1 Introduction .................................................................................................... 95
4.2 Characterization of Mixed Cesium Sulphate-Phosphates ………………….
96
4.2.1 Synthesis of the compounds ………………………………………… 97
4.2.2 Structural features of room temperature phases …………………….
98
4.2.3 Structural features of high temperature phases ……………………… 104
4.2.4 Key features of the superprotonic phase transitions ………………… 107
4.3 Introductory Comments on Entropy Rules …………………………………. 117
4.4 Entropy Rule for Room Temperature Structures …………………………… 118
4.4.1 Entropy of CsHSO4 and Cs6(H2SO4)3(H1.5PO4)4 ⇒ZERO! ……….. 120
4.4.2 Entropy evaluation for CsH2PO4 −the disordered hydrogen bond …. 121
4.4.3 Entropy of Cs3(HSO4)2.50(H2PO4)0.50 and Cs3(HSO4)2.25(H2PO4)0.75 −
partially occupied hydrogen bonds …………………………………..
125
4.4.4 Room temperature entropy of Cs3(HSO4)2(H2PO4) ……………….... 129
4.4.5 Room temperature entropy of Cs5(HSO4)3(H2PO4)2 ………………..
130
4.4.6 Room temperature entropy of Cs2(HSO4)(H2PO4) …………………. 135
4.4.7 Summary of entropy evaluations for the room temperature phases … 137
4.5 Entropy Rules for the High Temperature Phases …………………………..
138
4.5.1 Plakida’s theory of the superprotonic phase transition in CsHSO4 ….. 138
4.5.2 Ice rules type model for superprotonic transitions ……………......... 140
4.6 Calculated Transition Entropies for the CsHSO4-CsH2PO4 System of
Compounds ……………………………………………………………….
145
4.6.1 Entropy calculations for CsHSO4 …………………………………… 146
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4.6.2 Entropy calculations for CsH2PO4 ………………………………….
148
4.6.3 Entropy calculations for pure cubic phases ......................................... 150
4.6.4 Entropy calculations for mixed tetragonal/cubic compounds ………. 151
4.6.5 Entropy calculations for Cs6(H2SO4)3(H1.5PO4)4 ……………………. 155
4.6.6 Summary of entropy calculations for high temperature phases……... 158
4.6.7 ∆Strans and comparison with experimental ∆Strans …………………... 159
4.6.8 Application of the adjusted ice rules to other superprotonic transitions 163
5 Superprotonic Phase Transition of CsHSO4 : A Molecular Dynamics
Simulation Study with New MSXX Force Field
170
5.1 Introduction ………………………………………………………………… 170
5.2 Characterization of CsHSO4 ……………………………………………….
171
5.2.1 Crystal structures of CsHSO4 ……………………………………….
171
5.2.2 Nature of the superprotonic transition of CsHSO4 ………………… 175
5.3 MD simulation of superprotonic transition of CsHSO4 …………………… 176
5.3.1 Overview ……………………………………………………………. 176
5.3.2 Calculation details: Force fields …………………………………….
176
5.3.3 Calculation details: Simulations …………………………………….
184
5.4 Results ……………………………………………………………………… 185
5.4.1 Phase II at room temperature: Calculation vs. experiment …………. 185
5.4.2 Phase transition: Cell parameters …………………………………… 189
5.4.3 Phase transition: Volume and energy change across Tsp ……………. 193
5.4.4 Phase transition: X-ray diffraction ………………………………….. 196
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5.4.5 Vibrational spectrum of Phase I CsHSO4 …………………………… 197
5.4.6 Orientation of the HSO4 groups …………………………………….. 199
5.4.7 Reorientation of the HSO4 groups …………………………………... 204
5.5 Parameters Effecting the Phase Transition Temperature …………………… 208
5.5.1 Oxygen charge distribution …………………………………………. 211
5.5.2 Hydrogen bond strength …………………………………………….. 214
5.5.3 Torsional barrier height ……………………………………………... 224
5.6 Summary and Conclusions …………………………………………………. 230
6 Conclusions
234
Appendix
238
A.1 Chapter 3 ……………………………………………………………. 238
A.1.1 β-CsHSO4-III ……………………………………………………… 238
A.1.2 Cs2Li3H(SO4)3*H2O ………………………………………………. 243
A.2 Chapter 4 ……………………………………………………………. 248
A.2.1 Causes for discrepancies in experimental data between published
values and those reported in Chapter 4 …………………………….
248
A.2.2 CsHSO4 ……………………………………………………………..
249
A.2.3 Cs3(HSO4)2.50(H2PO4)0.50 …………………………………………...
251
A.2.4 Cs3(HSO4)2.25(H2PO4)0.75 …………………………………………… 252
A.2.5 Cs3(HSO4)2(H2PO4) ………………………………………………… 254
A.2.6 Cs5(HSO4)3(H2PO4)2 ……………………………………………… 256
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A.2.7 Cs2(HSO4)(H2PO4) …………………………………………………. 257
A.2.8 Cs6(H2SO4)3(H1.5PO4)4 …………………………………………… 259
Bibliography
263
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List of Figures
1.1 Effects of symmetry on strong, medium, and weak bonds
17
1.2 Simple hydrogen-bonded networks found in solid acids
19
1.3 Room temperature structures for CsHSO4 and CsH2PO4
20
1.4 Tetragonal structure of KH2PO4
21
1.5 Structure of monoclinic K3H(SO4)2
22
1.6 Vehicle mechanism of proton transport
24
1.7 Grotthuss mechanism of proton transport
25
1.8 Representation of the Grotthuss mechanism in ice
27
1.9 Normal and interstitial hydrogen bonds proposed for room temperature
phases of KH2PO4 and MH3(XO4)2 classes of compounds
31
1.10 Possible conduction paths for proton vacancy/interstitial defects in H-bond
zigzag chains
31
1.11 Structure of CsHSO4 above its superprotonic phase transition
34
2.1 Equivalent circuit for a dielectric material between two electrodes
45
2.2 Separation of bulk, grain boundary, and electrode resistances
46
2.3 Realistic impedance plot
47
3.1 Measurements on the α, β, γ-CsHSO4-III compounds
59
3.2 Crystal structures of the mixed Cs/Na compounds
63
3.3 DSC and conductivity measurements on CsNa(HSO4)3 and CsNa2(HSO4)3
64
3.4 Characteristic lengths of MHSO4 compounds as a function of average cation
radius
66
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3.5 Average hydrogen bond length versus mean cation radius
68
3.6 Structure of Cs2(HSO4)(H2PO4)
73
3.7 Cubic phase of Cs2(HSO4)(H2PO4)
74
3.8 Thermal analysis of the M2(HSO4)(H2PO4) compounds
76
3.9 Conductivity measurements along the b-axis of the M2(HSO4)(H2PO4)
compounds
77
3.10 Cation size effect on the room temperature conductivities
79
3.11 Compensation law for M2(HSO4)(H2PO4) compounds and other solid acids 81
3.12 Characteristic distances for the M2(HSO4)(H2PO4) compounds
86
3.13 Changes in the characteristic distances of Cs2(HSO4)(H2PO4), CsHSO4 and
CsH2PO4 across superprotonic transitions
88
3.14 Average thermal parameters of the oxygen atoms versus distances
90
3.15 Cation radius versus polarizability
92
3.16 Schematic representation of the potential wells for oxygen atoms
93
4.1 Room temperature structures for CsHSO4 and CsH2PO4
102
4.2 X-ray powder diffraction patterns of the mixed cesium sulfate-phosphates at
room temperatures (~25˚C)
104
4.3 X-ray powder diffraction patterns of the mixed cesium sulfate-phosphates
above superprotonic phase transitions
105
4.4 Proposed superprotonic structures for CsHSO4 and CsH2PO4
106
4.5 Protonic conductivity of the mixed cesium sulfate-phosphate compounds
108
4.6 Various transition properties versus phosphate percentage
112
4.7 Arrangement of the hydrogen-bonded tetrahedra
120
4.8 Disordered hydrogen bonds in CsH2PO4
121
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4.9 Room temperature structure Cs3(HSO4)2.50(H2PO4)0.50
126
4.10 Structure of Cs3(HSO4)2(H2PO4)
129
4.11 Structure of Cs5(HSO4)3(H2PO4)2
131
4.12 Probable effect of local order in the mixed S/P sites on neighboring
disordered hydrogen bonds
134
4.13 Structure of Cs2(HSO4)(H2PO4)
135
4.14 Local variants in the structure of Cs2(HSO4)(H2PO4)
136
4.15 Disordering of protons across the superprotonic transition
139
4.16 Hexagonal ice
141
4.17 Possible configurations of the sulfate tetrahedral in the superprotonic phase 147
4.18 Cubic structure of CsH2PO4
149
4.19 Configurational entropy loss due to a proton transfer from the cubic to
tetragonal phase
152
4.20 Possible source of extra entropy in the cubic phase of
Cs6(H2SO4)3(H1.5PO4)4
157
4.21 Measured versus calculated transition entropies
160
4.22 Transition volume versus enthalpy
168
5.1 Crystal structure of CsHSO4, as proposed by Jirak
173
5.2 Possible configurations of the sulfate tetrahedral in the superprotonic phase
174
5.3 Structures used to adjust the Dreiding parameters
179
5.4 Potential energy curves for an HSO4
- ion with fixed O(1)-S-OD-H torsional
angles
184
5.5 Cell parameters as a function of temperature (MD simulations)
191
5.6 Potential energy and volume as a function of temperature from MD
simulations
195
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5.7 Calculated X-ray powder diffraction patterns
197
5.8 Calculated IR spectra for MD simulations
198
5.9 Probability distribution functions for the S-O vectors
201
5.10 Probability distribution functions for all S-O vectors in phase I
203
5.11 Orientation/reorientation of an HSO4
- ion defined by its S-OD vector
205
5.12 Autocorrelation functions for all 32 tetrahedra
207
5.13 Average angular velocity of all 32 S-OD vectors versus temperature
208
5.14 Results of equal oxygen charge MD simulations
211
5.15 Calculated X-ray diffraction patterns for equal oxygen charge MD
simulations
213
5.16 Simulation results with the binding energy of the H-bonds increased by 150
and 200 percent
215
5.17 Autocorrelation functions for original simulation and simulations with
increased H-bond strength
219
5.18 X-ray diffraction patterns for simulations with increased H-bond strength
below and above the low temperature transitions
222
5.19 Rearrangements of the sulphate tetrahedral across the low temperature
transitions of the simulations with the increased H-bond strength
223
5.20 Results of the simulations with lowered torsional barrier
225
5.21 Results for simulations with torsional barrier 10 times value in original FF 227
5.22 Autocorrelation functions for simulations with decreased and increased
torsional barrier heights
229
A.1 Crystal structure of β-CsHSO4-III
239
A.2 H+ NMR measurements on β-CsHSO4-III and true CsHSO4-III
242
A.3 Structure of Cs2Li3H(SO4)3*H2O
243
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A.4 TGA and DSC measurements on Cs2Li3H(SO4)3*H2O
247
A.5 Conductivity of Cs2Li3H(SO4)3*H2O
247
A.6 PXD patterns of CsHSO4 taken at various temperatures
250
A.7 PXD patterns of Cs3(HSO4)2.50(H2PO4)0.50 taken at various temperatures
251
A.8 PXD patterns of Cs3(HSO4)2.25(H2PO4)0.75 taken at various temperatures
253
A.9 PXD patterns of Cs3(HSO4)2(H2PO4) taken at various temperatures
255
A.10 PXD patterns of Cs5(HSO4)3(H2PO4)2 taken at various temperatures
256
A.11 PXD patterns of Cs2(HSO4)(H2PO4) taken at various temperatures
258
A.12 PXD patterns of Cs6(H2SO4)3(H1.5PO4)4 taken at various temperatures
259
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List of Tables
1.1 Correlation between hydrogen bond strength, Odททท Oa, and Od—H distances 15
1.2 Hydrogen-bonded networks in solid acids by their H:XO4 ratio
19
3.1 Superprotonic phase transitions for MHXO4 class of compounds
51
3.2 Compounds synthesized in the mixed Cs-KD/Na/Li systems
57
3.3 Hydrogen bond parameters for the MHSO4 compounds
69
3.4 Cystallographic data for the M2(HSO4)(H2PO4) compounds
71
3.5 Successful synthesis conditions for the M2(HSO4)(H2PO4) compounds
75
3.6 High temperature transition parameters for the M2(HSO4)(H2PO4) compounds 75
3.7 Activation energy and pre-exponential term for the proton conduction in the
room temperature phases of the M2(HSO4)(H2PO4) compound
80
3.8 Cation/anion radius ratios for the M2(HSO4)(H2PO4) and MH2PO4
compounds
85
4.1 Synthesis of the mixed cesium sulfate-phosphates
97
4.2 Structural parameters of the mixed cesium sufate-phosphates in their room
and high temperature phases
99
4.3 Thermodynamic parameters of the superprotonic phase transitions
115
4.4 Values for the configurational entropy of the room temperature structures
137
4.5 Calculated entropies for high temperature phases
159
4.6 Calculated experimental transition entropies
162
4.7 Application of the ice rules to other solid acid superprotonic phase transitions 164
5.1 Force field for CsHSO4
177
5.2 Force field parameters for CsHSO4
178
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5.3 ESP charges for CsHSO4
181
5.4 Phase II at room temperature: calculation vs. experiment
185
5.5 Atomic positions for MD simulation at 298 K
186
5.6 Hydrogen bond comparison between MD and experiment in phase II
187
5.7 HSO4 group arrangement: QM and FF calculations vs. MD and experimental
values in phase II
188
5.8 MD vs. experimental parameters for tetragonal phase I CsHSO4
192
5.9 MD vs. experimental atomic positions for Cs and S in phase I CsHSO4
193
5.10 Characteristic values of the superprotonic phase transition in CsHSO4
194
5.11 Proposed librations in CsHSO4 phase I compared to simulation results
204
A.1 Atomic coordinates and equivalent displacement parameters (ล2) for
β-CsHSO4-III. Ueq = (1/3)Tr(Uij)
238
A.2 Anisotropic thermal parameters (ล2) for β-CsHSO4-III
240
A.3 Data collection specifics for β-CsHSO4-III, (CsHSO4)3
240
A.4 Atomic coordinates and equivalent displacement parameters (ล2) for
Cs2Li3H(SO4)3*H2O. Ueq = (1/3)Tr(Uij)
244
A.5 Anisotropic thermal parameters (ล2) for Cs2Li3H(SO4)3*H2O
244
A.6 Data collection specifics for Cs2Li3H(SO4)3*H2O
245
A.7 Variation of the transition enthalpy for CsHSO4 from pure and mixed cation
solutions
249
A.8 Results of rietveld analysis on CsHSO4 PXD patterns taken at various
temperatures
250
A.9 Results of rietveld analysis on Cs3(HSO4)2.50(H2PO4)0.50 PXD patterns
252
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taken at various temperatures
A.10 Microprobe data on Cs3(HSO4)2.25(H2PO4)0.75.
253
A.11 Results of rietveld analysis on Cs3(HSO4)2.50(H2PO4)0.50 PXD patterns
taken at various temperatures
254
A.12 Results of rietveld analysis on Cs3(HSO4)(H2PO4) PXD patterns taken at
various temperatures
255
A.13 Results of rietveld analysis on Cs5(HSO4)3(H2PO4)2 PXD pattern in cubic
high temperature phase
257
A.14 Results of rietveld analysis on Cs2(HSO4)(H2PO4) PXD patterns taken at
various temperatures
258
A.15 Results of rietveld analysis on Cs6(H2SO4)3(H1.5PO4)4 PXD patterns taken
at various temperatures
260
A.16 Atomic coordinates and equivalent displacement parameters (ล2) for
Cs6(H2SO4)3(H1.5PO4)4
260
A.17 Anisotropic thermal parameters (ล2) for Cs6(H2SO4)3(H1.5PO4)4
261
A.18 Data collection specifics for Cs6(H2SO4)3(H1.5PO4)4
261
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Chapter 1 Introduction
1.1 Overview
Solid acids, or acid salts, are a class of compounds with unique properties arising
from the incorporation of “acid” protons into a crystalline structure: e.g.,
ฝ Cs2SO4 + ฝ H2SO4 > CsHSO4. Initial research into these compounds focused on the
ferroelectric properties that many solids acids, such as KH2PO4, express below room
temperature due to ordering of the protons within their potential wells1. Near room
temperatures, the structural proton leads to protonic conductivity on the order of Log(σ) ~
-6 to –9 in most solid acids. This conductivity is due to local defects in the structure and
subsequent protonic hopping2.
While most early studies focused on low temperature behavior of solid acids, in
1981 it was observed that CsHSO4 had a first-order phase transformation at 141ฐC3. Not
long after, it was discovered that as a result of this solid-solid phase transformation, the
protonic conductivity increased by over three orders of magnitude4. Since then, there has
been increasing interest in the high temperature properties of these compounds and their
first-order phase transformations.
Most solid acids with superprotonic phase transitions have monoclinic symmetry
in their room temperature phase5. Above the phase transition temperature, the symmetry
of the compounds increases and to accommodate the higher symmetry, the oxygens
become disordered. The partial occupancy of the oxygen sites gives a nearly liquid-like
nature to the protons as the previously static hydrogen bonded system becomes highly
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dynamic6,7. In this dynamic system, the XO4 groups librate at ~1011 Hz with inter-
tetrahedra hopping of the proton occurring at ~109 Hz8. This fast reorientation of the
tetrahedra in conjunction with proton translations leads to the jump in conductivity across
the phase transition and the “superprotonic conduction” many solid acids exhibit in their
high temperature phases.
With the discovery of superprotonic conductivity in CsHSO4, other known solid
acids were investigated to reveal if they exhibited similar properties, resulting in many
new superprotonic conductors being found. The three most extensively studied families
of solid acids with superprotonic phase transitions have formulas M3H(XO4)2, MHXO4,
and MH2YO4 (X=S, Se; Y=P, As; M=Li, Na, K, NH4, Rb, Cs). The high temperature
behavior of these compounds has been analyzed by a myriad of techniques including, but
not limited to, X-ray diffraction, impedance spectroscopy, thermal calorimetry and
gravimetric analysis, infrared and Raman spectroscopy, acoustic absorption, neutron
diffraction and scattering, and NMR spectroscopy. There is therefore a good physical
understanding of these phase transition. They are order-disorder transitions of first order
that are entropically driven. Below the transition, the protonic transport is of the intrinsic
type due to proton defects in the static hydrogen bonded network. Above the transition,
symmetry increases and proton transport is due to fast reorientations of the XO4
tetrahedra in combination with proton translation along a “dynamically disordered
network of hydrogen bonds”9.
However, in spite of this plethora of theoretical and experimental data, there were
only generalities for the question of which chemical and structural properties influence
superprotonic phase transitions in solid acids. The objective of this thesis work was,
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therefore, to uncover the chemical and structural parameters that favor superprotonic
phase transitions over melting or decomposition in the MHXO4, MH2YO4, as well as the
new mixed MHXO4-MH2YO4 classes of compounds and to thereby gain some ability to
“engineer” the properties of solid acids for applications.
1.2 Ionic Conductivity10-12
In general, the total ionic conductivity of a material, under the influence of an
electric field, will be the sum of the conductivities of each mobile species in the material.
The conductivity of each ionic species is directly proportional to the number density of
the ions, their mobility and the charge per ion. The total conductivity is then
∑
∑ =
=
i
ii
i
i
i
ezN ต
σ
σ total
(1-1)
where i refers to the species, i
N is the number of mobile ions per unit volume, i
ต is their
mobility, and ezi equals the ion’s charge (charge per electron times valence of ion). For a
pure ionic conductor in which the current is carried by only one type of ion, the total
conductivity simplifies to
i
i
ezN ต
σ =
i
(1-2)
The evaluation of the conductivity can then be reduced to calculating i
N and i
ต .
In the calculation of i
N we must consider the mechanism of ion mobility. For any
crystalline material, the diffusion of atoms will be caused by the presence of defects in its
Page 22
4
structure. These defects allow the atoms of the material to move on an otherwise fixed
lattice. The intrinsic defect concentration can be evaluated as follows.
Thermodynamically, the very presence of these defects is due to the increase in
entropy when some number of defects are added to the material. For an ideal solution,
this increase in entropy per mole can be written
)]
ln(
)
1ln()
1[(
1
1
1
1
N
N
N
N
R
Smix
+
−
−
−=
(1-3)
where here, 1
N is now the mole fraction of defects. The increase in entropy per mole of
material, mix
S∆
, due to a small addition to the mole fraction of defects,
1
N
∆ , is then
1
1
1
1
1
1
ln
N
N
N
R
N
dN
dS
S
mix
mix
∆





