Addressing Thermodynamic Inefficiencies of Hydrogen Storage in Transition Metal Hydrides - CaltechTHESIS

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Addressing Thermodynamic Inefficiencies of Hydrogen Storage in Transition Metal Hydrides
Citation
Weadock, Nicholas Joseph
(2019)
Addressing Thermodynamic Inefficiencies of Hydrogen Storage in Transition Metal Hydrides.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/ANY4-VA70.
Abstract
Transition metal hydrides (MH) are an attractive class of materials for several energy technologies. Primary benefits include their large volumetric storage capacity (often exceeding that of liquid hydrogen) and capability to absorb and desorb hydrogen for hundreds of cycles. In this thesis, we set out to understand two of the thermodynamic inefficiencies of MH: the pressure hysteresis associated with hydrogen absorption and desorption and the corrosion and dissolution of high capacity MH alloys in high pH electrolyte environments.
The volume change associated with hydriding transitions can exceed 10%, and a macroscopic nucleation barrier resulting from coherency strains has been proposed as the origin of the pressure hysteresis. We investigated this hypothesis for the palladium-hydrogen system. The hysteresis and phase transformation characteristics of bulk and nanocrystalline PdH were characterized with coupled
in situ
X-ray diffraction and pressure composition isotherm measurements. Size effects are observed in the total hydrogen uptake and hydrogen solubility in the hydride phases. Experimentally determined hysteresis energies were found to be comparable to the misfit strain between the Pd and PdH phases and much larger than the energy for dislocation formation. Theoretical predictions of pressure hysteresis overestimate the experimentally measured hysteresis, and we suggest methods of accommodation which could explain the discrepancy. Finally, we propose that an effect of the nucleation barrier is to split the coherent spinodal phase diagram and introduce directionally dependent phase boundaries.
We report a successful development of Ti
29
62-x
Ni
Cr
(x = 0, 6, 12) body-centered cubic (BCC) MH electrodes for MH batteries by addressing vanadium corrosion and dissolution in potassium hydroxide electrolytes. The effectiveness of a limited oxygen environment and vanadate ion addition against corrosion are compared to the effects of Cr substitution. By identifying oxygen as the primary source of corrosion and eliminating oxygen with an Ar-purged cell, the Cr-free alloy electrode achieved a maximum capacity of 594 mAh/g, double the capacity of commercial AB
MH electrodes. With modified coin cells suppressing oxygen evolution, the cycle stability of the Ti
29
62
Ni
alloy electrode was greatly improved with either vanadate ion additions to the electrolyte or Cr-substitution in the alloy. Both approaches lead to reversible capacity of 500 mAh/g for 200 cycles.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Metal hydrides, batteries, hysteresis, X-ray diffraction
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Fultz, Brent T.
Thesis Committee:
Faber, Katherine T. (chair)
Johnson, William Lewis
See, Kimberly
Fultz, Brent T.
Defense Date:
22 January 2019
Funders:
Funding Agency
Grant Number
NSF
UNSPECIFIED
Department of Energy (DOE)
DE-SC0001057
Record Number:
CaltechTHESIS:02112019-143327096
Persistent URL:
DOI:
10.7907/ANY4-VA70
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Article adapted for Chapter 3.
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Author
ORCID
Weadock, Nicholas Joseph
0000-0002-1178-7641
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Deposited By:
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Deposited On:
20 Feb 2019 20:36
Last Modified:
04 Oct 2019 00:24
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Addressing Thermodynamic Inefficiencies of Hydrogen
Storage in Transition Metal Hydrides

Thesis by

Nicholas J. Weadock

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

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2019
Defended January 22, 2019

ii

Nicholas J. Weadock
ORCID: 0000-0002-1178-7641

iii

ACKNOWLEDGEMENTS
“...meddle first, understand later. You had to meddle a bit before you had anything
to try to understand."
Sir Terry Pratchett, Interesting Times
First and foremost I would like to thank my advisor, Professor Brent Fultz, for giving
me the opportunity to explore the topics and experiments I found interesting. His
guidance and expertise helped me to think critically and develop my fundamental
understanding of materials science. My goal in coming to Caltech was to do just
that, so I am eternally grateful to Professor Fultz for helping me achieve this.
I must thank Michelle Shearer and Sheryl Ehrman for challenging me early on to
be a better and more clever scientist. Ichiro Takeuchi and Raymond Phaneuf, your
teaching and mentoring are what drove me to desire to understand the fundamentals
of materials science. Lourdes Salamanca-Riba and Liangbing Hu, thank you for
giving me the opportunity to discover my passion for experimental work.
I have learned a great amount from current and former members of the Fultz group.
Ratnakumar Bugga, Heng Yang, and Hongjin Tan taught me all they know about
metal hydrides and electrochemistry, and from Maxwell Murialdo and Nicholas
Stadie I learned about gas adsorption and absorption. Hillary Smith taught me
about neutron scattering but also provided sound advice on my research in general.
Channing Ahn gave great advice on experimental design and always had an amusing
anecdote to share. Thank you also to Lisa, Dennis, Fred, Jane, Yang, Peter, Cullen,
Bryce, Claire, Camille, Stefan, and Olle for your support. Aadith, thank you for all
your assistance in the lab.
Finally I must thank my friends and family for keeping me sane. The Steuben house
was a great four years, and the friendships started there will last for many more years
to come. Jon, thank you for always being up for a skiing or biking trip. Dee Dee,
thank you for being a wonderful and supportive partner. I will always appreciate
you showing me around LA and having a real interest in learning about my research.
Mom, Dad, and Zack, I can never thank you enough for your support over the years.

iv

ABSTRACT
Transition metal hydrides (MH) are an attractive class of materials for several energy
technologies. Primary benefits include their large volumetric storage capacity (often
exceeding that of liquid hydrogen) and capability to absorb and desorb hydrogen for
hundreds of cycles. In this thesis, we set out to understand two of the thermodynamic
inefficiencies of MH: the pressure hysteresis associated with hydrogen absorption
and desorption and the corrosion and dissolution of high capacity MH alloys in high
pH electrolyte environments.
The volume change associated with hydriding transitions can exceed 10%, and a
macroscopic nucleation barrier resulting from coherency strains has been proposed
as the origin of the pressure hysteresis. We investigated this hypothesis for the
palladium-hydrogen system. The hysteresis and phase transformation characteristics of bulk and nanocrystalline PdH were characterized with coupled in situ X-ray
diffraction and pressure composition isotherm measurements. Size effects are observed in the total hydrogen uptake and hydrogen solubility in the hydride phases.
Experimentally determined hysteresis energies were found to be comparable to the
misfit strain between the Pd and PdH phases and much larger than the energy for
dislocation formation. Theoretical predictions of pressure hysteresis overestimate
the experimentally measured hysteresis, and we suggest methods of accommodation which could explain the discrepancy. Finally, we propose that an effect of the
nucleation barrier is to split the coherent spinodal phase diagram and introduce
directionally dependent phase boundaries.
We report a successful development of Ti29 V62−x Ni9 Cr x (x = 0, 6, 12) bodycentered cubic (BCC) MH electrodes for MH batteries by addressing vanadium
corrosion and dissolution in potassium hydroxide electrolytes. The effectiveness
of a limited oxygen environment and vanadate ion addition against corrosion are
compared to the effects of Cr substitution. By identifying oxygen as the primary
source of corrosion and eliminating oxygen with an Ar-purged cell, the Cr-free
alloy electrode achieved a maximum capacity of 594 mAh/g, double the capacity
of commercial AB5 MH electrodes. With modified coin cells suppressing oxygen
evolution, the cycle stability of the Ti29 V62 Ni9 alloy electrode was greatly improved
with either vanadate ion additions to the electrolyte or Cr-substitution in the alloy.
Both approaches lead to reversible capacity of 500 mAh/g for 200 cycles.

PUBLISHED CONTENT AND CONTRIBUTIONS

N. J. Weadock, and B. Fultz. Elastic energy and the hysteresis of phase transformations in palladium hydride. In Preparation.
N.J.W. conceived of the project, performed the experiments, analyzed the
data, and wrote the manuscript.
H. L. Smith, N. J. Weadock, F. C. Yang, N. Butch, T. J. Udovic, C. W. Li, and B.
Fultz. Hydrogen Dynamics in Laves-phase hydride YFe2 H2.6 under pressure.
In Preparation.
N.J.W. assisted with sample preparation, beamtime experiments, and data
analysis.
M. Murialdo, N. J. Weadock, Y. Liu, C. Ahn, S. Baker, K. Landskron, B.
Fultz. High-pressure hydrogen adsorption on porous electron-rich covalent
organonitridic frameworks. ACS Omega, 4:444-448, December 2018. doi:
10.1021/acsomega.8b03206
N.J.W. performed surface area and skeletal density measurements, and participated in data analysis and preparation of the manuscript.
H. Yang†, N. J. Weadock†, H. Tan, and B. Fultz. High capacity V-based metal
hydride electrodes for rechargeable batteries. Journal of Materials Chemistry
A, 5:21785-21794, September 2017. doi: 10.1039/C7TA07396H.
N.J.W. participated in the conception of the project, performed characterization and electrochemical experiments, prepared and analyzed the data, and
co-authored the manuscript.
†These authors contributed equally to the manuscript.

vi

PATENT APPLICATIONS

H. Yang, N. J. Weadock, B. Fultz, B. Edwards. High capacity corrosion resistant
V-based metal hydride electrodes for rechargeable metal hydride batteries.
U.S. Application No. 15/996,390. Filed June 2018. Application Pending.
N. J. Weadock, H. Tan, B. Fultz, H. Yang. Metal hydride alloys with improved
rate performance. U.S. Application No. 15/046,104. Filed February 2016.
Application Pending.

vii

TABLE OF CONTENTS

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Published Content and Contributions . . . . . . . . . . . . . . . . . . . . . .
Patent Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Metal Hydrides as Energy Materials . . . . . . . . . . . . . . . . . .
1.2 Chemisorption of Hydrogen by Metal Hydrides . . . . . . . . . . . .
1.3 Hysteresis in Metal Hydrides . . . . . . . . . . . . . . . . . . . . .
1.4 Nickel-Metal Hydride Batteries . . . . . . . . . . . . . . . . . . . .
Chapter II: Elastic Energy and the Hysteresis of Phase Transformations in
Palladium Hydride . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter III: High Capacity V-based Metal Hydride Electrodes for Rechargeable Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Corrosion of Vanadium in Aqueous Environments . . . . . . . . . .
3.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter IV: Summary and future work . . . . . . . . . . . . . . . . . . . . .
4.1 Principles of Metal Hydride Hysteresis . . . . . . . . . . . . . . . .
4.2 New Models for Hysteresis . . . . . . . . . . . . . . . . . . . . . .
4.3 Metal Hydride Electrodes . . . . . . . . . . . . . . . . . . . . . . .
4.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A: Supplementary Information for Elastic Energy and the Hysteresis of Phase Transformations in Palladium Hydride . . . . . . . . . . . .
A.1 Pressure composition isotherm measurements in Sievert’s apparatus
and in situ hydrogen environment chamber . . . . . . . . . . . . . .
A.2 Two-Dimensional finite Eshelby model for an eccentric circular inclusion in a circular domain . . . . . . . . . . . . . . . . . . . . . .

iii
iv
vi
vii
ix
xv
17
19
19
19
20
29
38
39
39
39
41
43
55
60
61
61
62
63
64
65
66
66

viii
Appendix B: Supplementary Information for High capacity V-based metal
hydride electrodes for rechargeable batteries . . . . . . . . . . . . . . . .
B.1 Alloy and Electrode Characterization . . . . . . . . . . . . . . . . .
B.2 Energy density calculations of a MH-Air battery cell . . . . . . . . .
Appendix C: Shoulder Removal from X-ray Diffraction Data . . . . . . . . .
C.1 Inel CPS120 Detector . . . . . . . . . . . . . . . . . . . . . . . . .
C.2 Anomalous Peak Shoulders . . . . . . . . . . . . . . . . . . . . . .
C.3 Shoulder Removal with Deconvolution . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72
72
78
84
84
85
86
97

ix

LIST OF ILLUSTRATIONS

Number
Page
1.1 Schematic illustrating two methods of hydriding a hydride-forming
metal. On the left, hydriding the metal (gray particles) occurs by
electrochemical reduction of water in an aqueous electrolyte. The
right side illustrates hydriding from the gas phase; a high partial
pressure of hydrogen gas is used to drive the hydriding transition. . . 3
1.2 Composite PCT for the V-H system as published by Yukawa, et al.
and Reilly and Wiswall. Yukawa investigated the monohydride transition electrochemically, whereas Reilly and Wiswall characterized
the dihydride transition in the gas-phase. . . . . . . . . . . . . . . . 7
1.3 Experimentally determined temperature-composition phase diagram
for the V-H system. Black circles represent data points, and the
connecting lines serve as approximate phase boundaries. The β/(β +
γ) phase boundary is an average value due to the finite width of the
vertical component of the PCTs in Figure 1.2. . . . . . . . . . . . . . 8
1.4 Full pressure-composition isotherm for 200 mesh Pd powder measured at 333 K. The Pd powder had been cycled two times prior
to this PCT measurement. A hysteresis of 0.88 was calculated using Equation 1.5. Dashed lines illustrate the graphical construction
method used to determine phase boundaries in the sloping regions of
the plateau. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Comparison of pressure hysteresis values reported in the literature
for bulk Pd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 High-resolution TEM image of as-received nanocrystalline Pd powder prior to hydrogen exposure. . . . . . . . . . . . . . . . . . . . . 21
2.2 Inverted dark field TEM micrograph of the nanocrystalline Pd with
inverted electron diffraction pattern (330 mm camera length) inset.
The dark field image was acquired with a 10 µm objective aperture
capturing 111 diffracted beams. A 40 µm selected area aperture was
used when acquiring the electron diffraction pattern. Scale bar for
the electron diffraction pattern is 2 nm−1 . . . . . . . . . . . . . . . . 22

2.3

2.4

2.5

2.6

2.7

2.8

a) Pressure-composition isotherms for bulk and nanocrystalline PdH.
An additional isotherm of the bulk PdH was measured at 435 K. The
inset plots the plateau region on a linear pressure scale to highlight
the shape of the isotherm curves. Closed symbols denote absorption,
and open symbols correspond to the subsequent desorption. b) 333
K minor loop for bulk PdH measured in situ. After hydriding to
approximately 80% transformed, the isotherm was reversed and the
sample was dehydrided. . . . . . . . . . . . . . . . . . . . . . . . .
In situ X-ray diffraction patterns of hydrogen absorption (left) and
desorption (right) by bulk Pd powder. The color of each trace corresponds to the total hydrogen concentration (in H/M) as indicated by
the central legend. . . . . . . . . . . . . . . . . . . . . . . . . . . .
In situ X-ray diffraction patterns of hydrogen absorption (left) and
desorption (right) by nanocrystalline Pd powder. The color of each
trace corresponds to the total hydrogen concentration (in H/M) as
indicated by the central legend. . . . . . . . . . . . . . . . . . . . .
Refined α phase fraction for the a) bulk and b) nanocrystalline PdH
powders. The black arrows indicate the direction of transformation,
and shading of the traces indicates the error bars. . . . . . . . . . . .
a) Refined lattice parameters of the a) bulk and b) nanocrystalline Pd
powders during hydrogen absorption and desorption. The red and
blue traces correspond to the solid solution α phase and hydride β
phase, respectively. Error bars are indicated by the shaded region. . .
Variation of dimensionless strain energy with inclusion position. An
0.4R inclusion is subjected to a uniform isotropic eigenstrain field
i∗j = 21  ∗ δi j . Strain energy density is normalized by (4µ ∗2 )/(κ + 1)2 .
Inset are heat maps of strain energy density for particles with inclusions located at the origin (left) and displaced 0.6R (right). The
matrix boundary is constrained by traction-free conditions; displacements due to the inclusion are not shown. . . . . . . . . . . . . . . .

24

25

26

28

30

34

xi
2.9

3.1

3.2
3.3
3.4

3.5

3.6

Absorption and desorption spinodal phase diagrams determined from
terminal compositions of bulk and nanocrystalline PdH. Bulk and
nanocrystalline PdH data from this study are plotted as circles and
triangles, respectively. Additional bulk data from Wicke et al. are
plotted as upside down triangles. 6 and 4 nm nanoparticle PdH data
from Vogel et al. are plotted as squares and diamonds, respectively.
Filled markers denote absorption, open markers denote desorption.
The black line denotes a hypothetical equilibrium boundary for a
barrier-free transformation. . . . . . . . . . . . . . . . . . . . . . . . 36
Pourbaix diagram of V with the potential of the Hg/HgO reference
electrode indicated by the short-dash blue line. The orange box
outlines the operational pH and potential ranges for MH batteries,
and the green lines indicate how equilibrium shifts with varying
concentrations of dissolved V (in units of grams V per kilogram
H2 O). Line a: 2H+ + 2e− → H2 ; and line b: 2H2 O → O2 + 4H+ + 4e− 40
X-ray diffractograms of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloys
after hydrogen activation and pulverization of the arc melted ingots. . 44
Backscattered electron images at (a) low and (b) high magnification
of a polished Ti29 V50 Ni9 Cr12 ingot. . . . . . . . . . . . . . . . . . . 45
Hydrogen absorption isotherms of Ti29 V62−x Ni9 Cr x (x = 0, 6, and
12) alloys as measured on a Sievert’s apparatus at room temperature
(298 K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Characterization of the three alloy electrodes: (a) First cycle charge/discharge
curves for the alloy electrodes in a beaker cell. Ex situ experiments
were performed at the numbered points on the graph. (b) Diffractograms of the three alloy electrodes at corresponding states of charge.
Hydride phases are marked with squares (BCC), triangles (BCT), and
circles (FCC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
The charge/discharge curves for (a) Ti29 V62 Ni9 and (b) Ti29 V50 Ni9 Cr12
electrodes in an Ar-purged three-electrode cell. . . . . . . . . . . . . 52

xii
3.7

3.8
3.9

A.1
A.2

A.3
A.4

A.5

A.6

A.7

Cycling performance of coin cells containing (a) Ti29 V62 Ni9 electrodes with KVO3 additions to the KOH electrolyte and (b), (c)
Ti29 V62−x Ni9 Cr x electrodes with KOH electrolyte. The MH electrodes were charged to 550 mAh/g in (a) and (b), and charged to 400
mAh/g in (c). In (a), cycling was interrupted after 110 cycles and
restarted after two weeks for the cell containing KOH with 500 mM
KVO3 . In (b) and (c), cycling was interrupted for two weeks after the
100th cycle for the Ti29 V56 Ni9 Cr6 and Ti29 V50 Ni9 Cr12 electrodes. . .
Schematics illustrating the (a) operational and (b) local oxidation that
occurs for V in the Ti29 V62 Ni9 alloy electrodes. . . . . . . . . . . . .
Gravimetric and volumetric energy density analysis of a MH air
cell as a function of the specific capacity and thickness of the MH
electrode. The shaded areas indicate the published energy density
ranges for 18650 type Li-ion batteries. . . . . . . . . . . . . . . . . .
Scanning electron micrograph of a bulk Pd particle consisting of
coalesced grains. The inset shows the scale of individual particles. . .
Comparison of pressure composition isotherms measured in a Sievert’s apparatus and in situ hydrogen environment chamber. Isotherms
for bulk Pd are plotted in a) and for nanocrystalline Pd in b), both at
333K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displacement field u1 for the case published by Zou. Displacement
is normalized by (1 − ν)/r ∗ to be unitless. . . . . . . . . . . . . . .
Displacement fields u1 for 0.4r inclusions located a) at the center and
b) displaced to the edge of the domain. Displacement is normalized
by (4r ∗ )/(κ + 1) to be unitless. . . . . . . . . . . . . . . . . . . . .
Displacement fields u2 for 0.4r inclusions located a) at the center and
b) displaced to the edge of the domain. Displacement is normalized
by (4r ∗ )/(κ + 1) to be unitless. . . . . . . . . . . . . . . . . . . . .
Stress fields σ11 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by
(4µ ∗ )/(κ + 1)2 to be unitless. . . . . . . . . . . . . . . . . . . . . .
Stress fields σ12 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by
(4µ ∗ )/(κ + 1)2 to be unitless. . . . . . . . . . . . . . . . . . . . . .

