# Ionic Conductivity and Phase Transition Behaviour in 4AgI-(1-x)PbI2-2xCuI System

Authors: Mohammed Hassan; Rafiuddin
Journal: Research Letters in Physics
 (2008)

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## Abstract

Samples of general formula 4AgI-(1-x)PbI2-2xCuI, x=0–0.4, have been prepared and investigated by XRD, DSC, and temperature-dependent conductivity studies. X-ray diffractograms showed the presence of binary system consisting of AgI and PbI2 in the sample x=0. Cu-substituted samples showed very similar diffractograms to that of the pure compound which indicates that no effect for the substitution on the nature of the binary system. DSC curves showed the presence of phase transition whose temperature increased with Cu+ ratio in the system. Ionic conductivity measurements confirmed the occurrence of the phase transition and showed that the high temperature phase is superionic conducting, whose conductivity increases with the increasing Cu+ amount in the system.


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## Body

## 1. Introduction

Superionic conductors are solid
compounds in which electric current is carried by charged atoms, that is, by ions. The passage
of current is thus associated with mass transfer. Such ionic conductors are
sometimes called “solid electrolytes,” by analogy to liquid electrolyte
solutions, and have permitted development of a new scientific discipline,namely, solid state electrochemistry. The associated technology is termed
solid-state ionics, in contrast to solid-state electronics.AgI is the most investigated
superionic conductor which has high ionic conductivity in itsα-phase stable
above 147°C. Below 147°C silver iodide exists in
several modifications based on zinc blend and wurtzite structures, both of
which favour ionic diffusion via face sharing polyhedra. Many attempts have
been made to stabilize this high conducting phase at room temperature by
substitution leading to a growing group of silver ion conductors in which the
transitions temperatures to the superionic phase are lower or higher than that
of the α-AgI.(AgI)x(PbI2)1-x is one such system which
has been studied extensively owing to the improved transport properties of AgI.
The phase diagram of the system was studied by many workers [1–4]. The recent work
by Hull et al. [5] has shown that the system contains a superionic phase of composition
4AgI-PbI2 stable at T≥400K. This phase has the ionic conductivity
of 0.1Scm−1. The structure of the phase has been resolved and was
found to have an fcc Structure I− sublattice with majority of
cations (over 90%) located in octahedral 4(b) cavities and the remainder within
tetrahedral 8(c) interstices. Extensive work has been done to study the effect
of substitution of mobile cation on the ionic conductivity of AgI-based
superionic conductors. However, not much work seems to have been done on the
substitution of immobile cations. The present
work is an attempt to study the effect of substitution of immobile
cation Pb+2 by Cu+ on the ionic conductivity, phase transition temperature, and dielectric
constant of 4AgI-PbI2 system. Two Cu+ ions replace each Pb+2 ion; therefore, the extra Cu+ ion
is expected to occupy interstitial position and participate in the conduction
process thereby enhancing the ionic conductivity of the system.


## 2. Experimental

AgI was prepared by the precipitation from
ammonical silver nitrate solution by the addition of ammonium iodide solution.PbI2 was prepared by the precipitation
from lead nitrate solution by potassium iodide. CuI was taken from Ottockemi, India,
with stated purity of 99%. Appropriate amounts of the
starting materials were mixed to produce the series 4AgI-(1-x)PbI2-2xCuI where x=0–0.4. The materials were then heated for 20 hours
at 480 K with intermittent grinding.Pellets for conductivity
and capacitance measurements were prepared by pouring different molar ratio
mixtures into stainless steel die and pressed under the pressure of 4 tonnes/cm2 with the help of a
hydraulic press. All the samples were annealed at 310 K for 6 hours to
eliminate any grain boundary effects. The pellet was mounted on stainless steel
sample holder between two copper leads using two polished platinum electrodes.
The copper leads were electrically insulated from the holder by Teflon sheets.
The electrical conductivity and capacitance of  samples were measured in the temperature
range of 300 K–470 K using Gen Rad 1659 RLC Digibridge at a single frequency
of 1 KHz. The heating rate was maintained at 2°C/min.Impedance measurements were performed
using HIOKI3532-50 LCR meter in the frequency rang of 40 Hz–5 MHz. DSC scanning
was traced by Perkin Elmer instrument using alumina as a reference. XRD were
recorded using RIGAKU D/MAX-B diffractometer withCuKα radiation.


