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Theory of the Power Spectrum and Scattering Properties of Three‐Dimensional Disordered Systems Having a Variable Degree of Short‐Range Order. I. Continuous Spectrum
Author(s) -
Celasco M.,
Mazzetti P.,
Stepanescu A.
Publication year - 1984
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221220204
Subject(s) - lattice (music) , mathematics , spectral density , position (finance) , statistical physics , convolution (computer science) , invariant (physics) , scattering , spectrum (functional analysis) , degree (music) , mathematical analysis , physics , quantum mechanics , computer science , mathematical physics , statistics , artificial neural network , economics , acoustics , finance , machine learning
A new approach to power spectrum calculation of structures characterized by a spatial distribution of localized physical events, which has the advantage of being flexible enough to describe practically any type of local order and of giving the results in a very compact and general form, is given. Starting from a completely ordered three‐dimensional structure, with the elementary events arranged according to an arbitrary crystallographic order, the disorder is introduced by displacing the elementary events from their lattice position. The displacements are described from a probabilistic point of view by means of three general distribution functions which can be related to the interaction forces acting between nearest neighbour events and using a convolution technique for describing self‐consistently the whole structure, whose statistical properties remain translationally invariant. A simple analytic expression is obtained where different degrees of short‐range order with any local crystallographic configuration can be introduced and characterized.