54
57

59
65

67
69

69

70

70

71

xiii
A.8

B.1
B.2

B.3
B.4

B.5

B.6

B.7

B.8
B.9

Stress fields σ22 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by
(4µ ∗ )/(κ + 1)2 to be unitless. . . . . . . . . . . . . . . . . . . . . . 71
Lattice parameters of dehydrided Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12)
alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Backscattered electron images of (a) Ti29 V62 Ni9 and (b) Ti29 V56 Ni9 Cr6
alloy ingots. Compositions superimposed on the image indicate average compositions of the V-rich (dark) and Ni-rich (light) regions as
determined by EDS. . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Discharge curve of Ti29 V62 Ni9 electrode in various KOH electrolytes.
Plateaus associated with V and Ni oxidation are indicated with arrows. 75
XPS spectra of V, Cr, Ni, and Ti prior to charge [1] and after full
discharge [4] of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy electrodes.
Boxed numbers correspond to the state of charge indicated in 3.5a. . . 76
Cycle performance of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy
electrodes in various electrolytes. All tests were performed in airsaturated beaker cells. Cells were charged to 800 mAh/g, then discharged following the three-step discharge procedure up to -0.75V
vs. Hg/HgO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Operation potential for the Ni(OH)2 /NiO(OH) electrode used in coin
cells. Current density is based on the mass loading of the Ni(OH)2
electrode powder mixture. Closed and open symbols correspond to
the plateau potentials for charge and discharge, respectively. The
boxed region indicates the current density range associated with the
MH electrode (10 to 100 mA/g for a 3 mg/cm2 loading). . . . . . . . 78
Charge/discharge curves of a). Ti29 V62 Ni9 and b). Ti29 V50 Ni9 Cr12
electrodes in the coin cell configuration. The cells were charged for
550 mAh/g and three-step discharged at 100, 40, and 20 mA/g to
1.10V. The decrease of discharge capacity at the high current step
shows that the rate capability of the MH electrode decreases with
cycling, despite excellent capacity retention. . . . . . . . . . . . . . . 79
Top view (left) and 3D sinde view (right) drawings of the 100-Wh
MH-air cell. Dimensions not to scale. . . . . . . . . . . . . . . . . . 82
Plot of electrode potential versus current density for the air electrode
manufactured by Electric Fuel.[120] . . . . . . . . . . . . . . . . . . 83

xiv
C.1

C.2

C.3

C.4

C.5
C.6
C.7

C.8

C.9

C.10

Raw diffraction data from the NIST Standard Reference Material
640b (powdered Si) collected with the Inel CPS 120 Detector. Tick
marks indicate expected peak positions from Mo Kα1 (red) and Kα2
x-ray wavelengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Diffraction pattern of the NIST SRM 640b (Si) obtained on the Inel
CPS 120 detector with output lines switched. The anomalous shoulder peaks are still observed to the right of the main peak, as indicated
by the black arrows. . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Comparison of peak shape of signal obtained through Pb slits to Bragg
reflection of a Si standard. The Si Bragg peak is approximately twice
as wide as the signal passed through the Pb slits. . . . . . . . . . . . 90
Primary and shoulder peak separation (in channel numbers) as a
function of channel number of the primary peak. Both peaks are fit
with a separate Lorentzian function. . . . . . . . . . . . . . . . . . . 91
Relative magnitude of the shoulder peak as a function of channel
number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Half-width at half maximum of the shoulder peaks as a function of
channel number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Plot illustrating the instrument function determination. The dotted
line is raw data obtained from the Pb slit/GeO2 setup, the dashed
line is a Lorentzian fit to the main peak, and the solid line plots
the result of convolving the instrument function with the Lorentzian
peak. Examples of the instrument function are provided in Figure C.8. 93
Two (solid and dashed lines) of 18 instrument functions describing
shoulder behavior of the Inel CPS120 detector. The functions consist
of a delta function at 4096 and a small peak resulting in a shoulder
in the raw diffraction data. . . . . . . . . . . . . . . . . . . . . . . . 94
Raw (dotted red line) and deconvoluted (solid blue line) bulk Pd
diffraction patterns acquired with the CPS 120 detector. Primary
peak shapes are well preserved. . . . . . . . . . . . . . . . . . . . . 95
Raw (dotted red line) and deconvoluted (solid blue line) nanocrystalline Pd diffraction patterns acquired with the CPS 120 detector.
Primary peak shapes are well preserved. . . . . . . . . . . . . . . . . 96

xv

LIST OF TABLES
Number
Page
2.1 Terminal compositions of the hydriding transition for bulk and nanocrystalline PdH obtained from in situ XRD results at 333 K. High temperature (435 K) compositions for the bulk Pd are evaluated from the
pressure composition isotherm. . . . . . . . . . . . . . . . . . . . . 27
2.2 Variation of lattice parameter with hydrogen concentration da/dc
(Å/H) in single phase regions. All data are fitted with a linear function
according to Vegard’s Law. Empty entries correspond to regions with
insufficient data points to fit. . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Comparison of experimentally determined hysteresis values to those
predicted by S-K theory. S-K hysteresis values are calculated according to Equation 1.8 with values listed in this section. Experimental
hysteresis values for the 300 nm nanoparticles are determined from
refs. [24] and [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Summary of hysteresis energies and measured and estimated misfit
strain values for bulk and nanocrystalline PdH at 333 K. Misfit strains
are estimated from hysteresis energies according to Equation 2.2. . . 33
3.1 Summary of the compositions of the majority V-rich and minority
Ni-rich regions within the alloy ingots. The reported compositions
are the average compositions as determined by EDS. . . . . . . . . . 44
3.2 Results from ICP-MS analysis of KOH electrolyte collected from
cells containing Ti29 V62−x Ni9 Cr x (x = 0, 6, 12) alloy electrodes.
Electrolyte was collected from cells fully charged, discharged to 0.75 V, and discharged to -0.50 V, as indicated in Figure 3.5. Data
from a cell cycled 10 times are also presented. . . . . . . . . . . . . 50
B.1 ICP-MS analysis of KOH electrolytes in which Ti29 V62−x Ni9 Cr x (x
= 0 and 12) alloy electrodes were stored for 10 days. . . . . . . . . . 73
B.2 Input values and energy density results for an example case of a 100
Wh MH-Air cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Chapter 1

INTRODUCTION
In the late 1860s, Thomas Graham published "On the Occlusion of Hydrogen Gas
by Metals" in which he reported on the absorption and desorption of hydrogen
gas by iron, platinum, and palladium.[1] Pure Pd was found to absorb the most
hydrogen with a stoichiometry of PdH0.772 obtained at 11◦ C and 756 mmHg pressure.
Measurements of electrical conductivity and magnetic properties of PdH led Graham
to incorrectly conclude that hydrogen itself is a white, lustrous metal. Following
Graham, work by Troost, Hautefeuille, and especially Winkler uncovered hydrides
of K, Na, Ce, Ca, Sr, Ba, Y, Th, Zr, and La. One of the first applications of
these metal hydrides involved calcium hydride; an apparatus containing CaH was
mounted to a carriage to allow for portable production of hydrogen with which to
fill the ballast of dirigibles.[2]
Metal hydride research has expanded significantly since early work by Graham
et al. The ability to absorb significant quantities of hydrogen, oftentimes with
hydrogen densities greater than liquid hydrogen itself, has driven the development
of metal hydrides for various technical applications which involve gas compression
or hydrogen as an energy source. Recent results have demonstrated that gaseous
hydrogen can be produced without CO2 emissions through photoelectrochemical
water splitting or methane decomposition.[3, 4]. Hydrogen can therefore be used as
an energy carrier or energy storage medium for a renewable energy infrastructure.
Solar and wind power generated hydrogen can be stored for later use to run fuel cells,
or be distributed via pipelines for use in the transportation sector. Recently, hydrogen
fuel cell-powered commercial transit options have been introduced including the
Toyota Mirai automobile and the Coradia iLint commuter train.[5]
1.1

Metal Hydrides as Energy Materials

Metal hydrides (MH) as initially discovered, and as will be referred to for the rest
of this thesis, consist of an elemental or alloy metal lattice with hydrogen atoms
occupying interstitial sites. Rare-earth MH were previously utilized prominently as
anode materials in nickel-metal hydride (Ni-MH) batteries, although niche applications including nuclear reactor cladding material, switchable mirrors, and cryogenic
cooling for the European Space Agency’s Planck mission were developed.[6–9]

Other applications of transition MH include thermal energy storage and multi-stage
hydrogen compressors for hydrogen filling stations.[10, 11]
Another class of MH, called complex metal hydrides, is also intensely studied.
Complex metal hydrides typically contain an alkali metal cation ionically bonded
to a metal- or metalloid-based anion. In these systems, the hydrogen is bonded
with heavy covalent character to the anion species. Recently, Li+ , Na+ , and Mg2+
borohydride-based compounds have been demonstrated as potential solid state electrolytes for their respective eponymous ion batteries.[12]
Computational modeling has predicted the existence of several high temperature
superconducting MH.[13, 14] These materials contain very high hydrogen concentrations (H/M ≥6) and require high pressure and temperature synthesis in a diamond
anvil cell. Despite these difficulties, synthesis of superconducting lanthanum superhydride with Tc approaching 280 K has been reported in the literature.[15] This
thesis will not discuss these materials further; interested readers can find more
information in the numerous reviews and papers on these topics.
Several academic questions still exist regarding thermodynamics and kinetics of
more traditional transition metal and elemental MH. The remainder of this Introduction will provide a brief overview of MH using examples from transition metal
and rare-earth MH. An initial overview of basics of hydrogen absorption/desorption,
the metal-hydrogen phase diagram and (de)hydriding phase transitions will provide
context for theories of hysteresis in MH.
1.2

Chemisorption of Hydrogen by Metal Hydrides

Methods of Hydriding
The absorption of hydrogen (hydriding) by elemental metals or intermetallic and
solid solution alloys has been well documented in the literature, with over 2400
hydride-forming metals identified. Typical MH absorb up to 2 hydrogens per metal
atom (H/M), with hydrogen residing in tetrahedral or octahedral interstitial sites.[7,
16] Absorption of hydrogen causes lattice expansions greater than 10% by volume
and oftentimes a transition to a different crystal structure.
One convenient aspect of MH is that hydrogen as a solute can be introduced to a host
metal which is in the solid state. The diffusivity of hydrogen in elemental metals
approaches 10−5 cm2 /s at room temperature, allowing for hydriding transitions to
be driven by an external source of hydrogen.[17] Typically, hydrogen is introduced
to a hydride-forming metal either electrochemically or from the gas phase. These

Figure 1.1: Schematic illustrating two methods of hydriding a hydride-forming
metal. On the left, hydriding the metal (gray particles) occurs by electrochemical
reduction of water in an aqueous electrolyte. The right side illustrates hydriding
from the gas phase; a high partial pressure of hydrogen gas is used to drive the
hydriding transition.

processes are illustrated schematically in Figure 1.1.
Electrochemical hydriding occurs by redox processes at the surface of an electrode
which contains the hydride-forming metal.[7] Reduction of water in an aqueous
electrolyte produces an adsorbed hydrogen atom, which diffuses into the hydrideforming metal and subsequently forms an MH. The redox equation associated with
this process (see Equation 1.9) is provided in the left panel of Figure 1.1. To desorb
hydrogen, the current is reversed, and hydrogen recombines with a hydroxide ion
(OH− ) to form water.
Gas-phase hydriding occurs in a similar manner to electrochemical hydriding, and
is illustrated in the right panel of Figure 1.1. Hydrogen gas is introduced into a
pressure vessel containing a hydride-forming metal. The chemical potential µ of
the gas is:
pH
(g)
(1.1)
µH2 = µ0 + RT ln 2
p0
with R the gas constant, T the temperature, and p the partial pressure of the gas
species. Increasing the hydrogen partial pressure will increase the chemical potential, µ, of hydrogen gas until hydride formation becomes thermodynamically
(g)
favorable (i.e. 1/2µH2 > µMH ).[16] Hydrogen molecules will adsorb on the surface of the hydride-forming metal, dissociate, and diffuse into the metal to form a
hydride. Reducing hydrogen chemical potential by reducing partial pressure in the
pressure vessel will drive a dehydriding transition, and hydrogen will be released
from the MH.
Electrochemical and gas-phase (de)hydriding are related two ways; by electrode
potential and hydrogen partial pressure, and by total hydrogen capacity. Electrode
potential is defined by the Nernst equation:
E = E0 +

RT
ln K
nF

(1.2)

where E is electrode potential, E0 the standard potential, n the number of electrons
in the redox reaction, F is Faraday’s constant, and K the reaction quotient (often
given as the ratio of activities of the reacting species). For metal hydride batteries
in an alkaline aqueous electrolyte (6 M potassium hydroxide (KOH) solution, pH =
14) at 293 K, n = 1, the Nernst equation becomes[7]:
EMH,eq (V vs. Hg/HgO) = −0.9234 − 0.0291 log

p(H2 )
p0

(1.3)

An Hg/HgO standard reference electrode is typically used in alkaline electrolytes,
giving the value of -0.9234 V for the H2 O/H2 redox couple. The reaction quotient
K is evaluated as the ratio of activity for H2 O and H2 , which can be expressed as the
ratio of activity of H2 O to fugacity of H2 times partial pressure of H2 gas. Activity
and fugacity values at T = 293 K in 6 M KOH are used to evaluate the leading
coefficient in the last term on the right hand side of Equation 1.3.[7] Thus the MH
electrode potential in an electrochemical cell can be directly connected to hydrogen
partial pressures required for gas phase hydriding.
Electrochemical specific capacity is expressed in mAh/g, whereas gas-phase specific
capacity is expressed as either mole fraction (H/M) or weight percent (wt.%). The
connection between gas-phase and electrochemical capacity can be determined
through simple dimensional analysis. Consider 100 g of MH containing 1 wt.% of
hydrogen:
1e− 1.008 mol H
1000 mA
1 hr
1.0g H
× 96, 500
100g MH 1H
1.0 g H
mol
3600 sec
mAh
= 266

(1.4)

Thus 1 wt.% of gas-phase storage corresponds to 266 mAh/g of electrochemical
capacity.
The Metal-Hydrogen Phase Diagram
Metal-hydrogen phase diagrams are constructed from pressure-composition isotherms
(PCTs). A PCT is measured by iteratively dosing a reactor containing a hydrideforming metal with an aliquot of hydrogen and allowing the hydrogen partial pressure
to equilibrate. With each dose, some amount of hydrogen is absorbed by the metal.
This process is reversed to characterize hydrogen desorption.1 The hydrogen concentration in the metal is evaluated either volumetrically (by accounting for the
change in moles of hydrogen gas) or gravimetrically (tracking changes in mass).
A phase transition begins when the chemical potentials of two hydride phases are
equal. Hydrogen is absorbed or desorbed as one phase replaces the other at a
constant partial pressure known as the plateau pressure. Plotting hydrogen partial
pressure (or hydriding potential as given by Equation 1.3) on the ordinate indicates
the relative stability of the hydride phase; low partial pressures correspond to a
1 Throughout this thesis, pressure composition isotherms are referred to as absorption or desorp-

tion isotherms to designate the direction of the reaction.

hydride phase that readily absorbs hydrogen but is difficult to remove hydrogen
from.
Figure 1.2 shows a composite 343 K PCT for the V-H system.[18, 19] Vanadium
can absorb up to 2 H/M and goes through two phase transformations; the bodycentered cubic (BCC) solid solution α phase transforms to a tetragonally distorted
BCT monohydride β phase at low hydrogen partial pressures. The monohydride
phase then transforms to the face-centered cubic (FCC) dihydride γ phase at significantly higher partial pressures. Characterization of the monohydride transition
was performed electrochemically due to the difficulty in accurately measuring the
low partial pressures with pressure transducers.[18] Plateau pressures for elemental
or intermetallic MH phase diagrams are constant. When energetic heterogeneities
are introduced in solid solution alloys, these plateaus develop a slope.
Temperature-composition phase diagrams are produced from measurements of PCTs
at several temperatures. Phase boundaries are determined from terminal compositions of the plateaus in PCTs, and often narrow with increasing temperature. The
temperature-composition phase diagram for VH, as measured by Reilly and Wiswall,
is reproduced in Figure 1.3.[19]
1.3

Hysteresis in Metal Hydrides

After Graham’s work on the absorption of hydrogen by platinum, iron, and palladium, several researchers noticed a peculiarity in the absorption and desorption of
hydrogen by palladium[20]:
When rα < r < r β (r the hydrogen concentration) the isotherm is flat;
the pressure has a special value, but the amount of hydrogen dissolved
is not controlled by it. In this region the system is sluggish, different
curves being obtained when hydrogen is added or removed. These
“hysteresis" curves, as they are called...
This phenomena of non-reversibility of hydrogen absorption and desorption by MH
is known as hysteresis. Pressure hysteresis is conveniently quantified with respect
to absorption and desorption pressure[16]:
pabs
(1.5)
Hysteresis = ln
pdes
At a constant temperature, the absorption pressure is greater than desorption pressure. Hysteresis also manifests as a difference in terminal compositions at phase

Figure 1.2: Composite PCT for the V-H system as published by Yukawa, et al.
and Reilly and Wiswall. Yukawa investigated the monohydride transition electrochemically, whereas Reilly and Wiswall characterized the dihydride transition in the
gas-phase.

Figure 1.3: Experimentally determined temperature-composition phase diagram for
the V-H system. Black circles represent data points, and the connecting lines serve
as approximate phase boundaries. The β/(β + γ) phase boundary is an average value
due to the finite width of the vertical component of the PCTs in Figure 1.2.

boundaries for absorption and desorption, a phenomenon known as solvus hysteresis. Pressure and solvus hysteresis in PdH are apparent in the 333 K PCT plotted
in Figure 1.4. With absorption and desorption plateau pressures of 75 and 31 Torr,
respectively, the pressure hysteresis is 0.88. Solvus hysteresis is less convenient to
quantify; the sloping nature of the plateau pressure at the end of the phase transformations makes determination of the phase boundary difficult. Frieske and Wicke used
a graphical construction in which the plateau pressure is extended until it intersects
with the opposite isotherm branch.[21] The composition at which the intersection
occurs is taken as the phase boundary. By this method, the solvus hysteresis in Figure 1.4 is 0.61−0.56 = 0.05 at the β phase boundary and 0.04−0.015 = 0.025 at the
α phase boundary. Dashed lines in Figure 1.4 illustrate the graphical construction
method.
Hysteresis in MH has been studied extensively, with the majority of the work
focusing on PdH and other MH with experimentally convenient transition pressures
and temperatures. It is well established that hysteresis decreases with temperature
and will disappear above a critical temperature Tc . Figure 1.5 plots hysteresis
as a function of temperature for several bulk PdH studies.[21–23] At 333 K, the
reported hysteresis varies by a factor of 2, indicating that hysteresis may have a size
dependence. Recently, several investigations of PdH nanostructures have revealed
that hysteresis increases with particle size, up to a maximum size of 300 nm.[24,
25] Despite decades of research, no analytical model has been developed which
completely describes hysteresis in MH.
Theories of Metal Hydride Hysteresis and Equilibrium
Early work regarding hysteresis was primarily focused on determining which branch
of the PCT is closer to equilibrium. Initially, researchers hypothesized that true
equilibrium resides halfway between the two branches. Lacher developed a statistical
mechanics model using a Bragg-Williams approximation which was subsequently
fit to PdH isotherms[20]:
log10 p1/2 (atm.) = log10

+ 2.3009 − (445.6 + 986.7θ)/T
1−θ

(1.6)

with θ the fraction of filled H sites in the lattice. The model accurately reproduces
isotherms above Tc , and the pressure is assumed to be constant in a two phase region
below Tc . Lacher claims that hysteresis is due to increased vapor pressure of the
nucleating phase due to a small initial size. As a result, a supersaturated α phase
forms during absorption, and an “undersaturated" β phase forms during desorption.

