Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T23:16:13.400Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of crystal lattices. I

Published online by Cambridge University Press:  24 October 2008

Max Born
Max Born
Affiliation:
The UniversityEdinburgh
Get access Rights & Permissions [Opens in a new window]

Extract

The stability of lattices is discussed from the standpoint of the method of small vibrations. It is shown that it is not necessary to determine the whole vibrational spectrum, but only its long wave part. The stability conditions are nothing but the positive definiteness of the macroscopic deformation energy, and can be expressed in the form of inequalities for the elastic constants. A new method is explained for calculating these as lattice sums, and this method is applied to the three monatomic lattice types assuming central forces. In this way one obtains a simple explanation of the fact that the face-centred lattice is stable, whereas the simple lattice is always unstable and the body-centred also except for small exponents of the attractive forces. It is indicated that this method might be used for an improvement of the, at present, rather unsatisfactory theory of strength.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 2 , April 1940 , pp. 160 - 172
Copyright
Copyright © Cambridge Philosophical Society 1940

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)Voigt, W.Lehrbuch der Kristallphysik (Leipzig, 1910).Google Scholar
(2)Born, M.Atomtheorie des festen Zustandes (Leipzig, 1923).CrossRefGoogle Scholar
(3)Zwicky, F.Phys. Z. 24 (1923), 131.Google Scholar
(4)Niggli, P.Z. f. Kristallogr. 74 (1930), 375.CrossRefGoogle Scholar
(5)Goldschmidt, V. M.Fortschr. d. Mineral. 15 (1931), 73.Google Scholar
(6)Born, M. and Goeppert-Meyer, M.Handbuch der Physik (Berlin, 1933), 24, pt. 1 (2nd ed.), article 4, p. 733.Google Scholar
(7)Blackman, M.Proc. Roy. Soc. A, 148 (1935), 365; 149 (1935), 117; 159 (1937), 416; 164 (1938), 62; Proc. Cambridge Phil. Soc. 33 (1937), 94.Google Scholar
(8)Herzfeld, K. and Lyddane, R. H.Phys. Rev. 54 (1938), 846.CrossRefGoogle Scholar
(9)Born, M.J. Chem. Phys. 7 (1939), 591.Google Scholar
(10)Kellermann, W.Phil. Trans. Roy. Soc. (in the Press).Google Scholar