−
−=∆
=
∆
(1-4)
As this function shows, the initial increase in entropy per vacancy added is
extremely large:
∞→
∆ mix
S
as
0
1 →
N
. Therefore, for a material at equilibrium there
will always be a finite number of defects. To calculate this equilibrium number, we can
use the fact that the change in Gibbs free energy, G, of a system in equilibrium is zero for
any small displacement. The change in the Gibbs free energy, ∆G, with the addition of
1
N
∆
defects to a mole of crystal already containing a concentration 1
N of defects is
N
N
N
S
T
N
N
HGd
1
1
1
∆
∂
∂
−
∆
=∆
(1-5)
Page 23
5
where N is Avagadro’s number, and
N
Hd / and
)/1)(
/(
1
N
NS
∂∂
are the increase in
enthalpy and entropy, respectively, in the crystal per defect added. The enthalpy increase
is due to local distortions to the atomic and electronic configuration resulting from the
incorporation of a defect into the crystal structure. The entropy term includes the ideal
entropy of mixing given in Eq. (1-3) plus another term due to the change in vibrations of
the atoms when a defect is included, NS
d / . Substituting these entropy terms into Eq. (1-
5) gives
N
N
N
N
RT
TS
H
G
d
d
1
1
1
1
ln
∆






−
+
−
=∆
(1-6)
Now, if the concentration of defects is very low, they are unlikely to interact and
d
H and d
S should be independent of 1
N . This equation then is most appropriate when
1
1 <<
N
. This is certainly true for most metals and ionic solids, where
4
1
10−
<
N
(Shewman, p70, 160). Using
1
1 <<
N
, Eq. (1-6) becomes
[
]
N
N
N
RT
TS
H
G
d
d
1
1
ln
∆
+
−
=∆
(1-7)
Since
0
=∆
G
for any small displacement,
1
N
∆ , from equilibrium, we can write the
equilibrium concentration of 1
N as
)/
exp()/
exp(
1
RT
H
RS
N
d
d
equil
−
=
(1-8)
or,
Page 24
6
)/
exp(
1
RT
G
N
d
equil
−
=
(1-9)
where
d
d
d
TS
H
G
−
=
is the free energy change to the crystal per one mole of defects
added, on top of the entropy of mixing.
For ionic solids, the dominant defect will be a vacancy or interstitial10. Also,
defects must leave the material charge neutral. These two facts lead to two types of
disorder in ionic solids: Schottky and Frenkel. For Schottky disorder, an equal number of
anion and cation vacancies are formed. It is found in materials where the energies of
formation of a defect on either lattice are similar and the motion of both defects can be
measured. However, experimentally it is observed that the mobility of cation vacancies is
often much greater than that of anion vacancies, due mostly to the fact that cation
vacancies are usually smaller than their companion anion vacancies. Cation vacancies are
therefore responsible for most ionic conductivity by the Schottky defect mechanism.
Using the results from Eq. (1-9), we find that at equilibrium in an ideal solution where
defects do not interact,
]/)
(
exp[
)
)(
(
RT
G
G
N
N
vc
va
equil
vc
equil
va
+
−
=
(1-10)
where
va
va
va
TS
H
G
−
=
and
vc
vc
vc
TS
H
G
−
=
are the molar free energy of formation of
an anion and cation vacancy, respectively. Now,
equil
vc
equil
va
N
N
=
, so we can write Eq. (1-
10) as
]2/
exp[
]2/)
(
exp[
RT
G
RT
G
G
N
S
vc
va
equil
va
−
=
+
−
=
(1-11)
Page 25
7
where S
G is the molar free energy to form the pair of vacancies. Schottky defects are
found in alkali halides, e.g., NaCl and CsCl.
If the Frenkel type of disorder is dominant, the molar free energy to form a cation
interstitial, ic
G , is much less than that to form an anion vacancy, va
G . Cation vacacies
will then be charged balanced by cations jumping to interstitial sites rather than anion
vacancies. Hence, the equilibrium concentration of cation interstitials, equil
ic
N
, and cation
vacancies, equil
vc
N
, will be equal. As opposed to the Schottky mechanism where only the
cation vacancies were significantly mobile, for Frenkel defects, cation mobility is due to
both the vacancy and interstitial mechanism. If these defects are randomly located (i.e.,
do not interact), we can again use Eq. (1-9) to get
)/
exp(
]/)
(
exp[
)
)(
(
RT
G
RT
G
G
N
N
F
vc
ic
equil
vc
equil
ic
−
=
+
−
=
(1-12)
or, since equil
ic
N
= equil
vc
N
,
)2/
exp(
]2/)
(
exp[
RT
G
RT
G
G
N
F
vc
ic
equil
ic
−
=
+
−
=
(1-13)
where F
G is the molar free energy of formation for the cation interstitial-vacancy pair.
This type of disorder is found in AgCl and AgBr.
We will now look at the other unknown in Eq. (1-2), the mobility of the charge
carrier, i
ต . Because the movement of an ion under the influence of an electric field is
governed by the same atomistic mechanisms as diffusion of atoms due to a concentration
Page 26
8
gradient, the ionic mobility can be directly related to the ion’s diffusivity. This is
expressed by the Nernst-Einstein equation:
Tk
D
ez
B
ion =
ต
(1-14)
where B
k is Boltzmann’s constant (8.62x10-5 eV/K), T is the temperature in degrees
Kelvin and D is the diffusion coefficient. Regardless of the method of transport, if we
assume that the jumps of the ion are uncorrelated and random, then the diffusion
coefficient is equal to
Γ
=
2
o
a
D
γ
(1-15)
where γ is a geometric constant derived from the structure, o
a is the jump distance and
Γ is the jump frequency. As the jumping of the atom necessarily involves some amount
of energy, we can give the jump frequency an Arrhenius-type temperature dependence:
)
/
exp(
Tk
G
b
o
jump
o
−
=Γ ν
(1-16)
where o
ν is the attempt frequency, and
o
jump
o
jump
o
jump
TS
H
G
−
=
is the jump activation
energy per ion. The exact value of o
ν is difficult to determine from theory. It is
comparable to a phonon frequency and is often approximated by the Debye frequency.
The attempt frequency can be measured directly by experiments; usually by neutron
scattering, nuclear magnetic resonance, or light scattering techniques. The exponential in
(1-16) represents the probability that any given oscillation will cause a jump. Replacing
Γ in Eq. (1-15) with the right side of Eq. (1-16) gives
Page 27
9
)
/
exp(
2
Tk
G
a
D
b
o
jump
o
o
−
= νγ
(1-17)
If we set
oo
o
a
D
νγ2
=
, then Eq. (1-17) becomes
)
/
exp(
Tk
G
D
D
b
o
jump
o
−
=
(1-18)
Using Eqs. (1-18) and (1-14) we can now express the conductivity as
( )
Tk
D
ez
N
b
i
2
i =
σ
(1-19)
( )







 −
=
Tk
G
Tk
D
ez
N
b
o
jump
b
o
i
exp
2
i
σ
(1-20)
or
( )







 −
=
Tk
G
Tk
a
ez
N
b
o
jump
b
o
o
i
exp
2
2
i
νγ
σ
(1-21)
with
oo
o
a
D
νγ2
=
.
From Eq. (1-9), we can solve for i
N since
)/
exp(
1
RT
G
N
N
N
N
d
o
o
equil
i
−
=
=
(1-22)
where o
N is the number of lattice sites of the mobile ion per molar volume of the crystal.
We can convert the exponential in Eq. (1-22) to the same units as the exponential of Eq.
(1-21) by substituting
A
b
NkR
=
(1-23)
where A
N is Avagadro’s number = 6.023x1023. Eq. (1-22) then becomes







