铁电铁弹材料的自然构形(II)———多晶材料
The Spontaneous Configuration of Ferroelectric-Ferroelastic Materials:Ⅱ ———Polycrystalline Materials
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摘要: 由于铁电铁弹单晶材料的内能密度函数是变形梯度张量和自极化电位移向量的非凸函数,在自然条件 下(即无外力和无外加电场作用)的铁电铁弹多晶材料的自极化稳定构形,一般呈现出一种粗糙的混合构形,即 每一晶粒不可能由单一电畴或有限的电畴组成。在这种混合结构中,各电畴的体积比受到位移和电位移场在晶 界上必须满足的连续性条件约束。由于材料中可以形成多种形式的孪晶,变形体积比和电畴体积比取决于晶界 的取向、两侧晶粒的取向以及孪晶的形式外,电畴体积比还与孪晶区域的形状有关。Abstract: As the internal energy densityof ferroelectric-ferroelastic single cystals is the non-convexfunction of the transformation gradients and the electric displacements in the process of polarization, in natural conditions (i.e., without external forces and external electric fields), the stable spontaneous configuration of a ferroelectric-ferroelastic polycrystalline material consists of a coarse mixture of various ferroelectric domains. In this coarse mixture, the volume fractions of electric domains are determined by the continuity requirements of the displacement and the electric displacement on the grain boundaries. Because various kinds of twins can be formed in the material, the volume fraction of the domainswith the same spontaneous deformation gradient depends upon the orientations of the grain boundaries, the orientations of the twining crystal lattices, and the twiningmode. In addition, the volume fraction of ferroelectric domains also depends upon the shape of the twining regio
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Key words:
- ferroelectrics /
- ferroelasticity /
- spontaneous polarization /
- mixture /
- electric domains /
- polycrystal
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