## 3. Results and Discussion

### 3.1. X-Ray Diffraction and DSC

X-ray diffractograms of the pure and substituted samples are
shown in Figure1. Two phases can be identified in the diffractogram of the
pure compound, namely, AgI and PbI2. This agreed with the previous
studies which reported that the fcc high temperature phase whose formula is Ag4PbI6 dissociates to its primary compounds at temperatures below the phase transition
temperature [5]. The substituted samples show very similar
diffractograms to those of the pure system. Substitution by Cu+ does
not seem to affect the crystal structure of the final mixture and Cu+ ions
appeared to occupy the voids in the lattices of the binary system, since no
peaks related to CuI can be identified in the diffractograms.Room temperature X-ray diffractograms of4AgI-(1-x)PbI2-2xCuI samples.
(a)(b)(c)(d)DSC curves of the pure and substituted samples are shown in
Figure2. The pure compound shows the expected thermal arrest at the
temperature 130°C which was reported to be originated from the
formation of the fcc superionic phase [5]. Substituted compounds showed gradual
increase in the phase transition temperaturewith Cu+ ratio
without any saturation observed within the concentration range studied. The α-β transition
temperature in AgI has also increased upon incorporating Cu+ in its
lattice [6]. No Other peaks were observed in the DSC curve of these samples
other than a very weak arrest which was detected at 177°C in the
sample 4AgI-0.4PbI2-0.8CuI which
might have resulted from insignificance decomposition of the superionic phase
at high concentrations of Cu+. The absence of any thermal arrest before
the phase transition temperature indicates that the binary system persists below
this temperature without any other phase formation.Figure 2
DSC curves of4AgI-(1-x)PbI2-2xCuI samples.The variation in the phase
transition temperature with the incorporation of substituent ion can be attributed to two reasons: (i)
the distortion of the lattice due to the “wrong” sized  substituent and (ii) the
increased  defect concentration in the lattice lead to the stronger
defect-defect interaction which affects the phase transition temperature.The relation between the defect-defect interaction and phase
transition temperature is given [7] by
(1)T=W−λ/2k(1+ln⁡ν),
where W
is the energy difference between the interstitial position and the lattice
sites, λ represents the defect-defect interaction
parameter and ν=((ω1/ω2)3(N1/N2)), ω1, and ω2 are the
vibration frequencies of the ions at interstitial positions and lattice sites,
N1 and N2 are the number of interstitials and original
lattice sites per unit volume and k is Boltzmann's constant. However, the crucial role in
affecting the phase transition temperature arises from lattice distortion which
is proportional to size mismatch between the host and guest cation [8].


