Symmetry of flexoelectric coefficients in crystalline medium

Flexoelectric effect, which is defined as strain gradient–induced polarization or electric gradient–induced strain in crystalline solids, can be presented as a fourth-rank tensor. The symmetry of the flexoelectric coefficients in matrix form is studied. The results indicate that the direct flexoelectric coefficients should be presented in 3 × 18 form and the converse flexoelectric coefficients in 6 × 9 form, rather than 6 × 6 form, like elastic constants. In addition, non-zero and independent elements in the matrices have been calculated for 32 point groups and 7 Ci groups. These results will provide valuable reference to the theoretical and application studies of flexoelectric effect.