Relation between Elastic Tensors of Wurtzite and Zinc-Blende Structure Materials

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Abstract
A transformation is derived which relates the fourth-rank elastic tensors of the two common modifications of tetrahedrally coordinated compounds, cubic zinc blende (ZB), and hexagonal wurtzite (Wz). The basic assumptions are that the local tetrahedra extending to second neighbors about each atom are rotated but otherwise identical in the two structures, and that differences between ZB and Wz for third and more distant neighbors are negligible. The procedure involves Robinson's rotations which apply to any tensorial property, to which is added internal strain between the two inequivalently oriented tetrahedra in the Wz structure. Good agreement is found with empirical constants of ZnS which have been measured in both structures. The transformation permits a simple derivation of "effective" cubic constants for Wz compounds, which are sufficient to extract the most important information on average tetrahedral forces. Effective constants are compared with measured ZB constants for the entire range of tetrahedrally coordinated compounds.