Ag₂CdI₄ compound belongs to the so called superionic materials of A₂BI₄ type (A = Cu, Ag, In, Tl; B = Hg, Cd, Zn), that undergo phase transition into superionic state. Structural investigation of superionic materials Ag₂HgI₄, Cu₂HgI₄ and others show the existence of low temperature b-phase, as a rule, tetragonal syngony, and high temperature a-phase [1,2]. It is considered that during b®a phase transition iodine sub-lattice remains, while there in a phase A⁺, B²⁺ ions and stoichiometric vacancies, , which are distributed randomly in crystal lattice determine high conductivity of the material.

Ag₂CdI₄ compounds possess smeared phase transitions into the superionic state in the temperature region 330 - 380 K. The solid fast ion conductor Ag₂CdI₄ exhibits a number of solid state phase transitions upon heating. Room temperature, covalent phase Ag₂CdI₄ crystallizes in a well-defined structure. Ag₂CdI₄ at T < 330 K belongs predominantly to hexagonal, with space group P₆/mmm and unit cell dimensions a = 4.578 Ǻ and C = 7.529 Ǻ and changes to cubic at T > 380 K with space group Pm3m and unit cell dimension a = 5.05 Ǻ [3].

Sudharsanan et al. [4,5] studied the IR and Raman spectra of this compound. Bolesta et al., [6] calculated the band structure of Ag₂CdI₄ by semi-empirical method using strong band approximation. Yunakova et al. [7], studied the temperature dependence of the spectral position and half-width of the A band in the range 90 - 430 K in Ag₂CdI₄. Nair et al. [8] studied the behaviour of Ag⁺ in Ag₂CdI₄ by cation substituted smaller Li⁺ and the larger Tl⁺ ions. Beeken et al. [9] tried to determine the effect of Cu-substitution on the conductivity and phase transition temperature of Ag₂CdI₄. Inspired by the results we have tried to prepare Ag₂CdI₄ and study the effect of K⁺ substitution on the conductivity and phase transition temperature of Ag₂CdI₄.

The temperature dependence of conductivity is given by the Arrhenius expression

where n is the number of ions per unit volume, e the ionic charge, l the distance between two jumps positions, n the jump frequency, g the intersite geometric constant, k the Boltzmann constant and DG^*, DS^* and DH^* are activation free energy, entropy and enthalpy terms. The equation can be written in a simpler form as

where s_o = ne2l2ng/k exp (–DS^*/k) and DH^* = Ea, i.e., the activation enthalpy equals experimental activation energy for ionic motion, which may include a defect formation enthalpy contribution [10].

Figure 1 shows a typical heat and cool mode plots of log σT vs 1/T for undoped Ag₂CdI₄, using Equation (4). It observed that the conductivity data were reproducible within experimental error (≤ ±2%) for heating and cooling cycles. The conductivity values of undoped Ag₂CdI₄ were found to have increased slowly initially but a sharp increase in conductivity was noted above 380 K. The presence of hysterisis loop in the heating and cooling phase of conductivity in the unannealed sample of Ag₂CdI₄ confirm the fact that abrupt change in conductivity is due to the phase transition.

Electrical conductivity (σ), measurements were performed on several potassium doped Ag₂CdI₄ sample throughout the temperature range 298 - 473 K. Arrhenius plot of pure Ag₂CdI₄ shows gradual increase in conductivity up to 380 K and above this temperature a sharp change in conductivity indicates the occurrence of phase transition at 380 K (Figure 2). The conductivity data of doped Ag₂CdI₄ samples with K⁺ ion found to exceed in conductivity as compare to the Li⁺ and Na⁺ ions [2,8].

The conductivity increase observed in the present investigation can be explained on the basis of the space charge model reported by Maier et al. [11]. In thermal equilibrium, the surface and grain boundaries of an ionic crystal may carry an electric charge resulting from the presence of excess ions of one sign. This charge is just compensated by a space charge cloud of the opposite sign

adjacent to the boundary. For a pure material, this charge arises if the energies to form anion and cation vacancies or interstitials at the boundary are different. The magnitude and sign of the boundary charge changes if there are aliovalent solutes present in the matrix which alter the concentration of the lattice defects in the crystal. Space charge effects will be predominantly important in very small crystals since the grain boundaries contain a large number of defects compared to the coarser grained polycrystalline materials.

K⁺ ion was chosen as the dopant with the expectation that it would enhance the conductivity of Ag₂CdI₄ on the basis of lattice expansion due to the larger K⁺ radius, (= 133 pm and = 129 pm). But during the course of reaction the conductivity of Ag₂CdI₄ doped with different mol % of K⁺ ions was found to decrease. This observed decrease likely results from decrease in free volume as larger potassium ion entering Ag₂CdI₄ lattice which is unchanging in size. Another important feature observed in the K⁺ doped Ag₂CdI₄ is erratic conductivity behaveiour in the post transition region of 9 and 10 mol% K⁺ doped Ag₂CdI₄. After 433 K the conductivity further decreases which are due to the collapse of framework and subsequently recovered on cooling which implies the restructuring of that sub-lattice [12].

The dielectric constant, e' of Ag₂CdI₄ was calculated over the frequency range 100 Hz to 10 KHz and in the temperature range of 298 - 473 K using relation mentioned in experimental section.

The plot between log e' and temperature (Figure 3), shows almost linear increase in e' with temperature. There is a small upward shift in the values of e' with decrease of frequencies near the transition temperature of Ag₂CdI₄, the slope of the graph before and after the transition remains the same.

This increase in dielectric constant of Ag₂CdI₄ with temperature may be attributed due to the reason that the

molecules cannot orient themselves in dielectrics. As temperature rises, the orientation of dipoles is facilitated and ionic polarization increases resulting in the increase of dielectric constant (e') [13,14]. Also at higher temperatures, the conductivity due to the hopping of mobile ions becomes important and increased dielectric constant results.

According to Samara [15], higher the dielectric constant of an ionic crystal, lower the energy of formation of lattice defects. Since the grain boundary of nanoparticles contain a large density of defects [16,17], it can be argued that the dielectric constant of nanoparticles should have higher values.

Nano-crystalline materials consist of grain or interphase boundaries. These boundaries contain defects such as dangling bond, vacancies, vacancy clusters etc. [18]. These defects can cause a positive or negative space charge distribution at interfaces. The space charges can move under the application of an external field and when they are trapped by the defects, lots of dipole moments are formed (space charge polarization). Hence the space charge effect will be an important factor which decides the dielectric properties in materials with small particles sizes [11]. In addition, ion jump polarization may also be greater in nanocrystalline materials since there will be a number of position in the grain boundaries for the ions to occupy. Thus the high values of the dielectric constant in Ag₂CdI₄ may be attributed to the increased ion jump orientation effect and the increased space charge effect exhibited by nanoparticles.

Electrical conductivity (σ) plots of several K⁺ doped Ag₂CdI₄ samples show decrease in conductivity. This observed decrease in conductivity was due to decrease in free volume which results from the larger potassium ion entering Ag₂CdI₄ lattice. The erratic conductivity behaveiour observed in the post transition region of K⁺ doped Ag₂CdI₄ was due to the collapse of CdI₄ framework. The dielectric constant of Ag₂CdI₄ was found to increase with temperature which facilitates the orientation of dipoles in Ag₂CdI₄.

We thankfully acknowledge Department of Chemistry, Aligarh Muslim University, Aligarh, India, for providing necessary facilities to carryout this work.