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On the stability of crystal lattices. II

Published online by Cambridge University Press:  24 October 2008

Rama Dhar Misra
Rama Dhar Misra
Affiliation:
The UniveristyEdinburgh
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Extract

On the assumption that the potential energy of the three cubic lattices of the Bravais type consists of two terms, an attractive one proportional to r−m and a repulsive one proportional to r−n, n > m, stability conditions are expressed in the form that two functions of the number n should be monotonically increasing. These functions have been calculated numerically for n = 4 to 15, and are represented as curves with the abscissa n. The result is that the face-centred lattice is completely stable, that the body-centred lattice is unstable for large exponents in the law of force, and that the simple lattice is always unstable,—in complete agreement with the results of Part I.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 2 , April 1940 , pp. 173 - 182
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

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