A new method of calculating interatomic spacing: the equal‐ratio method

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Marco E. Ciriotti
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A new method of calculating interatomic spacing: the equal‐ratio method

Messaggio da Marco E. Ciriotti » ven 05 apr, 2019 13:26

Referenza:
▪ Fan, Q. (2019): A new method of calculating interatomic spacing: the equal‐ratio method. Journal of Applied Crystallography, 52, 289-295.

Abstract:
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 (x2, y2, z2) or its equi‐position atom (e + x2, f + y2, g + z2) (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 (x1, y1, z1), the distance between the two atoms can be calculated by the formula d[uvw](1/r) = d′[uvw]/r, where d′[uvw] = (u2a2 + v2b2 + w2c2 + 2uvabcosγ + 2vwbccosα + 2uwaccosβ)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 (x2 − x1), (y2 − y1) and (z2 − z1). 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 SiO2 structure and Cu3Au I superstructure as well as face‐centred cubic, body‐centred cubic and hexagonal close‐packed structures.
Marco E. Ciriotti

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