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On the kinetics of Cu(I) transfer through the solid CuI-Cu interface
Materials Chemistry and Physics, 24 (1990)
ON THE KINETICS
J.C.
OF Cu(1) TRANSFER
THROUGH
473
THE SOLID
INTERFACE
CuI-Cu
, M.R. Prat and J.A. Schmidt*
Baz&*
Dpto. de Quimica
e Inp. Quimica,
8000 Bahia Blanca Received
413-485
Universidad
National
de1 Sur
(Argentina)
July 31, 1989; accepted
September
13, 1989
ABSTRACT The Cu(1) transfer vanostatic
transient
through
the Cu/_d,(l),o(-CuI
technique.
for both the anodic and cathodic rate controlling to the CuI
according
theoretical
for the Cu/_b,p-CuI
side to the electrolyte
calculation
range
of the energy
by a gal-
energies
obtained
steps are postulated
as
: a) the ion incorporation
interface
surface
barrier
was studied
activation
two different
processes,
to the temperature
solid electrolyte
from the metallic
interface
From the experimental
in-
and b) the ion transfer
at the Cu/o(-CuI
interface.
for the ion transfer
A
is also pre-
sented.
INTRODUCTION The study of the electrodic of interest electrolytes
in energy
on the subject and metals
has been conducted
of Ag(1)
the present
conversion
[I]. The cationic
some attention, transfer
reactions
due to the increasing
but mainly through
on interfaces
devices.
study conducted
involving
solid oxygen interface
[2]. In
has already
cells is a matter
Cientificas
conductors has received
this laboratory
been studied
on the Cu/CuI electrode
de Investigaciones
solid
Most of the work done
conductor
ion conductors interface
systems
involving
conductor/electronic
for silver
*Research Fellows, Comision Aires (CIC) (Argentina). 0254-0584/90/$3.50
and gas sensing
the Ag/AgI
paper a similar
in solid state galvanic
use of electrochemical
the
/3]. In
is reported
de la Prov. de Buenos
0 Elsevier Sequoia/Printed
in The Netherlands
on.
474
EXPERIMENTAL CuI was synthesized The solid precipitate maintained diameter
by reaction
nitrogen
and about 0.3 cm thickness
Copper metal of 99.999%
were prepared
respectively.
The cell was placed
in a vertical
In order to assure
the solid-solid
tained on the working
Preliminary
electrode
experiments
to 460°C and was maintained
latively
glass furnace contact,
electrodes electrode.
nitrogen.
of 13 Kg/cm2 was main-
temperature. was obtained
an alternating
current
for about one hour. The working beta- and alpha-CuI
phases,
by previous of 1kHz fre-
temperature namely
covered
from 330°C
fl"C.
pulses
ranging
in time were applied.
low values,
at 2000 Kg/cm2.
and working
under purified
a pressure
that reproducibility
cell by passing
range of the gamma-,
Short galvanostatic
by pressing
of 1 cm
and the cell was heated at about 500°C during at
showed
quency and lo-20 mV amplitude
10 to 4Op.s
10 hours. Pellets
It was also used as reference
before going to the working
of the working
the stability
for about
purity was used for the counter
of 1 cm and 0.3 cm diameter
'activation'
quality.
was washed and dried at 120°C. After that the powder was
at 550°C under purified
least 30 minutes,
KI, both of proanalysi
of CuSO4 with
in order
from 2~10~~ to 8~10-~ A in current and from
The applied
to perturb
current
values were limited
the electrode
surface
to re-
as little as po-
sible. The measuring combined
circuitry
with a Datalab
was integrated
DL 902 transient
by a Mega Physics recorder
IM 400 galvanostat
and a Telequipment
storage
oscilloscope.
RESULTS Figure 1 shows a typical ohmic
resistance
those calculated
A linear
normally condition
values
portion
for linearizing
0.04 V. This upper lues employed
as shown
was obtained
dimensions
between
values
expression
used here, this condition
value of overpotential
(j) and the
resistances, exponential
as expressed equation.
is given by vF<
is met at potentials
corresponds
The At
under
with the higher current
temperatures
relationship
current
2 and 3. The slopes of
transfer
of a Butler-Volmer-type
that exponential
show an exponential
in Fig.4.
the applied
as charge
here. Only at the lower working
which
with
and the conductivity
('7). as shown in Figs
lines are interpreted
temperatures
From the initial jump the
The values were consistent
.
relationship
by the linear
the working
obtained,
[4]
overpotential
those straight
(2) response.
was obtained.
from the solid electrolyte
from the literature
stationary
overpotential
of the electrolyte
va-
are higher qvalues
with the galvanostatic
current,
475
T ft -
-
---
-----L-
1 bi
q.lsi
+
1
ImV
Fig. l.A typical
4
galvanostatic
8
transient
12
I8
response.
