Surfaces, Shapes, and Bulk Properties of Crystals

We study the interplay between surface and bulk properties of macroscopic materials. It is demonstrated that the so-called polar surfaces may be stabilized through a charge redistribution between the complete set of surfaces that depends upon the overall shape of the sample and the nature of the material. This charge redistribution, in turn, is governed by certain constraints that we call generalized Tasker conditions. The same surface, but for samples of different shapes, may have different surface charges. Besides its stabilizing effect, the charge redistribution is also shown to particularly affect the dipole moment per repeat unit, a bulk property. For the latter, it is established that essentially any physically meaningful value is possible (depending upon the shape and material), in contrast to the often made assumption that different samples of the same material will have values that differ by, at most, a lattice vector. Finally, some recent experimental and theoretical results for polar surfaces are discussed in terms of the analysis presented here.