Lognormal Distribution Function for Describing Anelastic and Other Relaxation Processes I. Theory and Numerical Computations

Such phenomena as dielectric, magnetic, and anelastic relaxation are often described in terms of a distribution of relaxation times. It is shown that a relaxation process which exhibits a Gaussian distribution in the logarithm of the relaxation times (a “lognormal” distribution) can be specified completely by three parameters. These are: the mean relaxation time (τ
m
), the width of the distribution (β), and the magnitude of the relaxation (δJ). The relationships of these parameters to experimentally measurable functions are usually complicated. These relationships were obtained in numerical form by machine computation. Finally, a simple formula is derived which expresses the parameter β in terms of the widths of the distribution of the activation energies and that of the attempt frequencies.