Phenomenological description of order-disorder by means of general correlation functions I. General properties of correlations functions. Disordered state

Abstract

A concept of phenomenological description of order-disorder in binary systems is developed in which the necessity of macroscopic character of ordering parameters is emphasized. Particular configurations of the system are described by means of so-called marking functions. Correlation functions of marking functions are determined for certain configurations and their properties are analyzed. The mean values of correlation functions over configurational ensemble related to the preparation of the sample are defined as ordering parameters, refering to the correlation between arbitrary complexes of ions. The connection between mean correlation functions andn-density functions introduced by Murakami and Ono is found. The averages, mean square fluctuations and statistical moments of correlation functions and of their Fourier transforms are evaluated for the case of completely disordered state. The functions introduced in the paper are e.g. suitable for the description of relaxation phenomena due to two magnon scattering in non-stoichiometric ferromagnets. Especially, the Fourier transform of the two-ion correlation function was proved to be proportional to the amplitude of two-magnon scattering.