ISSN 10637834, Physics of the Solid State, 2013, Vol. 55, No. 7, pp. 1377–1380. © Pleiades Publishing, Ltd., 2013.
Original Russian Text © V.G. Pleshchev, N.V. Selezneva, N.V. Baranov, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 7, pp. 1281–1284.
1377
1. INTRODUCTION
Dichalcogenides of transition metals of Groups IV
and V elements having the general formula
TX
2
exhibit
a natural layered structure in which hexagonally
packed layers of a transition metal (
T
) are located
between two chalcogen layers (
X
). A weak coupling
between the neighboring chalcogen layers provides a
way of inserting (intercalating) atoms of other ele
ments into the interlayer space and, thus, causing sig
nificant changes in the physical properties of the com
pounds [1–3]. Among compounds of this class, in last
decades much attention has been paid to the study of
intercalated titanium dichalcogenides
M
x
Ti
X
2
, which
exhibit a wide variety of behavior of the physical prop
erties depending on the kind and concentration of
introduced atoms (
M
) and on the type of the matrix
compound. In particular, the intercalated titanium
dichalcogenides demonstrate the formation of super
structures, phase transitions to the chargedensity
wave state, the occurrence of the superconducting
state or various magnetic states [4–6]. Of a specific
interest are the studies of the electronic and ionic
charge transfer in similar compounds which can open
new possibilities of their application in practice. For
example, some lithiumintercalated dichalcogenides
of transition metals are already used as electrodes of
chemical current sources [7, 8]. According to available
data, significant ionic conductivity can also take place
in
M
x
TX
2
compounds, in which intercalated atoms
M
are copper and silver atoms. The study of the electron
density distribution of copper ions in the Cu
x
TiS
2
compounds shows that the copper ions are weakly
coupled with sulfur ions in adjacent layers. As a result,
they can exhibit significant mobility, which makes
these and similar compounds promising as electrodes
for chemical current sources [9]. In addition, there are
experimental data on the ionic conductivity in tita
nium and zirconium chalcogenides due to the transfer
of silver ions [10–12]. In particular, the Ag
x
TiS
2
com
pound is found to have quite high coefficients of con
jugated chemical diffusion
D
~ 10
–5
cm
2
/s and the
ionic conductivity
σ
i
~ 10
–1
S/cm at temperatures of
450–550 K [12].
Despite fact that the hafnium dichalcogenidebased
intercalated compounds are scantly known, nevertheless,
several Ag–Hf–S compounds with a layered structure
were found, which exhibit a quite high (~10
–3
S/cm)
ionic conductivity at room temperature [13]. Our stud
ies of the Ag
x
HfSe
2
samples [14] showed the existence
in them of polarization phenomena, which, according
to [15, 16], are characteristic of materials with a mixed
electronic–ionic conductivity. In this work, the
Ag
x
HfSe
2
compounds are studied by impedance spec
troscopy and the method of electrochemical cell emf to
obtain additional data on the charge and masstrans
fer in intercalated dichalcogenides of transition metals.
2. SAMPLE PREPARATION
AND EXPERIMENTAL TECHNIQUE
The Ag
x
HfSe
2
(
x
= 0.1, 0.2) samples were prepared
from materials synthesized and attested for previous
SEMICONDUCTORS
Specific Features of the Charge and Mass Transfer
in a SilverIntercalated Hafnium Diselenide
V. G. Pleshchev
a
,
*, N. V. Selezneva
a
, and N. V. Baranov
a
,
b
a
Institute of Natural Science, Ural Federal University named after the First President of Russia B.N. Yeltsin,
ul. Kuibysheva 48, Yekaterinburg, 620083 Russia
* email: Valery.Pleschov@usu.ru
b
Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences,
ul. Sofii Kovalevskoi 18, Yekaterinburg, 620990 Russia
Received December 28, 2012
Abstract
—The specific features of the charge transfer in intercalated samples of Ag
x
HfSe
2
have been studied
for the first time by alternating current (ac) impedance spectroscopy. It has been found that relaxation pro
cesses in an ac field are accelerated with increasing silver content in the samples. The complex conductivity
(
Y
) shows a frequency dispersion described by power law
Y
~
ω
s
, which is characteristic of the hopping con
ductivity mechanism. The Ag
x
HfSe
2
compounds demonstrate shorter relaxation times as compared to those
observed in hafnium diselenide intercalated with copper atoms, and this fact indicates that the charge carrier
mobility in the silverintercalated compounds is higher. The possibility of silver ion transfer in Ag
x
HfSe
2
is
confirmed by the measurements performed by the method of electrochemical cell emf.
DOI:
10.1134/S1063783413070238
1378
PHYSICS OF THE SOLID STATE
Vol. 55
No. 7
2013
PLESHCHEV et al.
studies of the system [14]. The samples under study
were 2mmthick pellets 10 mm in diameter. The
impedance spectra of the samples were measured by a
Z3000 impedance meter in the range of linear fre
quencies (
ν)
from 10 Hz to 3 MHz. The chemical
potential difference of silver in the samples was deter
mined with respect to metallic silver using the electro
chemical cell Ag1/RbAg
4
I
5
/Ag
x
HfSe
2
/RbAg
4
I
5
/Ag2.