10

%%%

/((.-,&)(+**)('&

%%

9+:;&'6&<*.=>)(?@&222A
&BC*.(D=4.5
&E)*.(D=4.5

%0%

%0

%0!

%02

%0"

3&45&'6&,378/

%01

%0#

Figure 1.4: Full pressure-composition isotherm for 200 mesh Pd powder measured
at 333 K. The Pd powder had been cycled two times prior to this PCT measurement.
A hysteresis of 0.88 was calculated using Equation 1.5. Dashed lines illustrate the
graphical construction method used to determine phase boundaries in the sloping
regions of the plateau.

11

Figure 1.5: Comparison of pressure hysteresis values reported in the literature for
bulk Pd.

12
This conclusion suggests hysteresis affects both branches of the isotherm equally,
and true equilibrium exists halfway between these branches. Despite hypothesizing
that hysteresis arises from mechanical constraints on the nucleating phase, Lacher’s
theory does not incorporate lattice expansion of Pd with H.
Everett and Nordon provided a critical review of Lacher’s theory, demonstrating that
Equation 1.6 does not accurately fit both absorption and desorption branches of PdH
PCTs below the critical temperature.[26] Rather, separate functions are required for
the α and β phase indicating that the vibrational partition function or proton-site
interaction energy is different in both phases. The phase transformation is not
considered complete until a hydrogen concentration is reached at which equations
describing absorption and desorption are equal. This fact led Everett and Nordon to
question if two-phase reversible equilibrium is possible in PdH. Lacher’s description
of the origin of hysteresis, however, was accepted and expanded upon by Everett
and Nordon. Nuclei of small size in an infinite crystal will have growth suppressed
by hydrostatic forces exerted by the matrix. This barrier can only be overcome, the
authors claim, by increasing hydrogen pressure. Furthermore, deviations from a flat
plateau (evident at the end of the transition in Figure 1.4) were proposed to be due
to changes in the energetics of any remaining parent phase caused by lattice strains.
Flanagan et al. carefully studied single phase regions of PdH isotherms and noticed
an increase in hydrogen solubility in the α phase of an unannealed Pd sample
as compared to an annealed sample.[27, 28] Similar solubility enhancements were
observed in the β to α transition, leading the authors to propose that hydrogen cycling
is accompanied by creation of a high density of dislocations in the metal. Solubility
does not increase continually with cycling, therefore dislocations generated beyond
an equilibrium dislocation density must be annihilated during the subsequent PCT
branch. Flanagan and Clewley proposed that hysteresis is due to the energetic cost
of generating dislocations during (de)hydriding and can be expressed in terms of
the enthalpy of dislocation formation ∆Hdisl [29]:
4∆Hdisl
pabs
(1.7)
ln
pdes
RT
Analysis of pressure hysteresis is extended to solvus hysteresis, and the change in
terminal composition is expressed as a function of the equilibrium pressure and phase
boundary compositions.[29] In Flanagan’s analysis, the equilibrium values exist
halfway between experimentally observed absorption and desorption isotherms.

13
Other groups claim that the desorption branch represents the true equilibrium of
(de)hydriding transitions. Several experiments from the group of Wicke et al.
demonstrate that absorption pressure decreases with cycling, whereas the desorption pressure stays relatively constant.[21, 30] Their isotherm measurements on bulk
Pd foil and Pd black (i.e. nanocrystalline Pd) revealed a large difference in absorption pressure, but no change in desorption pressure between the samples. Wicke and
Blaurock also performed a detailed analysis of solvus hysteresis in PdH and PdD
to determine critical hydrogen concentration (nc ) at Tc .[30] Analysis of isotherms
measured above Tc yielded nc = 0.257 ± 0.004, and analysis of subcritical isotherms
yielded 0.25 < ncdes < 0.26 and 0.29 < ncabs < 0.30. Agreement between the equilibrium supercritical concentration and equilibrium concentration determined on
desorption provided additional evidence to the hypothesis that desorption isotherms
represent true strain-free equilibrium.
Schwarz and Khachaturyan (S-K) presented a material-agnostic analysis of hysteresis which considers how elastic strains modify thermodynamics of two-phase
hydriding and dehydriding phase transitions.[31, 32] When nucleation proceeds
coherently, an elastic energy term is introduced, which depends solely on the total concentration c of solute atoms (and not volume fraction or solute distribution
between two phases). This is known as the Bitter-Crum theorem, a result derived
from Eshelby’s theory for elastic inclusions in an infinite matrix.[33–35] In the
Bitter-Crum theorem, the two phases are required to have the same elastic constant
and be elastically isotropic. All strains are purely dilatational, the crystal is assumed
infinite, and no interactions between solute atoms are included.
According to S-K theory, the free energy of a coherent system is equal to the sum
of the “chemical" free energies of the two phases plus a coherent strain energy
term.[31, 32] The hydriding and dehydriding transitions begin at the compositions
cαcoh and ccoh
β , which are determined from the common tangent construction between
these chemical free energies. In the incoherent case, the free energy of the system
becomes a weighted sum of free energies (chemical plus elastic) of each phase, there
is no additional coherency term. The miscibility gap in this case is determined by
a common tangent construction between the total free energy curves. Incoherent
coh
terminal compositions are cαinc < cαcoh and cinc
β > cβ .
For coherent nucleation, the consequence of the elastic strain energy depending
solely on the total solute concentration is that the chemical potential in the two
phase region is no longer determined by a common tangent construction and instead

14
decreases linearly with c. In the case of hydriding, the inclusion of the energy
barrier shifts the system to the total free energy curve (chemical plus elastic) with
a corresponding increase in chemical potential. The α to β transition begins at
end
coh
µ(cαcoh ) > µ(ccoh
β ), and is complete when c = c β > c β . The effect is similar for
coh
end <
dehydriding; the transition begins at µ(ccoh
β ) < µ(cα ) and ends with c̄ = cα
cαcoh . In an open coherent system, this macroscopic nucleation barrier can only be
overcome by increasing (or decreasing) the chemical potential of hydrogen gas to
match the shift between free energy curves.2 In S-K theory, the presence of the
barrier results in a pressure hysteresis given by:
 8ν G 1+σ  2 (ccoh − ccoh )
0 s 1−σ 0 β
pabs
ln
pdes
k BT

(1.8)

where Gs is the shear modulus, σ the Poisson ratio,  0 the fractional change in lattice
coh
parameter with respect to hydrogen concentration, and ccoh
β and cα as defined above.
ν0 is the molar volume of the hydride-forming metal. If total strain energy associated
with hydriding overcomes the elastic limit, coherency will be lost and hysteresis will
be reduced. As such, these results provide an upper bound on pressure hysteresis.
The formalism developed by Schwarz and Khachaturyan also accounts for the solvus
hysteresis, although no explicit expression is derived.
Qian and Northwood recognized that large stresses associated with hydriding will
cause yielding at the matrix-precipitate interface and developed an expression for
the hysteresis in terms of irreversible work due to elastoplastic deformation associated with accommodating a growing precipitate.[36] Their analysis also considered
changes in mechanical properties with composition and size. The accommodation
energies depend on the yield stress of the matrix; if mechanical properties of the
hydride phase are different than the metal, hysteresis will not be symmetric. Accommodation energy is also modified by particle size. When precipitate size is
comparable to the matrix, e.g. in nanoparticles, internal stresses are mitigated by
“image" forces at the free surface. If stresses are reduced below the yield stress of
the matrix, no plastic deformation will occur and the transformation will be entirely
elastic.
Recently, Griessen et al. developed a mean field model to predict size dependent
spinodal pressures and associated hysteresis in Pd nanostructures.[24] Unlike some
earlier models mentioned, elastic and electronic H-H interactions are included (as2 This result is also proposed by Everett and Nordon, however Schwarz and Khachaturyan

provided a rigorous thermodynamic derivation to prove this statement.

15
sumed to be the same as in bulk Pd). This model assumes a coherent core-shell
hydriding geometry with differing hydrogen concentrations in each component and
accounts for the associated surface tension and clamping contributions. Enthalpies
of formation for the core and shell are obtained from fits to several datasets. Experimental hysteresis values are reproduced for numerous Pd nanostructures (some
not included in the initial fitting) by assuming a coherent transition with a modified
surface-shell-core coupling. However, recent experimental studies demonstrate that
spherical cap nuclei are energetically favorable to core-shell geometries assumed
in the Griessen, et al., model.[25, 37] An increased solubility of hydrogen in the
α phase and reduction in total capacity is attributed to thermodynamically-distinct
absorption sites on or near nanostructure surfaces.[24, 38, 39]
Other theories of hysteresis have been published in the literature, with experimental
studies of hysteresis existing for PdH, LaNi5 H, NbH, UH, ZrNiH, and others.[40]
In all cases, the proposed origin is either elastic or plastic deformation or some
combination of the two. As such, this section of the Introduction is not exhaustive
and instead serves to introduce hysteresis and provide relevant recent examples from
the literature.
Chapter 2 presents an experimental study of hysteresis in bulk and nanocrsytalline
Pd. A comparison of isotherm measurements and in situ X-ray diffraction observations of the phase transformations are used to evaluate aforementioned theories of
hysteresis and "equilibrium" PCTs.
Effects of Metal Hydride Hysteresis
The effect of hysteresis in MH systems is that hydrogen absorption and desorption
are no longer reversible in the thermodynamic sense below Tc . In this temperature regime, desorption of hydrogen from a metal hydride will not occur along
the absorption branch. As will be demonstrated in Section 2.3, reversing even
an incomplete hydrogen absorption process (a so called “minor loop")[41] is not
possible. Thus, the existence of hysteresis results in a thermodynamic inefficiency
for engineering systems which utilize MH. These inefficiencies manifest for both
gas-phase and electrochemical hydrogen absorption and desorption, as evidenced
by the following examples:
• Consider a hydrogen fuel cell with a MH tank as the hydrogen storage medium.
The fuel cell requires a hydrogen pressure of 30 psig to run, so an MH must
be chosen which will desorb hydrogen at a partial pressure greater than 30

16
psig at the operating temperature.[42] At 100◦ C, LaNi5.68 Sn0.32 desorbs
hydrogen at 43 psi.[43] Due to the hysteresis, hydrogen absorption at the
same temperature occurs at 47 psi. Thus an additional work term associated
with the compression of hydrogen to 47 psi must be considered in calculating
the efficiency of this MH-fuel cell system.
• Hysteresis inefficiencies in an electrochemical MH system (Ni-MH battery)
are apparent from the Nernst equation (1.3). From the second term on the
right-hand side, we see that the potential changes by 29.1 mV per decade
of pressure. For LaNi5 -based metal hydride electrodes, hysteresis can result
in charge/discharge overpotentials up to 20 mV for a cell with an operating
voltage of 1.2V.[44]
In both cases, the inefficiency may not represent a large portion of the useful work
obtained from the system, but with continued cycling of the system, these small
losses will sum to a significant amount.
In addition to theoretical work regarding the origin of hysteresis, there has been
significant effort in developing strategies to reduce or eliminate it. Alloying of
pure elemental or intermetallic hydrides has been demonstrated to reduce hysteresis
and the width of the two phase region. Substitution of up to 10% of Ni with
Ge in LaNi5 reduces hysteresis by a factor of five at room temperature, with a
reduction in hydrogen capacity of 25%.[44] Alloying Pd with several metals, most
notably Ag, reduces and in some cases eliminates the two phase region at a constant
temperature.[45] Wang et al. found a near elimination of hysteresis in an internally
oxidized Pd/Cr2 O3 composite at 493 K, a temperature at which pure Pd still exhibits
significant hysteresis.[41] The authors propose this is a microstructure effect but
provide no microstructural analysis.
Another avenue of reducing hysteresis is to use a nanosized MH. As demonstrated
in Section 2.3, nanocrystalline Pd has a smaller hysteresis than bulk Pd at the
same temperature, but also a smaller capacity. It is apparent that there is a trade
off between a decreased capacity or reduced hysteresis. When designing an MH
system, it is therefore important to weigh which aspect will have a more deleterious
effect on the overall performance of the system.

17
1.4

Nickel-Metal Hydride Batteries

The most well-known application of MH is the Ni-MH battery, which served as the
rechargeable battery of choice prior to the introduction of Li-ion batteries. In these
systems, a Ni(OH)2 /NiO(OH) cathode is paired with a hydride-forming metal anode,
and charge/discharge reactions at the anode proceed according to the schematic in
Figure 1.1. The redox reaction at the anode is:
H2 O + M + e −

OH− + MH

(1.9)

with the redox potential determined by Equation 1.3. On the cathode side, the redox
reaction is:
Ni(OH)2 + OH−
NiO(OH) + H2 O + e−
(1.10)
with an associated redox potential of 0.41 V vs. Hg/HgO. In Equations 1.9 and 1.10,
moving from right to left corresponds to charging.
There are additional constraints when using MH for electrochemical hydrogen storage. In an aqueous electrolyte, the charging potential must be less negative than
the potential for hydrogen evolution to facilitate absorption of evolved hydrogen.
Otherwise, the pressure of the cell can increase, resulting in catastrophic failure. If
the MH cannot catalyze the reduction of water to form hydrogen, an electrocatalyst must be incorporated into the electrode formulation to evolve hydrogen to be
absorbed by the hydride-forming metal. The final constraint is that the MH should
be stable against corrosion in the aqueous alkaline electrolyte. Corrosion can be
addressed with alloying or encapsulation with an inert metal (such as Pd), but both
options often result in a loss of specific capacity.[18, 46, 47] In Chapter 3, an alternative option of electrolyte modification is presented as a promising way to mitigate
corrosion.
The first Ni-MH battery was demonstrated by Battelle in 1967 and utilized a TiNibased AB alloy as the anode.[7, 48] State-of-the-art commercial MH alloys are
“AB5 ” alloys based on the Haucke phase of LaNi5 . These alloys have been heavily
developed, with substitutions on both the La and Ni sites to reduce cost, alter the
hydride stability, and improve the lifetime.[7] Lanthanum is often substituted with
mischmetal, (Mm) a less expensive mixture of rare-earth metals primarily composed
of Ce (30 - 52 wt%) and La (13 - 25 wt%). Other La site substitutions include Ce,
Pr, Nd, Zr, and Hf. Substitutions on the Ni site include Sn, Al, Mn, Cu, Co,
Cr, Fe, Si, and Zn.[7, 44] These AB5 alloys offer a reversible capacity of around
300 mAh/g.[49–51] Development of a higher capacity anode would make Ni-MH

18
batteries competitive with Li-ion batteries in terms of energy density, with the added
safety benefit of using an aqueous electrolyte rather than an organic one.
For many years, vanadium-based BCC alloys have been proposed as higher capacity alternatives to AB5 materials.[52–55] Pure V absorbs up to 2 H/M, which
corresponds to 3.9 mass% hydrogen storage capacity, or 1037 mAh/g theoretical
electrochemical capacity. The VH ↔ VH2 phase transformation takes place at 4
atm hydrogen equilibrium pressure at 313 K, which can be altered to some extent
by alloying with other transition metals.[19, 56, 57] The V ↔ VH phase transformation occurs at a very low hydrogen equilibrium pressure (on the order of 10−6
atm), and this monohydride transition is generally considered to be too stable for
electrochemical applications.[18] This limitation has been thought to restrict the accessible electrochemical capacity of V-based BCC alloys to half of their theoretical
values.[47] There is little physical evidence, however, of the extent of the phase transformation or even if electrochemical dehydrogenation of the monohydride phase is
possible at all.
Vanadium is often alloyed with titanium for lower cost and faster hydrogen absorption kinetics.[18, 58–60] Nickel is indispensable for electrochemical activity,
and many studies focused on the Ti-V-Ni ternary system as electrode materials for
Ni-MH batteries.[54, 61] The Ti-V-Ni-based alloys tend to unmix chemically on the
BCC lattice, forming an electrocatalytically active Ni-rich minority region (maximum hydrogen capacity of 1.3 mass%) and a majority V-rich region which forms
a high capacity MH.[47, 52, 53, 62–66] One of the highest capacity BCC alloy
compositions is TiV2.1 Ni0.3 , or Ti29 V62 Ni9 . The hydrogen absorption capacity for
Ti29 V62 Ni9 was reported to be 4.0 mass% in gas-phase reactions; electrochemically,
however, it discharges 470 mAh/g initially before quickly losing one third of its
capacity in 10 cycles.[47] Dissolution of V from the electrode was identified as the
cause of the electrode failure. The cycle performance was improved by alloying with
Cr, but the capacity of Ti29 V62−x Ni9 Cr x (x ≤ 12) alloy electrodes still decreased
substantially over 30 cycles.[46] Recently, the same group reported further improvement of cycle stability for a Ti29 V44 Ni9 Cr18 alloy, but with a much lower reversible
capacity of about 300 mAh/g.[67] The trade-off between long cycle life and high
capacity suggests it may not be possible to develop Ti-V-Ni-based alloy electrodes
by Cr-substitution alone. Chapter 3 is focused on the development of stable V-based
BCC MH electrodes.

19
Chapter 2

ELASTIC ENERGY AND THE HYSTERESIS OF PHASE
TRANSFORMATIONS IN PALLADIUM HYDRIDE
2.1

Chapter Overview

The palladium-hydrogen system is the prototypical metal hydride (MH), and a convenient one for studying hysteresis. Face-centered cubic (FCC) palladium undergoes
an isostructural expansion of approximately 10% when it absorbs up to 0.7 H per
Pd.[68] Hydrogen absorption and desorption occurs quickly, and at convenient hydrogen partial pressures in the range of 103 to 105 Pa. The hysteresis behavior
of both bulk and nanoscale PdH has been studied previously, and there is a clear
trend of size dependence.[24, 25, 37, 69–76] The (de)hydriding transitions of bulk
and nanoscale PdH are characterized with simultaneous measurements of pressure
composition isotherms and in situ X-ray diffraction. This is the first such study
for nanoscale PdH. Previous in situ studies on nanoscale PdH have used hydrogen
partial pressure, lattice parameter, luminescence, or plasmon intensity as a proxy for
hydrogen concentration.[37, 69, 71, 74, 75, 77, 78] Directly measured hysteresis,
composition dependent phase fractions, and lattice parameters are used to evaluate
some of the theories of hysteresis in metal hydrides presented in Chapter 1, and
show a directional dependence of the coherent spinodal phase diagram.
2.2

Experimental Details

Palladium powder (200 mesh, 99.95% metals basis) was purchased from Alfa Aesar
(Ward Hill, MA, USA). The powder was annealed at 1273 K for one hour under
N2 flow in a Lindberg horizontal tube furnace before any hydriding experiments.
Palladium nanopowder (99.95%) was purchased from US Research Nanomaterials,
Inc., (Houston, TX, USA) and degassed at 353 K for at least 8 hours prior to any
hydriding experiments.
In situ X-ray diffraction (XRD) experiments were performed using an Inel CPS 120
powder diffractometer utilizing Mo Kα radiation. A Si h110i single crystal oriented
in the h220i direction was used as the incident beam monochromator. Two-theta
calibration of the CPS 120 detector was performed with a NIST SRM 660a (LaB6 ).
More details of the diffractometer alignment and data processing can be found in
Appendix C. At least 200 mg of sample was first loaded into a temperature controlled

20
vertical sample holder, then placed into a stainless steel chamber (980 mL) with a
Be window. This reactor is connected to a gas manifold with VCR fittings and MKS
Baratron pressure transducers. Prior to hydrogen uptake, the sample was evacuated
at 353 K for 72 hours. Each sample was cycled at least once prior to collection
of data presented here. At least two complete isotherms were measured for each
temperature.
Electron micrographs of annealed bulk Pd powder were acquired with a high resolution Zeiss 1550VP Field Emission scanning electron microscope (SEM). Nanocrystalline Pd powder was analyzed with bright and dark-field transmission electron
microscopy (TEM) using an FEI Tecnai F-30UT STEM. The powder was dispersed
in isopropanol and sonicated one hour to reduce agglomeration before loading on
an amorphous carbon grid for TEM characterization.
Pressure-composition isotherms of bulk Pd powder and nanocrystalline Pd powder
were also measured on an independent volumetric Sievert’s type apparatus. At least
1.0 g of sample were loaded into an AISI 316L stainless steel reactor (5 mL) and
evacuated (baseline 10−5 Pa) at 473 K (bulk Pd) or 353 K (nanocrystalline Pd) for
8 hours. Each sample was cycled at least once prior to collection of data presented
here, and at least two complete isotherms were measured.
Hydrogen concentrations in the sample were calculated volumetrically with the
NIST REFPROP database.[79, 80] Absorption and desorption isotherms were measured at 333 K for both the in situ XRD and Sievert’s-type apparatus experiments.
An additional pressure composition isotherm was measured on the Sievert’s-type
apparatus for bulk Pd at 435 K. At each hydriding (dehydriding) step, equilibration
was reached when pressure in the reactor did not change for a period of 15 minutes. After equilibration, the next quantity of hydrogen was added (removed for
dehydriding) from the reactor.
2.3

Results

The structure of the bulk and nanocrystalline Pd powders were investigated with
SEM and TEM, respectively. A high-resolution TEM image of nanocrystalline Pd
is provided in Figure 2.1, and SEM images of bulk Pd are provided in Appendix A
(Figure A.1). Annealed bulk Pd particles are 43.5 ± 12.90 µm in size with easily
distinguishable coalesced grains 3.0 ± 1.26 µm in diameter. The nanocrystalline Pd
consists of agglomerated crystallites 7.47 ± 2.35 nm in diameter, as measured from
dark field images. A representative dark field TEM image (inverted) is provided in

21

Figure 2.1: High-resolution TEM image of as-received nanocrystalline Pd powder
prior to hydrogen exposure.

