Premium
A new method of calculating interatomic spacing: the equal‐ratio method
Author(s) -
Fan Quncheng
Publication year - 2019
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/s1600576719001018
Subject(s) - atom (system on chip) , hexagonal crystal system , crystallography , crystal (programming language) , crystal structure , lattice (music) , atomic physics , physics , chemistry , computer science , acoustics , embedded system , programming language
Based on a simple principle of analytical geometry, a new equal‐ratio method has been developed to calculate the interatomic spacing of crystal structures. If an atom ( x 2 , y 2 , z 2 ) or its equi‐position atom ( e + x 2 , f + y 2 , g + z 2 ) ( e , f and g are integers) is located at the 1/ r ≤ 1 of one interatomic spacing period d ′ [ uvw ] on the [ uvw ] atomic row passing through the atom ( x 1 , y 1 , z 1 ), the distance between the two atoms can be calculated by the formula d [ uvw ] (1/ r ) = d ′ [ uvw ] / r , where d ′ [ uvw ] = ( u 2 a 2 + v 2 b 2 + w 2 c 2 + 2 uvab cosγ + 2 vwbc cosα + 2 uwac cosβ) 1/2 is the interlattice point spacing of the corresponding primary lattice of the crystal structure, 1/ r is the interatomic spacing coefficient, and r is equal to the reciprocal of the common factor of ( x 2 − x 1 ), ( y 2 − y 1 ) and ( z 2 − z 1 ). The reliability and advantages (no auxiliary view is required, suitable for arbitrary directions and for all crystal structures) of the equal‐ratio method have been examined by calculations for the β‐cristobalite SiO 2 structure and Cu 3 Au I superstructure as well as face‐centred cubic, body‐centred cubic and hexagonal close‐packed structures.