Such a cell design allows one to transmit an ionic cur
rent through it owing to the use of RbAg
4
I
5
having a
high ionic conductivity [17] and also to measure elec
tromotive forces appeared between electrodes Ag1 and
Ag2 and corresponding crosssections of the samples
as the external circuit is disconnected. All the mea
surements were carried out at room temperature.
3. RESULTS
The impedance spectra measured on the Ag
x
HfSe
2
(
x
= 0.1, 0.2) samples are shown in Fig. 1 as the depen
dences of the imaginary part of the impedance
(
⎯
Im
Z
) on the real part (Re
Z
). At the complex plane,
these dependences are circle arcs whose radii decrease
with increasing silver concentration in the samples.
According to [18, 19], such a shape of the depen
dences can be described in an approximation of the
equivalent circuit consisting of an active resistor and
capacitor connected in parallel. However, as one can
see, the curves obtained are not ideal semicircles. In
particular, we can note some asymmetry of these
curves and also the shift of the center of the semicircles
below the abscissa axis. These distortions demonstrate
an inconsistence of the impedance behaviors in the
samples to the Debye relaxation model and can be
related to either the existence of several discrete
parameters of the equivalent circuit or a continuous
distribution of these parameters around an average
value. In particular, the deviations from the Debye
relaxation model can be related to the charge transfer
processes over both the grain bulk and the grain
boundaries, and each process is characterized by vari
ous values of the parameters.
The frequencies at which the impedance imaginary
part shown in Fig. 1 takes the maximum value (
ω
m
=
2
πν
m
) are 615 kHz and 4.1 MHz for the samples with
x
= 0.1 and 0.2, respectively. These data allow us to
find the characteristic relaxation times
τ
= 1/
ω
m
which
are 1.6
×
10
–6
s and 2.4
×
10
–7
s and can be interpreted
as the lifetimes of the charge carriers. The values
obtained are substantially lower than those found in
our similar studies performed on coppercontaining
samples of comparable compositions [20]. This differ
ence testifies that, when the same matrices (HfSe
2
) are
used for intercalation, the charge transfer in the silver
containing samples is faster than that in the copper
containing samples; this fact seems to be related to
higher mobility of the silver ions. In turn, the latter can
be result of a lower binding energy of the intercalated
silver ions with the matrix lattice as compared to the
copper ions.
The data of impedance spectroscopy can give use
ful information on the microscopic mechanism of the
charge carrier motion. Figure 2 shows the frequency
dependences of the complex conductivity (
Y
) in the
logarithmic scale. Two regions can be separated in
these dependences for both samples. The first region is
a frequencyindependent plateau, and the second
region is the region of frequency dispersion that can be
described by expression
Y
~
A
ω
s
. The power depen
dence of the complex conductivity on frequency is
characteristic of many materials, in which the charge
carriers behave by the hopping mechanism, and is
known as “universal dynamic response” (UDR) [21–
23]. According to the theoretical concepts [24], in the
20
Re
Z
, k
Ω
10
12
8
4
16
0
15 25 30
ω
x
= 0.2
5 35
x
= 0.1
−
Im
Z
, k
Ω
Fig. 1.
Impedance spectra of Ag
x
HfSe
2
.
10
ln
ω
[Hz]
6
−
9.2
−
9.6
−
10.0
−
8.4
8 12 14
x
= 0.2
4 16
x
= 0.1
ln
Y
[S]
2
−
10.4
−
8.8
Fig. 2.
Frequency dependences of the complex conductiv
ity of Ag
x
HfSe
2
. The arrows indicate the region of the tran
sition to the frequency dispersion.
PHYSICS OF THE SOLID STATE
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2013
SPECIFIC FEATURES OF THE CHARGE AND MASS TRANSFER 1379
case of hopping conductivity, exponent
s
in the expres
sion of the frequency dispersion must be smaller than
unity. The values of
s
determined by approximation of
the dependences in the highfrequency region are 0.58
and 0.44 for the samples with
x
= 0.1 and 0.2, respec
tively. These values are close to the frequency disper
sion exponents for the Cu
x
HfSe
2
samples (0.55 and
0.41) [20], which indicate the identity of the conduc
tivity mechanisms in these compounds. However, the
frequencies (
ω
), at which the frequency dispersion
begins to be pronounced in the Ag
x
HfSe
2
samples and
which are called hopping frequencies [25], are 270 and
1190 kHz for
x
= 0.1 and 0.2, respectively. These hop
ping frequencies are almost twice as high as those
obtained earlier for the Cu
x
HfSe
2
samples identical in
composition; this result adequately correlates with the
above noted decrease in the relaxation times obtained
from the comparison of the impedance spectra of
these two systems.
We studied the masstransfer in the samples
using the electrochemical cell
Ag1/RbAg
4
I
5
/Ag
x
HfSe
2
/RbAg
4
I
5
/Ag2 that allows the
transmission of an ionic current through the sample.
