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A further solution for a two‐dimensional model of crystal‐growth disorder
Author(s) -
Welberry T. R.
Publication year - 1977
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/s0021889877013582
Subject(s) - lattice (music) , statistical physics , symmetry (geometry) , constraint (computer aided design) , crystal (programming language) , statistical model , crystal growth , crystal structure , atom (system on chip) , reflection symmetry , plane (geometry) , reflection (computer programming) , physics , condensed matter physics , materials science , mathematics , crystallography , chemistry , geometry , computer science , thermodynamics , statistics , programming language , acoustics , embedded system
The paper refers to a previously described two‐dimensional model of crystal‐growth disorder in which the type of molecule or atom at a given lattice site is dependent on the previous neighbour in the two crystal directions. It is shown that a special case of the model for which some mathematical and simulation results have been published corresponds to the situation when the statistical properties of the lattice are symmetric to reflection in a plane. This symmetry may be achieved by applying a constraint to the growth probability parameters and, moreover, enables a solution to be found for the statistical properties of the lattices.