### 3.2. Electrical Conductivity

Complex impedance plots of the investigated samples are shown
in Figure3. They are typical plots of ionic conductors showing a semicircle at
high frequency side and a spike at lower frequency for
all of the samples. Two overlapped semicircles are shown in case of Ag4Pb0.7Cu0.6I6 sample, the one at higher frequency resulted from bulk resistance while
that at low frequency results from grain boundary resistance contribution.  The relaxation times of the two contributions
are very close in the other sample which results in a depressed semicircle. The
spike in the lower frequency range is attributed to the blocking electrodes due
to ion migration. The appearance of the spikes is an indication that the
conduction in these materials is ionic in nature [9].Rom temperature complex impedance spectra of4AgI-(1-x)PbI2-2xCuI samples.
(a)(b)The temperature dependence of ionic
conductivity is given by the Arrhenius expression,(2)σT=σ0exp⁡(−EakT),
where σ0 is the
pre-exponential  factor and Ea is the activation energy of ionic motion.Arrhenius plots of the samples are shown in Figure4.
Ionic conductivity measurements showed higher phase transition temperature in
Cu-substituted samples which is in agreement with the DSC results.Figure 4
Arrhenius plots of4AgI-(1-x)PbI2-2xCuI samples.The ionic
conductivity decreased gradually with increasingCu+ ratio in the
low temperature region while significant enhancement is observed at the high
temperature phase. Cu+, which is less mobile than Ag+,
accumulates in the vacancies available in the lattice of AgI and partially
blocks Ag+ ions motion through these vacancies leading to the
overall decrease in the ionic transport. While in the high temperature region,
the conductivity results from the hopping of the interstitial Ag+ ions, hence the presence of Cu+ does not block the migration of these
ions but enhances the ionic conduction through its mobility in the lattice.The activation energies calculated from the slope of
Arrhenius plot in the low and high temperature regions are presented in Table1.
Significant enhancement in the activation energies of Cu-substituted samples is
observed in the low temperature region. This directly reflects the increase of
the potential barrier which has to be overcome by the mobile ion to hope from
one position to another. The increase in activation energy in the substituted
samples is due to the restricted movement of Ag+ ions due to the substitution. The comparable values of
the activation energies for the various substitutions suggest that an identical
hopping mechanism is responsible for the transport in all the samples [10].Table 1
Activation energies in the low and high temperature regions of4AgI-(1-x)PbI2-2xCuI samples.
x/mole fractionActivation energies in prephase transition region/eVActivation energies in postphase transition region/eVx=00.2620.118x=0.10.4200.304x=0.20.4390.199x=0.30.4570.195x=0.40.4650.150The activation energies in the high temperature region
are much lower than those in the low temperature region which is explained by
the greater disorder possessed by the high temperature phase. In general, Cu-substituted
samples show higher activation energies compared to the pure one. In
spite of the enhancement of conductivity which results from the participation
ofCu+ in the conduction process, replacement of the larger size cation
(rPb+2=1.21Å) by the smaller one (rCu+=0.67Å) leads to the contraction of the lattice  of the high temperature phase and
hence decreasing the bottle-neck size through which ion hopping takes place.
Therefore, higher thermal energy is required by Ag+ ion to overcome
this potential barrier. Activation energy decreases in
the high temperature region which is explained by the increasing
importance of Cu+ conduction at the higher concentrations of the ion.


## 3.1. X-Ray Diffraction and DSC

X-ray diffractograms of the pure and substituted samples are
shown in Figure1. Two phases can be identified in the diffractogram of the
pure compound, namely, AgI and PbI2. This agreed with the previous
studies which reported that the fcc high temperature phase whose formula is Ag4PbI6 dissociates to its primary compounds at temperatures below the phase transition
temperature [5]. The substituted samples show very similar
diffractograms to those of the pure system. Substitution by Cu+ does
not seem to affect the crystal structure of the final mixture and Cu+ ions
appeared to occupy the voids in the lattices of the binary system, since no
peaks related to CuI can be identified in the diffractograms.Room temperature X-ray diffractograms of4AgI-(1-x)PbI2-2xCuI samples.
(a)(b)(c)(d)DSC curves of the pure and substituted samples are shown in
Figure2. The pure compound shows the expected thermal arrest at the
temperature 130°C which was reported to be originated from the
formation of the fcc superionic phase [5]. Substituted compounds showed gradual
increase in the phase transition temperaturewith Cu+ ratio
without any saturation observed within the concentration range studied. The α-β transition
temperature in AgI has also increased upon incorporating Cu+ in its
lattice [6]. No Other peaks were observed in the DSC curve of these samples
other than a very weak arrest which was detected at 177°C in the
sample 4AgI-0.4PbI2-0.8CuI which
might have resulted from insignificance decomposition of the superionic phase
at high concentrations of Cu+. The absence of any thermal arrest before
the phase transition temperature indicates that the binary system persists below
this temperature without any other phase formation.Figure 2
DSC curves of4AgI-(1-x)PbI2-2xCuI samples.The variation in the phase
transition temperature with the incorporation of substituent ion can be attributed to two reasons: (i)
the distortion of the lattice due to the “wrong” sized  substituent and (ii) the
increased  defect concentration in the lattice lead to the stronger
defect-defect interaction which affects the phase transition temperature.The relation between the defect-defect interaction and phase
transition temperature is given [7] by
(1)T=W−λ/2k(1+ln⁡ν),
where W
is the energy difference between the interstitial position and the lattice
sites, λ represents the defect-defect interaction
parameter and ν=((ω1/ω2)3(N1/N2)), ω1, and ω2 are the
vibration frequencies of the ions at interstitial positions and lattice sites,
N1 and N2 are the number of interstitials and original
lattice sites per unit volume and k is Boltzmann's constant. However, the crucial role in
affecting the phase transition temperature arises from lattice distortion which
is proportional to size mismatch between the host and guest cation [8].


