Internal and external thermal expansions of wurtzite ZnO from first principles

Many crystals contain “internal” structural parameters not completely constrained by symmetry. These vary with temperature T, similar to the variation of “external” structural parameters that describe the unit cell. The term “thermal expansion” most often refers to the external parameters, which are more easily and accurately measured. Here we use “thermal expansion” to mean both external and internal parameters. Internal thermal expansion impacts a wide range of applications, but has been given less attention. In this study, the thermal expansion behavior of wurtzite ZnO is studied from first principles with the generalized Grüneisen theory in the framework of quasi-harmonic approximation (QHA). Negative external thermal expansions are found below the temperature of 150 K. We demonstrate that the so-called “zero static internal stress approximation” (ZSISA) gives the correct external but incorrect internal thermal expansions, due to the neglect of the clamped-lattice internal contribution contained in the generalized Grüneisen theory. Although accurate at low T, at higher T the QHA may need to be supplemented by higher order anharmonic corrections.