The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines. The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design. However, as of now a method to compute efficiently, yet with high accuracy the thermodynamic properties of such alloys has been missing. One of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent alloys. In this work, a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.

多种主要成分合金的独特和出乎意料的性能，重新焕发了合金设计的领域，并引起了科学界的浓厚兴趣。巨大的成分参数空间通过计算设计使这些合金成为独特的勘探领域。然而，到目前为止，仍缺乏一种有效计算且具有高精度的方法，这些合金的热力学性质。潜在的原因之一是，对于这些化学复杂的多组分合金，缺乏精确而有效的方法来计算振动自由能（包括非谐性）。在这项工作中，基于热力学积分和机器学习潜能的结合，开发了一种基于密度泛函理论的方法来克服这一问题。