Flux-independent theory of nonlinear diffusion for Vegard's law solutions
Flux-independent theory of nonlinear diffusion for Vegard's law solutions
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DOI：
10.1016/j.msea.2006.08.073
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发表时间：
2007-01
期刊：
影响因子：
6.4
通讯作者：
J. Kirkaldy
中科院分区：
文献类型：
--
作者：
J. Kirkaldy
现象学Boltzmann-Matano （B-M）分析认为，浓度相关的扩散系数D(X)与溶质守恒的、通量表示的非守恒摩尔分数X的非线性抛物方程的无限二元扩散偶实验有关。与此相反，这一贡献证明了对于稳定的替换维加德定律解，其中D(X)由一系列增量偶经验定义，这个D(X)必须始终在右边的二阶导数之外。因此，碱方程被金兹堡-朗道变分方程所取代，其中不允许溶质守恒通量进入理论结构。在三元推广中，溶质通量同样没有定义，因此必须重新检查“零通量平面”的概念。此外，在这个三元体系中，体积和摩尔质量保持守恒，并且在二元体系中，它们对应的中性面并不重合。
The phenomenological Boltzmann–Matano (B–M) analysis argues that a concentration-dependent diffusion coefficient D(X) relates to infinite binary diffusion couple experiments by the solute conserving, flux-formulated non-linear parabolic equation in terms of the non-conserved mole fraction X:In contradiction, this contribution proves that for stable substitutional Vegard's law solutions, in which D(X) is empirically defined by a series of incremental couples, this D(X) must consistently lie outside the second derivative on the right. The base equation has accordingly to be replaced by a Ginzburg–Landau variational equation in which a solute-conserving flux is denied entry to the theoretical structure. In the ternary generalization solute fluxes are likewise not defined so the concept of a “zero-flux plane” must be re-examined. Furthermore, in this ternary formulation volume and molar mass remain conserved, and as in the binary case their corresponding neutral planes are not coincident.