Temperature dependence of the thermal expansion of GaN

The thermal expansion of hexagonal GaN bulk crystals was studied in an extended temperature range from $12\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1025\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The lattice parameters $a$ and $c$ were measured by high-resolution x-ray diffraction. The temperature dependence of the derived thermal expansion coefficients along the $a$ and $c$ directions could be well described over the entire temperature range within both the Debye model and the Einstein model. Debye temperatures of $(868\ifmmode\pm\else\textpm\fi{}20)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $(898\ifmmode\pm\else\textpm\fi{}24)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and Einstein temperatures of $(636\ifmmode\pm\else\textpm\fi{}13)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $(662\ifmmode\pm\else\textpm\fi{}18)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ were derived along the $a$ and $c$ axes, respectively, and compared to available literature values.