Why is E3 zero for cubic symmetry?

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    Cubic Symmetry Zero
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Discussion Overview

The discussion revolves around the electric field components in a cubic symmetry context, specifically focusing on why the component E3 is considered to be zero. Participants explore the implications of this condition on the overall electric field, including the roles of other components like E0, E1, and E2, and the relationship between these fields and lattice geometry.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant states that E3 is the dipolar field from other dipoles, suggesting that its contribution vanishes due to averaging over all orientations and distances in a cubic lattice.
  • Another participant questions whether E3 being zero implies that the polar fields at each site are spherical and whether this relates to the spherical cavity represented by E2.
  • A different viewpoint emphasizes a preference for visualizing interactions among the contributors to the total electric field rather than relying solely on equations.
  • One participant proposes that the cavity should maintain cubic symmetry but notes that the procedure is approximate and shouldn't be overly generalized.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding regarding the implications of E3 being zero, with some agreeing on its relation to dipolar fields while others seek clarification on its geometric interpretations. The discussion remains unresolved with multiple competing views on the implications of cubic symmetry.

Contextual Notes

The discussion includes assumptions about the nature of dipolar fields and their contributions, as well as the approximations involved in the analysis of electric fields in cubic symmetry. There are unresolved questions regarding the relationship between E2 and E3.

Who May Find This Useful

Individuals interested in electrostatics, solid-state physics, and the effects of symmetry on electric fields may find this discussion relevant.

cruz_johann
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The total electric field is given as Etotal = E0 +E1 +E2 +E3
Where E0 is the applied field, E1 is the depolarization, E2 is caused by polarization of a hypothetical sphere while E3 is the one dependent on lattice geometry... How come E3 is zero for cubic symmetry? Can I picture this as summation of forces? Is the sphere the imagined atom itself?
 
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Well, E3 is the dipolar field of the other dipoles in this approximation. The summation over the cubic lattice is more or less equivalent to an averaging of the dipolar field over all orientations and distances. As the dipolar field changes sign with angle theta, it is not too surprising that this contribution vanishes.
 
Kinda get it. But have some clarification, E3 being zero in cubic symmetry does that mean that the polar fields in each site is spherical? Dose this one have to do with spherical cavity of E2? E3 somehow related to E2 in this case?

Thanks for the help DrDu
 
I find it more satisfying to visualize how the contributors to the total electric field interacts than to go with the equations.
 
I would guess that the cavity should in principle respect at least the cubic symmetry. But the whole proceedure is only approximate, so it shouldn't be streched too far.
 

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