By extending the concept of Wulff construction, we demonstrate that ECSs can nevertheless be obtained for this class of materials. It is found that for each semipolar plane, the relative energy with respect to its neighboring polar plane can be unambiguously computed as a function of chemical potential. This energy difference, corresponding to the crystal radius along the polar axis, is the important quantity that governs the crystal shape.
We have exemplified our approach with wurzite GaN. Taking into account several bulk-truncated surfaces, ECSs have been constructed. These crystals exhibit a rodlike shape along the polar c axis, with top and bottom geometries depending on the chemical potential, while the side walls are formed by both types of nonpolar surfaces. Our results can well explain the experimentally observed nanowire shapes. They also open a perspective to gaining insight into morphologies of the entire class of polar materials, concerning point groups of 6, 6 mm, 4, 4 mm, 3, 3 mm, 2, and 2 mm, where such polar axes exist.