Studies of electrochemical properties of TiNi alloy used as an MH electrode - I. Discharge capacity

Article abstract of DOI:10.1016/S0013-4686(98)00007-3

The electrochemical properties of TiNi alloy used as an MH electrode were investigated. A mathematical model for the electrochemical discharge capacity of TiNi electrode was developed. The model was used to study the effects of various parameters on the discharge capacity, and cycle life. The predicted results from the model fit well with the experimental results. Increasing the discharge current density and charge/discharge cycling current density decreases the discharge capacity, but a high charge/ discharge cycling current density increases the cycle life of the hydride electrode. Increasing the exchange current density, or the diffusion coefficient of hydrogen or reducing the particle size increases the discharge capacity. Upon increasing the discharge current density the controlling steps of discharge capacity change from hydrogen diffusion in α phase (including oxide film) to the charge-transfer reaction on the hydride electrode surface. However for the TiNi alloy electrode the discharge capacity still depends mainly on the diffusion ability of hydrogen even at high discharge current density (200 mA/g). There exists an optimum dissolved hydrogen content of the α phase, C^opt_αβ, at which the discharge capacity reaches a maximum value. Also C^opt_αβ increases with increasing discharge current density.

Full text of DOI:10.1016/S0013-4686(98)00007-3

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Electrochimica Acta, Vol. 43, Nos 21±22, pp. 3193±3207, 1998
# 1998 Published by Elsevier Science Ltd. All rights reserved
Printed in Great Britain
PII: S0013-4686(98)00007-3
0013±4686/98 $19.00 + 0.00
Studies of electrochemical properties of TiNi
alloy used as an MH electrode Ð I.
Discharge capacity
C. S. Wang*, Y. Q. Lei and Q. D. Wang
Department of Materials Science and Engineering, Zhejiang University, Hangzhou, 310027 P.R. China
(Received 29 October 1997; in revised form 12 January 1998)
AbstractÐThe electrochemical properties of TiNi alloy used as an MH electrode were investigated. A
mathematical model for the electrochemical discharge capacity of TiNi electrode was developed. The
model was used to study the e€ects of various parameters on the discharge capacity, and cycle life. The
predicted results from the model ®t well with the experimental results. Increasing the discharge current
density and charge/discharge cycling current density decreases the discharge capacity, but a high charge/
discharge cycling current density increases the cycle life of the hydride electrode. Increasing the exchange
current density, or the di€usion coecient of hydrogen or reducing the particle size increases the dis-
charge capacity. Upon increasing the discharge current density the controlling steps of discharge capacity
change from hydrogen di€usion in a phase (including oxide ®lm) to the charge-transfer reaction on the
hydride electrode surface. However for the TiNi alloy electrode the discharge capacity still depends
mainly on the di€usion ability of hydrogen even at high discharge current density (200 mA/g). There
exists an optimum dissolved hydrogen content of the a phase, Coabpt, at which the discharge capacity
opt
reaches a maximum value. Also C increases with increasing discharge current density. # 1998 Elsevier
ab
Science Ltd. All rights reserved
F
f
Faraday's constant, 96547.6 (J V 1 mol 1), or
LIST OF SYMBOLS
1
26800 (mA h mol
@Qd
)
@Qd
1
(g mA 1 s
)
Cab, Cba
The hydrogen concentration of a or b phase
equilibrating with Peq at the interface between
Ratio of
to
@ꢀDAa =r2o†
Discharge current density (mA g )
@Io
1
Id
Ic
3
)
the a and b phase (mol cm
Optimum value of Cab, at which the discharge
Charge/discharge cycling current density
opt
ab
1
C
(mA g
Exchange current density (mA g
Barrier coecient of phase transformation
)
3
1
capacity getting the maxim (mol cm
)
Io
1/k
)
Cmax
Ca
Hydrogen concentration of b phase equilibrat-
3
1
ing with 1 atm pressure (mol cm
Actual hydrogen concentration of a phase at
the interface between the and phase
)
(mol s g
)
Km
m
Percentage of active alloy.
Particle numbers
Average radius of the particle (cm).
a
b
3
)
(mol cm
ro
Cs
Hydrogen concentration of a phase on the
ra
Radius of unreacted
process (cm).
b phase in discharge
3
)
surface of particle (mol cm
COH, CH O Concentration of OH and H2O (mol cm
3
)
2
gc
Decline coecient of maximum discharge
capacity.
A
Da
Apparent hydrogen di€usion coecient in a
phase including hydrogen di€usion though the
gk
r
Z
Decline coecient of kinetics.
Density of TiNi alloy (g cm 3).
Overpotential V
oxide ®lm on the surface and transfer from
)
the absorbed sites to adsorbed sites (cm2 s
Qd, Qmax Discharge capacity and the maxim discharge
1
w
weight per mole of the TiNi alloy
(106.68 g mol 1).
1
)
capacity, (mA h g
Qabs
Maximum capacity of hydrogen absorption
for the hydride electrode.
INTRODUCTION
Much attention has recently been given to nickel-
hydride batteries using hydrogen storage alloys as the
*Author to whom correspondence should be addressed.
Fax: +86 5717951358; E-mail: phycsw@ema.zju.edu.c.n
3193

