Variations in ß(T)-function due to addition of LiI-4AgI system

Univ. Sci. 22 (2): 113-121, 2017. doi: 10.11144/Javeriana.SC22-2.vifd Bogotá original article Variations in β(T)-function due to addition of LiI-4AgI system Carlos Alberto Lozano Zapata1 a, Diego Peña Lara2 b, Hernando Correa Gallego3 c Edited by Juan Carlos Salcedo-Reyes () 1. Grupo de Estadística y Matemática Aplicada, Pontificia Universidad Javeriana, Cali, Colombia. 2. Departamento de Física, Universidad del Valle, A.A. 25 360, Cali, Colombia. 3. Laboratorio de Optoelectrónica, Universidad del Quindío, Armenia, Colombia. a. b. c. Received: 13-09-2016 Accepted: 10-05-2017 Published on line: 26-05-2017 Citation: Lozano Zapata CA, Peña Lara D, Correa Gallego H. Variations in β(T)-function due to addition of LiI-4AgI system, Universitas Scientiarum, 22 (2): 113-121, 2017. doi: 10.11144/Javeriana.SC22-2.vifd Funding: N/A Electronic supplementary material: N/A Abstract Impedance spectroscopy measurements of the LiI-4AgI samples, in the frequency range 20 Hz–1 MHz, and in the temperature range between 353 K and 378 K were made. Both pure and lithium-doped silver iodide showed blocking phenomena in the electrodes and the grain boundary. The blocking phenomena allowed a change in the transport properties of the pure compound in respect to the doped compound as the temperature varied. The curves of electrical modulus in the LiI-4AgI system show asymmetric peaks corresponding with a weak correlation between mobile ions in the diffusion process. The electrical conductivity in the AgI-LiI system can be described using a stretched relaxation function of the Kohlrausch-Williams-Watts (KWW) type. We speculat e that the phase of lithium dissolved in the silver iodide favors the formation of islands that disperses the conductivity due to the modification of the relationship among the microscopic energies: microscopic energy and migration energy. Keywords: Electrical modulus; Ionic conductivity; Silver iodide; Lithium iodide; KWW function. Introduction The high diffusion of ions in the so-called superionic or fast-ion conductor materials can be seen in the superionic phase for temperatures T ≥ Tt , where Tt is the transition temperature from low-conducting to high-conducting phases. The influence of mobile ions such as Na+ , Li+ , Ag+ [1,2], among others, has been studied in these systems. The phase transition is characterized by an abrupt increase in ionic conductivity, a low activation energy, a latent heat typical for a first-order transition, a crystalline structure with vacancies available for mobile ions, and, in general, a change in the symmetry of the lattice. For these materials the structural disorder, below the melting point, is important for the increase of the ionic diffusion rate when either it is heated or a voltage is applied. One of the most used experimental techniques to characterize the dynamics of ionic transport is the so-called impedance spectroscopy. In order to study the dielectric Universitas Scientiarum, Journal of the Faculty of Sciences, Pontificia Universidad Javeriana, is licensed under the Creative Commons Attribution 4.0 International Public License 114 Variations in β(T)-function properties of materials using the impedance spectroscopy technique, an impedance bridge is used. It provides conductance (G), capacitance (C), and phase angle (θ) measurements as a function of the angular frequency ω [3]. All the experimental information about electric relaxation at a given temperature is found in G[ω] and C[ω]. These physical quantities are transformed in the complex permittivity ε? [ω], complex conductivity σ ? [ω] = jωε? [ω], complex resistivity ρ? [ω] = 1/σ ? [ω], and complex electrical modulus M ?[ω] = 1/ε?[ω] [4]. Electric answer due to ion dynamics By applying a Heaviside step function to the electric displacement vector D, we have that for t > 0 the internal electric field E decreases due to the ion conventional hopping mechanism. This condition is expressed mathematically introducing the cm [t] function [5,6], that defines the electric field change with time: E[t] = cm [t]E[0] (1) cm [t] represents the relaxation of E at the interior of the material when a step function is applied to D, E[0] is the value of E at the instant t > 0: D0 E[0] = (2) ε0 ε∞ where ε0 is the electrical permittivity of vacuum and ε∞ is the electrical permittivity at the high-frequency limit. The time derivative of (1) is: dE[t] D0 dcm [t] = . dt ε0 ε∞ dt (3) By denominating Φm [t] = − dcm [t] dt (4) as the relaxation function and integrating the Eq. (3)   Z t 1 0 0 E[t] = D[t] − D0 Φm [t ]dt ε0 ε∞ 0 (5) In the Eq.(5), the notation E[t] and D[t] are defined over the whole interval −∞ < t < ∞. Fourier transform of (5) is: E[ω] = D[ω](1 − Φm [ω]) ε0 ε∞ (6) where Φm [ω] is the electrical susceptibility. From (6) and D[ω] = ε0 ε[ω]E[ω], the electrical modulus is: M ? [ω] = M∞ (1 − Φm [ω]) (7) being M∞ ≡ 1/ε∞ . For the case of an assembly of dipoles or ions non-correlated or Debye behavior (cm [t] ∼ e−t/τ ), the electrical modulus would be:    Z ∞ de−t/τ −jωt M ? [ω] = M∞ 1 − − e dt dt 0 √ with j = −1. Universitas Scientiarum Vol. 22 (2): 113-121 (8) http://ciencias.javeriana.edu.co/investigacion/universitas-scientiarum 115 Lozano Zapata et al. The solution of (8) gives the spectrum of M ? [7]:   1 ? M [ω] = M∞ 1 − 1 + jωτ (9) For the case of some compounds that do not follow the Debye type behavior, i.e., when the interactions between the ions and the structural disorder are taken into account, Havriliak-Negami proposed a susceptibility function of the form [8]: Φm,HN [ω] = 1 [1 + (jωτHN )α ]γ (10) where the exponents α, γ and the characteristic time τHN are chosen in such a way that they satisfy the experimental data which are asymmetric curves of slope different from one for the right branch, therefore expression (7) may be rewritten as:   ∂cm [t] M ? [ω] =F (11) 1− M∞ ∂t where the new susceptibility must be equal to the susceptibility for the Debye case, multiplied by the time distribution function: Φm,HN = ρ[t] 1 1 + jωτ (12) carrying out the inverse transform: β cm [t] = e−(t/τ ) [T ] (13) That is, a stretched relaxation function of the Kohlrausch-Williams-Watts (KWW) type [9,10]. Thus the expression (8) takes the form M ? [ω] = M∞    Z ∞ β ∂ e(−t/τ ) −jωt e dt 1− − ∂t 0 (14) This is the expression used to fitting experimental data. Preparations of samples Polycrystalline AgI powder were recrystallized using the solution technique with highpurity reagents [11] starting from 99.99% (Aldrich) high-purity compound. Pure single crystals of 0.5 cm in diameter were achieved. The obtained single crystals were subjected to thermal treatment at 413 K during 24 hours before the measurements to eliminate the γ-phase. The single crystals of chemical composition LiI-4AgI were prepared using the same method, mixing AgI and LiI Aldrich compounds of 99.99% in purity. During the recrystallization process, both AgI and LiI compo (...truncated)