20
24
28
] [mA cm-*] Fig. 2.Plot of overpotential
(v) against
current
density
(j), anodjc
runs.
476
8
4
12
16
20
24
28
j [mA cm21 Fig. 3.Plot of overpotential
-
(2) against
current
density
(j). Cathodic
runs.
density
(j) at low temperature
Tt336.C
220
180
I40 T E -Km d 60
20 I 2
I
1 6
I
j
[mA
I IO
I
I I4
1
I I8
cW2]
Fig. 4.Plot of overpotential (q) against showing the exponential relationship.
current
477
Hence the apparent expression
exchange
current
densities
jo were calculated
from the
:
j = j. vF/RT
(I)
The obtained beta-CuI
values
varied
between
7~10~~ and 160~10-~
range and from 0.35 to 0.7 A/cm2
The j. data follow an Arrhenius-type in Figs.5
and 6 for the anodic
rent slopes
are observed
relationship
and cathodic
: one for the gamma-beta
zone of the beta-alpha-CuI
The data dispersion
is higher
in this case the electrode anodic
alpha-CuI
respectively.
CuI and another, plot coincides
as shown Two diffe-
lower than the with the tem-
perturbation
plots, which
is acceptable
should be higher than in the
runs.
02 1
.o
198 .o Z6 C
i 3.4 4.2 54
132
1.36 1.40 1.44 l&a
152
1s
180
lfi
[f.&-] Fig. 5.Arrhenius Anodic data.
phase.
transition.
for the cathodic
surface
for the gamma-
with temperature
processes,
first, for the alpha CuI. The knee of the Arrhenius perature
A/cm'
for the high temperature
plot of In exchange
current
density
(j,) against
I/T.
for
478
02.6 .: 3.4 4,2 5,o
1,32 1,36 1,40 1.44 l,? [ Fig. 6.Arrhenius Cathodic data.
assebled
Table
average
in Table
current
values of the apparent
average
Besides,
which
l/T.
energies
(E,) are
activation
energies
Phase gamma-beta
405-460
citance
(jo) against
activation
values of the apparent
Eai$G$ic 300-405
density
I.
I. Calculated
Tempetgure
p/q
plot of In exchange
The calculated
1.52 1,56 1,60 1..64
alpha
from the initial
was calculated.
172.4
28.0
42.7
slopes of the 9 -t transients
The obtained
is a figure considerabily
lid electrolyte
interfaces
Ea~Y:zJ
152.3
133.
the double
values were of the order of 10 -2
lower than the reported
layer capapF/cm2
values for other metal/so-
479
DISCUSS[ON The activation
energies
As assumed to involved
and the controlling
in other similar
the following
cases
[3, 53
by b) C&(I)
and the reverse
for the cathodic
assure
that different
obtained
reaction
is considered
: a) Cu(1) transfer
surface,
ion incorporation
From the different
, the reaction mechanism
two steps for the anodic
from the metal to the solid electrolyte
followed
steps
into the crystal
lattice,
direction.
values of the activation
steps control
the electrodic
energy,
reaction
it is easy to
at each temperature
range. For the lower temperatures,
CuI phases, the obtained ionic migration reasonable
are similar
inside the crystal,
of the gamma and beta
to the energies
which
to the movement
between
in the
II.
rate is controlled
step, for to do that, the Cu(I) ion must overcome
to that corresponding
involved
are shown in Table
to assume that in this case the reaction
corporation similar
process
in the range of stability
Ea values
It
an energy
equivalent
then
is
by the inbarrier
sites in the crys-
tal structure.
Table
11. Migration
Phase Temperat/; range
energies
vacancy and intersticials in solid CuI C4].
of copper
Migration
energy
for
Migration energy for copprJ;;;j-sticial
coPP;J;;;ncY
alpha-CuI (420-470)
18.37
beta-CuI
11.56
107.53
----..--
156.54
120.50
(390-400)
L
gala-CuI (325-350)
On the other hand, the activation densities
at higher
tion energy ticials
(Tables
predominates
ion transfer
temperatures
I and II),
energy
is somewhat assuming
with a migration
step could be assumed
obtained
from the exchange
that in this case the movement
energy
current
higher than the corresponding
(Em) of about
to be rate controlling.
migra-
via inters-
12.5 kJ/mol. Thus,
the
In Fig.7 an schematic drawing of the different energy barriers is presented. For the low temperature the addition
of the Ea for incorporation
corresponding justify
to Cu(1) in the metal
the higher
Em (o<-(3).
flects
energy
the ionic transfer
plus the difference
process
obtained
apparent
cui,,f)
an estimation ion transfer the double
of the energy barriers
calculation
Following
curve).
The diagram
the cathodic
higher stability
re-
and anodic for the
t
I
;
Theoretical
between
to the
of alpha-CuI,
lower (dotted
be rate controlling.
a relatively
This would
E, as compared
is considerably
difference
the energy
than in the crystal.
