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ERIC Number: EJ907125
Record Type: Journal
Publication Date: 2011-Jan
Pages: 11
Abstractor: As Provided
Reference Count: 16
ISSN: ISSN-0143-0807
Common Misconceptions about the Dynamical Theory of Crystal Lattices: Cauchy Relations, Lattice Potentials and Infinite Crystals
Elcoro, Luis; Etxebarria, Jesus
European Journal of Physics, v32 n1 p25-35 Jan 2011
The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used solid-state textbooks. Frequently, pair interaction is even considered to be the most general situation. In addition, it is shown that the demand of rotational invariance in an infinite crystal leads to inconsistencies in the symmetry of the elastic tensor. However, for finite crystals, no problems arise, and the Huang conditions are deduced using exclusively a microscopic approach for the elasticity theory, without making any reference to macroscopic parameters. This work may be useful in both undergraduate and graduate level courses to point out the crudeness of the pair-potential interaction and to explore the limits of the infinite-crystal approximation. (Contains 1 table, 1 figure, and 4 footnotes.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A