22

Figure 2.2: Inverted dark field TEM micrograph of the nanocrystalline Pd with
inverted electron diffraction pattern (330 mm camera length) inset. The dark field
image was acquired with a 10 µm objective aperture capturing 111 diffracted beams.
A 40 µm selected area aperture was used when acquiring the electron diffraction
pattern. Scale bar for the electron diffraction pattern is 2 nm−1 .

23
Figure 2.2 with the corresponding electron diffraction pattern inset.
Pressure-composition isotherms measured on a Sievert’s apparatus for bulk and
nanocrystalline Pd are plotted in Figure 2.3a. Uptake values of approximately
0.6 and 0.7 H/M are found for the nanocrystalline and bulk PdH, respectively,
consistent with other reports.[38, 39, 73] The 333 K pressure hysteresis measured
from the isotherms (according to the left hand side of Equation 1.8) is 0.37 for
nanocrystalline PdH and 0.88 for bulk PdH. High temperature hysteresis of the bulk
PdH at 435 K is 0.37. A significant reduction in the absorption plateau pressure
for the nanocrystalline PdH (from 10 kPa to 6.9 kPa) contributes primarily to the
reduction in the hysteresis at 333 K. Only a small increase in the desorption plateau
is observed for the nanocrystalline PdH. Another important difference is that the
transition is more gradual for the nanocrystalline PdH; a sharp initial transition is
observed for the bulk PdH.
Figure 2.3b plots a minor loop isotherm for PdH measured on the in situ system in
which the hydriding transformation was stopped at 80% completion then reversed.
Rather than traversing back along the absorption branch, the pressure decreases to
the desorption branch before significant quantities of hydrogen are removed. Similar
results have been reported previously.[41]
Isotherms measured during the in situ hydriding experiments are consistent with
those plotted in Figure 2.3a. They are compared in Figure A.2 and discussed in
Appendix A. The hysteresis measured in both apparatuses are the same.
The in situ diffraction patterns from a full hydriding and dehydriding cycle for the
bulk and nanocrystalline PdH powders are shown in Figures 2.4 and 2.5, respectively.
Raw diffraction data were initially processed with a deconvolution algorithm to
remove instrument effects. Rietveld refinement with the GSAS-II software package
was subsequently used to extract phase fraction and lattice parameter data from the
deconvoluted in situ XRD results.[81] The bulk and nanocrystalline PdH data were
both fit to a two-phase model consisting of the solid solution α-phase and hydride
β-phase, with the sum of the phase fractions constrained to be unity.[77] Crystallite
size for nanocrystalline PdH was set at 7 nm, as determined by TEM and consistent
with XRD.
The phase fraction of α phase as a function of hydrogen content for both bulk and
nanocrystalline Pd is plotted in Figure 2.6. Our direct measurement of hydrogen
content in nanocrystalline PdH is different than other studies which convert lattice

24

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Figure 2.3: a) Pressure-composition isotherms for bulk and nanocrystalline PdH.
An additional isotherm of the bulk PdH was measured at 435 K. The inset plots
the plateau region on a linear pressure scale to highlight the shape of the isotherm
curves. Closed symbols denote absorption, and open symbols correspond to the
subsequent desorption. b) 333 K minor loop for bulk PdH measured in situ. After
hydriding to approximately 80% transformed, the isotherm was reversed and the
sample was dehydrided.

25

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Figure 2.4: In situ X-ray diffraction patterns of hydrogen absorption (left) and
desorption (right) by bulk Pd powder. The color of each trace corresponds to the
total hydrogen concentration (in H/M) as indicated by the central legend.

26

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Figure 2.5: In situ X-ray diffraction patterns of hydrogen absorption (left) and
desorption (right) by nanocrystalline Pd powder. The color of each trace corresponds
to the total hydrogen concentration (in H/M) as indicated by the central legend.

27
Table 2.1: Terminal compositions of the hydriding transition for bulk and nanocrystalline PdH obtained from in situ XRD results at 333 K. High temperature (435 K)
compositions for the bulk Pd are evaluated from the pressure composition isotherm.
Sample

cαabs
cabs
cαdes
cdes

Bulk
Nanocrystalline
333 K 435 K
333 K
0.04
0.63
0.013
0.56

0.10
0.59
0.07
0.51

0.125
0.47
0.115
0.46

parameter to hydrogen content using a 3(∆a/a0 ) = 0.19∆c relationship reported for
bulk PdH.[17, 69, 77] In Figure 2.6a, the rate of transformation in bulk PdH is greater
than linear until an inflection point halfway through the transformation. Past this,
the rate of transformation remains linear until the phase transformation is complete.
This is in contrast to the results for nanocrystalline PdH (Figure 2.6b) which exhibit
a much more linear transformation. The phase fraction data is used to determine
terminal compositions of the two-phase region. Terminal compositions are identified
as the composition at which the α-phase fraction changes from a constant value in
the single phase region of the isotherm. These compositions are reported in Table
2.1. Other studies use graphical constructions or analytical models to determine
terminal compositions.[30, 69, 82] Vogel et al. report a much larger solvus hysteresis
in PdH nanoparticles than we report for nanocrystalline PdH powder. Their in
situ isotherms contain fewer data points and do not directly measure hydrogen
concentration, however.[77] No in situ data was measured for bulk PdH at 435 K
because the hydrogen environment chamber is not suited to accommodate required
hydrogen partial pressures. In this case, terminal compositions were determined by
the graphical method proposed by Wicke et al. in which the plateaus are extended
to the opposite isotherm branch, and the intersection point is taken as the terminal
composition.[30]
Refined lattice parameters are plotted in Figure 2.7. Variation of lattice parameter
with hydrogen concentration in single phase regions was fit to a linear function
(Vegard’s law); the results are summarized in Table 2.2. Within the two-phase
region, lattice parameters for bulk phases are constant but there is variation in
nanocrystalline Pd. This is apparent in the continual increase in α phase lattice
parameter during absorption. Lattice parameters for both phases are larger for

28

Figure 2.6: Refined α phase fraction for the a) bulk and b) nanocrystalline PdH
powders. The black arrows indicate the direction of transformation, and shading of
the traces indicates the error bars.

29
Table 2.2: Variation of lattice parameter with hydrogen concentration da/dc (Å/H)
in single phase regions. All data are fitted with a linear function according to
Vegard’s Law. Empty entries correspond to regions with insufficient data points to
fit.
Region

Bulk

Nanocrystalline

αabs
αdes
βabs
βdes

0.174 ± 0.058
0.183 ± 0.050
0.151 ± 0.011

0.099 ± 0.015
0.071 ± 0.041
0.140 ± 0.012
0.132 ± 0.029

absorption than desorption, with a significant difference for bulk Pd (Figure 2.7a).
2.4

Discussion

Hysteresis of Bulk Palladium
The hysteresis and phase transformation behavior of bulk PdH indicate that a large
nucleation barrier exists which is likely due to strains generated by a new phase.
des
abs
des
Our results (Table 2.1) for bulk PdH show that cabs
β > c β and cα > cα . The shift
in terminal composition to lower values on desorption is consistent with behavior
predicted by Flanagan and S-K theory.[29, 31, 32] Furthermore, the abrupt transition
to the plateau at the start of the (de)hydriding transition (Figure 2.3a) indicates the
presence of a large nucleation barrier.
Changes in the terminal compositions affect both lattice parameter and phase fraction. A decrease in terminal composition corresponds to a reduction in lattice
parameter, as seen in Figure 2.7a. During absorption, a β = 4.034Å, whereas
a β = 4.025Å on desorption. Refined phase fractions for bulk PdH deviate from a
linear behavior during initial stages of the phase transformation. During desorption,
the β phase disappears slower than expected, whereas for absorption the α phase
transforms faster. In the presence of a barrier, an undersaturated β phase could form;
rather than nucleating an α precipitate, the β matrix continues to desorb hydrogen,
retarding the transformation. Similarly, a supersaturated α phase could form during
hydriding. Once a β phase precipitate forms, it draws hydrogen from both the
supersaturated α phase as well as the gas phase. In this scenario, hydrogen in the
supersaturated phase segregates to form additional β phase and a saturated α phase.
The nucleation barrier disappears as the transformation progresses. Refined phase
fractions shift to a linear slope past the halfway point of the transformation, at a

30

Figure 2.7: a) Refined lattice parameters of the a) bulk and b) nanocrystalline
Pd powders during hydrogen absorption and desorption. The red and blue traces
correspond to the solid solution α phase and hydride β phase, respectively. Error
bars are indicated by the shaded region.

31
hydrogen concentration at which isotherms begin to deviate from a constant-valued
plateau pressure.
Comparison of Bulk and Nanocrystalline Behavior
Nanocrystalline PdH has a smaller hysteresis, smaller total hydrogen capacity, and
narrower miscibility gap than bulk PdH. A narrower miscibility gap corresponds to
increased hydrogen solubility in the α phase and decreased solubility in the β phase
as seen in Figure 2.3. In Figure 2.7, we see that during absorption, aα approaches
3.92Å for nanocrystalline PdH, whereas aα = 3.903Å for bulk PdH. Similarly, a β
for nanocrystalline PdH never exceeds 4.03Å, the minimum value measured during
absorption in bulk PdH.
The variation of lattice parameter with hydrogen content, da/dc, is less in nanocrystalline than bulk PdH, especially for the α phase. This means that the volume
distortion and subsequent elastic energy contribution is less per hydrogen, allowing
for increased solubility of hydrogen in the α phase. It has been hypothesized that
increased solubility of hydrogen in the α phase and reduction in total capacity is due
to a significant fraction of energetically favorable interstitial sites near the particle
surface.[24, 38, 39] A high fraction of grain boundaries are visible in Figure 2.1
within the nanocrystalline Pd. Existence of energetically favorable sites or grain
boundaries could provide a means for relaxation of elastic energy resulting in the
reduced value of da/dc which we observe.
Phase fractions for nanocrystalline PdH are plotted in Figure 2.6b. The transformation proceeds linearly, in contrast to trends for bulk PdH. Nanocrystalline PdH
isotherms do not exhibit abrupt transitions at the beginning of the plateau as in bulk
PdH. Instead, the transition is more gradual (see inset in Figure 2.3), corresponding
to a lower nucleation barrier. Additionally, a smaller hysteresis and a smaller difference in terminal compositions further indicate that the nucleation barrier is less for
nanocrystalline than bulk PdH.
Hysteresis and Hysteresis Energies
The S-K pressure hysteresis of Equation 1.8 is evaluated at 333 K with ν0 =
coh
1.47×10−29 m3 , σ = 0.39,  0 = 0.063, and (ccoh
β −cα ) as determined from our phase
fraction data (Table 2.1).[17, 83] Shear moduli of G s = 44 and 35 GPa are used for
bulk and nanocrystalline PdH, respectively.[84] S-K hysteresis values are compared
to experiment in Table 2.3, and the S-K theory significantly overestimates hysteresis.
Furthermore, we test the predicted temperature dependence by comparing ratios of

32
hysteresis at two temperatures. For bulk PdH, the measured ratio between 435 K and
333 K is 0.42, whereas the predicted ratio is 0.7. S-K theory does not quantitatively
describe the thermodynamics of hysteresis.
Hydrogen absorption and desorption by PdH nanostructures has been demonstrated
to occur without any plastic deformation, and the critical size below which no
dislocation formation is observed is 300 nm. Hysteresis increases with particle size
up to this critical size, with a maximum value of 1.41 evaluated from data reported
by Ulvestad, et al.[24, 25] It is likely that the hydriding transition occurs coherently
for nanoparticles below 300 nm, yet hysteresis predicted by the S-K theory is still
an overestimate.
Table 2.3: Comparison of experimentally determined hysteresis values to those
predicted by S-K theory. S-K hysteresis values are calculated according to Equation
1.8 with values listed in this section. Experimental hysteresis values for the 300 nm
nanoparticles are determined from refs. [24] and [25].
Experiment
Bulk, 333 K
0.88
Bulk, 435 K
0.37
7 nm nanocrystalline, 333 K
0.37
300 nm nanoparticle, 300 K
1.41

S-K Theory
5.2
3.6
2.8
2.5

Hysteresis energy can be expressed as the difference in chemical potential between
absorption and desorption plateaus:
pabs
(2.1)
∆µhyst = k BT ln
pdes
Assuming that hysteresis is due to a macroscopic energy barrier, we can equate half
the hysteresis energy to an elastic energy of the form:
Eel =

1 2
Bδ

(2.2)

where B is bulk modulus (187 GPa for Pd) and δ is a fractional change in volume.[83]
For cubic crystals δ is 3(∆a/a). Combining Equations 2.1 and 2.2, we estimate a
misfit strain (∆a/a = |a β − aα |/aα ) between α and β phases and compare it to
that obtained from lattice parameter data. The results are summarized in Table 2.4.
Misfit strains estimated from hysteresis energies are within a factor of four of those
obtained from lattice parameter measurement, indicating that hysteresis is due in
large part to the existence of a macroscopic elastic energy barrier. That the estimated

33
value is less, however, indicates that misfit strain is mitigated in some way in both
bulk and nanocrystalline PdH.
Table 2.4: Summary of hysteresis energies and measured and estimated misfit strain
values for bulk and nanocrystalline PdH at 333 K. Misfit strains are estimated from
hysteresis energies according to Equation 2.2.
meV
Ehyst [ atom
mis f it measured

mis f it estimated

Bulk
6.3
0.033
0.010

Nanocrystalline
3.1
0.027
0.007

The elastic energy can depend strongly on the shape of a precipitate. For example, Nabarro calculated the energy of a misfitting ellipsoid embedded in an elastic
medium, assuming the ellipsoid is incompressible and all elastic energy is in the
surrounding medium.[85] This classic result showed that a sphere gives the highest
energy, but this is reduced by shaping the precipitate as a thin oblate spheroid. The
elastic energy per volume is reduced to zero as the precipitate becomes arbitrarily
thin. Alpha-phase precipitates are observed to be shaped as thin plates, so there is
a large reduction of total elastic energy compared to the case of spherical precipitates.[86] This is counteracted to some extent by surface energy. Nevertheless, we
expect hydriding to proceed with a lower elastic energy barrier than for the spherical
precipitates of the S-K analysis.
Other theories propose that hysteresis is due to continued formation of dislocations
as hydriding transitions occur.[29] The energy of these dislocations is analogous to
stored energy of cold work, or the energy released as dislocations are annealed out
of cold-worked metals. In cold-worked FCC metals, stored energy is on the order
of 0.1 meV/atom, far less than hysteresis energies calculated in Table 2.4.[87]
We observe in Figure 2.3a that the reduction in hysteresis of the nanocrystalline Pd is
primarily due to a reduction in absorption pressure. This asymmetry in the hysteresis
indicates that the mitigation of elastic energy could occur differently for absorption
and desorption, adjusting the relative magnitudes of the nucleation barriers.
Strain effects on hysteresis
Schwarz and Khachaturyan’s theory for hysteresis is derived from Eshelby’s model
for a misfitting precipitate in an infinite matrix. When the matrix becomes finite
with respect to precipitate size, edge effects are important.[36] Recently, a solution

34

Figure 2.8: Variation of dimensionless strain energy with inclusion position. An
0.4R inclusion is subjected to a uniform isotropic eigenstrain field i∗j = 21  ∗ δi j .
Strain energy density is normalized by (4µ ∗2 )/(κ + 1)2 . Inset are heat maps
of strain energy density for particles with inclusions located at the origin (left)
and displaced 0.6R (right). The matrix boundary is constrained by traction-free
conditions; displacements due to the inclusion are not shown.

35
to the finite Eshelby problem in two dimensions was reported for eccentrically
placed circular inclusions in a circular matrix.[88, 89] We use this analysis to model
effects of precipitate position within the matrix on displacement, stress, and strain
energy (details in Supporting Information). The total strain energy of a precipitate
of radius 0.4R in a particle of radius R is plotted against precipitate center position
in Figure 2.8, with inset plots of strain energy density for a centered inclusion and
an inclusion displaced by 0.6R. Additional plots showing for displacements and
stresses are provided in Appendix A. A reduction in strain energy by more than a
factor of two is achieved by shifting the precipitate to the particle edge. Further
reduction of strain energy is possible by replacing the circular precipitate with a
circular cap.[25]
The combined results from experiment and modeling demonstrate that accommodation of (de)hydriding stresses occurs differently in bulk and nanocrystalline PdH,
altering isotherm behavior. Stresses imposed by both changing hydrogen concentration in single phase regions and by coherent nucleation of new phases are mitigated
by surface effects in nanocrystalline PdH. It is likely that such surface effects could
account for the smaller hysteresis of nanocrystalline PdH listed in Table 2.3. In bulk
PdH, coherency stress can be reduced by precipitate shape or loss of coherency.[86]
This distinction manifests as nucleation barriers with different slopes; a steep barrier for bulk and a more moderate barrier for nanocrystalline PdH. As particle size
increases, so would the slope of the barrier and the hysteresis.
Hysteresis Effects on the Spinodal Phase Diagram
Solvus hysteresis effects are apparent when plotting terminal compositions on the
spinodal phase diagram. Figure 2.9 includes data from Table 2.1 and the literature.[30, 77] For bulk and nanocrystalline PdH, the absorption curve is shifted to the
right compared to desorption. Wicke, et al., proposed that desorption is closer to
true “strain-free" equilibrium, and thus should be used for the phase boundaries.[30]
Our results in Figure 2.6a show that desorption in bulk PdH still exhibits a nucleation barrier and thus is not a stress-free transition. Nanocrystalline PdH has a lower
nucleation barrier and hysteresis, so the shifts in terminal composition are smaller.
As a result of the splitting, the phase boundaries become directionally dependent.
When hydrogen is added, the transition proceeds according to the phase boundary
denoted by filled symbols in Figure 2.9, and when hydrogen is removed, the boundary
shifts to that denoted by open symbols. This shift occurs even for partial isotherms,

36

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Figure 2.9: Absorption and desorption spinodal phase diagrams determined from
terminal compositions of bulk and nanocrystalline PdH. Bulk and nanocrystalline
PdH data from this study are plotted as circles and triangles, respectively. Additional
bulk data from Wicke et al. are plotted as upside down triangles. 6 and 4 nm nanoparticle PdH data from Vogel et al. are plotted as squares and diamonds, respectively.
Filled markers denote absorption, open markers denote desorption. The black line
denotes a hypothetical equilibrium boundary for a barrier-free transformation.