 −
=




 −
=




 −
=
Tk
G
N
Tk
NG
N
TNk
G
N
N
b
o
defect
o
b
A
d
o
A
b
d
o
i
exp
/
exp
exp
(1-24)
Page 28
10
The term o
defect
G
represents the free energy of formation for one defect. So, Eq. (1-24)
simply states that the equilibrium concentration of defects will equal the number of
possible defects sites per unit volume times the probability (Boltzman) that a defect will
exist. Substituting the right side of Eq. (1-24) into Eq. (1-21) for i
N gives
( )







 −







 −
=
Tk
G
Tk
G
N
Tk
a
ez
b
o
jump
b
o
defect
o
b
o
o
exp
exp
2
2
i
νγ
σ
(1-25)
( )








+
−








+
=
Tk
H
H
k
S
S
Tk
aezN
b
o
jump
o
defect
b
o
jump
o
defect
b
oo
o
)
(
exp
exp
2
2
i
νγ
σ
(1-26)
using the fact that
o
jump
o
jump
o
jump
TS
H
G
−
=
and
o
defect
o
defect
o
defect
TS
H
G
−
=
.
Eq. (1-26) can be further simplified to:





 −
=
Tk
Q
T
A
b
exp
i
σ
(1-27)
where
( )








+
=
b
o
jump
o
defect
b
o
o
o
k
S
S
k
a
ez
N
A
exp
2
2 νγ
(1-28)
and
o
jump
o
defect
H
HQ
+
=
(1-29)
The parameters A and Q will vary from material to material, but are independent of
temperature. Eq. (1-27) then relates the underlying structural and thermodynamic
properties of an ionic solid to its conduction. Experimentally, we find A and Q from an
Arrhenius plot of Eq. (1-27) in the form of
)
ln( Ti
σ
versus 1/T. Q is often called the
Page 29
11
activation energy for migration: the energy required to both form ( o
defect
H
) and move
( o
jump
H
) a defect to an adjacent lattice site. These two terms can be resolved by either
calculations of the electronic energy change due to defect formation/migration or by
experimentation.
For ionic solids, these experiments usually involve doping of the sample. If a
material is heavily doped, then there will exist some low temperature range where the
number of defects due to doping (Ndp), which is fixed, will be greater than the number of
intrinsic defects ( equil
va
N
, equil
ic
N
, and equil
vc
N
), which increases/decreases exponentially with
increasing/decreasing temperature. In this low temperature region, then, the concentration
of defects is independent of temperature and a plot of
)
ln( Ti
σ
versus 1/T will give a
slope proportional to
o
jump
HQ
=
. The conductivity of the material in this region is called
“extrinsic” as it depends on the dopant concentration and not the inherent properties of
the crystal.
For sufficiently high temperatures, the number of intrinsic defects will be much
greater than the number of defects due to doping. For this high temperature range, the
concentration of defects will vary with temperature according to Eqs. (1-10) and (1-12),
for Schottky and Frenkel defect mechanisms, respectively. The slope of
)
ln( Ti
σ
versus
1/T in this region will be proportional to
o
jump
o
defect
H
HQ
+
=
, as the conductivity will be
due to both defect formation and migration. Not surprisingly, the conductivity of this
region is labeled “intrinsic.” The change in slope going from the extrinsic to intrinsic
regions should then be equal to o
defect
H
.
Page 30
12
The only variable not yet evaluated in Eq. (1-27) is then
o
jump
o
defect
o
total
S
S
S
+
=
. A
direct measurement of the entropy of ionic conduction is difficult and since it is
independent of temperature, it is often simply lumped into o
σ and forgotten. However, it
can be estimated from theory. Both o
defect
S
and o
jump
S
are due to changes in the vibrational
spectrum when a defect is created or an ion jumps, respectively. We can calculate this
change by using the harmonic oscillator approximation of the vibrational partition
function13:
Tkh
Tk
i
Tk
i
i
Tk
vib
b
b
b
bi
e
e
e
e
Z
/
)/(2/1
]/)2/1[(
)/(
1
ν
ν
ν
ε
−
−
+−
−
−
=
=
=
∑
∑
h
h
(1-32)
where the partition function is over all possible states of one harmonic oscillator. We can
then use the definition of the Helmholtz free energy, relative to that at absolute zero, to
get
∑






−
−=
−=
−
i
Tk
h
b
vib
b
b
i
e
Tk
ZTk
F
/
1
1
ln
ln
ν
(1-33)
where the summation is now over all frequencies of the crystal (i.e., system of harmonic
oscillators). We can substitute Eq. (1-33) into the thermodynamic equation
V
TF
S )/(
∂∂−=
(1-34)
and get
∑












