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Limitations of Crystal Symmetry on Physical Phenomena with Particular Reference to Diamagnetic Magnetostriction

Published online by Cambridge University Press:  24 October 2008

D. Shoenberg
D. Shoenberg*
Affiliation:
Coutts Trotter Student, Trinity College
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Extract

A direct method of obtaining the limitations of crystal symmetry on physical phenomena is described and discussed in greater detail for the case of diamagnetic magnetostriction. Formulae are obtained for the variation of the longitudinal and transverse effects with crystal orientation in the case of bismuth.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 2 , April 1935 , pp. 265 - 270
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* Voigt, W., Lehrbuch der Kristallphysik (Teubner, 1928)Google Scholar.

† Kapitza, P., Proc. Roy. Soc. A, 135 (1932), 537.Google Scholar

‡ We use the strict tensor definition of strain as in Jeffreys, , Cartesian Tensors, p. 72.Google Scholar

* Essentially Voigt's method applies the symmetry conditions to the thermodynamic potential instead of directly to the tensor involved.

† It is important to note that the transformation law (3) holds for an inversion of axes only if the tensor is polar (as our m rs ab ). For an axial tensor a minus sign has to be added (only for this particular transformation) and so all its components must vanish if it is of even rank, but there is no restriction if of odd rank. As regards the other transformations which we shall consider, there is no distinction between axial and polar tensors.

* Bridgman, P. W., Phys. Rev. 42 (1932), 858 CrossRefGoogle Scholar; Allen, Mildred, Phys. Rev. 42 (1932), 848.CrossRefGoogle Scholar

† Kohler, M., Ann. der Phys. 20 (1934), 891 Google Scholar; Shoenberg, D., Proc. Cambridge Phil. Soc. 31 (1935), 271.Google Scholar

‡ This particular example is chosen since it was necessary for the interpretation of some experiments of the author, an account of which is to be published shortly.

* To be published shortly.