37
as seen in the minor loop in Figure 2.3b. When the transformation is reversed
within the two-phase region, the system shifts to the opposite isotherm branch (and
associated spinodal) before any significant changes in phase fractions occur. Neither
phase boundary is a chemical equilibrium boundary, but due to the existence of a
nucleation barrier, they are physically relevant as coherent spinodals.
The coherent spinodal differs from the chemical spinodal owing to the elastic energy
in the unmixed state. This energy is positive, suppressing the phase boundary for
unmixing, and lowering the critical temperature of the coherent spinodal below
that of the chemical spinodal. The unmixing boundary for nanocrystalline PdH is
lower than for bulk PdH, but the elastic energy barrier of hysteresis is smaller in
nanocrystalline PdH. This elastic energy barrier for the hysteresis therefore cannot be
responsible for the lower critical temperature of nanocrystalline PdH. The reduction
in critical temperature for nanocrystalline PdH must originate with either a different
type of elastic energy in the material, or more likely in our opinion, with a change
in the hydrogen-vacancy interactions.
Cahn predicted that a coherent spinodal could shift for a system in which two phases
have different elastic moduli, with the direction of the shift dependent on the phase
that is nucleating.[90] For anisotropic cubic materials, the elastic modulus of interest
is Y(100) = (C11 + 2C12 )(C11 − C12 )/C11 .[90] This modulus is 277 and 274 GPa
for bulk Pd and PdH, respectively.[91] The largest difference in modulus between
the two phases is 12% for the C44 shear modulus, however Cahn does not quantify
what difference is required for a shift. In Cahn’s theory, spinodal boundaries are
determined by a common tangent construction, however S-K theory states that the
nucleation barrier invalidates this approach.[31, 32, 90] The splitting we observe in
the PdH system may be due to a different phenomenon than Cahn predicted.
Accessing chemical spinodal boundaries requires eliminating the nucleation barrier.
One method to achieve this would be to increase temperature above the critical
temperature, dose with an amount of hydrogen equal to the critical concentration,
and slowly cool below the spinodal. Initially, strain will be minimized as there
is a small difference in terminal compositions between the α and β phases. As
temperature decreases, hydrogen is desorbed from the α phase and absorbed from
the β phase. Growth of these phases will occur without a nucleation barrier. As a
result, we predict that a “strain-free" spinodal boundary will follow the desorption
branch (open symbols) at low H concentrations, and the absorption branch for high
H concentrations. This boundary is denoted in Figure 2.9 by the dashed black line.

38
2.5

Conclusions

We investigated pressure hysteresis associated with absorption and desorption of
hydrogen by bulk and nanocrystalline Pd. Hysteresis energies were found to be
comparable to elastic energies associated with lattice mismatch between α and β
phases, and significantly larger than stored energy of dislocations. Size effects are
observed in several aspects of the isotherm, including hysteresis, miscibility gap,
and terminal compositions of absorption and desorption. Lattice parameters and
phase fractions refined from in situ XRD data are consistent with changes in terminal
compositions. Nanocrystalline Pd has a smaller value of da/dc than the bulk, and the
reduced elastic energy per added hydrogen suggests a mechanism for the increased
solubility in the α phase.
These experimental results indicate the existence of a nucleation barrier caused
by elastic coherency strains of the misfitting nuclei. A quantitative comparison
was made between the experimental hysteresis and that calculated by SchwarzKhachaturyan theory. The theory predicted a much larger hysteresis than measured.
Likewise, for the measured hysteresis, the associated elastic energy predicted a
much smaller misfit strain than measured by XRD. We suggest this is caused by
microstructural accommodation of the new phase by forming plate-like precipitates,
reducing the coherency energy. A further reduction in elastic energy by a factor of
two or more occurs for the hydriding of nanocrystalline Pd. Here, the edge effects
play a big role, even for small precipitates of the new phase. The large fraction of
atoms at grain boundaries in the nanocrystalline Pd could also offer interstitial site
energies that are higher and lower than the bulk, causing both a slope and narrowing
of the two-phase plateau of hydriding.
Additionally, the presence of a nucleation barrier splits the coherent spinodal phase
boundaries, creating a directionally dependent phase diagram with the absorption
boundaries greater in composition than desorption. Further work is warranted in
investigating elastic energy effects on the coherent spinodal.

39
Chapter 3

HIGH CAPACITY V-BASED METAL HYDRIDE ELECTRODES
FOR RECHARGEABLE BATTERIES
3.1

Chapter Overview

Vanadium-based body-centered (BCC) alloys are an attractive high-capacity alternative to AB5 -based metal hydrides (MH) for Ni-MH batteries. Implementation of
these alloys in commercial systems is hindered by the short cycle life of V-based
BCC alloy electrodes due to the corrosion and dissolution of V in aqueous alkaline
environments. An in-depth summary of the development of these alloys is provided
in Chapter 1. In this Chapter, we investigate the corrosion behavior of V-based
Ti29 V62−x Ni9 Cr x BCC alloy electrodes and demonstrate techniques to mitigate the
corrosion. Furthermore, the performance of a novel MH-air battery utilizing Vbased BCC electrodes is modeled and compared to state-of-the-art Li-ion batteries.
3.2

Corrosion of Vanadium in Aqueous Environments

The corrosion behavior of Ti-V-Ni-Cr quaternary alloys may be qualitatively understood by using elemental Pourbaix diagrams and experimental corrosion studies.
Of these four transition metals, Ti, Ni, and Cr show passivation behavior in strong
alkaline environments by forming a metal oxide or hydroxide on the surface.[92–99]
Figure 3.1 shows the Pourbaix diagram of V plotted with corrected data from Post,
et al.[92, 100, 101] According to the Pourbaix diagram, V corrodes and dissolves
in strong alkaline solution as VO3−
4 (vanadate) ions, which is the only stable pentavalent V species at a pH above 13.[102] Liu et al. studied the redox behavior of
vanadate ions in alkaline solutions with a glassy carbon electrode and observed the
reduction process of VO3−
4 at -1.93 V versus a saturated calomel electrode, which
is well outside the operational voltage window for MH electrodes.[103] This shows
that corrosion-induced V dissolution is irreversible, but the rate of corrosion may
be controlled by adjusting the electrochemical and chemical environment of the
V-based alloy electrode. For example, Al-Kharafi et al. investigated the electrochemical behavior of V and found that the corrosion rate decreased upon removing
oxygen from the alkaline solutions.[104] It should be noted that the Pourbaix diagram is a thermodynamic prediction with no information on kinetics. Furthermore,
the corrosion of an alloy may differ from its elemental constituents. A systematic

40

Figure 3.1: Pourbaix diagram of V with the potential of the Hg/HgO reference
electrode indicated by the short-dash blue line. The orange box outlines the operational pH and potential ranges for MH batteries, and the green lines indicate how
equilibrium shifts with varying concentrations of dissolved V (in units of grams V
per kilogram H2 O). Line a: 2H+ + 2e− → H2 ; and line b: 2H2 O → O2 + 4H+ + 4e−

41
investigation of the corrosion behavior of alloy electrodes is still appropriate.
Further improvement of Ti29 V62−x Ni9 Cr x alloy electrodes requires a better understanding of the phase transformations and corrosion that occurs during electrochemical hydriding/dehydriding cycles. In this work, we characterize structural changes
and address corrosion by exploring the effects of pH, electrode potential, alloy composition, and the oxygen and vanadate ion concentration in the KOH electrolyte.
By understanding and accounting for the limitations imposed on these electrodes
by corrosion, we were able to develop an MH anode system that reversibly delivers
500 mAh/g capacity for up to 300 cycles.
3.3

Experimental Methods

Ti-V-Ni-Cr alloy preparation
High purity Ti, V, Ni, and Cr metals were weighed then arc-melted under an
argon atmosphere. The ingots were turned over and remelted three times to improve
compositional homogeneity. The ingots were then crushed, weighed, and transferred
to a Sievert’s apparatus for activation. The crushed ingots were first subject to high
vacuum at 653 K for several hours before the reactor was pressurized with 30 atm of
high-purity hydrogen gas. The reactor was then cooled to room temperature. This
process was repeated five times. After gas-phase activation, the ingots were ground
in an Ar glovebox and sieved to a fine powder (200 mesh). This alloy powder was
used for X-ray diffraction (XRD) analysis and electrode preparation.
Isotherm measurements
Room temperature hydrogen absorption isotherms were performed on a volumetric
Sievert’s type apparatus. At least 1 gram of activated alloy powder was loaded into
an AISI 316L stainless steel reactor and evacuated (baseline 10−5 Pa) at 673 K for 8
hours. The reactor was allowed to cool to room temperature before the absorption
measurements were performed. For each hydriding step, equilibration was reached
when the pressure in the reactor did not change for a period of 15 minutes. After
equilibration, the next quantity of hydrogen was introduced into the reactor.
Electrode preparation
The alloy electrodes were prepared by pressing a mixture of alloy and Inco 525 Ni
powder (1:3 mass ratio) onto an extruded Ni mesh (Dexmet Corporation) or Ni foam
(MTI Corporation) current collector. Approximately 100 mg of powder mixture was
hydraulically pressed onto a Ni mesh current collector with a surface area of 1.33

42
cm2 . This high loading procedure follows those commonly adopted in literature
for evaluation of the electrochemical properties of metal hydride electrodes.[105,
106] These electrodes were used to assemble air-saturated beaker cells, which were
convenient for post-cycling analysis by methods such as XRD, X-ray photoelectron
spectroscopy (XPS), and inductively coupled plasma mass spectrometry (ICP-MS).
A smaller electrode was prepared by pressing approximately 5 mg of powder mixture
onto Ni foam (0.32 cm2 ). This type of electrode is more suitable for cycle stability
tests, because the porous nature of the Ni foam produced an electrode that was more
mechanically robust.
Cell assembly and testing
The electrolyte used in this study was an aqueous 30 wt% KOH solution (Alfa Aesar). For the open-air beaker cells, a Ni mesh based MH electrode was sandwiched
between two sintered NiO(OH)/Ni(OH)2 electrodes (4 cm2 each) with nylon separators. The electrode stack was placed in a three-electrode beaker cell with Hg/HgO
reference electrodes. The cell was filled with 24 mL electrolyte and let rest for at
least 2 hours before testing. Coin cells were assembled in open air using Ni foam
MH electrodes, 200 µL electrolyte, and NiO(OH)/Ni(OH)2 positive electrodes. (See
Figure B.6 and its accompanying description for the design and preparation of coin
cells.) Both the beaker cells and coin cells were cycled with an Arbin multichannel
potentiostat.
The Ar-purged three-electrode cells consist of a Ni foam MH anode, NiO(OH)/Ni(OH)2
positive electrode (BASF-Ovonic, Rochester Hills, MI, USA), and a Hg/HgO reference electrode inside a 4-neck flask, with the necks sealed by septums. 24 mL of
KOH was added, and Ar was allowed to bubble through for 30 minutes before the
electrodes were lowered into the electrolyte. Cycling of the cell under continuous Ar
flow was controlled by a Princeton Applied Research Versastat 4 potentiostat. All
cells were charged at 100 mA/g. Two discharge protocols were used: (1) single-step
discharge at 20 mA/g and (2) three-step sequential discharge at 100, 40, and 20
mA/g with a 5 minute rest period between each step. The charge capacities and
cut-off voltages are specified in the text.
Characterization
Polished pieces of the alloy ingot were characterized using backscattered electron
imaging (BES) and energy dispersive X-ray spectroscopy (EDS) on a Zeiss 1550VP
Field Emission scanning electron microscope (SEM) equipped with an Oxford X-

43
Max EDS system with a silicon drift detector (SDD). X-ray diffraction analysis of
the alloy and electrodes was performed with a PANalytical X’Pert Pro diffractometer
utilizing Cu Kα radiation. The alloy powder or electrode powder was ground before
XRD measurements. The 2θ positions of the diffraction peaks from the electrode
powders were calibrated by the diffraction peaks of the internal Ni conductive
binder. X-ray photoelectron spectroscopy (XPS) was conducted on the Ni mesh
electrodes before and after electrochemical experiments with a Kratos Ultra XPS.
Chemical analysis of the used electrolyte was determined by an Agilent ICP-MS.
The electrolyte samples for ICP-MS were collected from beaker cells and diluted
with 3% nitric acid.
3.4

Results

Microstructure and thermodynamics
The microstructure and composition of three alloys (Ti29 V62−x Ni9 Cr x , x = 0, 6,
and 12) were characterized by XRD, SEM, and EDS (Figures 3.2 and 3.3). Xray diffractograms of all three alloy compositions exhibit only the BCC structure
(Figure 3.2). The diffraction peaks shift to higher angles with increasing Cr content,
corresponding to a smaller lattice parameter for these alloys (Figure B.1). Smaller
secondary peaks are also observed in the diffractograms for alloys with low Cr
content, consistent with no change in crystal structure during chemical unmixing.
Backscattered electron images of polished Ti29 V50 Ni9 Cr12 ingots are provided in
Figures 3.3a and 3.3b. These images reveal that the microstructure of the alloy is
composed of a minority Ni-rich network (light) dispersed in a majority V-rich matrix
(dark). The Ti29 V62 Ni9 and Ti29 V56 Ni9 Cr6 alloys show similar a microstructure
(Figure B.2). The average composition of the majority and minority regions within
the Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloys are listed in Table 3.1. For all three
alloys, the composition of the V-rich region is close to the designed stoichiometric
ratio, while the Ni-rich region contains a Ti:Ni ratio of roughly 1:1. The Ni-rich
region contains little V and almost no Cr.
The microstructure of the Ti29 V62−x Ni9 Cr x alloys is similar to what has been reported previously.[46] The differences in the scale of the microstructure and compositional distribution are expected from the different cooling rates. These BCC
alloys tend to unmix during cooling into V-rich and Ni-rich regions. The alloy
as a whole is BCC, but the compositional unmixing generates regions with larger
(V-rich) and smaller (Ni-rich) lattice parameters. The expected lattice parameters of

44
Table 3.1: Summary of the compositions of the majority V-rich and minority Nirich regions within the alloy ingots. The reported compositions are the average
compositions as determined by EDS.
Alloy
Ti29 V62 Ni9
Ti29 V56 Ni9 Cr6
Ti29 V50 Ni9 Cr12

V-rich region
Ti29 V65 Ni6
Ti28 V59 Ni6 Cr7
Ti23 V57 Ni6 Cr14

Ni-rich region
Ti47 V8 Ni45
Ti49 V8 Ni42 Cr1
Ti46 V7 Ni47

.%#&"- ,+*)( '#&%"$#"!

9&6:;01<&:=*>6

9&6:;03<&:=*3

9&6:;36<&:

51

50

41

40

01

00

31

30

21

20

/1

67 (8.

Figure 3.2: X-ray diffractograms of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloys after
hydrogen activation and pulverization of the arc melted ingots.

/0

45

a)

100 μm

b)

10 μm

Figure 3.3: Backscattered electron images at (a) low and (b) high magnification of
a polished Ti29 V50 Ni9 Cr12 ingot.

46
the two regions can account for the primary and secondary peaks visible in Figure
3.2. The composition of the Ni-rich region is relatively constant with increasing Cr
concentration, while the V-rich region is not. As a result, we observe that the lattice
parameter of the V-rich region decreases with increasing Cr content, shifting the
peak position to the right in Figure 3.2 until it overlaps the peaks associated with
the Ni-rich region.
Room temperature hydrogen absorption isotherms of the alloys are provided in Figure 3.4. The maximum hydrogen absorption capacity decreases with increasing Cr
content from 3.2 mass% (Ti29 V62 Ni9 ) to 2.8 mass% (Ti29 V50 Ni9 Cr12 ), which translates to electrochemical capacities of 854 to 748 mAh/g. This hydrogen absorption
capacity is lower than that reported by Iwakura et al., which is likely caused by
difficulty in completely desorbing hydrogen from the solid solution BCC hydride
phase.[47] (Note: The isotherm curves for TiV2.1 Ni0.3 reported by Iwakura, et al.
show a maximum uptake of closer to 1.75 H/M (3.5 mass%), not 1.99 H/M as stated
in the text.)[47]
Chromium substitution also increases the plateau pressure. In the Ti29 V50 Ni9 Cr12
alloy, a significant amount of hydrogen is absorbed above 1 atm of hydrogen partial
pressure, indicating potential difficulties when fully charging the alloy in Ni-MH
cells at ambient pressure. The addition of Cr reduces the lattice parameter and
therefore the interstitial volume of the alloy, resulting in a destabilization of the
hydride. A higher chemical potential is therefore required for hydride formation.
Electrochemical properties and characterization
To understand the phase transformations and corrosion reactions associated with
cycling these alloy electrodes, electrode and electrolyte samples at various states of
charge were used for XRD, XPS and ICP-MS analysis. All samples were prepared
in beaker cells in air. The cells were charged to 1200 mAh/g, or 150% of the
maximum capacity estimated from the gas phase isotherm, and then discharged to
-0.5 V versus Hg/HgO. The cut-off potential was chosen to include a wide potential
window without oxidation of the conductive Ni binder at around -0.4 V (Figure
B.3).
The charge/discharge profiles for the first cycle are plotted in Figure 3.5. The
potential of the plateau during charge increases with Cr concentration, consistent
with the gas phase measurement. The charge capacity approaches 800 and 710
mAh/g for the alloy electrode with 0 and 6 at.% Cr, respectively, before the hy-

47

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I0;J<:2%;
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Figure 3.4: Hydrogen absorption isotherms of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12)
alloys as measured on a Sievert’s apparatus at room temperature (298 K).

48

Figure 3.5: Characterization of the three alloy electrodes: (a) First cycle
charge/discharge curves for the alloy electrodes in a beaker cell. Ex situ experiments were performed at the numbered points on the graph. (b) Diffractograms
of the three alloy electrodes at corresponding states of charge. Hydride phases are
marked with squares (BCC), triangles (BCT), and circles (FCC).