−
−





−
−=
−
−
i
Tkh
b
i
Tkh
b
b
i
b
i
eTk
hv
e
k
S
1
1
1
1
ln
/
/
ν
ν
(1-35)
or for temperatures well above the Debye temperature, where
>>
Tkb
i
hv ,
Page 31
13
(
)
∑
−=
i
b
i
b
Tkhv
k
S
/
ln
(1-36)
The entropy change as the crystal is perturbed from its ideal structure is then:
( )
∑
−=
i
p
i
i
i
b
vv
k
S
/ln
(1-37)
where i
i
v and p
i
v are the vibrational modes of the ideal and perturbed crystal, and the
summation is over all vibrational modes of the crystal lattice. This summation is not
easily done, but by dividing the crystal into nearest neighbors, elastically stressed
neighbors, and the rest of the lattice, one can arrive at a good approximation.
It is possible then, at least in theory, to completely describe the ionic conductivity
in terms of the structural and thermodynamic properties of a material. This is done
experimentally most often by measuring not only the ionic conductivity of a material, but
also its diffusion coefficient or attempt frequency, so that the other parameters in Eq. (1-
27) can be resolved. More generally, Eq. (1-27) is used to calculate the activation energy
of ion transport and the overall structural parameter. These are then compared to like
compounds and the method of ionic transport is inferred from known conduction
mechanisms.
Page 32
14
1.3 Structural Features of Solid Acids
Before describing the mechanisms of proton transport, which differs quite
significantly from that of other ions, it is necessary to describe the structural features of
solid acids which influence proton conduction. Very generally, the structures of solid
acids are similar to that of other ionic solids in that the compounds are made up of two
lattices, one for cations and one for anions. However, the incorporation of the acid proton
leads to the fundamental structural difference between solid acids and their analogous
salts: the presence of hydrogen bonds. These hydrogen bonds link the anions together and
the conduction of protons will be greatly effected by both the types of and particular
arrangement of the hydrogen bonds found in a solid acid. Therefore, to properly explain
protonic conduction in solid acids, it is necessary to first describe the types of hydrogen
bonds and hydrogen-bonded networks that are found in them.
1.3.1 Characterization of Hydrogen Bonds
A hydrogen bond is said to exist if two electronegative species X and Y are
connected to each other through bonds to a hydrogen atom, H. Usually, one bond will be
stronger, written X―H, and is called the normal X―H bond while the weaker bond,
written HทททY, is termed the hydrogen bond. The X and Y atoms are termed the donor and
acceptor atoms, respectively. The dissociation energy of the X―HทททY complex is equal
to the strength of the HทททY bond or the hydrogen bond strength14. Hydrogen bond
strengths run in the range of 2 to 15 kcal/mole, which is significantly greater than other
intermolecular forces (e.g., van der Waals forces with energies in the range of 0.1 to 2
Page 33
15
kcal/mole for smaller molecules), but much less than intra-molecular covalent bonds (30
to 230 kcal/mole)15.
This bond energy is not entirely due to the electrostatic attraction between the
electronegative atoms and the hydrogen, but also involves a certain amount of covalent
character arising from the overlap of lone pair electrons from the Y acceptor atom with
those of X―H bond. As the hydrogen-acceptor distance decreases, the amount of
covalency increases and so does the hydrogen bond strength16. This correlation between
bond strengths and bond distances leads to hydrogen bonds being very generally labeled
as strong, medium, or weak depending upon their donor-acceptor and donor-hydrogen
lengths. As shown in Table 1.1 for X,Y = O, the hydrogens of strong hydrogen bonds are
more equally shared between the donor and acceptor oxygens (Od and Oa, respectively),
resulting in smaller OdทททOa and bigger Od―H distances when compared to weak
bonds17,18.
Table 1.1 Correlation between hydrogen bond
strength, Odททท Oa, and Od—H distances14,17,18
Bond Strength
dOdททท Oa(ล)
dOd—H(ล)
Strong
2.4 to 2.6
1.3 to 1.0
Medium
2.6 to 2.7
1.02 to 0.97
Weak
2.7 to ~3
Below 1.0
Which strength hydrogen bond favors protonic conductivity depends on a
material’s mechanism of proton transport. If protons are transported on a mobile species,
then strong hydrogen bonds would decrease the mobility of the carrier. Hence, weak
Page 34
16
hydrogen bonds are preferable for such a mechanism. However, if the mechanism of
proton transport requires both the translation of protons along hydrogen bonds and the
breaking of hydrogen bonds, then medium strength hydrogen bonds are preferable. This
is due to the trade-off between the energy required for proton translation, which decreases
with increasing hydrogen bond strength (decreasing OdทททOa distance), and the energy
required to break the bond, which by definition decreases with decreasing hydrogen bond
strength (increasing OdทททOa distance)19.
The local crystallographic symmetry also effects proton conduction as the
geometry of a hydrogen bond is partially determined by its site symmetry. This can be
seen in Figure 1.1 for an O―HทททO bond. For two oxygen atoms related by a center of
symmetry and bound by a strong hydrogen bond, the potential energy of the proton will
have a single minimum exactly between the two oxygens; the dual nature of each oxygen
is signified by the label Oa/d. If the oxygen atoms are not related by symmetry, the
hydrogen will reside slightly closer to one oxygen, but the hydrogen will be strongly
bound near the center of the OdทททOa complex.
In hydrogen bonds with medium OdทททOa distances, two minima exist in the proton
potential and the presence or absence of local symmetry influences the relative
population of each minima by the proton. For the symmetric case, the proton will be
found with equal probability in either minima and therefore can be considered “locally
disordered” as the proton will hop between the two sites17. When the potential well of the
proton is asymmetric, the proton will preferentially occupy one minimum over the other.
However, the proton will still occasionally hop to the second minimum, thus dramatically
increasing its intra-hydrogen bond mobility.
Page 35
17
Hydrogen Bonding
bond type
strong
medium
weak
symmetric
< 2.4ล
O
O
~1.3ล
Energy
H
~1.3ล
~
~2.0ล
~ 2.6ล
O
O
H
H
~1.2ล
Energy
not generally observed
asymmetric
< 2.4ล
O
O
~1.3ล
Energy
H
~1.3ล
~
~1.8ล
~ 2.6ล
O
O
~1.2ล
Energy
H
H
H
1 or 2
D
A
> 2.9ล
O
O
~1.0ล
Energy
H
~2.2ล
~
D
A
Figure 1.1 Effects of symmetry on strong, medium and weak hydrogen bonds18.
Page 36
18
Weak hydrogen bonds are almost always asymmetric, with only one minimum in
potential energy of the proton. Moreover, as stated earlier, a weak hydrogen bond
requires large energies to transfer the proton to the other side of the potential well (~2 to
10 times that of medium and strong hydrogen bonds, respectively)19. Consequently, the
local symmetry of the hydrogen bond has a much greater effect on the proton transport
properties of medium strength hydrogen bonds than it does on those of weak or very
strong hydrogen bonds. The hydrogen bonds found in solid acids are ~2.5 to 2.7 ล20 and
are thus, for both symmetric and asymmetric examples, of the moderately strong to
medium strength type of hydrogen bonds. Hydrogen bond energies associated with OทททO
distances of 2.5 to 2.7 ล are ~14 to 6 kcal/mole, respectively21.
1.3.2 Hydrogen-Bonded Networks in Solid Acids
Very generally, hydrogen bonds can link together molecules into structures of 0,
1, 2, 3 dimensions. Some simple hydrogen-bonded networks found in solid acids are
shown in Figure1.2. More complicated networks involve tetrahedra linking in such a way
as to give three-dimensional structures (e.g., branched chains or layers) or true 3-D
networks that run through out the crystal. To a certain degree, the type of hydrogen-
bonded network found in a solid acid is predetermined by the average number of
hydrogen-bonded oxygens per XO4 tetrahedra. This number is itself a function of the
compound’s H:XO4 ratio. Table 1.2 shows the hydrogen-bonded structures for an average
of 1, 2, 3, and 4 bonded oxygens per XO4 group. The example structures in this table
were selected from solid acids of interest to this work.
Page 37
19
Linear Dimers
Cyclic Dimers
Chains
Rings
Layers
Figure 1.2 Simple hydrogen-bonded networks found in solid acids.
Hydrogen Bonds are indicated by
lines.
Table 1.2. Hydrogen-bonded networks in solid acids by their H:XO4 ratio22
H:XO4 ratio Number of oxygens
involved in hydrogen
bonds per XO4
Type of
hydrogen-bonded
network
Examples from MHxXO4 and
M3H(XO4)2 compounds -
{ref}
1:2
1
Dimer
K3H(SO4)2 - 23
1:1
2
Cyclic dimer
Rings
Chains
KHSO4 [2] - 24
Cs2Na(HSO4)3 - 25
CsHSO4 - 26
3:2
3
Layers
Cs2HSO4H2PO4 - 27
2:1
4
Layers
3-dimensional
CsH2PO4 - 28
KH2PO4 - 29
Page 38
20
1.3.3 Common Structures Found in the Low Temperature Phases of
Solid Acids
The zigzag chains of Figure 1.2 are a very common feature in solid acids. Straight
chains are also observed, but more often than not a chain of tetrahedra will zig and zag as
will the surrounding cations to a give a “checker-board” appearance to the arrangement
of anions and cations30. This arrangement of atoms is shown in Figure 1.3 for the stable
room temperature structure of CsHSO4 (phase II)26.
Figure 1.3 Room temperature structures for CsHSO4 and CsH2PO4: a) the cxb
r
r
plane of
CsHSO4 showing zigzag chains of sulfate tetrahedra parallel to c
r
and b) view down the
c-axis revealing the checkerboard arrangement of cation and anion chains The rectangles
represent unit cells.
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21
These zigzag chains are often found in solid acids with higher dimensional
networks where they are cross-linked by other hydrogen bonds to form planes and three-
dimensional hydrogen-bonded networks 31,31,32. The zigzag chains found in CsH2PO4 are
cross-linked to form planes of hydrogen-bonded tetrahedra perpendicular to the [001]
direction32. In KH2PO4, each tetrahedron is connected to two zigzag chains at right angles
to each other to form a hydrogen-bonded network of tetrahedra that runs throughout the
structure, Figure1.4.
a)
b)
Figure 1.4 Tetragonal structure of KH2PO4 projected down a) the [001] and b) the [100]
directions. Chains of hydrogen-bonded PO4 tetrahedra extend along the [100] and [010]
directions in a) and the zigzag nature of these chains can be seen in b). Circles represent
K atoms and tetrahedra PO4 groups.
Another common structural type is found in solid acids belonging to the
M3H(XO4)2 family of compounds (M=Cs, Rb, NH4, K, Na; X=S, Se). In the ordered
(room temperature) phases of these compounds, the tetrahedra are hydrogen-bonded
together into dimers. These dimers and their companion cations are arranged in such a
way as to form planes with almost trigonal symmetry perpendicular to the [001]
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22
direction, the true symmetry being monoclinic, space group A2/a. For the compound
K3H(SO4)2, this arrangement of sulfate dimers and K+ ions is shown in Figure 1.532.
a)
b)
Figure 1.5 Structure of monoclinic K3H(SO4)2 projected down a) the c*-axis and b)
down the b-axis.
1.4 Protonic Conduction
1.4.1 Mechanisms of Proton Transport
Although the general concepts of ionic conduction apply to protonic conduction,
there is a fundamental difference between the two due to the fact that H+ is the only ion
with no core shell of electrons. It must therefore be solvated by the electrons of another
atom or atoms33,34. For nonmetallic materials, and in particular ionic solids, the proton
will be coordinated by only one or two atoms35. Due to the positive charge on the proton,
the coordinating atom is usually the most electronegative atom around: F,O, N and
sometimes Cl and S15,34.
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23
For most protonic conductors, the coordinating atom(s) is an oxygen. If the
oxygen is well separated from other oxygen atoms, the proton-oxygen pair forms an O-H
bond ~ 1 ล in length. As the distance to other electronegative species lessens, a hydrogen
bond, O-HทททO, will be formed, with OทททO distances in the range of 2.4-3 ล long20. As the
proton can never be free from the electron density of its neighbors, it must move by a
method where it is bonded to at least one atom during the entire process36. This restraint
leads directly to the two main methods of proton conduction: the vehicle and Grotthus
mechanisms2,37.
In the vehicle mechanism, the proton is attached to a mobile species (e.g.,
H2O+H+⇒H3O+). Protonic conductivity is then achieved by the diffusion of the vehicle
and counter-diffusion of unprotonated vehicles (here, H2O), as shown in Figure 1.6.
Clearly, in this mechanism the diffusion rate of the vehicle will determine the overall
conductivity of the proton38. This mechanism is responsible for the protonic conductivity
in oxonium β-alumina, hydrogen uranyl phosphate, and hydrated acidic polymers (e.g.,
NAFION)37,39.
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24
H
+
H
+
H
+
Figure 1.6 Vehicle mechanism of proton transport. Protons are carried to the left while
empty vehicles travel to the right37.
In contrast, the Grotthuss mechanism has the chemical species to which the
proton is attached remain translationally stationary on the timescale of proton transport.
By transfer of the proton within a hydrogen bond and subsequent structural relaxation
(i.e., a structural or dipole reorientation of the new carrier), the proton can diffuse through
the material40. This process requires that the protonic carriers have significant local
dynamics. The relevant rates for this mechanism are then that of proton transfer and
structural relaxation. Some materials that conduct protons by the Grotthuss process are
ice37, concentrated aqueous solutions and hydrates of acids (e.g., H3PO4, H2SO4, HCl,
etc.) 41,42 43, fused phosphoric acid44, the solid proton conductor HClO4
45, and solid acids
in both their low and high temperature phases 35,46,47. A schematic description of the
Grotthuss mechanism for ice is shown in Figure 1.7.
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25
H+
b)
H+
c)
H+
a)
Figure 1.7 Grothhuss mechanism of proton transport. Proton jumps to an adjacent
vehicle, a), which then reorients, b), to form a new hydrogen bond, c).
The ideal structure of normal (hexagonal) ice, first described by Bernal and
Fowler, has each oxygen atom tetrahedrally coordinated by four other oxygens at a
distance of 2.76 ล. Associated with each oxygen will be exactly two protons. Each
proton will form a hydrogen bond with OH and OHทททO distances of 0.95 and 1.81 ล,
respectively, resulting in each oxygen being involved in four hydrogen bonds48.
According to the prevailing theory, there are two pairs of defects responsible for protonic
conduction in ice. The first pair is created by reorientation of the water molecule, which
causes doubly occupied and empty hydrogen bond sites: D and L defects, respectively49.
This reorientation cannot be definitively labeled as a structural reorientation (with the
molecule rotating around an axis of symmetry) or a dipole orientation (with the proton
hopping from one site to another). Thermodynamically, both mechanisms must be
present to some degree, but which one dominates the structural relaxation involved in
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26
ice’s protonic conduction is difficult to determine. Intra-hydrogen bond translation of the
proton results in the formation of the second defect pair: the hydroxyl (OH−) and
hydronium ions (H3O+)50. Note that both steps require the protons to move from one to
another crystallographic proton site.
It is necessary for both types of defect pairs to exist for true translation of a proton
as each pair, alone, moves the protons in only a coordinated way, leaving the hydrogen-
bonded system “polarized” in the direction of proton transport. By traveling along the
same hydrogen-bonded system, the alternative pair can “unpolarize” this chain of
hydrogen bonds. In particular, a D defect traveling in the same direction as a hydronium
ion (and vice versa) will “unpolarize” the hydrogen-bonded system, as shown in Figure
1.8 c, d, and e. Similarly, an L defect following a hydroxyl ion (and vice versa) will allow
for a continuation of proton migration in the same direction37. Proton conduction in ice
then requires both proton transfer along hydrogen bonds and a reorientation of the proton
carriers, and hence occurs by the Grotthuss mechanism.
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27
−
+
+
D defect
L defect
a)
b)
c)
d)
e)
Figure 1.8 Representation of the Grotthuss mechanism in ice. Intra-hydrogen bond
transfer of the proton, a), leads to the formation of hydroxyl (OH-) and hydronium
(H3O+) ions, b). Reorientation of a water molecule, c), results in an L/D defect pair, d),
with further reorientations removing the defects and leaving the chain able to continue
proton conduction to the right, e).
For completeness, it should be mentioned that some materials exhibit mixed
vehicle and Grotthuss mechanisms of proton transport. This occurs when there is both a
high mobility for the proton carriers and a significant amount of proton transference
between carriers. Dilute aqueous solutions of acids and bases and solid acid hydrates with
high water content have mixed mechanisms of proton transport39. However, in general,
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28
these two mechanisms operate exclusively of each other. The presence of continuous
hydrogen-bonded pathways is essential to proton conduction via the Grotthuss
mechanism, but an extensive hydrogen-bonded network hinders the translation of mobile
species necessary to the vehicle mechanism51.
1.4.2 Room Temperature Proton Conduction in Solid Acids
Proton conduction in solid acids is similar to that in ice for the low temperature,
low symmetry, and (for the most part) ordered phases of solid acids that exist near room
temperatures. Migration of protons again requires both transfer of the protons along
hydrogen bonds and reorientations of the tetrahedral anions. As with ice, it is unclear as
to whether the necessary structural reorientations occur by a physical rotation of the
tetrahedra or by proton hopping leading to dipole reorientations. The transfer of protons
along hydrogen bonds will result in the formation of tetrahedra that are negatively and
positively charged when compared to average charge on the tetrahedra (e.g., 2(HSO4
−) →
SO4
−2 + H2SO4).
For solid acids with all tetrahedral oxygen atoms involved in hydrogen bonds, the
formation of D and L defects would seem essential for proton conduction and the
mechanism of proton conduction to be nearly identical to that found in ice. Indeed,
models proposed by Murphy52, O’Keeffe53 and Pollock54 relate the intrinsic conductivity
to the formation of D and L defects in KH2PO4 type solid acids. In KH2PO4, all oxygens
are involved in crystallographically symmetric hydrogen bonds (with OทททO distances of
2.491 ล), and the proton resides in a symmetric double minimum potential well55.
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29
Evidence of this symmetric double minimum over a single minimum is found in
KH2PO4’s low temperature ferroelectric properties56. The distance between the minima is
~ 0.37 ล, a distance much shorter than the van der Waals radius for hydrogen (r =
1.2 ล)15. D defects will therefore have a large electrostatic repulsive energy associated
with them1. To avoid the formation of such high energy defects, a model put forth by
Sharon57 involves the synchronous reorientations of multiple tetrahedra. Disadvantages to
this model are that it requires the breaking of multiple hydrogen bonds as well as the
coordinated rotation of multiple tetrahedra57.
All the above models require the proton to move from one normal
(crystallographic) site to another normal site; similar to the mechanism proposed for ice.
In contrast, Baranov suggests a mechanism of proton conduction where the protons hop
between normal and interstitial (i.e., non-crystallographic) sites, similar to a Frenkel
defect mechanism2. This mechanism requires neither the formation of D defects nor
rotations of the tetrahedra, since the protons jump between the normal and interstitial
sites without aid of tetrahedral reorientations 2. The necessary structural relaxation for a
Grotthuss proton conduction mechanism is accomplished by dipole reorientations in this
model. Intra-hydrogen bond transfer of the protons will still lead to tetrahedral
equivalents of hydroxyl and hydronium ions, but the equivalent of the D, L defect pair for
this model is a proton vacancy (L defect) and interstitial pair. The free energy of
formation of the proton vacancy/interstitial pair will be lowest for interstitial sites that
reform a hydrogen bond. Proton conduction is then possible by the migration of protons
within and between the normal hydrogen-bonded network and the instantaneous network
of interstitial hydrogen bonds.
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30
In KH2PO4, Baranov suggests probable interstitial sites with O(1)ทททO(2') distances
of 3.16 ล, which could form a weak to medium strength hydrogen bond after structural
relaxation 46. A representation of this interstitial site is shown in Figure 1.9 a. An
equivalent interstitial site in ice is not found as the next-nearest neighbor oxygens for
each oxygen atom are ~ 4.5 ล distant, too far away to form a hydrogen bond58. Baranov
states this mechanism of proton conduction seems even more likely for solid acids with
oxygens that are not structurally involved in hydrogen bonds, such oxygens acting as
“built-in” interstitial sites. The direction(s) of the interstitial hydrogen bond(s) are then
determined by finding the nearest oxygen atoms. In the M3H(XO4)2 compounds, the
pseudo-trigonal symmetry of the room temperature phases results in two interstitial sites
per tetrahedron and is schematically depicted in Figure 1.9 b46. For a solid acid
containing infinite chains of hydrogen-bonded tetrahedra similar to those found in
CsHSO4
26, a vacancy/interstitial proton conduction mechanism is shown in Figure 1.10.
The ideal structure of CsHSO4-II has O(3) and O(4) atoms not involved in hydrogen
bonds. An interstitial hydrogen bond between these two oxygens is proposed by Baranov
as the O(3)ทท O(4) distance is only 3.2 ล46.
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31
b)
a)
Figure 1.9 Normal and interstitial hydrogen bonds proposed for room temperature
phases of a) KH2PO4 and b) the M3H(XO4)2 class of compounds. Solid and dashed lines
denote normal and interstitial hydrogen bonds, respectively.
a)
b)
c)
d)
e)
f)
Figure 1.10 Possible conduction paths for proton vacancy/interstitial defects along and
in between hydrogen-bonded zigzag chains of anion tetrahedra. Notice the formation of
potential water molecules (i.e., an oxygen with two hydrogen bonds) is not a necessity for
proton transport.
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32
Although there is agreement in the literature that proton conduction occurs by the
Grotthuss mechanism in the low temperature phases of solid acids, in the end there is no
definitive proof of the particulars of the mechanism. Hence, there is a question as to
which pair is formed: D and L or vacancy/interstitial defect pairs. Similarly, it has not
been determined if the structural relaxation necessary for protonic conduction in these
low temperature phases occurs by actual rotations of the tetrahedra or simply by dipole
reorientations resulting from proton jumps.
1.4.3
High Temperature Proton Conduction in Solid Acids
For the high temperature superprotonic phases of solid acids, the mechanism of
proton conduction is not in dispute. A highly disordered state leads to fast local dynamics
of the anion tetrahedra and subsequent proton translation via the Grothhuss mechanism35.
It has been determined that the tetrahedra are librating much faster (1011 Hz) than protons
are being transferred (109 Hz) which indicates that the structural relaxation essential to
the Grotthuss mechanism is due to the physical reorientations of the tetrahedra in these
phases59,60. The increase in symmetry across the phase transition (typically monoclinic →
rhombohedral, tetragonal, or cubic) results in disorder on the oxygen sites, which are then
free to vibrate and librate between crystallographically identical positions. This nearly
free rotation of the tetrahedra creates many more crystallographically equivalent proton
sites than there are protons, resulting in a “dynamically” disordered hydrogen-bonded
network9.
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33
In contrast to protonic conduction in the room temperature phases of solid acids, it
is then possible for proton conduction through only “normal,” crystallographic proton
sites. The combination of fast tetrahedral dynamics and proton translations along
hydrogen bonds of a disordered network results in high protonic conductivity.
Superprotonic conduction is therefore a result of the ideal structure rather than intrinsic
defects60. In terms of Equation 1-1, this superprotonic conductivity is a product of the
increase in the proton’s mobility and the increase in the number of mobile protons (all of
them).
The structure proposed by Jirak for CsHSO4 in its superprotonic phase is given in
Figure 1.1161. It should be mentioned that there is some disagreement in the literature
over the exact position of the oxygen atoms, and hence the protons. This structure was
chosen as it gives the most realistic arrangement and length to the hydrogen bonds, as
well as its overall fit to experimental data (to be discussed in Section 4.6.1).
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34
a)
b)
Cs
H+
SO4
Figure 1.11 Tetragonal structure of CsHSO4 above its superprotonic phase transition
projected along the [100], c), and [010], d), directions. Two orientations of the tetrahedra
result in partially occupied proton sites and a disordered network of hydrogen bonds
(dashed lines).
The room temperature phase of CsHSO4-II is monoclinic, space group P21/c,
comprising zigzag chains of hydrogen bonded SO4 tetrahedra alternating with zigzag
rows of cesium atoms (Figure1.3). There are four crystallographically distinct oxygens,
two of which are involved in asymetric hydrogen bonds with O(1)ทททO(2) distances of
2.63 ล26. On the contrary, after transforming to the superprotonic tetragonal phase (space
group I41/amd), the oxygens become crystallographically identical and all oxygens
participate in hydrogen bonds. There are two possible orientations of the tetrahedra,
resulting in ฝ and ผ occupancy of the oxygen and proton sites, respectively. Hydrogen
bonds of average length 2.78 ล connect the oxygens61. Other proposed structures have a
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35
different number of tetrahedral orientations, hydrogen bond lengths and hydrogen bond
orientations. However, regardless of the exact configuration of oxygens and protons in
the superprotonic phase of CsHSO4, the method of proton conduction remains the same:
rapid reorientations of the SO4 group forming a dynamically disordered network of
hydrogen bonds through which protons can jump from one tetrahedron to the next.
This mechanism of proton transport is responsible for the high conductivity in all
superprotonic phases of solid acids, with any differences between their conductive
processes attributed largely to the relative symmetry of the specific material. For
example, CsHSO4, being tetragonal, shows a small anisotropy in its conductivity parallel
and perpendicular to its 4-fold axis62. In contrast, the compound Cs2(HSO4)(H2PO4),
which transforms to a cubic structure (space group Pm 3 m) exhibits isotropic
conductivity in the superprotonic phase63. Nevertheless, on a very local scale, the process
of proton transfer and reorientation is considered to be very similar in all superprontic
phases and conclusions reached for one compound should apply at least to structurally
related compounds, if not to the whole class of solid acids.
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Chapter 2. Experimental Methods
2.1 Synthesis
The solid acids analyzed in these studies were all grown by slow evaporation of
an aqueous solution containing high purity metal carbonates and the appropriate mineral
acids:
M2CO3 + HnXO4 + H2O  →

