The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with \(N\), the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of \(N\), and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.

合金的簇扩展形式主义用于构建三种难熔高熵合金（NbTiVZr，HfNbTaTiZr和AlHfNbTaTiZr）的替代模型。然后，将这些团簇扩展模型与蒙特卡洛方法和热力学积分一起使用，以计算这些难熔高熵合金随温度的配置熵。许多固溶体合金设计指南均基于理想的混合熵，该熵随合金中元素数量\（N \）单调增加。然而，我们的结果表明，在低温下，这些材料的构型熵在很大程度上与\（N \）无关。，并且上述假设仅在高温范围内成立。这表明基于理想混合熵的合金设计指南需要进一步研究。