Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-12T10:18:34.503Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of crystal lattices IX. Covariant theory of lattice deformations and the stability of some hexagonal lattices

Published online by Cambridge University Press:  24 October 2008

M. Born
M. Born
Affiliation:
The University, Edinburgh
Get access Rights & Permissions [Opens in a new window]

Extract

The theory of lattice deformations is presented in a new form, using the tensor calculus. The case of central forces is worked out in detail, and the results are applied to some simple hexagonal lattices. It is shown that the Bravais hexagonal lattice is unstable but the close-packed hexagonal lattice stable. The elastic constants of this lattice are calculated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 1 , January 1942 , pp. 82 - 99
Copyright
Copyright © Cambridge Philosophical Society 1942

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Born, M.Proc. Cambridge Phil. Soc. 36 (1940), 160.CrossRefGoogle Scholar
(2)Born, M.Atomtheorie desfesten Zustandes (Berlin: Leipzig, 1923).CrossRefGoogle Scholar
(3)Ricci, M. M. G. and Levi-Civita, T.Math. Ann. 541 (1901), 125.Google Scholar
(4)Synge, J. L.Proc. London Math. Soc. 24 (1926), 103.CrossRefGoogle Scholar
(5)Murnaghan, F. D.American J. Math. 59 (1937), 234.Google Scholar
(6)Brillouin, L.Les tenseurs en méchanique et én élasticité (Paris, 1938).Google Scholar
(7)Voigt, W.Lehrbuch der Kristallphysik (Leipzig, 1910).Google Scholar
(8)Keesom, W. H., de Smedt, J. and Mooy, H. H.Proc. Amsterdam Acad. Sci. 33 (1930), 814; Commun. Phys. Lab. Univ. Leiden, Nr. 209 d; Nature, London, 126 (1930), 757.Google Scholar
(9)Vegard, L.Z. Phys. 79 (1932), 471.CrossRefGoogle Scholar
(10)Voigt, W.Ann. Phys., Leipzig, 31 (1887), 474.CrossRefGoogle Scholar