−OH
2
→ single crystals
where M = Cs, Rb, NH4, K, Na, Li and X = S, P. Most crystals were grown at room
temperatures, but some compounds were found to grow only at elevated/lowered
temperatures. The compounds discussed in this work are primarily mixed cation sulfates
(Chapter 3) and cation sulfate-phosphates (Chapter 4). First attempts at their synthesis
were carried out in solutions with total metal to anion (M:XO4) ratios of 1:1. Therefore,
unless otherwise noted, it is safe to assume a compound was synthesized at ~25ฐC with a
solution M:XO4 ratio of 1:1.
After the formation of crystal samples, they were collected by either removing
individual crystals directly from solution, or by filtration over a porous ceramic (since the
solutions are still quite acidic and would eat through normal filters). If necessary, the
samples were washed with acetone or isopropanol to remove any excess solution clinging
to the crystals. Deliquescent compounds were placed in desiccated containers, while most
other samples were stored in ambient conditions.
For large quantities of a desired phase or to force the synthesis of a compound not
found to grow by the above method, organic solvents were used to precipitate powder
samples. The most common solvents used were acetone, methanol, and isopropanol. The
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37
powders were filtered from solution and washed with the precipitating liquid on ceramic
filters. Powder samples were stored in sealed containers to limit surface water absorption.
2.2 X-ray Diffraction
X-ray diffraction methods were almost exclusively used to identify the phases of
crystals grown as above. For the most part, the diffraction measurements were performed
on single crystal samples so as to provide very accurate phase determinations, single
crystal samples for other measurements, and the possibility of orienting the samples. If it
was necessary to analyze the abundance of different phases grown from the same
solution, a random sampling of crystals was finely ground together and a powder X-ray
diffraction (PXD) measurement taken.
Single crystal X-ray diffraction (SCXD) measurements also provided the data for
determining the structures of any novel compounds. SCXD samples were cut from single
crystals and shaped into rough cubes, on average ~ 0.15 mm a side. The small crystallites
were then attached to the top of a thin glass fiber by a common two-part epoxy and the
glass fiber mounted in a cylindrical brass holder. The brass holder was then placed in a
goniometer and the cube aligned in the center of the X-ray beam. Diffraction intensity
data for the aligned samples were obtained on a Syntex four-circle diffractometer using
Mo Kα radiation (λ = 0.71073 ล). Decay and absorption corrections were applied as
necessary and structural refinements performed on the resulting F2 data for the collected
reflections. The SHELXS86 and SHELXL93 (or SHELXL97) programs were used for
structure solution and refinement, respectively64,65. Visual inspection and depiction of the
structures were accomplished with the ATOMS program66.
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38
Unfortunately, the relatively large (~ 1 to 2 %) volume changes typical of
superprotonic transitions causes single crystal samples to turn polycrystalline and become
useless in SCXD measurements. Hence, the high temperature structures were determined
from PXD measurements taken above the phase transition temperature. Also, from
Reitveld refinements of PXD patterns taken at elevated temperatures the thermal
expansion coeffiecients for both low and high temperature phases were measured
allowing for accurate calculations of the transition volume changes. The program Rietica
was used in such refinements67. PXD measurements were also used to confirm the phase
purity of solvent precipitated samples. Calculated patterns were generated from published
data using the Micro-Powd program and then compared to the measured PXD patterns
with the program JADE68,69. Unless otherwise stated, the PXD measurements reported in
this work were taken on a Siemens D500 diffractometer with Cu Kα radiation (λ =
1.5418 ล).
2.3 Neutron Diffraction
Neutron diffraction on both single crystal and powder samples was performed to
take advantage of its sensitivity to light elements and atoms with similar atomic numbers.
Due to the difficulty in taking such measurements, a nuclear reactor or scintillation
source being required, neutron diffraction measurements were only taken when analysis
of the X-ray diffraction data failed to definitively resolve a crystal’s structure. For
compounds in this work, any ambiguity in their structures usually resulted from the
inability to accurately locate H/D atoms or to differentiate between sulfate and phosphate
groups. Both problems are a direct result of the fact that the scattering lengths for X-rays
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39
increases monotonically with atomic number. Hence, H/D atoms are fairly transparent to
X-rays, while SO4 and PO4 groups will scatter X-rays almost identically70.
Conversely, in neutron diffraction H and D atoms are easy to discern as their
coherent scattering lengths are -3.739 and 6.671 fm, respectively, making both atoms
strong neutron scatterers71. Also, the scattering lengths for S and P are quite different for
neutrons (5.13 and 2.847 fm, respectively), and it is usually straightforward to distinguish
between the two atoms or even determine their individual occupancies on a mixed S/P
site72. In particular, neutron diffraction was used in this work to resolve the H/D and O
positions for atoms involved in disordered hydrogen bonds in the otherwise ordered room
temperature phases. For the superprotonic phases, the H/D and O positions resulting from
the fast reorientations of the tetrahedra were also investigated, along with the possible
existence of superstructures do to potential ordering of the tetrahedra in mixed sulfate-
phosphate compounds. Measurements used thermal neutrons with wavelengths ~ 1 ล
generated from both reactor and spallation sources.
2.4 Thermal Analysis
The behavior of compounds with increasing temperature was probed by two main
techniques: differential scanning calorimetry (DSC) and thermal gravimetric analysis
(TGA). The presence and characterization of phase transitions both above and below
room temperature were accomplished by DSC measurements. A compound’s response to
heating was examined with a Perkin-Elmer DSC 7 calorimeter in a flowing nitrogen
environment. The most common heating rates were 5, 10, and 20ฐC/min. For low
temperature measurements, an in house apparatus was used which essentially consisted of
a Perkin-Elmer DSC 7 calorimeter immersed in a helium environment that had been cool
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40
by liquid nitrogen. A sample was therefore cooled to ~ -150ฐC (the limit for LN2) and
heated, at rates varying from 1-5ฐC, in 30ฐC intervals to limit instrument drift.
The onset of decomposition in a sample was probed by a Perkin-Elmer TGA 7 or
Neztsch STA 449 analyzer under flowing nitrogen and argon, respectively. Again, the
most common heating rates were 5, 10, or 20ฐC/min. The Neztsch system can
simultaneously take DSC and TGA data, but for consistency’s sake all DSC
measurements were taken on the Perkin-Elmer machines.
2.5 Chemical Analysis
The compositions of any new compounds were measured using a JEOL JXA-733
electron microprobe. Single crystal samples were mounted in an epoxy resin, polished
and then coated in carbon by evaporation. The polishing of single crystal samples was not
trivial as the compounds are water soluble. For some compounds, even best attempts at
polishing still resulted in poor quality surfaces for microprobe measurements. Hence,
pressed powder pellet samples (from ground up single crystals) were also analyzed, with
the advantage that the surfaces of the pellets were already flat and needed only to be
carbon coated. Microprobe data were taken at a minimum of seven points on a sample for
statistical averaging. High quality samples (single crystals or pellets) of compounds with
a like, but known, nature were used as standards. Measured X-ray peak intensities were
converted to elemental weight percentages using the CITZAF program73. For most
compounds (new/known solid acids and single crystal/pellet samples alike), visible beam
damage was observed during data collection. This damage is most likely the dehydration
of the surface when excited by the electrons in the beam. For this reason, larger rather
than smaller areas were scanned in the measurements.
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2.6 Optical Spectroscopy/Microscopy
Superprotonic phase transitions of some compounds were further investigated by
infrared (IR) spectroscopy and polarized light microscopy. The vibrational spectrum of
compounds pressed into optically transparent KBr pellets (sample:KBr mass ratio of
1:300) were measured on a Nicolet Magna 860 FTIR spectrometer in flowing nitrogen.
An in house heating stage was employed to heat the pellets and observe the changes in
their spectrums with temperature. Most attention was given to the changes with
temperature in the bending and stretching modes of the tetrahedrons (in the range of 450
to 1100 cm-1) as well as the OH stretching modes within the O-HทททO bonds. These modes
show up as three broad peaks ~ 1700, 2400, and 2800 cm-1 and are often referred to as the
“ABC bands” of hydrogen bonds14. From the behavior of the tetrahedral modes, the
increase in symmetry associated with almost all superprotonic transitions could be
observed, hopefully validating the assigned symmetry taken from PXD data.
Observations of the ABC bands not only confirmed the presence of hydrogen bonds, but
also revealed the general effect of a phase transition on these bonds.
Polarized light microscopy was most often used to judge the quality of single
crystal samples. This was accomplished by observing the sample under extension
conditions on a transmission Leica DMLB microscope. For a single domain crystal
without inclusions or attached crystallites the perceived image should be homogeneous.
By attaching a single crystal sample to a heating stage, high temperature transitions could
be observed. In most cases, single crystal samples would become completely opaque
above a superprotonic transition due to the high symmetry of the phases. This technique
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42
was also an easy way to determine if single crystal samples would turn polycrystalline or
not when undergoing a transition, which influenced other measurements.
2.7 NMR Spectroscopy
Pulsed Fourier transform H+ NMR measurements were performed on a finely
ground sample to characterize the proton environment of the compound. Specifically, the
number of crystallographically distinct hydrogen atoms and their relative amounts were
investigated. Also, the percent deuteration of a compound was accurately measured by
taking the ratio of the integrated intensities of deuterated and fully protonated samples.
All measurements were taken on either a Bruker DSX 500 MHz or a Bruker AM 300
MHz NMR spectrometer. The chemical shifts of the samples were referenced to
tetramethylsilane (TMS). Magic angle spinning (MAS) was employed to reduce the
proton-proton dipole broaden of the signal lines resulting from the local interactions of a
proton’s magnetic moment with the dipole fields generated its neighbors.
For most measurements, a 12 kHz spinning rate was used in conjunction with a 4
ตs, 90ฐ pulse. The spin-lattice relaxation time, T1, was on the order of 1000 s for all
compounds measured, revealing that the excited H+ nuclei in these solid acids interact
weakly with their surrounding lattices. The observed chemical shifts for the
crystallographic protons were ~ 10-12 ppm, typical values for protons residing in
medium strength hydrogen bonds74. There was often a very sharp peak seen at ~ 6 ppm
that was attributed to absorbed water based on its disappearance with heating and a
comparison to measurements on calcium phosphates, where similar peaks were observed
and assigned to surface water75.
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2.8 Impedance Spectroscopy
The conductivity of a compound was measured by a.c. impedance spectroscopy
using a 4284 LCR (inductance-capacitance-resistance) meter. Conductivity
measurements were taken on cut and polished single crystal samples along known
crystallographic directions (as determined by SCXD methods), while polycrystalline
samples were made from finely ground single crystals that had been uni-axially pressed
into pellets. Silver paint (Ted Pella cat. no. 16032) served as the electrode material.
Samples were prepared so as to have a large area to length ratio (A/L) with respect to the
direction of the applied field. Such a geometric ratio is desirable as it decreases a
sample’s effective resistance and gives better signal resolution. Measurements were made
over the frequency range of 20 Hz to 1 MHz with an applied voltage of 1 V under either
inert (dry argon or nitrogen) or ambient atmospheres. Heating and cooling rates were
0.5ฐC/min (unless otherwise noted). For most samples, the impedance spectra exhibited a
single arc in the Nyquist representation. The effective d.c. resistivity, ρ, was determined
by fitting such an arc to an equivalent (RQ) circuit using the least squares refinement
program EQUIVCRT76. The effective resistivities (ρ = R) were then converted into
geometry independent conductivities, σ= 1/(ρ*A/L), and plotted in an Arrhenius form to
facilitate the extraction of informative parameters from the data (see section 1.2). Since
this impedance spectroscopy method is probably the least well known technique used in
this work, its basic theory will be described below.
Page 62
44
2.8.1 Complex Impedance (from ref 77-79)
The simplest model for an electrode-sample system under an applied voltage is a
capacitor and resistor in parallel, Figure 2.1 a. The capacitor is a result of the sample’s
geometry, while the resistor represents the resistivity of the bulk. For such a circuit, the
response to an applied voltage,
tieoVtV
ω
=
)(
(2-1)
will be a current in the resistor,
R
tV
R
ti
e
o
V
RI
)(
=
=
ω
(2-2)
and a current in the capacitor,
)(
))((
)(
tCVi
ti
eoCVi
dt
ti
e
o
dV
C
dt
tCVd
dt
tdQ
C
I
ω
ω
ω
ω
=
=
=
=
=












