Refractory metal carbides, usually fabricated via solid state reactions, require precise control of their reactants and temperature, especially when they enter a complex compositional space, like high-entropy (multi-component) carbides. In this work, the solid-state reactions of tungsten based refractory metal carbides M-W-C (M = Ti, Zr, Hf, V, Nb, Ta) are systematically studied through first-principles thermodynamic calculations and percolation simulations, and its relationship with symmetric principles is unraveled. Symmetric hierarchy is defined by the group-subgroup Bärnighausen tree and the gap in their space group number. It suggests MC and WC/W2C are two possible reactants to form the highest symmetric M-W-C ternary carbides, and indicates the larger the gap in their space group number, the harder the reactions. From the symmetric hierarchy, we found the reaction path from MC to M-W-C ternary carbides is the most probable, supported by the Gibbs reaction free energy. Carbon percolation within the metal framework plays another role in the solid-state reactions of tungsten based refractory metal carbides. It reveals the phase transition from M6W6C to M3W3C undergoes a transient M2W2C. The success in predicting the phase relationship of M-W-C ternary system offers a new paradigm for the design and synthesis of high-entropy carbides, nitrides, and oxides.

中文翻译：

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通过第一性原理计算揭示钨基难熔金属碳化物固态反应中的对称层次结构


难熔金属碳化物通常通过固态反应制备，需要精确控制其反应物和温度，尤其是当它们进入复杂的成分空间时，如高熵（多组分）碳化物。本工作通过第一性原理热力学计算和渗流模拟，系统研究了钨基难熔金属碳化物 M-W-C （M = Ti， Zr， Hf， V， Nb， Ta） 的固相反应，并揭示了它与对称原理的关系。对称层次结构由群-子群 Bärnighausen 树及其空间群编号中的间隙定义。它表明 MC 和 WC/W2C 是形成最高对称 M-W-C 三元碳化物的两种可能反应物，并表明它们的空间群数间隙越大，反应越困难。从对称层次结构中，我们发现从 MC 到 M-W-C 三元碳化物的反应路径是最可能的，这得到了吉布斯反应自由能的支持。金属框架内的碳渗流在钨基难熔金属碳化物的固态反应中起着另一个作用。它揭示了从 M6W6C 到 M3W3C 的相变经历了瞬态 M2W2C。成功预测 M-W-C 三元系的相关系为高熵碳化物、氮化物和氧化物的设计和合成提供了新的范式。