Stress, Strain, Piezoresistivity, and Piezoelectricity

Strain in crystals is created by deformation and is defined as relative lattice displacement. For simplicity, we use a 2D lattice model in Fig.2.1 to illustrate this conception, but discuss the general conception in 3D cases. As shown in Fig. 2.1a, we may use two unit vectors \(\widehat{x}, \widehat{y}\) to represent the unstrained lattice, and in a simple square lattice, they correspond to the lattice basis vectors. Under a small uniform deformation of the lattice, the two vectors are distorted in both orientation and length, which is shown in Fig. 2.1b. The new vectors \(\widehat{{\rm x}}^{\prime}\) and \(\widehat{{\rm y}}^{\prime}\) may be written in terms of the old vectors: and in the 3D case, we also have