(2-3)
The total current in the circuit is then
)(
)(
tCVi
R
tV
CI
I
totalI
R
ω
+
=
+
=
(2-4)
Exactly like the conventional impedance, Z, the complex impedance is defined as the
ratio between the voltage and current, which is here:
Ci
R
tCVi
R
tV
tV
Z
ω
ω
+
=
+
=
1
1
)(
)(
)(
(2-5)
The impedance can be separated into its real, Z′, and imaginary, Z′′, parts to give
Page 63
45
( )
( )
ZiZ
C
R
C
i
C
R
R
Z
′′−′=
+
−
+
=












2
21
2
21
1
ω
ω
ω
(2-6)
A plot of Z′ vs. -Z′′ (as parametric functions of ω) will result in a semicircle of radius R/2
in the first quadrant, Figure 2.1 b. The time constant of this simple circuit is defined as
o
RC
o
ω
τ
1
=
=
(2-7)
and corresponds to the characteristic (dielectric) relaxation time of the sample.
Substituting
o
ω from Eq. (2-7) into Eq. (2-6) gives Z′ = R/2, Z′′ = R/2, so that the
characteristic frequency lies at the peak of the semi-circle. A plot of Z′ vs. -Z′′ is often
called a Nyquist plot.
Figure 2.1 Equivalent circuit for a dielectric material between two electrodes, a): Rb and
Cb represent the bulk resistance and capacitance, respectively. This circuit gives a semi-
circle in the complex impedance plot of Z′ vs. -Z′′. The frequency increase from right to
left and the characteristic frequency of the electrode-material system lies at the peak of
the semicircle.
Page 64
46
One of the major advantages of complex impedance spectroscopy over single
frequency or DC techniques is its ability to resolve the electrode, bulk, and grain
boundary (for polycrystalline samples) contributions to the resistance. In an ideal sample,
the impedance plot would show three semicircles and would be modeled as three (RC)
circuits in series, Figure 2.2. This type of impedance plot is often seen for pure ceramics
such as ZrO2, but almost never seen for the proton conducting compounds of this work.
Instead, only one (single crystal samples) or two semi-circles (polycrystalline samples)
were usually present at low temperatures, representing the bulk and grain boundary
responses to the applied voltage. This type of impedance plot was modeled by two (RC)
circuits in series, i.e., the first two circuits in Figure 2.2 a.
Figure 2.2 Separation of bulk, grain boundary, and electrode resistances is possible by
impedance spectroscopy if a sample’s complex impedance plot shows three separate
semi-cirlces, a), by fitting the data to a three element RC circuit, b).
Page 65
47
At elevated temperatures, the second arc (due to grain boundaries) virtually
always disappeared, which can be attributed to the grain boundaries having a higher (than
the bulk) activation energy for proton conduction. The total resistance of the grain
boundaries would then decrease much faster than the bulk, represented in the Nyquist
plots by an ever shrinking second arc with increasing temperature. In its place, a nearly
straight line was usually seen, caused by a variation of the effective resistance and
capacitance of some element(s) in the circuit with frequency, Figure 2.3 a. This variation
comes from a distribution of relaxation times in the sample as a result of inhomogeneties
in the material and/or when the diffusion of an uncharged (or effectively uncharged)
species responding to a chemical potential becomes the rate controlling step. For solid
electrolytes, the later situation typically refers to the mobile species diffusing through the
electrodes, which have an effective potential gradient of zero due to the presence of
majority electronic carriers. Such a process results in a straight line at 45ฐ degrees to the
Z′ (real) axis as proven by Warburg and Macdonald78,80.
b)
CPE
Rb
a)
-Z’’ (
)
Ω
Z’ ( )Ω
ω =1/
ο
R C
b
b
ω
Θ
R /2
b
R /2
b
CPE
CPE
Figure 2.3 Realistic impedance plot showing a depressed semi-circle with center below
the real axis and straight line at low frequencies, a). Both effects are due to the
distribution of characteristic frequencies in the sample and are modeled with a constant
phase element (CPE), b).
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48
However, lines observed in this work usually deviated from 45 degrees, attesting
to true physical inhomogeneities in the samples. The most common cause of such
inhomogeneous behavior is rough electrode/electrolyte interfaces, which causes the
microscopic resistivities and capacitances near the interface to be “distributed” around
the mean macroscopic values. Distributed relaxation times are also caused by variations
of local composition and/or structure. As well as the appearance of lines at low
frequencies, these inhomogeneities also result in depressed semi-circles with centers
below the real axis, Figure 2.3 a. Both these distributed effects are modeled by
introducing a constant phase element (CPE) with impedance
ψω
−
= )(
iA
CPEZ
(2-8)
The CPE equivalent of the normal RC circuit then has an impedance of
ψω
ψω
)(
1
1
)(
)(
)(
)(
iA
R
iA
tV
R
tV
tV
Z
+
=
−
+
=
(2-9)
The CPE reduces to an ideal capacitor for Ψ = 1 and to a resistor for Ψ = 0, and thus can
model the distribution of microscopic capacitors and resistors in a material.
For compounds with superprotonic transitions, the conductivity increases by ~
102-103 across the transition. Not surprisingly then, the semi-circle in Figure 2.3 a
disappears, usually leaving only a straight line visible in the Nyquist plots of the
superprotonic phases. The resistance of the bulk (and therefore the materials
conductivity) was then estimated by the intercept with the real axis of a least squares
Page 67
49
refinement on the line. This estimation was necessary as the frequencies associated with
superprotonic conduction exceeded the upper limit of our impedance meter (1 MHz), but
nevertheless gave highly reproducible values that also compared well with those in the
literature, and so was deemed acceptable.
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50
Chapter 3. Cation Size Effect on the
Superprotonic Transitions of MHnXO4
compounds (M = Cs, Rb, NH4; X = S, Se, P, As;
n = 1-2)
3.1 Introduction
The effect of alkali ion substitution on solid to solid phase transitions in the
MHnXO4 class of compounds has been well documented. The initial investigations of
these solid acids focused on the low temperature behavior of the MH2XO4 (M = Cs, Rb,
NH4, K; X = P, As) compounds, looking for ferroelectric transitions similar to that
discovered in KH2PO4 at 123K1. It was found that the K, Rb, and Cs phosphates and
arsenates all exhibited ferroelectric transitions with the average change in the transition
temperatures upon isovalent substitution being81:
4
4
40
36
14
OAs
PO
Cs
Rb
K
K
K
K
 →

 →

 →

−
⊕
⊕
(3-1)
From this it seems clear that larger cations inhibit the ferroelectric transitions in this class
of compounds.
After the discovery of the superprotonic phase transition in CsHSO4 at 142ฐC, the
high temperature properties of the entire class of compounds began to be examined3. In
contrast to the results of the low temperature transitions, increased cation size was found
to lower the superprotonic phase transitions, which were observed only in the compounds
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51
with the largest cations, Table 3.1. The explanation for this phenomenon was generally
held to be that the increased ionic radius of the cations resulted in larger X-X distances
(X = S, Se, P, As), thereby creating more room for the nearly free rotations of the
tetrahedra observed in the superprotonic phases39. The phosphate and arsenate
compounds are not listed on Table 3.1 as only the Cs compounds undergo superprotonic
phase transitions at 232 and 162ฐC for CsH2PO4 and CsH2AsO4, respectively46. Also, the
TlHSO4 compound is reported to have a superprotonic transition at 115ฐC, but its room
temperature structure has not yet been reported and hence the coordination of the Tl
cations is not known82. Since the ionic radius of the Tl ions varies from 1.76 to 1.60 in
going from a coordination of XII to VIII, respectively, it is not appropriate to compare
the properties of TlHSO4 to those of the other MHSO4 compounds until its structure is
known.
Table 3.1 Superprotonic phase transitions for MHXO4 class of compounds. The ionic
radii of the cations are based on their average coordination (superscripted Roman
numerals) in these materials. For the central ion of the tetrahedra, the covalent radii are
given for a four-fold coordination83.
Radius of M/X
(ล)
S IV
0.26
Se IV
0.43
Ref
CsX
1.81
Tsp = 142 ฐC
Mono, P21/c →
Tetra, I41/amd
Tsp = 128 ฐC
Mono, P21/c →
Tetra, I41/amd
84
85
RbVIII
1.61
Tsp = 227 ฐC at 0.31 GPa
Mono, P21/c →?
At 1 atm, Tmelt = 203 ฐC
Tsp = 174 ฐC
Mono, B2 →
Mono, C2h?
86
85,87
88
NH4
VIII
1.59
Tsp = 177 ฐC at 1.77 GPa
Mono, B21/a →?
At 1 atm, Tmelt = 146 ฐC
Tsp = 144 ฐC
Mono, B2 →
Mono, P21/b?
89
90
91
As was seen in the ferroelectric transitions, substitution of a larger central ion in
the tetrahedra lowers the superprotonic transition temperatures. This effect is evident in
Page 70
52
the fact that under ambient conditions the Rb and NH4 selenate compounds have
superprotonic phase transitions before melting, whereas in the analogous sulfate
compounds pressure must be applied to raise Tmelt above that of Tsp
86. Also, in the Cs
phosphate and arsenate compounds, the transition temperature drops 60 degrees when the
PO4 groups are replaced by the larger AsO4 tetrahedra. These results are at odds with the
statement that larger cations increase the volume in which the tetrahedra reorient since
one would then expect the bigger tetrahedra to require coordination by proportionally
larger cations for a superprotonic transition to be feasible. However, exactly the opposite
result is measured. The underlying cause for the observed behavior was therefore not
clearly understood with the limited number of data points given in Table 3.1, although the
overall effect of increasing the size of the cation and/or the tetrahedral ion is clearly to
promote superprotonic phase transitions in these compounds.
This work was carried out to better explain this connection between
cation/tetrahedral ion size and the presence of superprotonic transitions. The approach
taken was to synthesize compounds with mixed M+1 ions and thereby vary the average
cation size. Unfortunately, attempts to grow selenate compounds categorically failed; the
normal (and even abnormal) synthesis routes resulting in, almost exclusively, the M2SeO4
salts. Also, the phosphate and arsenate compounds were avoided due to the known
instability of the superprotonic phases of the pure cesium compounds92,93. Hence,
attention was focused on mixed cation sulfate compounds.
3.2 Mixed Cation Sulfate Systems
Attempts to deduce the correlation between a compound’s average cation size and
the presence/absence of a superprotonic phase transition started with investigations into
Page 71
53
the mixed Cs/K, Cs/Na, and Cs/Li systems. The emphasis on Cs is for the obvious reason
that CsHSO4 has a known superprotonic transition. On the other hand, the K, Na, and Li
hydrogen sulfate compounds all melt/decompose without transforming to a highly
conductive phase94-96. Therefore, replacing some of the Cs atoms with the smaller alkali
cations in CsHSO4 was hoped to have quite dramatic and quantifiable effects on the
superprotonic transition. Mixed Cs/Rb compounds were not explored as the Cs/Rb
system had already been investigated resulting in two new compounds, Cs0.9Rb0.1HSO4
and Cs0.1Rb0.9HSO4, which can be considered as structural modifications of end members
CsHSO4 (phase II) and RbHSO4, respectively97,98. The high temperature properties of
these compounds are nearly unchanged from those from which they were derived,
namely the cesium rich compound has a superprotonic transition ~ 142ฐC, while the
rubidium rich compound exhibits no high temperature transition before melting ~
177ฐC99. These compounds then confirm that a larger average cation radius encourages
superprotonic transitions, but do not further illuminate the fundamental correlation
between the two parameters since the structures and properties are nearly identical to
those of the end-member compounds.
Mixed Cs/NH4 compounds were avoided as the presence of the NH4 cations is
known to cause markedly different properties in solid acids. For example, the
(NH4)3H(SeO4)2 compound has a superprotonic phase transition at 27ฐC, whereas the
isostructural K and Rb compounds have transitions at 115ฐ and 185ฐC, respectively100,101.
Also, note that the NH4HSeO4 compound transforms to the superprotonic phase 30
degrees lower than the RbHSeO4 compound, Table 3.1. This anomalous behavior is
attributed to the fact that the hydrogen atoms of the ammonium ions often form hydrogen
Page 72
54
bonds to the tetrahedral oxygen atoms and that the NH4 groups typically show some
degree of disorder at room temperatures102-104. The bonding of the ammonium cations
will therefore be highly directional and/or highly variable when compared to the purely
electrostatic interactions of the spherical alkali metal cations. Analysis of any mixed
Cs/NH4 compounds would be complicated by such considerations, it being difficult to
resolve the cation size effect from the ammonium ion effect on a phase transition, and
therefore their synthesis was not attempted.
For the above reasons, only the mixed Cs- K/Na/Li systems were investigated.
These systems also had the additional advantage in that there is a large difference
between ionic radius of Cs versus K, Na, and Li. It was hoped that this difference would
highlight the essential structural properties associated with large cations and
superprotonic phase transitions. It should be mention here that the synthesis and
characterization of all the mixed systems Cs/M+1 mentioned here have been reported by
other researchers (primarily Mhiri et al.). The published results suggest that solid
solutions of the mixed cations are possible and that often the high temperature properties
gradually change from those of CsHSO4 to those of the MHSO4 compound in question.
This is in complete disagreement with the results of the present work and seems highly
implausible as none of the other MHSO4 compounds are isostructural to CsHSO4.
Moreover, except for work on crystals whose structure had been determined (e.g.,
Cs0.9Rb0.1HSO4 and Cs0.1Rb0.9HSO4), these investigations analyzed powder samples
created by grinding together crystals grown by aqueous synthesis99,105,106 107. It is
therefore not very surprising that they found very smooth changes in properties as the
percentage of substitutant M+1 cation in the solutions was increased. Also, the techniques
Page 73
55
used to characterize the powders measured only the average properties of the samples:
powder X-ray diffraction, Raman spectroscopy, differential scanning calorimetry, and
conductivity measurements of pressed powder pellets. For these reasons, this work will
not refer to these investigations.
3.2.1 Synthesis and Characterization Techniques
Crystals examined in these mixed cation systems were synthesized by mixing the
appropriate amounts of the metal carbonates (Alpha Aesar puratonic, assay 99.999%) and
sulfuric acid (98% aq. sol.) in an aqueous solution, followed by slow evaporation at room
temperatures:
(1-x)*Cs2CO3 +(x)*M2CO3 + H2SO4 + H2O  →

