机械力化学旋节分解：多组分结晶固体相变的唯象理论
Mechano-chemical spinodal decomposition: A phenomenological theory of phase transformations in multi-component, crystalline solids
摘要：
我们提出了一个唯象处理扩散驱动的马氏体相变在多组分晶体固体中产生的非凸自由能的机械和化学变量。的治疗描述了扩散相变，伴随着对称性破坏的晶体晶胞的结构变化，并揭示了机械化学旋节线的重要性，定义为应变组成空间中的自由能量密度函数是非凸的区域。该方法与相变有关，其中结构序参量可以表示为相对于高对称性参考晶体的应变的线性组合。描述机械化学旋节分解的控制方程是从自由能量密度函数变分推导的，该函数通过快速变化的应变和成分场的梯度来解释界面能。本文提出了一个处理耦合、高阶扩散和非线性应变梯度弹性问题的计算框架。因为在非均匀的、变形的微结构中的局部应变可以是有限的，所以弹性问题必须考虑几何非线性。可用的实验相图和第一性原理自由能的评估表明，机械化学旋节分解应发生在金属氢化物，如ZrH $_{2-2c}$。在二维和三维的几个数值例子中探索了丰富的物理学，并在锂离子电池和高温陶瓷的重要电极材料的背景下讨论了机制的相关性。
英文摘要：
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry breaking structural changes of the crystal unit cell and reveals the importance of a mechano-chemical spinodal, defined as the region in strain-composition space where the free energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechano-chemical spinodal decomposition are variationally derived from a free energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests mechano-chemical spinodal decomposition should occur in metal hydrides such as ZrH$_{2-2c}$. The rich physics that ensues is explored in several numerical examples in two and three dimensions and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high temperature ceramics.
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