Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T14:00:44.463Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of crystal lattices. III

An attempt to calculate the tensile strength of a cubic lattice by purely static considerations

Published online by Cambridge University Press:  24 October 2008

M. Born  and
R. Fürth
M. Born
Affiliation:
The UniversityEdinburgh
R. Fürth
Affiliation:
The UniversityEdinburgh
Get access Rights & Permissions [Opens in a new window]

Extract

The energy density of a cubic lattice, homogeneously deformed by a force acting in the direction of one axis, is calculated, and the equilibrium conditions and the stability conditions for any arbitrary small additional deformations are derived. A special assumption is made as to the law of force between the atoms, and the numerical calculations are performed for the face-centred lattice. In this way the strain as a function of the deformation is calculated and, from the stability conditions, the tensile strength is determined. The results are not in agreement with the experimental facts, and the possible reasons for this disagreement are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 4 , October 1940 , pp. 454 - 465
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)Polanyi, M.Z. Phys. 7 (1921), 323.CrossRefGoogle Scholar
(2)Born, M.Atomtheorie des festen Zustandes (Berlin, 1923).CrossRefGoogle Scholar
(3)Zwicky, F.Z. Phys. 24 (1923), 131.Google Scholar
(4)See e.g. Born, M. and Mayer, J.Z. Phys. 75 (1932), 1.Google Scholar
(5)Misra, R. D.Proc. Cambridge Phil. Soc. 36 (1940), 173.Google Scholar
(6)Lennard-Jones, J. E.Physica, 10 (1937)941.Google Scholar
(7)Born, M.Proc. Cambridge Phil. Soc. 36 (1940), 160.Google Scholar
(8)See e.g. Schmidt, E. and Boas, W.Kristallplastizität (Berlin, 1935).CrossRefGoogle Scholar
(9)Born, M.J. Chem. Phys. 7 (1939), 591.CrossRefGoogle Scholar
(10)Fürth, R. (in the press).Google Scholar
(11)Fürth, R.Nature, Lond., 145 (1940), 741.CrossRefGoogle Scholar