Mismatch strain due to an electric field

Phenomenologically, the relationship between imposed electric field i on a crystal and corresponding strain ij induced in the crystal is of the form (Auld 1973) 

Symmetry of the strain array Cjj under interchange of its indices implies that, of the 27 components of only 18 can be independent. Material S5nn-metry reduces the number of independent components further for most real crystals. The array of constants represents the components of a tensor, so that these components transform as tensor components between different sets of mutually orthogonal rectangular coordinate axes, as illustrated for the case of the stress tensor in (3.37). 

For purposes of calculation for a given orientation of the material with respect to some underlying rectangular coordinate system, the reduced matrix representation of the relationship (3.82) is again found to be convenient, following the convention adopted in Section 3.1. As before, the cost of this convenience is that the tensor character of the arrays representing physical quantities is lost. A reduced form of (3.82) is 

This representation presumes that the c—axis is aligned with the 0 3—direction. For a cubic crystal, such as gallium arsenide, only three components of the piezoelectric matrix are nonzero, and these are specified in terms of a single constant according to 

It is presumed that the cube axes are aligned with the rectangular coordinate axes in this case. 

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