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3194
C. S. Wang et al.
negative electrode materials due to the demand for
portable power sources with high energy density,
high-rate dischargeability, long cycle behavior, and
better environmental compatibility. The titanium-
based alloy TiNi has been known as one of the
most promising hydrogen storage materials [1].
all the studies mentioned above the e€ects of
the activation and degradation were neglected
altogether.
It is generally accepted that many factors a€ect
the activation and degradation processes of MH
electrodes. Considering the oxidation of hydrogen-
absorbing metallic elements as the main cause for
capacity deterioration of hydride electrodes,
Willems [7], Wakao and Yonemura [8] and Zuttel
et al. [9] proposed their own cycle life equations.
However, as the values of the parameters in these
equations were determined only from experimental
capacity data, they belong to semiempirical models.
In our previous studies [2], we presented a math-
ematical model describing the relationship of dis-
charge capacity to discharge current density and
cycle number of a hydride electrode. But the e€ect
of the charge/discharge cycling current density on
cycle life was neglected.
The electrochemical reactions taking place at the
metal±electrolyte interface, the pressure±composi-
tion isotherms of electrode alloys, the di€usion of
hydrogen and the phase transformation within the
bulk of a hydrogen storage alloy are the main fac-
tors a€ecting the performances of a metal hydride
electrode [2]. Yang et al. [3, 4] have established the
relationship between the hydrogen surface concen-
tration and overpotential for the galvanostatic
discharge of non-porous hydride electrodes.
Viitanen [5] developed a model for the discharge of
a cylindrical metal-hydride electrode that took into
account the ohmic losses in the electrolyte and in
the solid materials, the charge-transfer reaction on
the surface of the solid particles, and di€usion of
atomic hydrogen in the solid particles. Considering
the hydride electrode as a porous electrode, Vidts
et al. [6], on the assumption that the charge-transfer
reaction occurred on the surface of the metal-
hydride particles, developed equations which
included the mass transfer in the electrolyte and in
the solid metal-hydride particles, the ohmic loss in
the electrolyte and in the solid phase. However in
Applying fundamental electrochemical principles
to an oxide-covered metal electrode and phase
transformations, a mathematical model for the dis-
charge capacity of the TiNi electrode is presented
here. The electrochemical parameters, including
the exchange current density, the di€usion coe-
cient of hydrogen, the resistance of phase trans-
formation, are all determined from the
experimentally determined electrochemical proper-
ties of TiNi electrodes.
Fig. 1. Schematic diagram of hydrogen concentration in a spherical metal-hydride particle. (a) actual concentration of
hydrogen distribution, (b) simpli®ed concentration of hydrogen distribution.

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Electrochemical properties of TiNi alloys
3195
Fig. 2. Typical curve of pressure vs hydrogen content for metal-hydride electrode.
MODEL DEVELOPMENT
state to adsorbed state are treated together as the
apparent di€usion coecient of hydrogen in the a
phase Da (see Fig. 1).
For thin porous electrodes, the mass transfer of
OH and H2O and the ohmic drop in the electro-
lyte have little e€ect on the electrode potential
due to the large di€usion coecients of OH and
H2O and the high porosity of the metal-hydride
electrode [6]. The discharge process of a hydride
electrode in this case can be simply treated as the
discharge of hydrogen from MH particles.
Figure 1 shows a metal-hydride particle in the
electrode modeled in this work and Fig. 2 shows
the typical pressure±composition isotherm for the
electrode alloy.
The hydrogen desorption process during dis-
charge proceeds in the following sequence [2]:
(a) nucleation and growth of the a phase from b
phase, the rate of which mainly depends on the
di€erence of hydrogen concentration (Cab Ca) and
number of non-equilibrium defects, such as excess
vacancies, dislocations, stacking faults and in-
A
(d) electrochemical oxidation of hydrogen at the
electrode surface;
MHads ‡ OH , M ‡ H2O ‡ e
It is generally believed that part of the titanium
in the TiNi alloy is segregated to the surface and
exists in the form of oxide in 6 M KOH electrolyte
after electrochemical cycling [13]. When the oxide
®lm is thin, electrons are exchanged with the under-
lying metal itself, and the oxide ®lm acts as a bar-
rier for electron transfer, causing the exchange
current density to decrease strongly as the ®lm
thickness grows [14].
Let us assume that the hydride particles are
spherical, with an average radius ro, and that the
reaction occurs on the entire spherical surface uni-
formly, and the discharge process is in the quasi-
clusions in the alloy, which for simplicity will not steady state. The hydride electrode is cycled using
be discussed any further.
the same charge and discharge current density Ic,
but the discharge capacity is measured at discharge
current density Id. The discharge begins at the
hydrogen concentration Cmax, which is the hydro-
gen concentration in the alloy when it is fully
charged uniformly throughout the entire b region
with hydrogen pressure equaling 1 atm for open
cells. When the pressure plateau of hydrogen is
near to 1 atm, for approximation we can take Cmax
as Cba, which is the hydrogen concentration of the
phase hydride equilibrated with the a phase at the
plateau pressure Pplat, (see Fig. 2). For AB5 type
metal-hydride electrodes the above treatment is
(b) di€usion of hydrogen from the a phase
through the oxide ®lm to the near-surface region of
the particles [10, 11]. The drastic drop of hydrogen
concentration in the TiO2 ®lm (Fig. 1(a)) is due to
the much lower di€usivity of hydrogen in TiO2
compared with that in the alloy [12].
(c) Transfer of hydrogen from the absorbed site
in the near-surface region to adsorbed site on the
electrode surface [3, 4];
MHabs , MHads
For simplicity, the low hydrogen di€usivity in the
oxide ®lm and hydrogen transfer from the absorbed quite reasonable, but for the TiNi alloy electrode

