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A new method of calculating planar density: the position‐duplication‐number method
Author(s) -
Fan Quncheng
Publication year - 2016
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/s1600576716010827
Subject(s) - planar , bravais lattice , position (finance) , plane (geometry) , hexagonal crystal system , crystal (programming language) , crystallography , crystal structure , geometry , physics , mathematics , materials science , chemistry , computer science , computer graphics (images) , finance , programming language , economics
The traditional method of calculating planar density requires an auxiliary sectional view showing the arrangement of atoms on the plane, this being very difficult for those planes with higher indices. In the present paper, a new position‐duplication‐number method is developed to calculate the planar density of all Bravais lattices and all crystal structure types using the formula ρ ( hkl ) ( m / q ) = N ( hkl ) ( m / q ) d ′ ( hkl ) / V cell . The new method is illustrated for calculating planar densities of the (110) and (579) planes of the β‐cristobalite SiO 2 structure, with additional examples in hexagonal close‐packed, face‐centred cubic and body‐centred cubic systems. These examples show the advantages of the new method: it does not require any auxiliary sectional view, and it is suitable for all crystal structures and all plane indices.