49
drogen over-charge potential was reached at -0.97 V. The charge potential for the
alloy electrode with 12 at.% Cr reaches the over-charge potential immediately after
current is applied. On discharge, the midpoint potential for the first plateau (before
-0.75V) follows the trend on charge and is observed at -0.83 V for Ti29 V62 Ni9 ,
and -0.88 V for the Ti29 V56 Ni9 Cr6 and Ti29 V50 Ni9 Cr12 alloys. A second discharge
plateau was observed for the Ti29 V62 Ni9 electrode starting at -0.70 V, and for the
Ti29 V56 Ni9 Cr6 electrode at -0.55 V. A second discharge plateau was not observed
for the Ti29 V50 Ni9 Cr12 electrode within the potential window. This observation
seems to contradict previous studies ascribing the second discharge plateau to dehydrogenation of the monohydride phase, as Cr-substitution is expected to increase
the hydrogen plateau pressure (negative shift on electrochemical scale) of both
binary phase regions.[18, 52, 107] A more plausible hypothesis is continuous oxidation/dissolution of V at the second plateau, as indicated by the Pourbaix diagram
(Figure 3.1). The reduction of VO3−
4 is irreversible over this potential range, thus
the second plateau is not observed in the charging curve.[103]
Figure 3.5 shows X-ray diffractograms for the alloy electrodes collected at the corresponding states-of-charge (SoC) enumerated on Figure 3.5a. The alloys start in the
BCC phase and transform to a mixture of FCC and BCT phases after charging. The
FCC phase fraction decreases with increasing Cr content, consistent with less of the
dihydride transition occurring below 1 atm hydrogen partial pressure (Figure 3.4).
Diffraction patterns taken after the electrodes are discharged past the first potential
plateau (-0.75 V for Ti29 V62 Ni9 , Ti29 V56 Ni9 Cr6 and -0.50 V for Ti29 V50 Ni9 Cr12 )
contain only peaks from the BCT phase. Interestingly, the peak position of the BCT
phase for all three electrodes shifts to higher 2θ angles, corresponding to a reduced
lattice parameter from hydrogen desorption. The contraction of the BCT phase
indicates that the discharge capacity includes hydrogen from both the FCC↔BCT
transition and the BCT monohydride phase. A further shift of the BCT peaks occurs
for the Ti29 V62 Ni9 and Ti29 V56 Ni9 Cr6 electrodes after discharge to -0.50 V. This
peak shift was suspected to be caused by V dissolution, and prompted elemental
analysis of the electrolyte.
Table 3.2 shows the ICP-MS results for the electrolytes collected at the SoC indicated
in Figure 3.5. The results are presented as the percentage of each element (by mass)
which has dissolved from the pristine alloy electrode into the electrolyte. In the case
of Ni, the mass of the binder and current collector are not included in the calculation.
The amounts of dissolved Ti, Ni, and Cr (for the Cr containing alloys) are very small

50
for all samples. The concentration of dissolved V, however, is much greater. A
small amount of V dissolution is already observed after the first charge. During
charging, a cathodic (reduction) current is applied to the MH electrode, indicating
that V actively corrodes even when the electrode potential is the most negative.
In fact, V corrodes and dissolves when the cell is in the open circuit condition.
Table B.1 shows the ICP-MS results for electrolyte taken from beaker cells that
were left standing for 2 days, where 6% of the total V in the Ti29 V62 Ni9 electrode
has dissolved, compared to 2.47% from the Ti29 V50 Ni9 Cr12 electrode. The most
significant V dissolution, however, is observed for Ti29 V62 Ni9 and Ti29 V56 Ni9 Cr6
alloy electrodes discharged past -0.75 V, confirming our previous hypothesis that
the second potential plateau is related to continuous V oxidation into vanadate ions.
The total amount of V dissolved from the electrode after one cycle is 17.75%, 5.04
%, and 0.95% for the electrodes with 0, 6, and 12 at.% Cr, respectively. After 10
cycles, the Cr free electrode loses 74% of the total V content. These results also
demonstrate the ability of Cr substitution to significantly suppress V corrosion and
dissolution.
Table 3.2: Results from ICP-MS analysis of KOH electrolyte collected from cells
containing Ti29 V62−x Ni9 Cr x (x = 0, 6, 12) alloy electrodes. Electrolyte was collected
from cells fully charged, discharged to -0.75 V, and discharged to -0.50 V, as indicated
in Figure 3.5. Data from a cell cycled 10 times are also presented.

Electrode state
x = 0, charged
x = 0, -0.75 V
x = 0, -0.50 V
x = 6, charged
x = 6, -0.75 V
x = 6, -0.50 V
x = 12, charged
x = 12, -0.50 V
x = 0, 10 cycles

% Loss from electrode
Ti
Ni
Cr
0.33 1.24
0.7
0.04 2.16
0.01
0.21 17.75
0.09
0.02 1.34
0.18
0.38
0.05 0.92
0.30
0.20
0.08 5.04
0.33
0.19
0.04 0.40
0.64
0.14
0.03 0.95
0.15
0.19
0.04 74.03
0.24

We further characterized the surface of the electrodes by XPS, and the results are
presented in Figure B.4. Aside from Ti, the elemental XPS spectra for all three
electrodes shift to higher oxidation states associated with oxides or hydroxides.
An in-depth analysis to determine the exact oxide species is difficult due to the
multicomponent nature of the alloys, as well as the broad peaks in the V and Cr

51
spectra. The spectra confirm, however, that surface V has oxidized to a higher
oxidation state (that will dissolve into solution) as a result of deep discharge.
Corrosion suppression and electrochemical performance
The Pourbaix diagram indicates that V corrosion is affected by four factors that
modify the electrochemical and chemical environment of the alloy electrode: (1)
electrode potential, (2) pH, (3) vanadate ion concentration, and (4) oxygen concentration near the electrode surface. From our previous analysis (see Table 3.2), it
is clear that the Ti29 V62 Ni9 alloy electrodes must not be discharged past -0.75 V
to avoid catastrophic V dissolution. Figure B.5 further explores controlling factors
(2) and (3) in aerated KOH solution and shows no improvement in cycle stability.
Compared to these strategies, Cr-substitution within the alloy improves cycle performance in aerated electrolytes, although capacity loss is still high at over 40% for
50 cycles.
Figure 3.6 plots the first three charge/discharge cycles of Ti29 V62 Ni9 and Ti29 V50 Ni9 Cr12
alloy electrodes in a deaerated, Ar-purged three-electrode beaker cell. The electrodes
were charged to 1200 mAh/g and discharged at 20 mA/g to a cutoff potential of 0.75 V. The first charge process for both electrodes differs from that observed in
the aerated electrolyte (Figure 3.5a) in that the charge capacity exceeds the estimated gas-phase capacity of 800 mAh/g before the hydrogen over-charge potential
is reached. This capacity could be a result of side reactions occuring at the electrode
surface, such as an oxide film that can only be reduced in deareated electrolytes.
Future studies of the surface chemistry of the alloy electrodes may provide insight
into this question. The voltage profiles of the first discharge processes, however,
are consistent with that seen in Figure 3.5a, and the midpoint potentials are again
observed at -0.83 and -0.87 V vs. Hg/HgO for the Ti29 V62 Ni9 and Ti29 V50 Ni9 Cr12
electrodes, respectively. In the following two cycles, the charge and discharge
potential profiles are more symmetrical, with charge capacities slightly exceeding
discharge (aside from the overcharge region of the charging curve). The Ti29 V62 Ni9
electrode initially discharges 594 mAh/g capacity, which fades slightly over the next
two cycles. This capacity decay process occurs in conjunction with an increasing
potential hysteresis, indicating that corrosion still occurs but at a much slower rate.
After an initial activation cycle, the Ti29 V50 Ni9 Cr12 electrode reversibly discharges
520 mAh/g, together with stable potential profiles. Compared to a previous study
[46] and our preliminary data in air-saturated cells (Figure B.5), our results clearly
show that a higher reversible capacity can be attained by suppressing vanadium

52

Figure 3.6: The charge/discharge curves for (a) Ti29 V62 Ni9 and (b) Ti29 V50 Ni9 Cr12
electrodes in an Ar-purged three-electrode cell.

53
corrosion by using a deaerated electrolyte.
To explore the effects of Cr and vanadate ion addition on the long-term cycling
behavior of the Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy electrodes in deaerated
electrolyte, sealed coin cells were prepared with excess cathode material (at least 40
times the MH capacity). The cycling performance of these coin cells is presented in
Figure 3.7. An abundance of cathode material is used to prevent oxygen evolution
during charging and provide a relatively stable cathode potential to serve both as the
counter and reference electrode. The small internal volume of the coin cell limits
the amount of oxygen in the cell, even if the cell is sealed in ambient conditions
(see more details of coin cell preparation in Figure B.6 and description therein).
The coin cells were charged to either 550 or 400 mAh/g and discharged to 1.10 V
following the three-step discharge procedure.
The effect of vanadate ion concentration was investigated by preparing KOH electrolyte with 5, 50, and 500 mM of added KVO3 for use in coin cells with Ti29 V62 Ni9
electrodes (Figure 3.7a). Compounds such as LiVO3 , NaVO3 , and KVO3 may all
be used to prepare electrolytes containing vanadate ions.[103] We selected KVO3 to
avoid introducing another cation species into the KOH electrolyte. The valence state
of V in both solid KVO3 and aqueous VO3−
4 is 5+. The VO3 ions in an ionic compound are polymerically linked by a single oxygen atom.[108] This ionic compound
dissociates into the corresponding cations and VO3−
4 anions.
These cells were previously activated (not shown) by sequentially cycling 5 times
each to charge capacities of 100, 300, and 500 mAh/g. This step-activation process
was necessary to prevent early failure of the Ti29 V62 Ni9 electrodes (manifesting
as unstable capacity in Figures 3.7b, 3.7c). Despite this, the cycle stability of
Ti29 V62 Ni9 electrodes is rather poor in pure KOH electrolyte, but greatly improves
with increasing vanadate ion concentration. The cell with 5 mM KVO3 in KOH
electrolyte discharged 480 mAh/g maximum capacity, but began to fail after 130
cycles. The cells containing 50 mM KVO3 in KOH electrolyte performed best,
discharging nearly 500 mAh/g for 200 cycles. With the addition of 500 mM KVO3 ,
the cycle stability is maintained, but at a lower capacity of 400 mAh/g, probably due
to slower ion migration in the electrolyte. The capacity fluctuations at later cycles
are likely related to the repetitive formation and disruption of the surface oxide layer
during charge/discharge cycles.
We compared the proposed strategy of vanadate ion addition to that of Cr substitution in the same coin cell setup. Figure 3.7b compares the cycle stability of the

54

Figure 3.7: Cycling performance of coin cells containing (a) Ti29 V62 Ni9 electrodes
with KVO3 additions to the KOH electrolyte and (b), (c) Ti29 V62−x Ni9 Cr x electrodes
with KOH electrolyte. The MH electrodes were charged to 550 mAh/g in (a) and (b),
and charged to 400 mAh/g in (c). In (a), cycling was interrupted after 110 cycles
and restarted after two weeks for the cell containing KOH with 500 mM KVO3 .
In (b) and (c), cycling was interrupted for two weeks after the 100th cycle for the
Ti29 V56 Ni9 Cr6 and Ti29 V50 Ni9 Cr12 electrodes.

55
Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy electrodes in pure KOH electrolyte. It
was found that the step-activation process used in Figure 3.7a was not necessary for
the Cr-containing electrodes. The x = 6 and 12 electrodes exhibit excellent cycle
stability, delivering 500 mAh/g of capacity for 300 cycles. In some cases when
cells were stopped and restarted due to rearrangement of test channels or instrument
power failure during the 9 months of cycling (see Figure 3.7 caption), the capacity
was recovered after a few cycles. The capacity of the Ti29 V62 Ni9 electrodes was not
recovered, potentially indicating the formation of a thick passivation layer on the
electrode surface. The excellent cycle stability of Ti29 V62−x Ni9 Cr x (x = 0, 6, and
12) alloy electrodes is also seen in Figure 3.7c, in which the x = 6 and 12 electrodes
were charged to 400 mAh/g and cycled stably for 400 cycles with around 95%
coulombic efficiency after activation. Despite the excellent capacity retention, the
voltage hysteresis and rate capability decreases with cycling (Figure B.7), indicating
a growing surface oxide film.
3.5

Discussion

Extent of phase transformations
The VH x isotherm (Figure 1.2) exhibits two distinct two-phase regions (plateaus)
separated by 6 orders of magnitude in pressure.[18, 19] In contrast, the phase
boundaries of the Ti29 V62−x Ni9 Cr x alloys are much less distinct (Figure 3.4). Sloping plateaus are common in solid solution alloys because their heterogeneous local
chemistry creates a distribution of interstitial site energies for hydrogen occupancies.[18] The plateau associated with the BCT↔FCC phase transformation is apparent in these alloy isotherms, however it is more sloping and occurs over a smaller
range of hydrogen concentration than for pure V. As a result, part of the electrochemical capacity may be accessed from the wide, sloping BCT monohydride phase
region before the corresponding electrochemical potential favors oxidation.
Mechanisms of vanadium oxidation
To access the high capacity suggested by the gas-phase isotherms, the irreversible
dissolution of V must be suppressed. The oxidation/dissolution of V in the alloy
electrodes occurs by two distinct pathways, illustrated schematically in Figure 3.8.
When the MH electrode is electrochemically discharged past the V dissolution potential, the corresponding cathodic reaction is the reduction of NiO(OH) to Ni(OH)2 ,
and the anodic reaction is the oxidation of VO x to VO3−
4 . This process is mitigated
by imposing a discharge cut-off potential more negative than the dissolution poten-

56
tial. In addition to this “operational oxidation," local oxidation reactions take place
internally within the MH alloy electrode regardless of the presence of a Ni(OH)2
counter electrode (Figure 3.8b). In this case, the V oxidation is coupled with the
following reduction reactions:
2H2 O + O2 + 4e− ↔ 4OH−

(3.1)

or
(gas)

2H2 O + 2e− ↔ H2

+ 2OH−

(3.2)

with Equation (3.1) strongly favored in highly alkaline media.[109] During the VO x
formation in the left panel of Figure 3.8b, the oxidation state of V is less than +5.
The interaction with V and the OH− in the electrolyte was proposed by Al-Kharafi,
et al.[104] The heterogeneous nature of the alloy electrodes, consisting of the Ni
current collector and Ni binder in addition to the Ni-rich and V-rich regions of the
MH itself, likely results in a varying electrode potential across the surface. The
ICP-MS results of Tables 3.2 and B.1 show that V is the only element undergoing
significant corrosion, indicating that the V-rich region of the alloy is the anodic
component which donates electrons to other parts of the electrode to facilitate the
reduction reactions of Equations (3.1) and (3.2).
Corrosion suppression and capacity retention
A combination of a low oxygen environment and either vanadate ion additions to the
electrolyte or Cr substitutions to the alloy are necessary for suppressing V corrosion.
Without the removal of oxygen from the electrolyte, the capacity of the electrodes in
Figure B.5 begins to fade immediately. The vanadate ion additions have little effect
on the cyclability of Ti29 V62 Ni9 electrodes, whereas Cr additions do show limited
improvement. Much like its role in stainless steel, Cr has been thought to form a
passivating surface oxide layer on the MH which suppresses corrosion.
By itself, reducing the amount of oxygen in the system does not solve the issue
of continued V oxidation. An improvement in the cyclability of the Ti29 V62 Ni9
electrode is observed when it is cycled in the Ar purged cell (Figure 3.6) as compared
to the beaker cell (Figure B.5). As shown in Figure 3.7, the capacity of coin cells
with the Ti29 V62 Ni9 electrode in pure KOH electrolyte begins to fade after 50 cycles.
In this case, removing oxygen from the electrolyte forces the cathodic reaction to go
from reaction (3.1) to (3.2), which may be kinetically much slower.[104, 109]

57

Figure 3.8: Schematics illustrating the (a) operational and (b) local oxidation that
occurs for V in the Ti29 V62 Ni9 alloy electrodes.

58
The addition of vanadate ions to the electrolyte or substitution of Cr in the alloy
suppresses V corrosion in the low oxygen environment of the coin cells. As seen
in Figure 3.7a, the Ti29 V62 Ni9 electrode stably cycles at 500 mAh/g for 200 cycles
with the addition of 50 mM KVO3 to the KOH electrolyte. The improvement can be
explained with Le Chatelier’s principle: as the concentration of the product (VO3−
4 )
is increased, the equilibrium shifts towards the reactants (VO x ). The Ti29 V56 Ni9 Cr6
and Ti29 V50 Ni9 Cr12 electrodes cycled in coin cells exhibit excellent capacity and
cycle stability of 500 mAh/g for 300 cycles (Figure 3.7b) or 400 mAh/g for 400
cycles (Figure 3.7c).
Integration into rechargeable batteries
Commercial Ni-MH batteries rely on the MH electrode to reduce oxygen evolved
at the Ni(OH)2 positive electrode during cell over-charging. The combination of
a porous separator and electrolyte-starved design facilitate this protection mechanism.[110] The optimum Cr concentration for Ti-V-Ni-Cr-based alloys to survive in
this environment remains an open question. Increasing the Cr content beyond 12 at%
may further improve corrosion resistance, but this will likely reduce the reversible
capacity and require tailoring the alloy composition to maintain a suitable equilibrium hydrogen pressure.[67] It may also be prudent to adopt different charging
protocols for Ni-MH batteries utilizing the Ti29 V62−x Ni9 Cr x alloy electrodes.
Alternatively, the Ti29 V62−x Ni9 Cr x alloy electrodes can be incorporated into an
MH-air system. In an MH-air cell, an anion exchange membrane (AEM) stable in
alkaline media can be used to prevent oxygen crossover.[111] Replacing the heavy
Ni(OH)2 electrode with an air electrode will greatly improve the energy density.
We calculated the cell level energy density of a MH-air system as a function of
MH electrode capacity and thickness, and the results are plotted in Figure 3.9. A
description of the cell geometry and calculation details are provided in Appendix
B. This is an optimistic calculation assuming the BCC electrodes are engineered to
the same quality as modern AB5 MH electrodes. The shaded regions in the figure
correspond to the range of energy densities for 18650 type Li-ion cells.[112, 113]
With an anode capacity of 500 mAh/g, the maximum energy densities of 240 Wh/kg
and 550 Wh/L are obtained with an anode thickness of 2 - 2.5 mm. The gravimetric
energy density is comparable to 18650 type Li-ion cells, whereas the volumetric
energy density is approximately 15% less. The discrepancy in volumetric energy
density is due to the inclusion of the air channel in the 100 Wh cell volume; we
expect a similar loss in volumetric energy density when the volume of cooling

59

Figure 3.9: Gravimetric and volumetric energy density analysis of a MH air cell as
a function of the specific capacity and thickness of the MH electrode. The shaded
areas indicate the published energy density ranges for 18650 type Li-ion batteries.

60
channels between 18650 cells is considered.
3.6

Conclusions

The microstructure, hydrogen absorption, and electrochemical properties of
Ti29 V62−x Ni9 Cr x (x = 0, 6 and 12) alloy electrodes were investigated. Vanadium
dissolution leads to irreversible capacity loss, which can be addressed by a combination of strategies: (1) removing oxygen from the system, (2) increasing vanadate ion
concentration in the electrolyte, and (3) increasing Cr content in the alloy. Capacities
as high as 594 mAh/g and 520 mAh/g for the Ti29 V62 Ni9 and Ti29 V50 Ni9 Cr12 alloy
electrodes, respectively, were demonstrated with Ar-purged cells. Coin cells containing Cr-substituted alloy electrodes and Cr-free alloy electrodes with a vanadate
ion containing electrolyte delivered around 500 mAh/g for up to 300 cycles. These
V-based BCC MH electrodes achieve high capacity by accessing the monohydride
phase, once V corrosion was sufficiently suppressed. This may open the door for
future development of high capacity MH electrodes enabling safe and high energy
density aqueous batteries.

