Why is E3 zero for cubic symmetry?

[cruz_johann]

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?

 

[DrDu]

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.

 

[cruz_johann]

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

 

[cruz_johann]

I find it more satisfying to visualize how the contributors to the total electric field interacts than to go with the equations.

 

[DrDu]

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.