Analysis of electrical relaxation in lithium phosphate glasses

Abstract

The non-Debye relaxation (NDR) behavior in disordered solids is characterized either by the empirical form of stretched exponential ϕ( t)=exp[−( t/ τ) β ] or by the Curie–von Schweidler law j( t)∝ t − n . The physical meaning for the exponents β and n is described in terms of energy processes, where the smallness of the exponent β or n characterizes the degree of non-Debye behavior. In the frequency domain, the non-Debye behavior shows dispersion in conductivity σ′( ω)∝ ω n and permittivity loss ɛ″( ω)∝ ω n−1 above loss peak frequency ω p and are termed as Jonscher universal power law or Jonscher universal dynamic response. In the present article, the universal dynamic response is described using a non-Debye relaxation function ϕ( t)=exp[− t/ τ*], where τ*= τ g / i (1− g) and τ* is defined as non-Debye relaxation time. Correspondingly, in the frequency domain, the dielectric response function ɛ*( ω)= ɛ ∞+[( ɛ S− ɛ ∞)/(1+ i g ωτ g )] has a phase factor i g . The physical meaning for the exponent g is described in terms of energy processes. At the dielectric loss peak frequency, the dielectric loss tan[ δ p] which signifies the energy dissipation, attains a minimum and it is related to the exponent g. Expressions for real part of the ac conductivity σ′( ω) is derived from the permittivity loss, ɛ″( ω). All experimentally known features of the σ′( ω) and ɛ″( ω) are explained satisfactorily. The present model is used to analyze the experimental data of lithium phosphate glassy system. The results show an excellent agreement both in the conductivity and impedance representation.