## 3.2. Electrical Conductivity

Complex impedance plots of the investigated samples are shown
in Figure3. They are typical plots of ionic conductors showing a semicircle at
high frequency side and a spike at lower frequency for
all of the samples. Two overlapped semicircles are shown in case of Ag4Pb0.7Cu0.6I6 sample, the one at higher frequency resulted from bulk resistance while
that at low frequency results from grain boundary resistance contribution.  The relaxation times of the two contributions
are very close in the other sample which results in a depressed semicircle. The
spike in the lower frequency range is attributed to the blocking electrodes due
to ion migration. The appearance of the spikes is an indication that the
conduction in these materials is ionic in nature [9].Rom temperature complex impedance spectra of4AgI-(1-x)PbI2-2xCuI samples.
(a)(b)The temperature dependence of ionic
conductivity is given by the Arrhenius expression,(2)σT=σ0exp⁡(−EakT),
where σ0 is the
pre-exponential  factor and Ea is the activation energy of ionic motion.Arrhenius plots of the samples are shown in Figure4.
Ionic conductivity measurements showed higher phase transition temperature in
Cu-substituted samples which is in agreement with the DSC results.Figure 4
Arrhenius plots of4AgI-(1-x)PbI2-2xCuI samples.The ionic
conductivity decreased gradually with increasingCu+ ratio in the
low temperature region while significant enhancement is observed at the high
temperature phase. Cu+, which is less mobile than Ag+,
accumulates in the vacancies available in the lattice of AgI and partially
blocks Ag+ ions motion through these vacancies leading to the
overall decrease in the ionic transport. While in the high temperature region,
the conductivity results from the hopping of the interstitial Ag+ ions, hence the presence of Cu+ does not block the migration of these
ions but enhances the ionic conduction through its mobility in the lattice.The activation energies calculated from the slope of
Arrhenius plot in the low and high temperature regions are presented in Table1.
Significant enhancement in the activation energies of Cu-substituted samples is
observed in the low temperature region. This directly reflects the increase of
the potential barrier which has to be overcome by the mobile ion to hope from
one position to another. The increase in activation energy in the substituted
samples is due to the restricted movement of Ag+ ions due to the substitution. The comparable values of
the activation energies for the various substitutions suggest that an identical
hopping mechanism is responsible for the transport in all the samples [10].Table 1
Activation energies in the low and high temperature regions of4AgI-(1-x)PbI2-2xCuI samples.
x/mole fractionActivation energies in prephase transition region/eVActivation energies in postphase transition region/eVx=00.2620.118x=0.10.4200.304x=0.20.4390.199x=0.30.4570.195x=0.40.4650.150The activation energies in the high temperature region
are much lower than those in the low temperature region which is explained by
the greater disorder possessed by the high temperature phase. In general, Cu-substituted
samples show higher activation energies compared to the pure one. In
spite of the enhancement of conductivity which results from the participation
ofCu+ in the conduction process, replacement of the larger size cation
(rPb+2=1.21Å) by the smaller one (rCu+=0.67Å) leads to the contraction of the lattice  of the high temperature phase and
hence decreasing the bottle-neck size through which ion hopping takes place.
Therefore, higher thermal energy is required by Ag+ ion to overcome
this potential barrier. Activation energy decreases in
the high temperature region which is explained by the increasing
importance of Cu+ conduction at the higher concentrations of the ion.


## 4. Conclusion

The electrical conductivity and phase
transition behaviour in the system4AgI-(1-x)PbI2-2xCuI were
investigated. Formation of the fcc superionic phase at temperatures larger than
130°C in the pure and substituted compounds was confirmed by DSC as
well as electrical conductivity measurements. X-ray measurements
showed the presence of binary system at lower temperatures with no effect of
the substitution. The ionic conductivity enhanced markedly in the high
temperature phase with the incorporation of Cu+. Unfortunately, this
enhancement comes at the expense of the increasing phase transition temperature
beyond that of the unsubstituted system.



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