I
Fig. 7.Sketch tal inside.
obtained
between
is given by
interface,
in the range of stability
process would
is 16 f 8 kJ/mol making
ion in the metal
for the process
and at the electrolyte
inside the crystal
also the experimentally
Ea, which
energy
value of the experimentally
As for the electrode
the ion migration Therefore,
the activation
phases,
cJ(c”I)
for ion transfer
of the energy barrier
an approximate
approach
from metallic
layer thickness.
Cu(1) ion approaching
energy
for the Ag/AgI
against
distance
copper to the solid electrolyte To this end the separate
both surfaces
to the crys-
for the CutI) transfer
used earlier
was made of the potential
from the metal
interface
161,
curve for the Cu(1)
surface,
going through
curves of the interaction
at the Cu/alpha-CuI
interface
of
were calculated.
481
The potential with metallic
' = D x where
energy
copper was calculated
exp -[2*
j
(V) - distance
curve for the interaction
by means
of the Morse equation
(aj - a,)]- 2 exp -[&(aj
D is the dissociation
energy
between
(D= 33.03 kJ/mol),e(
distance
maximum
the three more probable
crystalline
used here (about lo-' A/cm2)
order of magnitude face, thus making
between
be only of coulombic that employed
into account
packed.
amounts
to a
that, at the current
the number of partaking
ions is about one
that only the next neighbours
or departing considered
for Madelung's
sur-
are going
ions.
are given elsewhere
a Cu(1) ion in the electrolyte
nature,
was
the (ill), (110)
and more densely
were taken, which
by taking
to consider
on the distances
The interaction
namely,
energy
lower than the number of atoms per sq.cm on the metallic it reasonable
to interact with the approaching More details
the interacting
[7]. The calculation
planes,
atoms the first and second neighbours
of 12 atoms. This is justified
densities
between
constant
the atoms at equilibrium.
and (loo), for these are the ones of lower surface As involved
:
a characteristic
The values of D and o( were taken from the literature made taking
ion
- a,)]
(in this case o( = 1.3588 i-l), aj the separation atoms and ae the distance
of a copper
[6].
surface was assumed
and was then calculated
using a method
constants
As most likely entrance
calculations.
analogous
to to or
exit plane, the (111) of the iodide ions was selected
following
[8]. The
iodide ions, in the plane
'gate' would
then be the space between
coulombically (copper
Thus, the approaching
with an assembly
ions) planes
placed
or departing
of alternate
at a constant
The total number of ions interacting ring the lattice
ions enclosed
the Cu(1) ion was always
Boyce and Hayes
ions. From that plane out the interaction
formed by the center of these was calculated.
three
ion was considered
negative
distance
(iodide
'seeing' a negative
to interact
ions) and positive
of 1.763 i from each other [9].
with the Cu(1) ion was varied
by half spheres
distance
of varying
radius.
by conside-
In such a way
charge of similar magnitude
to its
own. The calculated sidered
the reference around
energy
half spheres.
to the radius of the con-
a minimum
value of the different
value. The dispersion
is higher
curves
the greater
at about 1 i from also oscillates
the distance
to the
plane.
Figure 8 shows the curve obtained sing different comparison,
according
all of them go through
plane and the energy
an average
reference
curves are different
However,
numbers
of copper
the same minimum
for several
and iodide
distance
radii of the half sphere compri-
ions of the lattice.
is taken
For the sake of
for all the curves.
482 l 4
a
0
l 0
a
0
0 0
to 0
0
a0
me
.m
0 A
0
0
7.30
l
0
11.25 II.30
A
t1,50
0
53 740
a
1
2
3i [I
Distance
numbers of interacF&g. 8.Coulomb interaction curves for Cu ion 'seeing'different ting ions in the CuI crystal, according to the radius of the half spheres considered.
It is worthwhile charge
distributed
sidering
the interaction
among three iodide As a better which
to notice that these calculations in alternate
involves
the criterion neighbours
6 copper
metallic
positions.
to the half sphere of radius 5.3 i
as possible
This was selected
to that involving
on the
12 near
plane.
of the total potential
to fix both the separation
by con-
charge distributed
the minimum
ions and 7 iodide ions was chosen.
of having a circle as similar
double
show that the effect of the
the same as that obtained
placed on aproximately
curve the one corresponding
in the opposing
the electrical
is nearly
of the Cu(1) ion with one negative
ions trigonally
For the construction necessary
planes
distance
layer and the energy
energy against between
difference
distance
the minima between
curve it was
at both sides of
them.
483
-300 -300 7
-316
e -324 ._ Y \ -332 B g -340 w $j -340 5 -356 8 -364 -372 -300 -368 -396
Fig. 9.Calculated potential energy against distance curves for the Cu(1) transfer from metallic copper to the alpha-CuI interface. The Morse curves for the (loo), (110) and (111) planes are shown.
