The elastic constants of the Group-III nitrides, c-BN, AlN and GaN were calculated from first-principles using the full-potential linear muffin-tin orbital method and local density approximation. The relation between the elatic constants in zincblende and wurtzite is studied by means of a tensor coordinate transformation approach. The latter combined with a correction for the internal displacement of the rotated tetrahedra is found to provide good results for the Ch11 Ch12 and Ch44 but not for Ch13 and Ch33. These two require explicit calculations involving distortions along the c-axis. The calculations also provide information on the transverse optical phonons. By deriving Keating model parameters we show that BN is much stiffer against bond-angle distortions than the other nitrides.
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Kim, K., Lambrecht, W. & Segall, B. Elastic Constants and Related Properties of the Group III-Nitrides. MRS Online Proceedings Library 395, 399–404 (1995). https://doi.org/10.1557/PROC-395-399