  Crystal morphologies are important for the design and functionality of
devices based on low-dimensional nanomaterials. The equilibrium crystal shape
(ECS) is a key quantity in this context. It is determined by surface energies,
which are hard to access experimentally but can generally be well predicted by
first-principles methods. Unfortunately, this is not necessarily so for polar
and semipolar surfaces of wurtzite crystals. By extending the concept of Wulff
construction, we demonstrate that the ECSs can nevertheless be obtained for
this class of materials. For the example of GaN, we identify different crystal
shapes depending on the chemical potential, shedding light on experimentally
observed GaN nanostructures.