C
o
25~
→single crystals
where M = K, Na, or Li and the total cation to anion ratio, (Cs+M):SO4, was held at 1:1.
This process was carried out in 10% molar increments of the secondary cation, M, except
where the discovery of new compounds merited a smaller increment of 5%.
The phases of the resulting single crystals were identified by single-crystal X-ray
diffraction (SCXD) techniques. Differential scanning calorimetry (DSC) and thermal
gravimetric analysis (TGA) were used to measure the thermal properties of the single-
crystals at elevated temperatures. Finally, conductivity measurements on single crystals,
or single crystals ground-up and pressed into pellets, were performed to confirm the
presence/absence of a superprotonic transition and to compare with the conductivity of
CsHSO4. The emphasis here is that whenever possible, only single-crystal samples were
grown and only single-crystal samples were analyzed.
Page 74
56
3.2.2 Resulting Phases of the Mixed System Investigations
The above synthesis route resulted in the compounds listed in Table 3.2. At very high
cesium percentages, slight modifications to CsHSO4-III, the meta-stable phase of
CsHSO4 that grows out of aqueous solutions, were discovered for all three systems. The
evidence for incorporation of the smaller cations into CsHSO4-III was first seen in the
SCXD measurements. The lattice constants of the modified structures were nearly
identical to that of CsHSO4-III, in an alternative primitive cell, but with the length of the
c-axis tripled compared to the pure compound. This primitive cell is transformed into the
crystallographically correct cell of undoped CsHSO4-III by the transformation: a′ = a –
ฝ*c, b′ = b, c′ = 2*c. The amount of K, Na , and Li incorporated into CsHSO4-III’s
structure is quite small as full data collections were not able to locate the ions although
they did confirm the tripling of the c-axis. It would appear that the smaller cations are
substituted on the Cs sites where they are hidden by cesium’s much larger scattering
factor for X-rays108. In a similar manner, electron microprobe measurements were unable
to observe the lighter cations.
For the Na compound, both Na+ and H+ NMR measurements were performed. A
very small peak in the Na+ NMR measurement was observed, but it was impossible to
rule out small amounts of Na contaminants as the cause of this peak. The proton NMR
measurements were more conclusive, in that two distinct peaks of significant magnitude
were observed for the doped sample, whereas the scan of the reference, undoped,
CsHSO4 sample showed only one peak (see appendix A). The sodium ions then again
Page 75
57
Table 3.2 Compounds synthesized in the mixed Cs-K/Na/Li systems. The average cation radius was calculated using both the ratio and particular
coordination of the cations in a compound.
System
Solution
Composition
% M2CO3
Compound
Obtained
Space
Group or
Symmetry
Lattice
Parameters
Average
Cation
Radius
Phase Transitions
Above RT
Comments and
References
All Systems
0
CsHSO4-III
P21/n
a = 8.229(2) ล, b = 5.8163(9) ล
c = 9.996(3) ล, β = 106.46(2)ฐ
1.81 ล
~ 62ฐC→CsHSO4-II;
142 ฐC→supeprotonic
a
109
CsHSO4−KHSO4
10-30
α-CsHSO4-III
P21(?)
a = 7.311(5) ล, b = 5.818(4) ล
c = 16.52(2) ล, β = 101.55(4)บ
~ 1.81 ล ~ 67ฐC→CsHSO4-II?;
140 ฐC→supeprotonic
New modification
of CsHSO4–III
40
α-CsHSO4-III &
K3H(SO4)2
50-100
K3H(SO4)2
A2/a
a = 9.790(4) ล, b = 5.682(2) ล
c = 14.702(4) ล, β = 103.02(5)บ
1.51 ล
190 ฐC→supeprotonic
190 ฐC→supeprotonic
a; b
23,110
CsHSO4−NaHSO4
5-10
β-CsHSO4-III
P21/m
a = 7.329(5) ล, b = 5.829(4) ล
c = 16.52(1) ล, β = 101.55(3)บ
~ 1.81 ล ~73ฐC→CsHSO4-II?;
141 ฐC→supeprotonic
New modification
of CsHSO4–III
15-35
Cs2Na(HSO4)3
P63/m
a = 8.572(2) ล
c = 9.982(2) ล
1.55 ล
139ฐC→melt
new compound
25,111
40
Cs2Na(HSO4)3
&
CsNa2(HSO4)3
45-55
CsNa2(HSO4)3
P213
a = 10.568(2) ล
1.28 ล
125ฐC→melt
new compound
25,111
60-100
NaHSO4ทH2O
a
CsHSO4−LiHSO4
10
γ-CsHSO4-III
P21(?)
a = 7.316(10) ล, b = 5.818(7) ล
c = 16.50(2) ล, β = 101.54(5)บ
~ 1.81 ล ~108ฐC→CsHSO4-II?;
141 ฐC→supeprotonic
New modification
of CsHSO4–III
20-80
Cs2Li3H(SO4)3
•H2O
Pbn21
a = 12.945(3)
b = 19.881(4)
c = 5.111(1)
1.08 ล
105ฐC→slow
decomposition
new compound
90-100
Li2SO4 •H2O
a
a) Compound previously known.
b) High temperature properties not previously investigated.
Page 76
58
revealed their presence indirectly through their effect on the surrounding structure, in this
case, the environment of the protons.
The incorporation of the K, Na and Li ions also showed up in the DSC
measurements. Upon heating the modified forms of CsHSO4-III, the transition to
CsHSO4-II (another monoclinic form) was observed to be systematically shifted to higher
temperatures as the size of the secondary cation decreased, Figure 3.1 a. Also, for the
Cs/Na compound, β-CsHSO4-III, two exothermic transitions instead of only one where
observed upon cooling, Figure 3.1 b. For this reason, the β-CsHSO4-III compound was
more extensively studied than the others. Conductivity measurements along the b-axis
revealed three, rather than two transitions, Figure 3.1 c. This discrepancy between the
DSC and conductivity results is probably due to sample size, i.e., very small crystals and
very large crystals were used in the DSC and conductivity measurements, respectively.
Low temperature DSC measurements also revealed an apparently second order transition
at -123.25ฐC not found in CsHSO4, Figure 3.1d112.
The temperature of the superprotonic phase transition, however, was not
significantly effected by the small amounts of K, Na, and Li present, Figure 3.1 a,
although the transition enthalpy was consistently lower for the mixed CsHSO4-III
compounds (see appendix A). These compounds, as was the case with Cs0.9Rb0.1HSO4,
do little to illuminate the cation size effect: their superprotonic phase transitions and
structures being essentially identical to those of CsHSO4. On the other hand, they do
reveal how sensitive these solid acids are to the addition of a secondary cation. In fact,
trace levels would appear to be the upper solubility limit for K, Na, and Li in CsHSO4
Page 77
59
(and vice versa), the rest of the crystals synthesized being either line compounds or
compounds with a single type of cation, Table 3.2.
40
60
80 100 120 140 160
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
40
60
80 100 120 140 160
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Heat/Cool
rate = 5OC/min
under flowing N
2
*
b)
a)
Cs/Li
Cs/Na
Cs/K
Cs
He
at Flow (W
/g
)
Temperature (OC)
endo
exo
Cs/Na
*
*
*
*
Cs/Li
Cs
Cs/K
He
at Flow (W
/g
)
Temperature (OC)
Figure 3.1 (See figure caption on next page.)
Page 78
60
-125
-124
-123
-122
-121
0.0
0.1
0.2
0.3
0.4
2.2
2.4
2.6
2.8
3.0
3.2
-6
-5
-4
-3
-2
-1
0
1
180 160 140
120
100
80
60
40
Scan rate 0.1OC/min
Helium atmosphere
c)
d)
H
e a t F
l o
w
( m
c
a l / s e
c
)
Temperature (OC)
Heat/Cool rate = 0.5OC/min
under ambient atmosphere
heating
cooling
Temperature (OC)
L o g [
σ
T
]
Ω
-1
cm
-1
1000 / T (K-1)
Figure 3.1 Measurements on the α, β, γ-CsHSO4-III compounds. DSC curves upon
heating, a), and cooling, b) for all three modified forms of CsHSO4-III. Also, b-axis
conductivity and low temperature DSC measurements for the Na compound, c) and d),
respectively. Figure a) shows an increase in the phase III-II transition temperature with K
to Na to Li substitution. The difference of the Na compound from pure CsHSO4 is shown
in its two and three reverse transitions visible in the DSC, b), and conductivity data, c),
as well as the presence of a low temperature (apparently second order) transition, d).
Experimental parameters given on graphs.
For the Cs/K system, this insolubility phenomenon is particularly easy to see in
that only α-CsHSO4-III and K3H(SO4)2 crystals grew from the solutions. The K3H(SO4)2
compound belongs to another class of superprotonic conductors with general formula
M3H(XO4)2 (M = Cs, Rb, NH4, K, Na and X = S, Se). This compound had been
previously synthesized and its structure determined, but its high temperature properties
had not been sufficiently investigated23. Our studies revealed K3H(SO4)2 to have two high
temperature transitions before decomposition, both of which are superprotonic in nature
Page 79
61
and neither of which are analogous to the superprotonic transitions found in the other
M3H(XO4)2 compounds110. Typically, these transitions involve very small structural
changes from pseudo-trigonal to trigonal unit cells, with superprotonic conduction
primarily in the basal planes100. The tetrahedra in the superprotonic phases do not
undergo true rotations, but simply librate around a site with C3 symmetry113. These
librations primarily effect the positions of basal plane oxygen atoms, hence the
anisotropic proton conduction of the phases. It is therefore not appropriate to compare the
superprotonic transitions of the M3H(XO4)2 compounds to those of the MHXO4
compounds, and so the results for K3H(SO4)2 will not be included in this work.
The Cs/Li system resulted in a new mixed compound, Cs2Li3H(SO4)3ทH2O. DSC,
TGA and conductivity measurements show no evidence for a superprotonic transition
before the start of decomposition above 105ฐC (see appendix A). The lack of a
superprotonic transition is not surprising as the average radius for the four- and tenfold
oxygen coordinated lithium and cesium ions, respectively, is 1.078 ล83. Also, as this
compound is hydrated and has a cation to tetrahedra ratio of 5:3 (instead of the desired
1:1 ratio), any correlations between its structure and properties are not particularly
pertinent to the present discussion.
Fortunately, the Cs/Na system did produce two new mixed solid acids in the
MHXO4 family with chemical formulas of Cs2Na(HSO4)3 and CsNa2(HSO4)3
25. The unit
cell of Cs2Na(HSO4)3 is hexagonal while that of CsNa2(HSO4)3 is cubic, both novel
symmetries for the room temperature structures of the MHXO4 compounds. Moreover,
the single asymmetric hydrogen bond in both compounds links the SO4 groups into
unique three-membered (HSO4)3 rings. These rings are most likely due to the Na atom’s
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preference for a 6-fold oxygen coordination, with the resulting NaO6 octahedra serving as
a template for the (HSO4)3 units22. The Cs atoms in both compounds reside in irregular
polyhedra with a coordination of 9 to 12 oxygens, depending on the upper limit one sets
for the Cs−O bonds. The rings in Cs2Na(HSO4)3 are linked together by NaO6 octahedra to
form infinite Na(HSO4)3 chains that extend along [001], Figure 3.2 a and b, while in
CsNa2(HSO4)3 the rings form a distorted cubic close-packed array. In this array, the Cs
atoms are located within the “octahedral” sites and the Na atoms within the “tetrahedral”
sites, Figure 3.2 c and d.
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63
Figure 3.2 Crystal structures of the mixed Cs/Na compounds. The hexagonal structure
of Cs2Na(HSO4)3 is projected down [001]: a) unit cell contents from z = 0 to ฝ and b)
from z = ฝ to 1. Sodium atoms have elevations of z = 0 and ฝ, while those of the
cesiums are as indicated. Cubic structure of CsNa2(HSO4)3 projected along [100]: c) unit
cell contents from x = -ผ to +ผ and d) from x = +ผ to พ. Elevation of cations as
indicated. Some oxygen atoms have been omitted for clarity25.
Neither of these compounds undergoes a superprotonic phase transition before
melting at 139 and 125ฐC for Cs2Na(HSO4)3 and CsNa2(HSO4)3, respectively, as
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64
established by thermal analysis and visual inspection. The DSC curves for the
compounds are shown in Figure 3.3, along with conductivity measurements which show
the compounds to be fairly poor protonic conductors despite their high crystalline
symmetry.
70
-1
0
1
2
3
CsNa2(HSO4)3
Cs2Na(HSO4)3 - heat
Cs2Na(HSO4)3 - cool
end
o
exo
heat
cool
90
110 130 150 170 190
Temperature ( C)
O
He
a
t F
lo
w (W
/g
)
a)
b)
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
-7
-6
-5
-4
-3
-2
-1
0
1
160
140
120
100
80
T, OC
∆E
σ
=
0.26 eV
∆E
σ
= 0.66 eV
∆E
σ
~ 1.0 eV
lo
g
(σ
T) [
Ω-1
cm
-1
K]
1000/T (K-1)
Cs2Na a-axis
Cs2Na c-axis
CsNa2 pellet
CsHSO4 pellet
Figure 3.3 a) DSC and b) conductivity measurements on Cs2Na(HSO4)3 and
CsNa2(HSO4)3. Figure a) shows the melting transitions of the compounds beginning at
139 and 125ฐC, respectively. The cooling curve for CsNa2(HSO4)3 does not reveal a
solidification peak, which is in agreement with visual observations that the compound
solidifies as a glass upon cooling from the melt. Conductivity measurements revealed the
compounds’ protonic conductivity to be lower and activation energy higher than that of
CsHSO4’s room temperature phase. The observed curvature in the conductivity of
Cs2Na(HSO4)3’s a-axis is likely due to the onset of melting. DSC and conductivity
measurements taken under flowing N2 and dry argon atmospheres, respectively, with
heating/cooling rates of 10ฐC/min and 0.5ฐC/min, respectively.
3.2.3 Conclusions from Mixed System Investigations
Studies into the mixed CsHSO4-K/Na/LiHSO4 systems have resulted in six new
compounds, two of which are appropriate with the other MHXO4 compounds. Three of
the compounds (α, β, γ-CsHSO4-III) are slight modifications of CsHSO4-III, with
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65
correspondingly small changes to the structural and superprotonic parameters of the
parent compound. Analysis of these compounds with respect to the cation-
size/superprotonic-transition correlation tells us little we did not already know from
CsHSO4 itself. On the other hand, the new solid acid discovered in the Cs/Li system,
Cs2Li3H(SO4)3ทH2O, has a very different structure from the other MHXO4 compounds.
However, this compound also has a cation to anion ratio of 5:3 and is hydrated, both
properties which any cation-size effect conclusions drawn from this compound unsuitable
for comparision with those of the MHXO4 family of compounds.
Hence, the only compounds synthesized of use to the present discussion are the
mixed Cs/Na compounds, Cs2Na(HSO4)3 and CsNa2(HSO4)3. Using the structures of
these two compounds as well as those of the other MHSO4 compounds, we can create a
graph that depicts the changes to the characteristic distances of the crystals as a function
of the average cation radius, Figure 3.4. These distances act as crystal-chemical measures
of the cations’ role in the presence or absence of a superprotonic phase transition. Such
distances include the mean S-S, M-S, M-M, and M-O distances and the effective length
per formula unit (taken as the cube root of the volume per MHSO4 unit). The trend of the
mean S-S distance with cation radius is of particular interest because, as mentioned
earlier, the general consensus is that large X-X distances are necessary to lower anion-
anion interactions and thereby promote the rapid XO4 reorientations of the superprotonic
phases35. The most salient feature of Figure 3.4 is then that the average S-S distance in
Cs2Na(HSO4)3 is larger than that of CsHSO4. This result suggests that either the XO4 to
XO4 interactions are not critical to superprotonic transitions, or that the distance
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66
is not a useful measure of such interactions. The same can be said of the distance
as that of Cs2Na(HSO4)3 is also larger than that found in CsHSO4.
On the other hand, the average M-S, M-O and V1/3 distances all scale with the
mean cation radius. Of these three distances, the M-S distance varies much more across
the no-transition/transition line than the other two. This tends to confirm the observation
derived from the effects of substituting Se for S in the Cs, Rb, and NH4HXO4
compounds (Table 3.1) that the M-X distance reflects a truly critical crystal-chemical
parameter with respect to superprotonic phase transitions. Of course, these results do not
exclude the possibility that the M-O and V1/3 distances are of equal or more importance
than the M-X distance.
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
No
Transition Transition
Cs
Cs9Rb1
Cs1Rb9
Rb
NH
4
Cs
2
Na
K
CsNa
2
Na
LiHSO
4