The double nes, which
layer thickness
are defined
is fixed by the position
as the location
of closest
On the CuI side it is given by the last crystalline side it is determined electrons
by the boundary
of the outer Helmholtz
approach
co-ions
plane, whereas
of the zone of positive
pla-
[lo). on the metal
charge where
the
move.
The minimum equilibrium
energy
position
ne of the metallic
on the metal on the metal
surface.
side is associated surface,
the centre
with the copper
ion in an
of the ion lying on the li-
484
it was taken as the average
As for the Cu(1) ion radius, and ionic radii,
1.28 and 0.96 i respectively
as above mentioned,
the minimum
Thus the total distance The energy
which
difference
tion of equation
was located
resulted
between
(2), which
should
can be estimated
for plane
of reac-
e t
0
AG>l
Cu;Surf)
-
is the standard potential,
744.37
(loo), 442.24
crystal
enrgy of sublimation,
kJ/mol
on the
eiM,
+
kJ/mol
1131;
for plane
corresponds
b4] ; and nG(Surf) on the surface
to thenGo
from the cycle
nG(Surf)
ionization
correspond
eid
AG(Sub)
wherenG(Sub)
side,
was 2.24 i.
the minima
I
“(M)
the metallic
at 1 i from the (111) iodide plane.
cu(s)
'
between
[11]. On the solid electrolyte
257.28
kJ/mol
is the work function,
4,
and 475.97
(110)
to the energy
difference
kJ/mol between
'gate' and the ion at an infinite
[12]; I is the 431.63
for plane
kJ/mol
(111)
the ion placed distance
from the
the crystal. The last term can be approximated the minimum
position
the above mentioned ThenGO especially
approximation.
value obtained
energy
Besides
Table
Comparison
curves
an ion at
according
0 to 18.8 kJ/mol depending
In Table III
the
ob-
ones. The agreement
[15] a value of
p=
0.4 was
factor of the electrode.
of the Ea values obtained
Crystalline
may be
made for the calculations.
experimentally
and by a theoretical
calculation Activation energy
to
was 552 kJ/mol.
value of 9.2 kJ/mol was
curve shown in Fig.9. with the experimental
from the slopes of the linearized for the symetry
III.
Thus an average
under the rather crude assumptions
calculated
between
long distance,
The value thus obtained
values.
values of E, are compared
seen as satisfactory,
difference
from the cycle varied between
on the work function
used to draw the potential tained
by the energy
and the ion at a sufficientely
plane
(100)
(110)
(111)
anodic
48.4
43.2
52.0
cathodic
38.8
33.6
42.4
new
Average
f
activation
kJ/mol]
Experimental values [kJ/moa
47.86
42.7 t 8
38.27
28.0 f. 8
CONCLUSIONS The experimental for the electrode the metallic ration further
results
are interpreted
reaction,
for the anodic
namely,
side up to the solid electrolyte
into the crystal postulated
and the converse
lattice,
interactions
yields
agreement
a theoretical
a two-step
direction,
surface,
direction.
obtained
energy
It is
higher than
involving
value for the activation
with the experimentally
from
by b) the incorpo-
at temperatures
A simple model
mechanism
a) ion transfer
followed
for the cathodic
that step a) is rate controlling
400°C and step b) for lower temperatures.
factory
by postulating
only coulombic barrier
in satis-
one for step a).
ACKNOWLEDGEMENTS This work was supported thanks
by grants
the UNS for a fellowship.
her contribution
from CIC and CONICET
The authors
to the theoretical
are indebted
of Argentina.
M.R.P.
to Dra. L. E. Fasano for
calculations.
REFERENCES 1
See for instance
2
H. Drstak and M.W. Breiter,
R.G. Linford
3 4
T. Matsui
5
S. Toshima,
6
L.E. Fasano and J.C. Bazdn,
and S. Hackwood,
Chem. Rev.,81
(1981) 327.
Electrochim.
Acta, 33 (1988) 33 and references
J.C. Bazdn and L.E. Fasano,
Electrochim.
Acta, -34 (1989) 309.
and J.B.
J. Electrochem.
therein.
Wagner,
T. Ohsaki
and N. Kimura,
7
L.A. Girifalco
8
J.B. Boyce and T.M. Hayes
ASTM Powder
10 E. Bergmann,
13 CRC Handbook 14 id.
Heidelberg,
Acta, _2l_(1976) 469. 50(3)
(1989) 259.
Physics
of Superionic
Electrochim.
Reinhart
Conductors,
1979. Chap. 2.
(ASTM Phyladelphia
and M. Voinov, Holt,
(eoj
New York,
& Winston
1967) 6-0623.
Acta, -22 (1975) 459. (ed), Solid State Phy-
1976. Chap. 19.
0. Knacke and 0. Kubaschewsky,
Substances.