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3196
C. S. Wang et al.
some further approximations had to be made as no
obvious pressure plateau is observed as shown in
Fig. 3. For simplicity, we take the pressure at the
median of hydrogen composition (H/M = 0.45) as
the plateau pressure of the TiNi alloy electrode,
and still let Cba equal Cmax and the ®rst knee point
of P±C±T curve be considered as Cab. For TiNi
alloy the Cab is measured to be H/M = 0.1 (see
Fig. 3).
So the ratio of ra to ro is
ꢁ
ꢂ
1=3
ra
Qd
Qmax
1
ꢀ3†
ro
Because hydrogen di€usion occurs radially in
spherical particles and the interface between the a
phase and b phase is incoherent, the growth rate of
the a phase is [15]
dra
dt
kr2o
ra
ˆ
ꢀCab Ca†
ꢀ4†
r
The distribution of hydrogen in the a-phase (including
the oxide ®lm)
3
where Cab is the hydrogen concentration (mol cm
)
in the a phase equilibrated with hydride b at the
plateau pressure Pplat, 1/k is the barrier coecient
of phase transformation.
From the continuity of H ¯ow in the a-phase
(including the oxide ®lm) and Fick's ®rst law [2];
In general, phase polarization is not very large,
Ca Cab<<Cba, hence
ꢀ
ꢀ
dc
4pr2mKmDAa ˆ 4pr2omKmDaA
dc
dr
4pr3ormKmId
ˆ
3F
ꢀ
ꢀ
dr
rˆro
Cba Ca Cba Cab
ꢀ5†
ꢀ1†
From mass conservation at the boundary between
the a and b phases
where Km is the percentage of active particles, F is
Faraday's constant, mA h mol 1, m is the number
ꢀ
ꢀ
dra
dt
dc
dr
Idr3or
3Fr2a
ˆ DAa
ˆ
ꢀ6†
ꢀ
ꢀ
ꢀCba Ca†
of spherical particles, r is density of TiNi alloy,
1
g cm 3, Id is discharge current density, mA g
Integrating equation (1) with boundary condition
r = ro, C = Cs, r = ra, C = Ca,
.
rˆra
Substituting equations (3)±(6) into equation (2),
we obtain,
Idr2ro
ꢁ
ꢂ
Cs ˆCab
Idr2or ro
3FkraꢀCba Cab
†
Cs ˆ Ca
1
ꢀ2†
3DAa F ra
ꢃꢁ
ꢂ
ꢄ
1=3
Idr2or
3DAa F
Qd
1
1
ꢀ7†
Qmax
3
)
where Cs is the hydrogen concentration (mol cm
in the a phase on the electrode surface, Ca is the
actual hydrogen concentration (mol cm 3) in the a
phase at the interface between the a phase and b
phase mol/cm3, ra is the size of unreacted hydride.
When the electrode is discharged to the cut-o€
potential ( 0.6 v), the surface concentration of
hydrogen is close to zero, and the discharge ca-
pacity is equal to the value of F multiplied by the
amount of hydrogen in the volume generated by the
shaded area (Fig. 1). Also the shaded area can be
approximated to the square area as indicated in
Fig. 1. The discharge capacity Qd is given by;
ꢁ
ꢂꢃ
ꢁ
ꢂ ꢄ
3
FKm
r
Ca
ra
ro
Qd
Cba
1
2
ꢁ
ꢂꢃ
ꢁ
ꢂ ꢄ
3
FKmCa
ra
ro
ˆ
Qabs
1
2r
ꢃ
ꢁ
ꢂ ꢄ
3
ra
ro
ˆ Qmax
1
where Qabs and Qmax are the maximum charge
capacity and maximum discharge capacity of the
hydride electrode respectively.
Fig. 3. Typical electrochemical discharge P±C curve at the
5th charge/discharge cycle and a cycle current density of
Ic=50 mA/g for TiNi hydride electrode.