Abstract NbMoTaW refractory high entropy alloy (RHEA) has shown great potential applications for high temperature components due to its high temperature mechanical strength. However, the brittleness at room temperature hinders its engineering application and further development. To overcome this deficiency, refractory alloying elements with melting temperatures over 1850 °C, i.e., Cr, Zr, V, Hf, and Re, were chosen to enhance the mechanical performance of NbMoTaW RHEA in the present work. The effects of refractory alloying elements on the strength and ductility of NbMoTaW RHEA were investigated via a combination of theory and experiment. To be specific, the first-principle calculations based on density functional theory were employed to predict the mechanical properties of the alloyed NbMoTaWX (X = Cr, Zr, V, Hf and Re) RHEAs and explain the alloying effect from the atomic and electronic level. Moreover, the phase structures of the alloyed RHEAs were determined based on the formation enthalpy and cohesive energy, as well as some empirical parameters, such as the average valence electron concentration VEC and atomic size difference δ. In combination with the experimental results, the calculated elastic constants and modulus indicated that most of these alloying elements enhanced the strength of NbMoTaW RHEA, while only Zr-alloying significantly improved the ductility. The strengthening mechanism of different elements was well analyzed based on the total and partial density of states, overlapping Mulliken population, charge density contour, and atomic distance. The improvement of the ductility for Zr-alloying was attributed to the formation of Zr–Zr metallic bonds in the alloyed NbMoTaWX RHEAs. The theoretic predictions were confirmed by the experimental investigations. The present work provides a good guidance for design and construction of NbMoTaW RHEA.

中文翻译：

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合金元素对 NbMoTaWX（X = Cr、Zr、V、Hf 和 Re）难熔高熵合金机械和电子性能的影响

摘要 NbMoTaW 耐火高熵合金 (RHEA) 由于其高温机械强度而在高温部件中显示出巨大的潜在应用。然而，室温下的脆性阻碍了其工程应用和进一步发展。为了克服这一缺陷，在目前的工作中，选择熔化温度超过 1850 °C 的难熔合金元素，即 Cr、Zr、V、Hf 和 Re，来提高 NbMoTaW RHEA 的机械性能。通过理论和实验相结合，研究了难熔合金元素对NbMoTaW RHEA强度和延展性的影响。具体而言，采用基于密度泛函理论的第一性原理计算来预测合金化 NbMoTaWX (X = Cr, Zr, V, Hf 和 Re) RHEAs 并从原子和电子层面解释合金化效应。此外，合金化 RHEA 的相结构是根据形成焓和内聚能以及一些经验参数确定的，例如平均价电子浓度 VEC 和原子尺寸差 δ。结合实验结果，计算的弹性常数和模量表明，这些合金元素中的大多数都提高了 NbMoTaW RHEA 的强度，而只有 Zr 合金显着提高了延展性。基于总态密度和部分态密度、重叠穆利肯布居、电荷密度等高线和原子距离，很好地分析了不同元素的强化机制。Zr 合金化延展性的提高归因于合金化 NbMoTaWX RHEA 中 Zr-Zr 金属键的形成。理论预测得到了实验研究的证实。目前的工作为 NbMoTaW RHEA 的设计和构建提供了很好的指导。