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Stereological characteristics of atomic arrangements in crystals
Author(s) -
Mackay A. L.
Publication year - 1972
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1972.tb03721.x
Subject(s) - polyhedron , voronoi diagram , atom (system on chip) , dirichlet distribution , crystal (programming language) , simple (philosophy) , measure (data warehouse) , spheres , volume (thermodynamics) , crystal structure , statistical physics , crystallography , computer science , materials science , physics , combinatorics , mathematics , geometry , chemistry , mathematical analysis , data mining , thermodynamics , philosophy , epistemology , astronomy , programming language , boundary value problem , embedded system
SUMMARY A major problem in dealing with complex structures is to identify simple parameters which will summarize significant information. For crystal structures the simplest measure is volume per atom. The Voronoi polyhedron (or Dirichlet region) about each atom can be calculated exactly or statistically. This has been done for a number of structures with unexpected results. Algorithms for examining the local atomic configurations by the calculation of N ‐dimensional volumes are described. Other proposals for the statistical examination of known crystal structures are put forward. Crystals are significant in themselves and in that they provide model structures which can be handled exactly. Formulæ, convenient for handling the packing of spheres and polyhedra in N dimensions, are listed.