Multi-principal element solid solutions are prone to develop local chemical inhomogeneities, i.e., chemical order/clustering and/or compositional undulation. However, these structural details from short-range (first couple of nearest-neighbor atomic shells) to nanometer length scale are very challenging to resolve in both experimental characterization and computer simulations. For instance, Monte Carlo modeling based on density-functional-theory calculations is severely limited by the sample size and the simulation steps practical in the simulations. Adopting the cluster expansion approach, here we systematically reveal the local chemical inhomogeneity, including chemical order and compositional fluctuation, in three representative equiatomic TiZrNb-based body-centered cubic refractory high-entropy alloys (HEAs): TiZrNb, TiZrHfNb and TiZrHfNbTa. Ti-Zr pairs are found to exhibit the highest degree of chemical preference among all atomic pairs. Such chemical short-range order (CSRO) induces an accompanying compositional undulation, both extending to characteristic dimensions of the order of one nanometer. The chemical inhomogeneity trend uncovered for this series of TiZrNb-based HEAs is expected to impact their mechanical properties; e.g., incorporating the CSRO effects in a current model significantly improves its agreement with experimental measured yield strength.

多主元素固溶体容易产生局部化学不均匀性，即，化学顺序/聚类和/或成分波动。然而，这些从短程（第一对最近邻原子壳）到纳米长度尺度的结构细节在实验表征和计算机模拟中都非常具有挑战性。例如，基于密度泛函理论计算的蒙特卡罗建模受到样本量和模拟中实际的模拟步骤的严重限制。采用簇扩展方法，本文系统地揭示了三种具有代表性的等原子 TiZrNb 基体心立方难熔高熵合金（TiZrNb、TiZrHfNb 和 TiZrHfNbTa）的局部化学不均匀性，包括化学有序和成分波动。发现 Ti-Zr 对在所有原子对中表现出最高程度的化学偏好。这种化学短程有序（CSRO）引起了伴随的成分波动，两者都延伸到一纳米量级的特征尺寸。这一系列基于 TiZrNb 的 HEA 所揭示的化学不均匀性趋势预计会影响其机械性能；例如，在当前模型中加入 CSRO 效应可显着提高其与实验测量屈服强度的一致性。