发表机构
Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne; Materials department, University of California, Santa Barbara（洛桑联邦理工学院材料研究所材料设计与模拟实验室; 加州大学圣巴巴拉分校材料系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出两种基于第一性原理计算多组分合金热力学因子的方法，避免采样空位涨落，高效重现扩散矩阵，并推广至非平衡态，适用于介观输运模拟。
AI 中文摘要
从多组分合金的Onsager输运系数计算非稀薄扩散系数，需要热力学因子，该因子衡量自由能相对于成分的曲率。由于金属中的扩散由空位介导，因此关键的曲率并非无空位合金的曲率（这易于计算），而是携带稀浓度空位的合金的曲率。由此得到的矩阵接近奇异，且从中获取该矩阵的成分涨落在蒙特卡罗模拟中收敛缓慢。本文开发了两种避免采样空位成分涨落的途径。第一种途径由两个量构建热力学因子：无空位合金的自由能曲率和空位浓度。第二种途径在半巨正则配分函数中截断至单个空位，并恢复含空位合金的完整热力学因子。同样的分离表明，扩散矩阵的最大特征值是空位示踪扩散系数，适用于任意组分数和任意非理想程度，而其余特征值随空位浓度缩放。在Hf--Mo--Nb--Ti--Zr体系的二元至五元合金中，两种途径均能重现由完全收敛的蒙特卡罗模拟获得的扩散矩阵的特征值和特征向量。单空位展开以约十分之一的采样工作量达到此精度。一个标度关系将两种途径推广至远离平衡的局域空位化学势，无需额外模拟。这些结果使得来自原子模型或CALPHAD评估的热力学描述可直接用于介观尺度的质量输运模拟。
英文摘要
Computing non-dilute diffusion coefficients from Onsager transport coefficients of a multicomponent alloy requires the thermodynamic factor, which measures the curvature of the free energy with respect to composition. As diffusion in metals is mediated by vacancies, the curvature that matters is not that of the vacancy-free alloy, which is straightforward to compute, but that of an alloy carrying a dilute concentration of vacancies. The resulting matrix is nearly singular, and composition fluctuations from which it is obtained converge slowly in Monte Carlo simulations. Here we develop two routes that avoid sampling vacancy composition fluctuations. The first constructs the thermodynamic factor from two quantities, the free-energy curvature of the vacancy-free alloy and the vacancy concentration. The second truncates the semi-grand canonical partition function at a single vacancy and recovers the full thermodynamic factor of the vacancy-containing alloy. The same separation shows that the largest eigenvalue of the diffusion matrix is the vacancy tracer diffusion coefficient for any number of components and any degree of non-ideality, while the remaining eigenvalues scale with the vacancy concentration. Across binary through quinary alloys of the Hf--Mo--Nb--Ti--Zr system, both routes reproduce eigenvalues and eigenvectors of diffusion matrices obtained from fully converged Monte Carlo simulations. The single-vacancy expansion reaches this accuracy with roughly one tenth of the sampling effort. A scaling relation extends both routes to local vacancy chemical potentials away from equilibrium, without additional simulations. These results allow thermodynamic descriptions from atomistic models or CALPHAD assessments to be used directly in mesoscale simulations of mass transport.
