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The number of independent pair‐correlation functions in multicomponent systems
Author(s) -
De Fontaine D.
Publication year - 1971
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889871006174
Subject(s) - ternary operation , overline , interpretation (philosophy) , quadratic growth , order (exchange) , mathematics , range (aeronautics) , diffraction , crystal (programming language) , physics , chemistry , mathematical analysis , materials science , quantum mechanics , particle physics , finance , computer science , economics , composite material , programming language
An n ‐component substitutional solid solution in a perfect crystal can be characterized uniquely by n −1 independent composition functions. There are n ( n −1)/2 distinct short‐range‐order parameters α ij ( i,j = 1,2,... n −1) corresponding to these ( n −1) independent compositions. The SRO parameters are linearly but not quadratically independent: for example, in ternary systems, the following equation holds Σ[(1 −_{1}) (1 −2)α11α22 −1 2α 12 α 21 ] = 0 in which 1 and 2 are the average compositions pertaining to atomic species 1 and 2, the summation extending over all significant correlation ranges in the crystal. This relation can be used to reduce the uncertainty relative to the interpretation of diffraction experiments realized with less than the optimum number of radiations.