61
Chapter 4

SUMMARY AND FUTURE WORK
The work described in this thesis covers only a few small aspects of the broad
field of academic research involving metal hydrides (MH). Insights gained into
thermodynamics of the hydriding transition and MH stability, however, are important
to the entire MH field and beyond.
4.1

Principles of Metal Hydride Hysteresis

No theory in the literature completely describes the pressure and solvus hysteresis
in MH. However, by comparing hysteresis energy with misfit strain energies, we
show that the origin of hysteresis is a nucleation barrier resulting from coherency
strain energies associated with nucleating a new phase with a different molar volume. Plastic deformation can occur during the transition, above a critical size,
although the energies of dislocation formation fall short of hysteresis energies in
Pd. These observations allow us to quantitatively compare experimental hysteresis
values to those predicted by Schwarz and Khachaturyan, who developed a model
for hysteresis based on coherency strains. Their model significantly overestimates
the hysteresis. The large strains associated with hydride nucleation can be accommodated by forming energetically favorable plate-like precipitates, rather than the
spherical nuclei assumed in the S-K theory. Furthermore, size effects play a role in
mitigating the strain energy, as was demonstrated by a finite Eshelby model. Shifting
the location of a nuclei to the edge of a particle further reduces the nucleation barrier
and hysteresis in a way not available to bulk materials.
Solvus hysteresis was shown to split the coherent spinodal phase boundaries into
distinct boundaries for absorption and desorption. The splitting of the boundaries
results in a directional dependence of the phase diagram; phase boundaries are
set by whether hydrogen is being absorbed by or desorbed from the metal lattice.
Neither spinodal boundary is an “equilibrium" boundary in the sense of quasistatic
reversibility, as the effects of the nucleation barrier are present during both hydrogen
absorption and desorption. As a result, the split spinodals represent physically relevant phase boundaries that must both be reported when mapping out phase diagrams
for MH systems. Minor loop isotherms for bulk Pd show that solvus hysteresis is
present even for an incomplete transformation, providing further evidence to the ex-

62
istence of nucleation barriers. To the best of my knowledge, no minor loop studies
have been performed for nanosized Pd. I expect that minor loops in nanocrystalline
Pd would exhibit the same behavior as in bulk Pd as the nucleation barrier is still
present.
Exploration of the spinodal phase boundaries is an interesting avenue for future work.
As mentioned in Section 2.4, a potential method for exploring a “strain-free" spinodal
boundary would involve slowly cooling the MH below the critical temperature and
comparing in situ XRD results to those obtained during simultaneous measurement
of pressure composition isotherms. Unfortunately, the critical temperature and
pressure for bulk PdH is 566 K and 20 atm, experimental conditions which the in
situ hydrogen environment chamber is not able to achieve.[21, 114] Replacing bulk
Pd with nanoparticles has been demonstrated to reduce the critical temperature and
pressure of the coherent spinodal, possibly to values compatible with the current
experimental setup. These experiments can also provide a method for determining
why the phase diagrams for bulk and nanocrystalline Pd are different. Zabel and
Peisl performed in situ XRD experiments similar to these for the niobium-hydrogen
phase diagram.[115, 116] In these studies, hydrogen was introduced to the system
above Tc , and the sample was subsequently cooled below Tc . Zabel and Piesl claim
that with a fast cooling rate, the sample segregates according to the incoherent
spinodal, and an incoherent phase boundary can be traced.[116] Slow cooling of the
NbH sample, however, resulted in a smaller miscibility gap that was attributed to the
coherent spinodal boundary.[115] No comparison was made, however, to terminal
compositions obtained with standard PCT measurements.
4.2

New Models for Hysteresis

My PdH work provides strong evidence to validate theories which attribute coherent
strain energy as the origin of hysteresis. Incorporating the effect of precipitate size
and location should help to make the models more accurate. However, we make no
attempt at this because developing a single model which incorporates size effects
and accurately predicts hysteresis in all MH systems is extremely difficult. Current
theories can be divided into two categories, material-agnostic and material-specific.
Material-agnostic theories, such as that proposed by Schwarz and Khachaturyan,
contain several assumptions or simplifications which generalize any result (see
Introduction).[31, 32] In a real MH system, the assumptions will not hold up, and a
match to theoretical predictions may just be coincidental. One can either develop a
more robust model for a specific system with less assumptions, or various parameters

63
can be introduced which capture the deviations from assumptions. In either case,
the model will lose generalizability.
Developing a material-specific model in conjunction with experimental data also
has shortcomings. The mean field approach reported by Griessen et al. included
non-linear interactions and a reasonable core-shell model for the structure of the
metal hydride particle.[24] Fitting to a few datasets resulted in enthalpy values
which reproduced other results not included in the fitting. However, Ulvestad and
Narayan demonstrated that the core-shell model is not how the hydriding transition
proceeds.[25, 37] It seems that the eccentricities of the system were subsumed into
the fitting parameters and produced coincidentally correct results.
In either case, the current theories are developed enough to capture the origins of
pressure and solvus hysteresis in MH. Additionally, they also provide clues to ways
of mitigating hysteresis effects. The results from the study of hysteresis in PdH
demonstrate the continued utility of MH as model systems for materials research.
4.3

Metal Hydride Electrodes

Previous attempts in the literature to extend the cyclability of V-based BCC electrodes involved introducing corrosion-preventing elements into the alloy formulation. Improved cycling was achieved with substantial additions of Cr, however the
discharge capacity is significantly reduced.[46, 67] Examining the Pourbaix diagram
for V allowed us to develop alternative strategies to mitigate the corrosion that do
not sacrifice capacity. Specifically, by combining electrochemical cells designed
to minimize dissolved oxygen in the electrolyte with vanadate ion additions to the
electrolyte or Cr substitution in the alloy, stable cycling of 500 mAh/g is achieved
for up to 300 cycles. The cycle life is an order of magnitude improvement over
previous studies.
In addition to strategies for improved cycling, much was learned about other aspects
of V-based BCC alloy electrodes. Operational oxidation of the electrode which
occurs during deep discharge (less negative than -0.75 V vs. Hg/HgO) can be
mistaken for the monohydride to solid solution transition of VH. X-ray diffraction
results confirmed that the pristine BCC phase is not recovered after discharge to
-0.50 V, even though a voltage plateau was observed at -0.68 V vs. Hg/HgO for
Ti29 V62 Ni9 electrodes. Unfortunately, this limits the reversible capacity of V-based
BCC electrodes to about 500 mAh/g, or half of the theoretical capacity of 1000
mAh/g. The results of this work also demonstrate that, unlike for AB5 based Ni-

64
MH batteries, overcharging can prove detrimental to V-based BCC alloy electrode
lifetime. If the system is overcharged in a cathode-starved configuration (i.e. excess
MH is added to the anode), the oxygen evolved at the NiO(OH) cathode will corrode
the BCC anode.
The corrosion mitigation strategies developed in this work provide a platform for
further development of V-based BCC alloys. These alloys segregate into a V-rich
hydrogen storage region and electrocatalytic Ni-rich region when cooled from the
melt. If the scale of the segregation is reduced, the shortened diffusion length of
hydrogen between the two phases will improve charge/discharge kinetics. Furthermore, as the electrode is cycled and the alloy particles decrepitate (break apart),
some particles may lose their electrocatalytic regions and no longer contribute reversible capacity. A finer microstructure will prevent this from occuring, so long
as the scale of the microstructure is less than the critical size for decrepitation. We
have begun to investigate the kinetics of rapidly cooled V-based BCC alloys, which
have characteristic lengths of the V-rich and Ni-rich regions reduced by a factor of
4. The rapidly cooled alloys discharge more capacity at higher discharge currents,
and this trend continues with cycling.
Another avenue of further research into V-based BCC alloys is the incorporation
of Fe into the alloy formulation. Developing an alloy composition with Fe will
allow for the use of ferrovanadium feedstock, which is much cheaper than pure V
precursors.[117] The effect of Fe additions to V-based BCC alloys on gas-phase hydrogen storage has been explored, and while there is some loss in capacity, the alloys
are suitable for gas-phase storage applications.[117, 118] By utilizing the strategies
developed in this work to mitigate corrosion, the long-term cycling performance of
cheaper, Fe-containing V-based BCC alloys can be properly evaluated.
4.4

Outlook

Although the metal hydride systems presented in this thesis differ in their complexity
and applicability, understanding the processes that contribute to their inefficiencies
requires an in-depth knowledge of the underlying thermodynamics. Providing experimental confirmation of theoretical models will help future researchers better
understand the phenomenon of hysteresis, and the identification of strategies to reduce corrosion in metal hydride battery electrodes will lead to the development of
stable, high capacity metal hydride batteries.

65
Appendix A

SUPPLEMENTARY INFORMATION FOR ELASTIC ENERGY
AND THE HYSTERESIS OF PHASE TRANSFORMATIONS IN
PALLADIUM HYDRIDE

Figure A.1: Scanning electron micrograph of a bulk Pd particle consisting of
coalesced grains. The inset shows the scale of individual particles.

66
A.1

Pressure composition isotherm measurements in Sievert’s apparatus and
in situ hydrogen environment chamber

Pressure composition isotherms were measured during the in situ x-ray diffraction
studies for bulk and nanocrystalline Pd samples. Figure A.2 below compares the
in situ and Sievert’s pressure composition isotherms measured for bulk (a) and
nanocrystalline (b) Pd. For both samples, the plateau pressures for absorption and
desorption are slightly greater in the in situ setup than those measured for with the
Sievert’s apparatus. Hysteresis values, however, are equivalent between the two
measurements. We attribute these differences to temperature differences between
the apparatus; the difference in pressure corresponds to a temperature difference of
approximately 5◦ C.
A.2

Two-Dimensional finite Eshelby model for an eccentric circular inclusion
in a circular domain

Eshelby solved the problem of a misfitting elastic inclusion in an infinite threedimensional elastic matrix. It was further demonstrated that stress and strain fields
within an elliptic or ellipsoidal inclusion are uniform, providing for an equilibrium
inclusion shape. Schwarz and Khachaturyan used the results of the classical Eshelby
problem to calculate the coherency stresses associated with nucleation of a hydride
(solid solution) phase inside an infinite solid solution (matrix). These stresses were
used in developing an expression for pressure hysteresis.[31, 32]
For hysteresis in nanoparticles, the assumption of an infinite matrix is no longer valid.
Image forces and edge effects are thought to play a large role in accommodating
coherency stresses associated with a phase transformation. As such, stresses and
strains in both the inclusion and matrix should vary with position of the inclusion
for a finite matrix.
To test this hypothesis, we adapted the results of Zou et al., which solve the problem
(in two-dimensions) of an eccentrically placed circular inclusion in a circular matrix.[88, 89] Working in two dimensions (x, y) allows for use of the complex variable
(z = x + iy) method with arbitrary analytic Kolosov-Muskhelishvili potentials γ and
ψ. These potentials (and their derivatives with respect to z) can be used to express
displacement, stress, and strain energy densities associated with an inclusion in a
matrix.
We assume the matrix and inclusion are both homogeneous and isotropic. A uniform
isotropic eigenstrain i j = 0.5 δi j is applied to the inclusion. The displacements ui

67

.-&,+('*))('&

!/!

!/

!/"

+94:)3;*+9)<;=('>
+?3(@(';A)+9)<;=('>

!/#

!/$

!/%

!/1

!/0

!/%

!/1

2+34+&5+,267.

"!

.-&,+('*))('&

!/!

!/

!/"

+94:)3;*+9)<;=('>
+?3(@(';A)+9)<;=('>

!/#

!/$

2+34+&5+,267.

Figure A.2: Comparison of pressure composition isotherms measured in a Sievert’s
apparatus and in situ hydrogen environment chamber. Isotherms for bulk Pd are
plotted in a) and for nanocrystalline Pd in b), both at 333K.

68
and stresses σi j are evaluated with Equations (65) – (67) in Reference [88], and the
strain energy density is adapted from Equation (A.8) in Reference [89]. They are
reproduced here:
u1 + iu2
2r
1 (κ − 1)z − 2h
χω
4r /(κ + 1) 4(z − h) 8
z−h
R r z + r h(hz − 2R )
κr z
(A.1)
4η(R − hz)
4η(R2 − hz)
rh
(κ − 1)r z
4η(η − 1)R
2ηR2
σ11 + σ22
1 ω R2 r 2
r2
Re
8µ ∗ /(κ + 1)
η(η − 1)R2
(R2 − hz)2

(A.2)

σ22 − σ11 + 2iσ12 r 2 (1 − χω r 2 h 3R2 h − 2R2 z − h z
8µ ∗ /(κ + 1)
2η
2(z − h)2
(R2 − hz)3

(A.3)

ν
(κ
1)(A.2)
2(A.3)(A.3)
4µ ∗ /(κ + 1)2

(A.4)

For these equations, R is the domain radius, r the inclusion radius, h the complex
coordinates x + iy of the inclusion center, µ the shear modulus, and χω is either
1 or 0 if a point z = x + iy is interior or exterior to the inclusion, respectively.
The case of plane stress or plane strain is set by κ = κ(ν), with Poisson’s ratio
ν, and η defines the boundary conditions. For η = κ, we have the displacementfree Dirichlet case, and for η = −1 the traction-free Neumann case. Solutions for
individual displacement or stress components are obtained by linear combination of
real and imaginary components of the above equations.
All four equations are incorporated into a custom MATLAB code to solve for
displacement, stress, and strain energy density given Poisson’s ratio and inclusion
radius and origin as inputs. The MATLAB code was evaluated for correctness by
reproducing results from Zou, et al., (see below) who solved for an inclusion with
ν = 0.3, r = 0.3R, and h = 0.5R. A traction-free boundary condition η = −1 was
imposed and the plane strain case κ = 3 − 4ν considered.
The MATLAB procedure was then used to evaluate the variation of strain energy
with inclusion position for a finite matrix. In this case, the Poisson ratio is set to 0.39,
the value reported for Pd. As before, a traction-free boundary condition η = −1

69

Figure A.3: Displacement field u1 for the case published by Zou. Displacement is
normalized by (1 − ν)/r ∗ to be unitless.

Figure A.4: Displacement fields u1 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Displacement is normalized by (4r ∗ )/(κ + 1)
to be unitless.
was imposed to allow for surface relaxation and the plane strain case κ = 3 − 4ν
considered. The position of an 0.4R diameter inclusion was varied from the center
to the edge in 13 steps spaced 0.05R apart along the x-axis, and the total strain
energy was calculated at each position. These results are summarized in Figure 2.8.
Displacement and stress components were also computed and are included here for
the case of the centered and edge inclusions.

70

Figure A.5: Displacement fields u2 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Displacement is normalized by (4r ∗ )/(κ + 1)
to be unitless.

Figure A.6: Stress fields σ11 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by (4µ ∗ )/(κ + 1)2 to
be unitless.

71

Figure A.7: Stress fields σ12 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by (4µ ∗ )/(κ + 1)2 to
be unitless.

Figure A.8: Stress fields σ22 for 0.4r inclusions located a) at the center and b)
displaced to the edge of the domain. Stresses are normalized by (4µ ∗ )/(κ + 1)2 to
be unitless.

72
Appendix B

SUPPLEMENTARY INFORMATION FOR HIGH CAPACITY
V-BASED METAL HYDRIDE ELECTRODES FOR
RECHARGEABLE BATTERIES
B.1

Alloy and Electrode Characterization

The microstructure of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloys was characterized by
X-ray diffraction (XRD), scanning electron microscopy (SEM) with backscattered
electron imaging (BES), and energy dispersive x-ray spectroscopy (EDS). Alloy
samples characterized by XRD were pulverized to a fine powder via the procedures
outlined in the main text. For SEM and EDS, the samples were mounted in graphite
and polished to a mirror finish.
Measuring the lattice parameter is challenging because of the broad, overlapping
peaks from regions of the BCC phase with different chemical compositions. The
lattice parameter, a, of the majority V-rich region clearly decreases with higher

Figure B.1: Lattice parameters of dehydrided Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12)
alloys.

73
Cr content, however. From our analysis of the backscattered electron images, we
estimate the fraction of the Ni-rich region to be about 9 vol%. The small amount of
the Ni-rich region, the small number of reflections in the measured 2θ range, and
the broad, overlapping peaks make analysis of the lattice parameter of this region
difficult. Given that the second peak has nearly disappeared in the x = 12 sample,
we estimate that the lattice parameter of the Ni-rich region is slightly smaller, on the
order of 0.3065 – 0.307 nm.
Electrochemical cells were assembled using electrodes containing Ti29 V62−x Ni9 Cr x
(x = 0, 6, and 12) alloys. Three types of cells were used: (1) 3-electrode beaker
cells assembled in air, (2) a 3-electrode Ar purged cell, and (3) coin cells assembled
in air. In addition to electrochemical cycling, elemental analysis of the electrolyte
was performed with inductively coupled plasma mass spectrometry (ICP-MS), and
the surface oxidation states of the cycled electrodes were characterized by X-ray
photoelectron spectroscopy (XPS).
Figure B.3 shows the discharge curves of Ti29 V62 Ni9 electrodes in pristine 1 M
KOH, 6.9 M KOH, and 6.9 M KOH with 500 mM KVO3 . All three electrodes were
assembled in air in three-electrode beaker cells. The Hg/HgO reference electrodes
were prepared with the corresponding KOH solutions. The experiments were performed by discharging at a small current of 10 mA/g based on the loading of the
alloy powder. These cells were discharged without prior charging, so the capacity is
a result of metal oxidation rather than oxidation of absorbed hydrogen. According to
the Pourbaix diagram, V oxidation to vanadate ions is expected at around -0.9 V vs.
Hg/HgO (pH = 15) for a pure V electrode. The corresponding dissolution potential
for the alloy is approximately -0.7 V in 6.9 M KOH solution, consistent with that
reported in the main text (Figure 3.5a). Increasing the vanadate ion concentration
in the electrolyte or reducing the pH both shift the dissolution potential to a more
positive value, as predicted by the Pourbaix diagram. Slower kinetics may also
contribute to the shift in dissolution potential, however.
Table B.1: ICP-MS analysis of KOH electrolytes in which Ti29 V62−x Ni9 Cr x (x = 0
and 12) alloy electrodes were stored for 10 days.
% Loss from electrode
Alloy composition Ti
Ni
Ti29 V62 Ni9
0.04 6.77
0.11
Ti29 V50 Ni9 Cr12
0.09 2.47
0.07

Cr
0.15

74

Figure B.2: Backscattered electron images of (a) Ti29 V62 Ni9 and (b) Ti29 V56 Ni9 Cr6
alloy ingots. Compositions superimposed on the image indicate average compositions of the V-rich (dark) and Ni-rich (light) regions as determined by EDS.

75

Figure B.3: Discharge curve of Ti29 V62 Ni9 electrode in various KOH electrolytes.
Plateaus associated with V and Ni oxidation are indicated with arrows.
The XPS spectra for the Ti29 V62−x Ni9 Cr x (x = 0, 6, 12) electrodes before cycling
(spectra [1]) and after charging and discharging to -0.50 V (spectra [4]) are presented in Figure B.4. The V 2p3/2 metallic peaks disappear for the Ti29 V62 Ni9
and Ti29 V56 Ni9 Cr6 electrodes, and the oxide 2p3/2 peaks shift to a higher binding
energy. This shift corresponds to an increase in the oxidation state of the V. The
surface oxide is likely a mixed oxide and manifests as a broad peak. There are no
shifts in the Ti 2p3/2 or 2p1/2 peaks; the native oxide layer appears to be stable in
the electrolyte environment. The XPS spectra for Ni show a disappearance of the
metallic 2p3/2 and 2p1/2 peaks and emergence of the corresponding Ni(OH)2 peaks.
The NiO 2p3/2 and 2p1/2 peaks persist during cycling. The broad Cr 2p3/2 and 2p1/2
peaks have a small shift to higher energy and an increase in amplitude, indicating
that a CrO x layer has formed on the surface. Similar to V, the CrO x layer is likely a
mixed oxide.
The design of the coin cells considered the following factors: (1) with a small
internal volume, the cells can be sealed in air with a negligible amount of oxygen
trapped inside the cells (2) the MH electrode is paired with a much larger Ni(OH)2
positive electrode, so that the positive electrode does not evolve oxygen during cell
overcharge and the potential remains relatively stable as a reference electrode. This

76

Figure B.4: XPS spectra of V, Cr, Ni, and Ti prior to charge [1] and after full
discharge [4] of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy electrodes. Boxed numbers
correspond to the state of charge indicated in 3.5a.

