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The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal
Abstract
It is shown that for a crystal, under the assumption of harmonicity for the interatomic forces and as a consequence of the periodic structure, the frequency distribution function of elastic vibrations has analytic singularities. In the general case, the nature of the singularities depends only on the number of dimensions of the crystal. For a two-dimensional crystal, the distribution function has logarithmically infinite peaks. In the three-dimensional case, the distribution function itself is continuous whereas its first derivative exhibits infinite discontinuities. These results are elementary consequences of a theorem of Morse on the existence of saddle points for functions defined on a torus.
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Citations
Cited by
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Blakemore, J. S. (1982) · Journal of Applied Physics · doi:10.1063/1.331665 · Cited by 2,503
Loudon, R. (1964) · Advances in Physics · doi:10.1080/00018736400101051 · Cited by 2,388
Electronic Spectra of Crystalline Germanium and Silicon
Brust, D. (1964) · Physical Review · doi:10.1103/physrev.134.a1337 · Cited by 448
Cowley, R. A. (1968) · Reports on Progress in Physics · doi:10.1088/0034-4885/31/1/303 · Cited by 380
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Cook, A. M., M. Fregoso, B., de Juan, F., Coh, S., & Moore, J. E. (2017) · Nature Communications · doi:10.1038/ncomms14176 · Cited by 367
Metadata
- Authors
- Van Hove, L.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1953-03-15
- Volume
- 89
- Issue
- 6
- Pages
- 1189-1193
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2053093277
- Cited by
- 1,464
- References
- 0
- FWCI
- 17.85
- Type
- journal article
- Language
- en
- Open access
- closed
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- Van Hove, L. (1953). The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal. Physical Review. https://doi.org/10.1103/physrev.89.1189
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