基于多尺度模型解释固体中的挠曲电效应

挠曲电效应是一种跨尺度的多场耦合现象。当前的宏观挠曲电理论均是基于应变梯度局部破坏晶体反演对称这一微观机理对该现象进行唯象描述。该宏观理论与基于晶格动力学及密度泛函理论的微观挠曲电理论模型之间存在较大差异。难以将两者结合用以跨尺度地研究材料中的挠曲电效应。针对该现状，本文基于前人提出的原子场理论，建立了一种新的多尺度挠曲电模型。并在该多尺度模型框架下解释了应变梯度诱发极化的微观机理。一方面，与基于连续介质力学的唯象理论不同，本文从材料微结构演化的角度推导了原子位移与极化的关系。另一方面，与通过晶格波假设原子位移的微观理论不同，本文得到的极化表达式更加真实和广义地解释了挠曲电效应。其能够适用于材料边界存在机械力作用，材料内部存在缺陷等复杂的情况。本文所建立的多尺度挠曲电模型能够为后续多尺度挠曲电效应的研究提供一些思路。

Interpretation of the flexoelectric effect in solids based on multi-scale model

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.