The use of quantum green functions for the calculation of the frequency spectrum of the lattice vibrations of isotopic binary substitutional alloys. I

Abstract

The paper derives a new method for the calculation of the frequency spectrum of isotopic binary substitutional alloys. The distribution of the admixture in the alloys is described by means of an operator field. Thus an equation for the quantum Green function in the form of functional derivatives can be formulated. In a purely analytical way two methods of successive approximations for the solution of this equation and the expansion in the form of a series in powers of the mass defect are deduced. In the second part of the paper an expansion of the solution in the form of a series of concentrations of the admixture is deduced and a more detailed discussion of the character of the frequency spectrum is performed.