Non-Axisymmetric Needle
Crystals
•Unfortunately, there is no exact
generalization of the Horvay- Cahn 2-fold solution to the 4-fold
case.
•Instead, we perform an expansion for
the 4-fold correction, valid for small-amplitude perturbations to a parabola of
revolution.
•Horvay-Cahn solution is written in an
ellipsoidal coordinate system. We transform the solution to paraboloidal
coordinates, and expand for small eccentricity to find the expansion for a
2-fold solution
in paraboloidal coordinates.
•We then generalize the 2-fold solution
to the n-fold case (n = 3,4) in paraboloidal coordinates .