V1/3

Distance [Angstroms]
[Angstroms]
Figure 3.4 Characteristic lengths of MHSO4 compounds as a function of average cation
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67
radius. Crystallographic data taken from the following sources: LiHSO4, 114; α-NaHSO4,
115; CsNa2(HSO4)3, 25; KHSO4, 24; Cs2Na(HSO4)3, 25; NH4HSO4, 116, RbHSO4, 117;
Cs0.1Rb0.9HSO4, 98; Cs0.9Rb0.1HSO4, 97; CsHSO4-II, 26.
Another distance of possible significance is the average O-O distance of the
hydrogen bonds in these solid acids. This distance is proportional to the energy associated
with a compound’s hydrogen bonds. As the energy of a hydrogen bond exponentially
increases with decreasing O-O distance, shorter hydrogen bonds will require much more
energy to break than longer bonds21. One would then expect that the presence of longer
(weaker) hydrogen bonds would favor a compound transforming to a superprotonic
phase, where these bonds will have to be continually broken and reformed as the
tetrahedra reorient. Moreover, the hydrogen bonds of the superprotonic phases are nearly
always longer than those below the transition35. Therefore, shorter bonds at room
temperature should increase the required transition enthalpy to the high temperature
phase. Nevertheless, in plotting the mean hydrogen bond O-O distance versus average
cation radius, Figure 3.5, there is no apparent relationship between the hydrogen bond
lengths and the presence of a superprotonic transition. This is concluded from the fact
that LiHSO4, NaHSO4, CsNa2(HSO4)3, and Cs2Na(HSO4)3 all have longer HBOND
distances than CsHSO4 and Cs0.9Rb0.1HSO4.
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68
0.8
1.0
1.2
1.4
1.6
1.8
2.55
2.60
2.65
2.70
2.75
Cs
2
Na
CsNa
2
Na
CsHSO
4
LiHSO
4
N
o
Tra
n
sition
Transition
Distance [Angstroms]
[Angstroms]

HBOND
Figure 3.5 Average hydrogen bond length versus mean cation radius. The Li, Na, CsNa2
and Cs2Na compounds all have an average hydrogen bond length longer than that of
CsHSO4. This fact suggests it would require a smaller loss in hydrogen bond energy for
these compounds to transform to a superprotonic phase compared to CsHSO4.
There is, however, a problem to the above comparisons and the conclusions
drawn from them, which is simply that the structures of the compounds are not the same.
In particular, the mixed Cs/Na compounds are quite different from the other compounds.
First, the unit cell symmetries of CsNa2(HSO4)3 and Cs2Na(HSO4)3 are cubic and
hexagonal, respectively, versus the monoclinic or tetragonal cells found in the other
MHSO4 compounds. Second, the alternating rows of anions and cations almost always
observed in the MHSO4 compounds are replaced with either the channels or FCC-like
array of the mixed Cs/Na compounds31. Finally, the way in which the tetrahedra are
connected by hydrogen bonds in CsNa2(HSO4)3 and Cs2Na(HSO4)3, into three-membered
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rings, is completely unique for the MHSO4 family of compounds. It is then possible that
the properties of the mixed Cs/Na compounds are due to their unique structures, making a
comparison with the other MHSO4 compounds less than ideal.
A rigorous application of this argument also invalidates the comparison between
the remaining MHSO4 compounds for all but RbHSO4 and NH4HSO4, which are
isostructural to each other118. This fact is particularly evident when evaluating the
hydrogen bond lengths, which are very much connected to the types of hydrogen bonds
(single or double minimum; fully or partially occupied) and hydrogen-bonded networks
(dimers, rings, or chains) present in the compounds. As seen in Table 3.3, the differing
structures of the MHSO4 compounds result in their having a broad distribution of
hydrogen bond types and networks, possibly explaining the seemingly random trend seen
in Figure 3.5.
Table 3.3 Hydrogen bond parameters for the MHSO4 compounds. Single, double and
partial hydrogen bond types refer to ordered single minimum, disordered double
minimum and partially occupied hydrogen bonds, respectively. Shaded cells denote
isostructural compounds.
Compound
Space
Group
Mean O-
O distance
Types of H-bonds
present
H-bonded
networks present
ref
LiHSO4
P21/c
2.644
Single
Chains
114
α-NaHSO4
P 1
2.642
Single, double,
partial
Branched chains
115
CsNa2(HSO4)3
P213
2.674
Single
Rings
25
KHSO4
Pbca
2.596
Single, double
Dimers, chains
24
Cs2Na(HSO4)3
P63/m
2.728
Single, partial?
Rings
25
NH4HSO4
B21/a
2.556
Single, partial
chains
116
RbHSO4
P21/c
2.564
Single, partial
chains
117
Cs0.1Rb0.9HSO4
P21/c
2.541
Single, double
Chains
98
Cs0.9Rb0.1HSO4
P21
2.59
Single
Chains
97
CsHSO4-II
P21/c
2.636
Single
Chains
26
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70
The conclusions drawn from this work on the mixed Cs-K/Na/LiHSO4 systems in
conjunction with the other MHSO4 compounds therefore concur with the initial
observations that the distance seems to be a critical crystal-chemical measure of
whether a compound will have a superprotonic transition or not, rather than the X-X or
other characteristic distances in the compounds. However, a plausible argument against
this result is that the underlying structural differences in the compounds may have a much
more important role in determining the presence/absence of a transition than either the
cation or anion size effect. To deconvolute any structural effects from the cation/anion
size effect, it is necessary to find a system of compounds that remained isostructural
while the size of the cation/anion is changed. The results from such a system would
complement those of the above mixed systems, the problem having being approach from
both top and bottom, so to speak. If the same trends were observed, it would conclusively
confirm the M-X distance as the critical parameter in predicting superprotonic phase
transitions. Luckily, just such a system exists.
3.3 M2(HSO4)(H2PO4) Compounds
The M2(HSO4)(H2PO4) compounds are isostructural for M = K, NH4, Rb, and Cs
(Table 3.4), the Cs compound being discovered during the investigations of the CsHSO4-
CsH2PO4 system (Chapter 4). Characterization of Cs2(HSO4)(H2PO4) showed it to have a
superprotonic phase transition in the range of 61 to 110ฐC63. On the other hand, the
properties of the other M2 compounds at elevated temperatures were not known. The
combination of these compounds being isostructural and having a known superprotonic
transition makes this system ideal for exploring the cation size effect irrespective of
structure.
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3.3.1 Structures of the M2(HSO4)(H2PO4) compounds
These compounds crystallize in a monoclinic unit cell, space group P21/n, with
two formula units per cell. Their lattice parameters and other crystallographic data are
listed in Table 3.4. Each compound has six crystallographically distinct, non-hydrogen
atom sites: one for the M+1 cations, four for the oxygen atoms and one site on which the S
and P atoms are evenly distributed. The structures consist of loosely defined MOx
polyhedra and well-defined XO4 tetrahedra. For the K, NH4 and Rb compounds the
cations are coordinated by nine oxygens, while the Cs compound has CsO10 polyhedra.
These coordination numbers are not particularly well defined as they depend to a great
deal on the upper limit one puts on the M-O bonds. However, using the published
coordination numbers, the ionic radii of the cations are 1.55, 1.61, 1.63, and 1.81 ล, for
K, NH4, Rb, and Cs, respectively83. Here, the radius of the ammonium cations has been
scaled with those of the rubidium ions for the sake of consistency with the previous
section and because it is difficult to calculate a spherical radius for these cations due to
the presence of highly directional N-H-O hydrogen bonds119. Considering that the NH4
compound’s volume is slightly larger than the Rb’s, it might be closer to the truth if the
RNH4 > RRb, but as the difference between the compounds is minimal, setting RNH4 < RRb
should make little to no difference in the analysis.
Table 3.4 Crystallographic data for the M2(HSO4)(H2PO4) compounds
Cation Space
Group
a (ล) b (ล) c (ล) β (ล) Vol.
(ล3)
Z Dcalc
(g/cm3)
Radius
M2 (ล)
ref
Cs
P21/n 7.856 7.732 7.827 99.92 468.3 2 3.261 1.81
27
Rb
P21/n 7.632 7.552 7.448 100.47 422.1 2 2.872 1.63
120
NH4
P21/n 7.723 7.540 7.482 101.32 427.2 2 1.789 1.61
119
K
P21/n 7.434 7.341 7.148 99.56 384.7 2 2.350 1.55
121
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The M-O and X-O distances in these compounds are all quite regular. For
Cs2(HSO4)(H2PO4), the mean Cs-O distance is 3.27 ล, with a low of 3.055(4) and high of
3.622(4) ล, giving a calculated bond sum of 1.10. The bond valence sum at the X cation
site is 5.51, in good agreement with the value of 5.5 predicted from a site occupancy of
0.5 S6+ and 0.5 P5+. The tetrahedral angles for this compound range from 107.1(2) to
112.6(3)ฐ, as expected for PO4 and SO4 anions27. The average X-O distance varies very
little with the nature of the cation: the K, NH4, Rb, and Cs compounds having values of
1.508, 1.506, 1.505, and 1.503 ล, respectively. These values all lie between those
typically encountered in PO4 and SO4 tetrahedra, ~1.52 and ~1.47 ล, respectively,
agreeing with the assignment of a completely mixed S/P occupancy on the X site83.
More confirmation of this mixing on the X site is evident in the fact that each XO4
group is involved in exactly three hydrogen bonds, the mean value of the two and four
bonds expected for HSO4 and H2PO4 tetrahedra, respectively. Two of these hydrogen
bonds connects the XO4 tetrahedra into zigzag chains running in the [010], while the third
bond cross-links the chains into sheets that lie in parallel (-101), Figure 3.6 a) for
Cs2(HSO4)(H2PO4). The hydrogen bonds of the chains are ordered (single minimum
potential), while the cross-linking bonds are disordered (double minimum potential). The
zigzag chains of hydrogen-bonded tetrahedra alternate with rows of M+1 cations to give a
checkerboard pattern, shown for the Cs compound in Figure 3.6 b.
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Figure 3.6 Structure of Cs2(HSO4)(H2PO4): a) the sheets of hydrogen bonded tetrahedra
in the (-101) plane with zigzag chains running in [010] and cross-linking hydrogen bonds
connecting the chains in [100]. A projection down [010], b), shows the checkerboard
arrangement of anion and cation rows as well as the sheets of tetrahedra extending along
[101]27. A unit cell is outlined in each picture.
High temperature X-ray powder diffraction and infrared spectroscopy revealed
that the high temperature phase of Cs2(HSO4)(H2PO4) is cubic, with ao = 4.926(5) ล. The
suggested symmetry of the unit cell is Pm 3 m, in which the compound would take on a
CsCl structure, with Cs atoms at the corners of a simple cubic unit cell, and the XO4
groups at the center, Figure 3.763. The coordinates for the Cs and X atoms are therefore 0
0 0 and ฝ ฝ ฝ, respectively. The oxygen atoms were placed at ฝ ผ 0.323 based on X-O
and Cs-O distance considerations. The single, crystallographic oxygen resides on a 24l
site, resulting in 6 orientations of the XO4 tetrahedra. Rapid librations between these
orientations, facilitating proton transport between the tetrahedra, are thought to result in
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the high conductivity of this phase, a nearly identical process being known to occur in the
superprotonic phase of CsHSO4
60.
Figure 3.7 Cubic phase of Cs2(HSO4)(H2PO4). Cs atoms reside at the corners and S/P
atoms in the center surrounded by the partially occupied oxygen sites.
3.3.2 Synthesis of the M2(HSO4)(H2PO4) compounds
These M2(HSO4)(H2PO4) compounds were synthesized by slow evaporation from
aq