Abstract：The flexoelectric effect in solids is explained in this paper based on Chen's multi-scale model. The flexoelectric effect is a multi-field coupling phenomenon across scales. The current macroscopic flexoelectric theories are based on continuum mechanics and describe the phenomenon phenomenally according to the micro mechanism that the local crystal inversion symmetry is destroyed by the strain gradient. However, due to the great difference between the macroscopic theory and the microscopic flexoelectric theory based on lattice dynamics and density functional theory, it is difficult to combine these two theories to study the flexoelectric effect in materials across scales. In view of this point, according to the atomic field theory proposed by Chen, the relationship between atomic displacement and polarization is obtained from the perspective of material microstructure evolution, and a new multi-scale flexoelectric model is established to explain the micro mechanism of flexoelectric effect. By deriving the polarization expression, it is found that the distance between atoms and the center of the unit cell is an important micro quantity affecting flexoelectric polarization. The flexoelectric effect establishes the relationship with temperature and time through this micro quantity at the atomic scale. In addition, the order of magnitude of the distance between atoms and the center of the unit cell is Angstrom. Expressions of the piezoelectric polarization contain the linear term while the flexoelectric polarization contain the quadratic term of this position, this result in the fact that the flexoelectric effect is much smaller than the piezoelectric effect at the macro scale. The multi-scale flexoelectric model established in this paper can be suitable for complex situations such as internal defects of materials, and provides some ideas for the follow-up study of multi-scale flexoelectric effect.
2022, Vol. 43 