(1977) 300.
Phys. Rev., -114 (1959) 687.
File Inorganic
and N.D. Mermin,
sics, New York,
Electrochim.
in M.B. Salmon
H. Tannenberg
11 N.U. Ashcroft
12 I. Barin,
Berlin.
Diffraction
124(2)
J. Phys. Chem. Solids,
and W.G. Weizer,
Springer-Verlag, 9
Sot.,
Springer-Verlag, of Chemestry
Berlin,
Termochemycal
Heidelberg,
and Physics,
60
th
edn.,
Properties
New York, Chemical
of 1norgani.c
1977. Rubber Ohio,
E 68.
, E 82.
15 J.O'M.
Bockris
1970. Chap. 8.
and A.M. Reddy, Modern
Electrochemistry.
Plenum
Press, New York,
ON THE KINETICS
J.C.
OF Cu(1) TRANSFER
THROUGH
473
THE SOLID
INTERFACE
CuI-Cu
, M.R. Prat and J.A. Schmidt*
Baz&*
Dpto. de Quimica
e Inp. Quimica,
8000 Bahia Blanca Received
413-485
Universidad
National
de1 Sur
(Argentina)
July 31, 1989; accepted
September
13, 1989
ABSTRACT The Cu(1) transfer vanostatic
transient
through
the Cu/_d,(l),o(-CuI
technique.
for both the anodic and cathodic rate controlling to the CuI
according
theoretical
for the Cu/_b,p-CuI
side to the electrolyte
calculation
range
of the energy
by a gal-
energies
obtained
steps are postulated
as
: a) the ion incorporation
interface
surface
barrier
was studied
activation
two different
processes,
to the temperature
solid electrolyte
from the metallic
interface
From the experimental
in-
and b) the ion transfer
at the Cu/o(-CuI
interface.
for the ion transfer
A
is also pre-
sented.
INTRODUCTION The study of the electrodic of interest electrolytes
in energy
on the subject and metals
has been conducted
of Ag(1)
the present
conversion
[I]. The cationic
some attention, transfer
reactions
due to the increasing
but mainly through
on interfaces
devices.
study conducted
involving
solid oxygen interface
[2]. In
has already
cells is a matter
Cientificas
conductors has received
this laboratory
been studied
on the Cu/CuI electrode
de Investigaciones
solid
Most of the work done
conductor
ion conductors interface
systems
involving
conductor/electronic
for silver
*Research Fellows, Comision Aires (CIC) (Argentina). 0254-0584/90/$3.50
and gas sensing
the Ag/AgI
paper a similar
in solid state galvanic
use of electrochemical
the
/3]. In
is reported
de la Prov. de Buenos
0 Elsevier Sequoia/Printed
in The Netherlands
on.
474
EXPERIMENTAL CuI was synthesized The solid precipitate maintained diameter
by reaction
nitrogen
and about 0.3 cm thickness
Copper metal of 99.999%
were prepared
respectively.
The cell was placed
in a vertical
In order to assure
the solid-solid
tained on the working
Preliminary
electrode
experiments
to 460°C and was maintained
latively
glass furnace contact,
electrodes electrode.
nitrogen.
of 13 Kg/cm2 was main-
temperature. was obtained
an alternating
current
for about one hour. The working beta- and alpha-CuI
phases,
by previous of 1kHz fre-
temperature namely
covered
from 330°C
fl"C.
pulses
ranging
in time were applied.
low values,
at 2000 Kg/cm2.
and working
under purified
a pressure
that reproducibility
cell by passing
range of the gamma-,
Short galvanostatic
by pressing
of 1 cm
and the cell was heated at about 500°C during at
showed
quency and lo-20 mV amplitude
10 to 4Op.s
10 hours. Pellets
It was also used as reference
before going to the working
of the working
the stability
for about
purity was used for the counter
of 1 cm and 0.3 cm diameter
'activation'
quality.
was washed and dried at 120°C. After that the powder was
at 550°C under purified
least 30 minutes,
KI, both of proanalysi
of CuSO4 with
in order
from 2~10~~ to 8~10-~ A in current and from
The applied
to perturb
current
values were limited
the electrode
surface
to re-
as little as po-
sible. The measuring combined
circuitry
with a Datalab
was integrated
DL 902 transient
by a Mega Physics recorder
IM 400 galvanostat
and a Telequipment
storage
oscilloscope.
