A new anomalous relaxation function and electrical properties of disordered materials

Abstract

A new anomalous relaxation function φ*( t)=exp [− t/ τ*] is obtained, where τ*= τ g / i (1− g) , i= −1 . The exponent g is the phase or loss factor, related to the impedance loss through the tan ( δ p) at the impedance loss peak frequency ω p=1/ τ g . Origin of the g( δ p) is attributed to the free energy barrier variations because of the non-periodic potential and many-body interactions of the mobile charges in disordered material medium. The φ*( t) has the stretched exponential behavior and the phase factor g( δ p) is responsible for the stretching of relaxation time. Many experimentally known features of the real part, σ′( ω), of the complex conductivity σ*( ω) and the imaginary part, ε″( ω), of the complex permittivity ε*( ω) are explained satisfactorily. The experimental data of doped crystalline and glassy materials are analysed and results show excellent agreement.