Myint Philip C, Benedict Lorin X, Wu Christine J, Belof Jonathan L
Physics Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States.
Materials Science Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States.
ACS Omega. 2021 May 10;6(20):13341-13364. doi: 10.1021/acsomega.1c01300. eCollection 2021 May 25.
We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.
我们提出了一种全局优化方法，通过最小化吉布斯自由能来构建多组分混合物中的相界。本质上，这种最小化方法是单组分系统中使用的麦克斯韦构造法的扩展。对于给定的温度、压力和整体混合物组成，它能揭示热力学稳定相的摩尔分数以及这些相的组成。我们的方法基于粒子群优化算法（PSO），这是一种无梯度的随机方法。它不依赖于对相分数和组成的良好初始猜测，而这对于本研究中考虑的高压应用是一个重要要求，因为高压下相界的数据往往极其有限。该方法的一个实际用途是创建连续尺度多物理场代码所需的状态方程表，这些代码在高压科学中很常见。目前，还不存在一种能严格考虑混合导致的相界变化来生成此类表格的方法。我们进行了广泛的测试，以证明粒子群优化算法能够可靠地确定吉布斯自由能的最小值，并能捕捉共晶和包晶温度等重要特征，从而生成连贯的相图。作为测试的一部分，我们开发了一种基于粒子群优化算法的亥姆霍兹自由能最小化程序，用于交叉检验吉布斯自由能最小化的结果。我们最后对我们的方法进行了批判，并为未来的工作提供了建议，包括一种基于粒子群优化算法的熵最大化方法，该方法将使上述连续体代码能够对多组分混合物进行实时相平衡计算。