RESULTS Figure 1 shows a typical ohmic
resistance
those calculated
A linear
normally condition
values
portion
for linearizing
0.04 V. This upper lues employed
as shown
was obtained
dimensions
between
values
expression
used here, this condition
value of overpotential
(j) and the
resistances, exponential
as expressed equation.
is given by vF<
is met at potentials
corresponds
The At
under
with the higher current
temperatures
relationship
current
2 and 3. The slopes of
transfer
of a Butler-Volmer-type
that exponential
show an exponential
in Fig.4.
the applied
as charge
here. Only at the lower working
which
with
and the conductivity
('7). as shown in Figs
lines are interpreted
temperatures
From the initial jump the
The values were consistent
.
relationship
by the linear
the working
obtained,
[4]
overpotential
those straight
(2) response.
was obtained.
from the solid electrolyte
from the literature
stationary
overpotential
of the electrolyte
va-
are higher qvalues
with the galvanostatic
current,
475
T ft -
-
---
-----L-
1 bi
q.lsi
+
1
ImV
Fig. l.A typical
4
galvanostatic
8
transient
12
I8
response.
20
24
28
] [mA cm-*] Fig. 2.Plot of overpotential
(v) against
current
density
(j), anodjc
runs.
476
8
4
12
16
20
24
28
j [mA cm21 Fig. 3.Plot of overpotential
-
(2) against
current
density
(j). Cathodic
runs.
density
(j) at low temperature
Tt336.C
220
180
I40 T E -Km d 60
20 I 2
I
1 6
I
j
[mA
I IO
I
I I4
1
I I8
cW2]
Fig. 4.Plot of overpotential (q) against showing the exponential relationship.
current
477
Hence the apparent expression
exchange
current
densities
jo were calculated
from the
:
j = j. vF/RT
(I)
The obtained beta-CuI
values
varied
between
7~10~~ and 160~10-~
range and from 0.35 to 0.7 A/cm2
The j. data follow an Arrhenius-type in Figs.5
and 6 for the anodic
rent slopes
are observed
relationship
and cathodic
: one for the gamma-beta
zone of the beta-alpha-CuI
The data dispersion
is higher
in this case the electrode anodic
alpha-CuI
respectively.
CuI and another, plot coincides
as shown Two diffe-
lower than the with the tem-
perturbation
plots, which
is acceptable
should be higher than in the
runs.
02 1
.o
198 .o Z6 C
i 3.4 4.2 54
132
1.36 1.40 1.44 l&a
152
1s
180
lfi
[f.&-] Fig. 5.Arrhenius Anodic data.
phase.
transition.
for the cathodic
surface
for the gamma-
with temperature
processes,
first, for the alpha CuI. The knee of the Arrhenius perature
A/cm'
for the high temperature
plot of In exchange
current
density
(j,) against
I/T.
for
478
02.6 .: 3.4 4,2 5,o
1,32 1,36 1,40 1.44 l,? [ Fig. 6.Arrhenius Cathodic data.
assebled
Table
average
in Table
current
values of the apparent
average
Besides,
which
l/T.
energies
(E,) are
activation
energies
Phase gamma-beta
405-460
citance
(jo) against
activation
values of the apparent
Eai$G$ic 300-405
density
I.
I. Calculated
Tempetgure
p/q
plot of In exchange
The calculated
1.52 1,56 1,60 1..64
alpha
from the initial
was calculated.
172.4
28.0
42.7
slopes of the 9 -t transients
The obtained
is a figure considerabily
lid electrolyte
interfaces
Ea~Y:zJ
152.3
133.
the double
values were of the order of 10 -2
lower than the reported
layer capapF/cm2
values for other metal/so-
479
DISCUSS[ON The activation
energies
As assumed to involved
and the controlling
in other similar
the following
cases
[3, 53
by b) C&(I)
and the reverse
for the cathodic
assure
that different
obtained
reaction
is considered
: a) Cu(1) transfer
surface,
ion incorporation
From the different
, the reaction mechanism
two steps for the anodic
from the metal to the solid electrolyte
followed
steps
into the crystal
lattice,
direction.
values of the activation
steps control
the electrodic
energy,
reaction
it is easy to
at each temperature
range. For the lower temperatures,
CuI phases, the obtained ionic migration reasonable
are similar
inside the crystal,
of the gamma and beta
to the energies
which
to the movement
between
in the
II.
rate is controlled
step, for to do that, the Cu(I) ion must overcome
to that corresponding
involved
are shown in Table
to assume that in this case the reaction
corporation similar
process
in the range of stability
Ea values
It
an energy
equivalent
then
is
by the inbarrier
sites in the crys-
tal structure.
Table
11. Migration
Phase Temperat/; range
energies
vacancy and intersticials in solid CuI C4].
of copper
Migration
energy
for
Migration energy for copprJ;;;j-sticial
coPP;J;;;ncY
alpha-CuI (420-470)
18.37
beta-CuI
11.56
107.53
----..--
156.54
120.50
(390-400)
L
gala-CuI (325-350)
On the other hand, the activation densities
at higher
tion energy ticials
(Tables
predominates
ion transfer
temperatures
I and II),
energy
is somewhat assuming
with a migration
step could be assumed
obtained
from the exchange
that in this case the movement
energy
current
higher than the corresponding
(Em) of about
to be rate controlling.
migra-
via inters-
12.5 kJ/mol. Thus,
the
In Fig.7 an schematic drawing of the different energy barriers is presented. For the low temperature the addition
of the Ea for incorporation
corresponding justify
to Cu(1) in the metal
the higher
Em (o<-(3).
flects
energy
the ionic transfer
plus the difference
process
obtained
apparent
cui,,f)
an estimation ion transfer the double
of the energy barriers
calculation
Following
curve).