When a current passes through the cell, a silver ion
chemical potential gradient is formed in the sample
due to the formation of the concentration gradient
opposite to the direction of the transmitted current;
the gradient provides the diffusion transfer of a charge
from the positive pole of the current source to its neg
ative pole. The steadystate concentration gradient is
also retained at the moment of switching off the cur
rent. The difference of silver atom concentrations at
opposite sample boundaries can be controlled by mea
suring the electromotive forces (emf) induced in the
electrochemical cell between the silver electrodes and
corresponding boundaries of the Ag
x
HfSe
2
samples.
As known, the cell emf (
E
) is determined by the differ
ence of the chemical potentials of silver in the sample
and silver in the metallic silver (electrode) according
to the relationship [26, 27]
eE
= ( – ), where
is the chemical potential of silver in metallic silver,
and is the chemical potential of silver in the sam
ple. In the case of ideal solutions, the chemical poten
tial of particles is dependent on their concentration
(
C
) and is determined by the relationship
μ
=
μ
* +
RT
ln
C
. In nonideal systems, concentration
C
must be
replaced by the component activity
a
=
γ
C
, where
γ
is
the activity coefficient.
Figures 3 and 4 show the time dependences of the
electrochemical cell emf for the samples with
x
= 0.1
and
x
= 0.2 after transmitting the ionic current in the
direction from Ag1 to Ag2. In the plots, the emf sign
corresponds to the sign of the metallic electrode
potential. The lower
E
1
(
t
) curves correspond to the left
cell, i.e., to its edge which was connected with the pos
itive pole of the current source during transmitting
current, and it reflects the difference of the chemical
potentials between electrode Ag1 and the left sample
edge. At the initial instant of time after switching off
the current, the values of emf in the lower curves are
close to a zero within the experimental error, and this
fact corresponds to equilibrium with pure silver. At the
opposite cell edge, emf is markedly higher (upper
E
2
(
t
)
curves in Figs. 3 and 4), and this result corresponds to
higher difference of the chemical potentials between
electrode Ag2 and the right sample edge and, thus, to
lower silver concentration (activity) in this crosssec
tion of the samples. As is seen,
E
1
and
E
2
are equalized
in time tending to the same values for each of the sam
ples, which corresponds to the equalization of the sil
μ
Ag
Ag
μ
Ag
smp
μ
Ag
Ag
μ
Ag
smp
750
t
, min
250
0.3
0.2
0.1
0.5
500 1000
E
2
0 1250
0.27 V
E
1
,
E
2
, V
E
1
0
0.4
Fig. 3.
Time dependences of the emf of electrochemical
cells (
E
1
) Ag1/
F
/Ag
0.1
HfSe
2
and (
E
2
) Ag2/
F
/Ag
0.1
HfSe
2
(
F
= RbAg
4
I
5
).
750
t
, min
250
0.3
0.2
0.1
0.5
500 1000
E
2
0 1250
0.235 V
E
1
,
E
2
, V
E
1
0
0.4
Fig. 4.
Time dependences of the emf of electrochemical
cells (
E
1
) Ag1/
F
/Ag
0.2
HfSe
2
and (
E
2
) Ag2/
F
/Ag
0.2
HfSe
2
(
F
= RbAg
4
I
5
).
1380
PHYSICS OF THE SOLID STATE
Vol. 55
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2013
PLESHCHEV et al.
ver concentration along the sample length. These
steadystate values are (235
±
10) mV for Ag
0.1
HfSe
2
and (270
±
10) mV for Ag
0.2
HfSe
2
. After transmitting
the current in the opposite direction (from Ag2 to
Ag1), the initial value of
E
2
is close to a zero. The
curves of the time dependences of the emf for the cor
responding cells are changed by their places, but they
have similar shapes, and this fact demonstrates the
reversibility of the kinetic processes occurring in the
materials under study. This work is an important addi
tion to the previous data of studies of the polarization
phenomena in these materials [14] and confirms the
possibility of coexistence of the ionic charge and
masstransfer in the Ag
x
HfSe
2
compounds.
4. CONCLUSIONS
The ac complex impedance of polycrystalline sam
ples of silverintercalated hafnium diselenide has been
measured for the first time. The impedance spectra
have the shape of semicircles, which corresponds to
the equivalent circuit with parallel connection of an
active resistor and capacitor. It is found that the
increase in the silver content in the Ag
x
HfSe
2
com
pounds decreases the relaxation times from 1.6
×
10
–6
s at
x
= 0.1 to 2.4
×
10
–7
s at
x
= 0.2. These values are
substantially lower as compared to the relaxation times
in Cu
x
HfSe
2
[20]; this fact demonstrates higher charge
carrier mobility in the silverintercalated compounds.
This is also confirmed by the increase in the hopping
frequency, at which the frequency dispersion of the
complex conductivity begins to be observed.
The method of electrochemical cell emf used for
the first time for studying Ag
x
HfSe
2
confirms the con
clusion on the silver ion mobility in these compounds,
which was previously made based on the observation
of the polarization phenomena [14].
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Translated by Yu. Ryzhkov