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On the stability of crystal lattices VII. Long-wave and short-wave stability for the face-centred cubic lattice

Published online by Cambridge University Press:  24 October 2008

S. C. Power
S. C. Power
Affiliation:
The UniversityEdinburgh Communicated by M. Born
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Extract

It is shown that the theorem stated in Born's paper, and proved for the case of a linear lattice of N equal particles under certain restrictions concerning the forces between the particles, that macroscopic stability (stability for long waves) implies microscopic stability, may be extended to three dimensions for the particular case of a face-centred cubic lattice, where the effects of all neighbours, other than the first twelve neighbours, are neglected.

I take this opportunity of expressing my sincere thanks to Prof. Born for much valuable advice.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 1 , January 1942 , pp. 61 - 66
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

* Proc. Cambridge Phil. Soc. 36 (1940), 160, 173, 454, 466Google Scholar; 37 (1941), 37, 177.