The diagram
the cathodic
higher stability
re-
and anodic for the
t
I
;
Theoretical
between
to the
of alpha-CuI,
lower (dotted
be rate controlling.
a relatively
This would
E, as compared
is considerably
difference
the energy
than in the crystal.
I
Fig. 7.Sketch tal inside.
obtained
between
is given by
interface,
in the range of stability
process would
is 16 f 8 kJ/mol making
ion in the metal
for the process
and at the electrolyte
inside the crystal
also the experimentally
Ea, which
energy
value of the experimentally
As for the electrode
the ion migration Therefore,
the activation
phases,
cJ(c”I)
for ion transfer
of the energy barrier
an approximate
approach
from metallic
layer thickness.
Cu(1) ion approaching
energy
for the Ag/AgI
against
distance
copper to the solid electrolyte To this end the separate
both surfaces
to the crys-
for the CutI) transfer
used earlier
was made of the potential
from the metal
interface
161,
curve for the Cu(1)
surface,
going through
curves of the interaction
at the Cu/alpha-CuI
interface
of
were calculated.
481
The potential with metallic
' = D x where
energy
copper was calculated
exp -[2*
j
(V) - distance
curve for the interaction
by means
of the Morse equation
(aj - a,)]- 2 exp -[&(aj
D is the dissociation
energy
between
(D= 33.03 kJ/mol),e(
distance
maximum
the three more probable
crystalline
used here (about lo-' A/cm2)
order of magnitude face, thus making
between
be only of coulombic that employed
into account
packed.
amounts
to a
that, at the current
the number of partaking
ions is about one
that only the next neighbours
or departing considered
for Madelung's
sur-
are going
ions.
are given elsewhere
a Cu(1) ion in the electrolyte
nature,
was
the (ill), (110)
and more densely
were taken, which
by taking
to consider
on the distances
The interaction
namely,
energy
lower than the number of atoms per sq.cm on the metallic it reasonable
to interact with the approaching More details
the interacting
[7]. The calculation
planes,
atoms the first and second neighbours
of 12 atoms. This is justified
densities
between
constant
the atoms at equilibrium.
and (loo), for these are the ones of lower surface As involved
:
a characteristic
The values of D and o( were taken from the literature made taking
ion
- a,)]
(in this case o( = 1.3588 i-l), aj the separation atoms and ae the distance
of a copper
[6].
surface was assumed
and was then calculated
using a method
constants
As most likely entrance
calculations.
analogous
to to or
exit plane, the (111) of the iodide ions was selected
following
[8]. The
iodide ions, in the plane
'gate' would
then be the space between
coulombically (copper
Thus, the approaching
with an assembly
ions) planes
placed
or departing
of alternate
at a constant
The total number of ions interacting ring the lattice
ions enclosed
the Cu(1) ion was always
Boyce and Hayes
ions. From that plane out the interaction
formed by the center of these was calculated.
three
ion was considered
negative
distance
(iodide
'seeing' a negative
to interact
ions) and positive
of 1.763 i from each other [9].
with the Cu(1) ion was varied
by half spheres
distance
of varying
radius.
by conside-
In such a way
charge of similar magnitude
to its
own. The calculated sidered
the reference around
energy
half spheres.
to the radius of the con-
a minimum
value of the different
value. The dispersion
is higher
curves
the greater
at about 1 i from also oscillates
the distance
to the
plane.
Figure 8 shows the curve obtained sing different comparison,
according
all of them go through
plane and the energy
an average
reference
curves are different
However,
numbers
of copper
the same minimum
for several
and iodide
distance
radii of the half sphere compri-
ions of the lattice.
is taken
For the sake of
for all the curves.
482 l 4
a
0
l 0
a
0
0 0
to 0
0
a0
me
.m
0 A
0
0
7.30
l
0
11.25 II.30
A
t1,50
0
53 740
a
1
2
3i [I
Distance
numbers of interacF&g. 8.Coulomb interaction curves for Cu ion 'seeing'different ting ions in the CuI crystal, according to the radius of the half spheres considered.
