Isotropic crystal and energy band

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Discussion Overview

The discussion revolves around the characteristics of energy bands in isotropic crystals, particularly whether the energy band can be considered spherical due to the equivalence of all directions in such crystals. It touches on theoretical aspects of crystallography and the implications of symmetry in crystal structures.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that the equivalence of all directions in an isotropic crystal implies that the energy band is exactly spherical.
  • Another participant counters that true isotropic crystals do not exist, noting that even cubic crystals exhibit symmetry only with respect to specific axes, which affects the isotropy of higher order tensors.
  • A later reply questions whether the isotropic approximation disregards the actual crystal structure, implying a potential limitation in the assumption of isotropy.
  • One participant confirms the idea that the isotropic approximation indeed overlooks the complexities of the crystal structure.

Areas of Agreement / Disagreement

Participants express disagreement regarding the existence of isotropic crystals and the implications for energy band shape, with no consensus reached on the validity of the isotropic approximation.

Contextual Notes

The discussion highlights limitations related to the assumptions of isotropy and the dependence on specific definitions of crystal symmetry. The implications for higher order tensors and the nature of energy bands remain unresolved.

hokhani
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Since all the directions are equivalent in an isotropic crystal, can we deduce that the energy band is exactly spherical?
 
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The problem is that there are no isotropic crystals. Even cubic crystals are only symmetric with respect to four and threefold rotations about some special axes. However this is sufficient to render second order (but not higher order) tensors isotropic.
 
DrDu said:
The problem is that there are no isotropic crystals. Even cubic crystals are only symmetric with respect to four and threefold rotations about some special axes. However this is sufficient to render second order (but not higher order) tensors isotropic.
Do you mean that using the isotropic approximation we in fact disregard the crystal?
 
Yes, indeed.
 
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