77

Figure B.5: Cycle performance of Ti29 V62−x Ni9 Cr x (x = 0, 6, and 12) alloy electrodes in various electrolytes. All tests were performed in air-saturated beaker cells.
Cells were charged to 800 mAh/g, then discharged following the three-step discharge
procedure up to -0.75V vs. Hg/HgO.

configuration is also more sensitive to capacity degradation of the MH electrode.
Figure B.6 shows the operation potential of the Ni(OH)2 /NiOOH electrode used in
this study. These electrodes were obtained from BASF (BASF-Ovonic, Rochester
Hills, MI, USA) and punched into disks with a 1.27 cm diameter. The capacity of
each electrode is about 24 mAh. The results shown in Figure B.6 were obtained by
first charging a Ni(OH)2 electrode to 12 mAh, converting part of the Ni(OH)2 to
NiO(OH). The Ni(OH)2 /NiO(OH) electrode was then charged at the specific current
density shown in Figure B.6 for 7200 s, rested for 1200 s, and discharged at the same
current density for 7200 s. The charge (Ea ) and discharge (Ec ) plateau potentials
were recorded and plotted in Figure B.6. The smallest current for the discharge of
the coin cells was 20 mA/g, and the V dissolution potential for Cr-free alloy is at
about -0.7 V versus Hg/HgO (Figure B.3 and Figure 3.5). For these reasons, and to
allow a voltage window as large as possible, the cut-off voltage for all coin cells was
set at 1.10 V. All coin cells were assembled with the half-charged cathodes.
The Ti29 V50 Ni9 Cr12 electrodes in Figure 3.7 were charged for 550 mAh/g, which
is higher than their maximum discharge capacity as measured in Figure 3.6. The
Coulombic efficiency of these coin cells are also less than 100%. As a result, a
small amount of hydrogen is evolved during charging, which may be consumed on

78

Figure B.6: Operation potential for the Ni(OH)2 /NiO(OH) electrode used in coin
cells. Current density is based on the mass loading of the Ni(OH)2 electrode powder
mixture. Closed and open symbols correspond to the plateau potentials for charge
and discharge, respectively. The boxed region indicates the current density range
associated with the MH electrode (10 to 100 mA/g for a 3 mg/cm2 loading).

the positive electrode by reducing NiO(OH) to Ni(OH)2 .[119]
B.2

Energy density calculations of a MH-Air battery cell

Energy density calculations of the MH-air batteries are based on a prismatic cell
design. This MH-air cell has three electrodes: oxygen-reduction-reaction (ORR)
electrode, oxygen-evolution-reaction (OER) electrode, and an MH anode. The ORR
electrode is a commercial alkaline fuel cell air electrode from Electric Fuel (Electric
Fuel Limited, Bet Shemesh, Israel) with the catalytic MnO2 on a substrate film of
PTFE.[120] The OER electrode is made from Monel mesh. The MH anode is made
by pressing MH alloy powder onto a nickel mesh substrate. Figure B.8 shows the
layout of the two-sided prismatic cell. The cell consists of two ORR-MH-OER
stacks with the OER electrodes facing the interior of the cell. The OER electrodes
are separated by a channel through which electrolyte flows. Flowing electrolyte is
utilized to compensate for local changes in electrolyte concentration and pH due to
water loss or generation as the cell charges or discharges.

79

Figure B.7: Charge/discharge curves of a). Ti29 V62 Ni9 and b). Ti29 V50 Ni9 Cr12
electrodes in the coin cell configuration. The cells were charged for 550 mAh/g and
three-step discharged at 100, 40, and 20 mA/g to 1.10V. The decrease of discharge
capacity at the high current step shows that the rate capability of the MH electrode
decreases with cycling, despite excellent capacity retention.

80
The cell was designed to achieve 100 Wh with an overall dimension of 20.2 cm
x 10.2 cm x 1.13 cm. The cell discharge potential is determined from the ORR
overpotential data as a function of cell current density, provided by the vendor of
ORR electrode, and our cycling data for the MH anode. The air electrode potential
is presented in Figure B.9. The current density needed from the ORR electrode
is chosen to match the specifications of the MH anode for a given discharge rate.
The total weight of the cell also includes those of passive components of electrode
substrates, separators, frame, and seal materials. Key input parameters of this model
are the MH anode thickness and MH anode specific discharge capacity. Other input
parameters including dimension of the prismatic cell, dimensions of the two air
electrodes, and the cell discharge C-rate, are preset based on project targets and
some of the preliminary lab testing results.
Based on the preliminary experimental results of the cell similar to this design, the
MH anode specific discharge capacity is in a range of 150 – 550 mAh/g, and the
practical thickness of the anode is above 300 microns. The model varies the MH
anode capacity from 0 – 800 mAh/g, and thickness from 0.3 – 5 mm. Varying these
two parameters leads to a 2D contour plot of cell level gravimetric and volumetric
energy density as shown in Figure 3.9. The colored lines are regions of constant
energy density in Wh/kg or Wh/L. MH anodes containing Ti29 V62−x Ni9 Cr x (x =
0, 6, 12) were demonstrated in Chapter 3 to have a specific capacity of more than
400 mAh/g, making it possible to achieve 200 Wh/kg. From the sensitivity analysis
of Figure 3.9, there is also an optimized range of the MH anode thickness in this
prismatic model, based on the targeted energy density. For example, with a target of
200 Wh/kg, the MH anode thickness is optimally 2 – 2.5 mm. The inputs and results
from an individual calculation for the contour plots of Figure 3.9 are provided in
Table B.2 below. The input values in the Example Case column are based on the
specifications determined by Figure B.9 and our MH cycling data. For this example,
an anode capacity of 400 mAh/g and thickness of 2.2 mm are chosen. The nominal
cathode current is set to match the specifications of the MH anode with a discharge
rate of C/3. The model then returns a specific energy density of 207 Wh/kg and a
volumetric energy density of 427 Wh/L.

4.00E03
4.00E03
1.25E03
9.00E02
8.00E03
2.70E03
2.53E02
2.00E-01
1.00E-01
5.00E-03
5.00E-04
2.20E-03
5.00E-04
1.20E-04
1.00E-03
2.92E-03
5.00E-04
2.5E-01

kg/m3
kg/m3
kg/m3
kg/m3
kg/m3
kg/m3
kg/m3
g/g
m2
m2
m3
m3
kg
kg
kg
kg
kg
kg

Example Case
Cathode nominal current
1.3E03
Cathode nominal potential -1.44E-01
vs. Hg/HgO
Anode capacity
4.0E02
Anode nominal potential
-8.5E-01
vs. Hg/HgO
Anode thickness
2.2E-03
Cell nominal potential
7.06E-01
Anode C-rate
3.16E-01
Cell current
4.45E01
Cell Power
3.14E01
Cell theoretical capacity
1.41E02
Cell Nominal Energy
9.94E01
Specific Energy
2.07E02
Volumetric Energy
4.27E02

Table B.2: Input values and energy density results for an example case of a 100 Wh MH-Air cell.

Inputs
Cathode Density
Anode Density
KOH Density
Plastic Density
Stainless Steel Density
Aluminum Density
Nickel Mesh Density
Electrode Width
Electrode Length
Frame Width
Cathode Thickness
Anode Thickness
Aux Electrode Thickness
Separator Thickness
Frame Thickness
Channel Thickness
Cooling Thickness
KOH:MH Mass Ratio

Table of Cell Parameters
Outputs
Cell width
2.02E-01
Cell length
1.02E-01
Cell thick w/o frame
9.3E-03
Cell thick w/ frame
1.13E-02
Air electrode frame
2.90E-03
Active area, two sides 3.42E-02
Frame volume
1.15E-05
Whole cell volume
2.33E-04
Frame Weight
1.03E-02
Cathode Weight
8.00E-02
Anode Weight
3.52E-01
Aux Electrode Weight 2.50E-03
Total Weight w/o KOH 4.45E-01
Total Weight w/ KOH 4.81E-01

1/h
Ah
Wh
Wh/kg
Wh/L

Ah/kg

A/m2

81

Figure B.8: Top view (left) and 3D sinde view (right) drawings of the 100-Wh MH-air cell. Dimensions not to scale.

82

83

Figure B.9: Plot of electrode potential versus current density for the air electrode
manufactured by Electric Fuel.[120]

84
Appendix C

SHOULDER REMOVAL FROM X-RAY DIFFRACTION DATA
C.1

Inel CPS120 Detector

X-ray diffraction (XRD) patterns of the hydriding transition in palladium hydride
(see Chapter 2) were acquired using an Inel Curved Position Sensitive (CPS) 120
powder diffractometer detector utilizing Mo Kα radiation. The use of a curved
detector allows for the simultaneous collection of X-rays diffracted up to 120◦ 2θ,
enabling faster measurement times. The Inel CPS120 detector is based on the device
reported by Ballon et al., which improved upon wire-based chamber detectors by
replacing the anode wire with a metal blade.[121] This change allowed for these
detectors to be curved; ideal for X-ray crystallography experiments.
The detector chamber consists of the knife-edge anode, a set of evenly spaced cathode
readout strips, and a delay line. A pressurized mixture of argon and ethane flow
through the detector. X-ray photons ionize the argon atoms, and the ejected electrons
are accelerated by the electric field to the cathode. The cathode is connected to a
delay line, which generates a pulse that is output to additional electronics. Each
cathode strip is referred to as a channel, with 4096 channels total. The pulse is
amplified, and the time delay is converted to position in order to determine the exact
2θ position of the pulse.
Detector Calibration
A flat Si h110i single crystal oriented in the h220i direction (θ Bragg = 10.644◦ ) is
used as a non-focusing incident beam monochromator. A set of Pb slits are used to
select a beam profile of 6.0 x 0.5mm perpendicular to the beam direction. Diffuse
background scattering was limited with the incorporation of a Pb slit 2.0mm wide
immediately following the monochromator crystal.
The CPS 120 detector rotates around a goniometer circle to operate in either transmission or reflection diffraction geometries. As a result, the channel number to 2θ
relationship must be calibrated whenever the detector is moved. Additional alignment of the X-ray beam (by adjusting the tube tower) is required to ensure that the
beam intersects the sample at the center of the goniometer circle. Sample stage
alignment and two theta calibration of the detector was performed using a NIST

85
Standard Reference Material (SRM) 660a (LaB6 ) powder dispersed in Formvar
on a glass slide. The diffractometer geometry is configured in a flat-plate asymmetric reflection geometry, which is subtly but distinctly different than traditional
Bragg-Brentano geometries.[122, 123] In asymmetric reflection geometry, X-rays
are incident on the sample with a fixed angle ω from parallel. Peak shifts δ due to
displacements perpendicular to the sample stage are given by:
δ=

s1 sin 2θ 180
Rs sin ω π

(C.1)

with s1 the displacement distance and Rs the detector radius (250 mm in this case).
Alignment of the incident X-ray beam with the center of the goniometer circle was
performed iteratively. First, the beam position is shifted by small translations of the
X-ray tube tower. Then, diffraction patterns of the LaB6 standard are acquired at
high and low incidence angles ω. If there is no shift in peak positions δ between the
two diffraction patterns, the stage and beam are considered to be aligned (according
to Equation C.1) and the channel number to 2θ calibration can be performed. To do
this, peaks are fit to the raw detector data to obtain the centroid of each diffraction
peak in terms of channel number. These are matched to the expected 2θ diffraction
angles of SRM 660a (LaB6 ), calculated from Bragg’s Law:
nλ = 2d sin θ

(C.2)

The lattice parameter of SRM 660a as reported by NIST is 4.1569162±0.0000097Å
at 22.5◦ C. The Mo Kα1 wavelength is 0.7093Å. Two theta values are plotted as a
function of channel number, and a polynomial fit is used as the calibration formula.
C.2

Anomalous Peak Shoulders

During 2θ calibration of the CPS120 detector, secondary peaks were observed to the
right of each Bragg peak of the SRM. The secondary peaks were initially assumed to
be due to Kα2 radiation. By Bragg’s Law, the spacing between the two peaks should
increase with 2θ, however, they are nearly constant as a function of channel number
and therefore cannot be due to the Kα2 radiation. Figure C.1 plots the measured
raw signal from NIST SRM 640b (Si) acquired with Mo-Kα radiation. The tick
marks below each peak indicate the expected position of the Bragg reflections for
Kα1 (red) and Kα2 (blue) radiation.
It was expected that the shoulder may be caused by failing electronics as the equipment is nearly 30 years old. To confirm that secondary peaks are not due to stray

86

Figure C.1: Raw diffraction data from the NIST Standard Reference Material 640b
(powdered Si) collected with the Inel CPS 120 Detector. Tick marks indicate
expected peak positions from Mo Kα1 (red) and Kα2 x-ray wavelengths.
reflections in the XRD setup, the outputs from the detector to the processing electronics were flipped. This has the effect of flipping the diffraction pattern; lower
index peaks will now be “seen" at higher channel numbers. If the shoulder is due
to stray reflections, it should flip as well. Figure C.2 plots a flipped diffractogram
of a Si standard. Reflections from the Kα2 are visible to the left of the Kα1 peaks
as expected. The peak shoulder, however, remains to the right of the main peaks,
confirming detector electronics are to blame for the shoulder.
Initially, shoulders were removed from raw LaB6 data using a machine learning
algorithm.[124] The processed data was then fit to pseudo-Voigt functions using
the Wavemetrics Igor Pro analysis software. Calculated MoKα 2θ angles of LaB6
were plotted against the channel number x of the corresponding peak centers, and a
fourth-order polynomial was fit to the data:
2θ = 4.6536 ± 0.0504 + (0.031104 ± 0.00019)x
− ((3.97 ± 2.07) ∗ 10−7 )x 2 + ((2.02 ± 0.67) ∗ 10−10 )x 3
C.3

(C.3)

Shoulder Removal with Deconvolution

Determination of Instrument Function
A detector instrument function was determined and incorporated into a deconvolution procedure to obtain corrected diffraction profiles. To measure the instrument

87

.$"%!-',+*)('&"%$!#"!
4211

4011

/111

/411

/311

/211

/011

56)!!#7'8-9+#*

Figure C.2: Diffraction pattern of the NIST SRM 640b (Si) obtained on the Inel
CPS 120 detector with output lines switched. The anomalous shoulder peaks are
still observed to the right of the main peak, as indicated by the black arrows.

function, a sample of amorphous GeO2 was placed in the diffractometer sample
holder to give a broad signal across the detector. The detector was covered entirely
in Pb aside from a small slit which allowed for a very small (10) number of channels
to be illuminated. The slit was placed at random intervals between channel numbers
200 and 2000 (corresponding to a 2θ range of 10 to 64◦ ) to characterize any changes
in the shoulder as a function of channel number. An example of the signal obtained
through the Pb slits is provided in Figure C.3. Also plotted is a peak from the Si
standard (rescaled) to demonstrate that the width of the signal passing through the
Pb slits is less than that of a Bragg reflection. Similar results were observed when
compared to Bragg reflections from the LaB6 SRM. This consideration will make
for a more accurate determination of the instrument function.
All diffractograms collected from the GeO2 and Pb slit setup were fit to two
Lorentzian functions, one for the primary peak and one for the shoulder. These
fits were obtained with the MATLAB code lorentzfit. Figures C.4, C.5, and
C.6 plot peak separation, relative peak magnitude and shoulder peak half-width
at half maximum (HWHM), respectively, as a function of channel number. The
separation between primary and shoulder peaks is relatively constant with respect
to channel number, whereas magnitude and HWHM increase with channel number

88
until leveling off past channel 1000.
A custom MATLAB code (FitConvFunc) was used to determine instrument functions by taking as inputs raw Pb slit/GeO2 data and a Lorentzian fit to the primary
peak (the true signal). On a plot of the raw data, the user is asked to select a peak
corresponding to the true signal and at least one peak resulting from an instrument
function. A new instrument function is created which consists of Gaussians centered
at each selection. This instrument function is convolved with the true signal and fit
to the raw data with a non-linear least squares fitting procedure, lsqnonlin. Each
iteration refines the magnitude, center, and width of Gaussian peaks in the instrument function until the fit converges. A graphical example of the fitting procedure
is provided in Figure C.7, which plots raw Pb slit/GeO2 data, a Lorentzian fit of
the primary peak, and the simulated measured signal generated by convolving the
Lorentzian fit with the instrument function.
Individual instrument functions were evaluated for all 18 Pb slit/GeO2 datasets; two
are plotted in Figure C.8. Peak shoulders in raw data were accurately accounted
for with only two Gaussians in the instrument function: a delta function at zero
shift and a broad Gaussian some distance away. Characteristics of the second peak,
including magnitude, width, and separation from the central delta function vary in
a manner similar to the shoulder peak of the Pb slit/GeO2 data.
Deconvolution of Raw Data
Peak shoulders in raw X-ray diffractograms make Rietveld refinement of a multiphase system difficult, as GSAS-II attributes peak shoulders to their own phase.
Oftentimes the shoulders overlap with true peaks, and can distort lattice parameter,
peak width, and phase fraction refinement. Instrument functions evaluated from
the Pb slit/GeO2 data were used to remove shoulders from raw XRD data using
a convolution procedure similar to FitConvFunc. The deconvolution function,
FitConv, takes as input the raw data file and an instrument function. A test function
(initialized as a copy of the raw data) is generated, convolved with the instrument
function, and subsequently fit to the raw data file. The range for deconvolution is
fixed to be between channels 50 and 4000; a large range is necessary to accurately
capture the background signal. The intensity at each channel number is set as a free
parameter to be fit so there is no loss or artificial smoothing of the raw data. Each
dataset requires several minutes to process as a result of this large number of fitting
parameters.

89
To account for the variation in shoulder characteristics evident in Figures C.4, C.5,
and C.6, different sections of raw diffraction data were deconvoluted with different
instrument functions. These functions represent average values of the range of
corresponding channel numbers. It was found later that peak-shoulder separation
increased between the time of GeO2 data collection and in situ PdH measurements,
requiring manual adjustment of peak-shoulder separation values of the instrument
functions. For example, the initial separation values of 30 channels had to be
increased to 45 for better shoulder removal in the nanocrystalline Pd data.
Figure C.9 plots raw data, deconvolved data, and the difference for a single bulk
PdH scan. Obvious peak shoulders have been nearly eliminated (with the exception
of noise), and primary peak shape is well preserved with only a minimal loss in
intensity. Three separate instrument functions were used to fit channels 50 to 750,
751 to 1150, and 1151 to 1800. Differences between the three functions were
primarily in shoulder magnitude and width rather than peak-shoulder separation.
Deconvolution of the nanocrystalline PdH data was ultimately performed using a
single instrument function that represented average values for peak-shoulder separation and shoulder magnitude and width. No obvious differences existed for
data processed with a single function when compared to data processed with the
same three functions used to process bulk PdH data. A comparison of raw and
deconvoluted data nanocrystalline PdH is provided in Figure C.10.

90

Figure C.3: Comparison of peak shape of signal obtained through Pb slits to Bragg
reflection of a Si standard. The Si Bragg peak is approximately twice as wide as the
signal passed through the Pb slits.

91

Figure C.4: Primary and shoulder peak separation (in channel numbers) as a function
of channel number of the primary peak. Both peaks are fit with a separate Lorentzian
function.

Figure C.5: Relative magnitude of the shoulder peak as a function of channel
number.

92

Figure C.6: Half-width at half maximum of the shoulder peaks as a function of
channel number.

93

Figure C.7: Plot illustrating the instrument function determination. The dotted line
is raw data obtained from the Pb slit/GeO2 setup, the dashed line is a Lorentzian
fit to the main peak, and the solid line plots the result of convolving the instrument
function with the Lorentzian peak. Examples of the instrument function are provided
in Figure C.8.

94

Figure C.8: Two (solid and dashed lines) of 18 instrument functions describing
shoulder behavior of the Inel CPS120 detector. The functions consist of a delta
function at 4096 and a small peak resulting in a shoulder in the raw diffraction data.

95

Figure C.9: Raw (dotted red line) and deconvoluted (solid blue line) bulk Pd
diffraction patterns acquired with the CPS 120 detector. Primary peak shapes are
well preserved.

96

Figure C.10: Raw (dotted red line) and deconvoluted (solid blue line) nanocrystalline
Pd diffraction patterns acquired with the CPS 120 detector. Primary peak shapes
are well preserved.

97

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