It is worthwhile charge
distributed
sidering
the interaction
among three iodide As a better which
to notice that these calculations in alternate
involves
the criterion neighbours
6 copper
metallic
positions.
to the half sphere of radius 5.3 i
as possible
This was selected
to that involving
on the
12 near
plane.
of the total potential
to fix both the separation
by con-
charge distributed
the minimum
ions and 7 iodide ions was chosen.
of having a circle as similar
double
show that the effect of the
the same as that obtained
placed on aproximately
curve the one corresponding
in the opposing
the electrical
is nearly
of the Cu(1) ion with one negative
ions trigonally
For the construction necessary
planes
distance
layer and the energy
energy against between
difference
distance
the minima between
curve it was
at both sides of
them.
483
-300 -300 7
-316
e -324 ._ Y \ -332 B g -340 w $j -340 5 -356 8 -364 -372 -300 -368 -396
Fig. 9.Calculated potential energy against distance curves for the Cu(1) transfer from metallic copper to the alpha-CuI interface. The Morse curves for the (loo), (110) and (111) planes are shown.
The double nes, which
layer thickness
are defined
is fixed by the position
as the location
of closest
On the CuI side it is given by the last crystalline side it is determined electrons
by the boundary
of the outer Helmholtz
approach
co-ions
plane, whereas
of the zone of positive
pla-
[lo). on the metal
charge where
the
move.
The minimum equilibrium
energy
position
ne of the metallic
on the metal on the metal
surface.
side is associated surface,
the centre
with the copper
ion in an
of the ion lying on the li-
484
it was taken as the average
As for the Cu(1) ion radius, and ionic radii,
1.28 and 0.96 i respectively
as above mentioned,
the minimum
Thus the total distance The energy
which
difference
tion of equation
was located
resulted
between
(2), which
should
can be estimated
for plane
of reac-
e t
0
AG>l
Cu;Surf)
-
is the standard potential,
744.37
(loo), 442.24
crystal
enrgy of sublimation,
kJ/mol
on the
eiM,
+
kJ/mol
1131;
for plane
corresponds
b4] ; and nG(Surf) on the surface
to thenGo
from the cycle
nG(Surf)
ionization
correspond
eid
AG(Sub)
wherenG(Sub)
side,
was 2.24 i.
the minima
I
“(M)
the metallic
at 1 i from the (111) iodide plane.
cu(s)
'
between
[11]. On the solid electrolyte
257.28
kJ/mol
is the work function,
4,
and 475.97
(110)
to the energy
difference
kJ/mol between
'gate' and the ion at an infinite
[12]; I is the 431.63
for plane
kJ/mol
(111)
the ion placed distance
from the
the crystal. The last term can be approximated the minimum
position
the above mentioned ThenGO especially
approximation.
value obtained
energy
Besides
Table
Comparison
curves
an ion at
according
0 to 18.8 kJ/mol depending
In Table III
the
ob-
ones. The agreement
[15] a value of
p=
0.4 was
factor of the electrode.
of the Ea values obtained
Crystalline
may be
made for the calculations.
experimentally
and by a theoretical
calculation Activation energy
to
was 552 kJ/mol.
value of 9.2 kJ/mol was
curve shown in Fig.9. with the experimental
from the slopes of the linearized for the symetry
III.
Thus an average
under the rather crude assumptions
calculated
between
long distance,
The value thus obtained
values.
values of E, are compared
seen as satisfactory,
difference
from the cycle varied between
on the work function
used to draw the potential tained
by the energy
and the ion at a sufficientely
plane
(100)
(110)
(111)
anodic
48.4
43.2
52.0
cathodic
38.8
33.6
42.4
new
Average
f
activation
kJ/mol]
Experimental values [kJ/moa
47.86
42.7 t 8
38.27
28.0 f. 8
CONCLUSIONS The experimental for the electrode the metallic ration further
results
are interpreted
reaction,
for the anodic
namely,
side up to the solid electrolyte
into the crystal postulated
and the converse
lattice,
interactions
yields
agreement
a theoretical
a two-step
direction,
surface,
direction.
obtained
energy
It is
higher than
involving
value for the activation
with the experimentally
from
by b) the incorpo-
at temperatures
A simple model
mechanism
a) ion transfer
followed
for the cathodic
that step a) is rate controlling
400°C and step b) for lower temperatures.
factory
by postulating
only coulombic barrier
in satis-
one for step a).
ACKNOWLEDGEMENTS This work was supported thanks
by grants
the UNS for a fellowship.
her contribution
from CIC and CONICET
The authors
to the theoretical
are indebted
of Argentina.
M.R.P.
to Dra. L. E. Fasano for
calculations.
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See for instance
2
H. Drstak and M.W. Breiter,
R.G. Linford
3 4
T. Matsui
5
S. Toshima,
6
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and S. Hackwood,
Chem. Rev.,81
(1981) 327.
Electrochim.
Acta, 33 (1988) 33 and references
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T. Ohsaki
and N. Kimura,
7
L.A. Girifalco
8
J.B. Boyce and T.M. Hayes
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10 E. Bergmann,
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