In Ref.  the case of non-symmetrical particles was also discussed. More precisely, for small deviations from spheres and cubes, i.e., for weakly ellipsoidal or weakly rectangular particles, there is a corresponding weak first-order contribution
that adds up to
Hence, for an ellipsoid of revolution with axes and
cut out of an sc lattice so that the ellipsoid's axes are parallel to the crystallographic direction, one has that the first order anisotropy is given by :
energy contribution scales with the surface of the system.
It is necessary to mention that for crystal shapes such as spheres and cubes the contribution
vanishes by symmetry.
The ratio of the second to the first order surface contributions is:
It can be significant even for
due to the combined influence of the large particle size and the small deviation from symmetry,