A new anomalous relaxation function and electrical properties of disordered materials

A new anomalous relaxation function φ*(t)=exp [−t/τ*] is obtained, where τ*=τg/i(1−g), i=−1. The exponent g is the phase or loss factor, related to the impedance loss through the tan (δp) at the impedance loss peak frequency ωp=1/τg. Origin of the g(δp) 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(δp) 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.