  Until recently, the heat capacity of GaN had only been measured for
polycrystalline powder samples. Semiempirical as well as
\textit{first-principles} calculations have appeared within the past few years.
We present in this article measurements of the heat capacity of hexagonal
single crystals of GaN in the 20-1400K temperature range. We find that our data
deviate significantly from the literature values for polycrystalline materials.
The dependence of the heat capacity on the isotopic mass has also been
investigated recently for monatomic crystals such as diamond, silicon, and
germanium. Multi-atomic crystals are expected to exhibit a different dependence
of these heat capacities on the masses of each of the isotopes present. These
effects have not been investigated in the past. We also present
\textit{first-principles} calculations of the dependence of the heat capacities
of GaN, as a canonical binary material, on each of the Ga and N masses. We show
that they are indeed different, as expected from the fact that the Ga mass
affects mainly the acoustic, that of N the optic phonons. It is hoped that
these calculations will encourage experimental measurements of the dependence
of the heat capacity on isotopic masses in binary and more complex
semiconductors.
