A search for stable ordered phases in the nonstoichiometric cubic tantalum carbide TaC_0.8 has been performed by use of the evolutionary algorithm and symmetry analysis. Four stable Ta₅C₄ superstructures with tetragonal, monoclinic, orthorhombic, and triclinic symmetry have been predicted for the first time. The DOS values of these Ta₅C₄ superstructures and stoichiometric TaC_1.00 carbide have been calculated. All the tantalum carbide superstructures and stoichiometric TaC_1.00 carbide have metal conductivity. The disorder–order phase transition channels TaC_y → Ta₅C₄ associated with the formation of the considered model superstructures include superstructural vectors of non-Lifshitz stars {k₁}, {k₂}, and {k₄}. The distribution functions of carbon atoms over the sites of the tetragonal, monoclinic, orthorhombic, and triclinic Ta₅C₄ superstructures have been calculated. For the first time, the physically permissible sequence of disorder–order and order–order phase transitions is established for the detected phases of the Ta₅C₄ family. Based on the formation enthalpy and the cohesion energy magnitudes, the triclinic Ta₅C₄ superstructure is the most favorable among all Ta₅C₄ phases predicted. The composition of the predicted Ta₅C₄ superstructures corresponds to TaC_0.80 which possesses the highest melting temperature and hardness.

中文翻译：

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使用进化算法和对称性分析预测Ta5C4相中的无序和有序相变

通过使用演化算法和对称分析，已经在非化学计量的立方碳化钽TaC _0.8中寻找稳定的有序相。首次预测了具有四方，单斜，正交和三斜对称性的四个稳定的Ta ₅ C ₄超结构。已计算出这些Ta ₅ C ₄超结构和化学计量的TaC _1.00碳化物的DOS值。所有的碳化钽超结构和化学计量的TaC _1.00碳化物都具有金属导电性。无序有序相变通道TaC _y →Ta ₅ C ₄与考虑的模型超结构的形成相关的包括非Lifshitz星{ k ₁ }，{ k ₂ }和{ k ₄ }的超结构矢量。已经计算出碳原子在四方，单斜，正交和三斜Ta ₅ C ₄超结构的位点上的分布函数。首次为Ta ₅ C ₄族的检测相建立了物理上无序-有序和有序-有序相变的序列。基于形成焓和内聚能的大小，三斜Ta ₅ C ₄在所有预测的Ta ₅ C ₄相中，上部结构是最有利的。预测的Ta ₅ C ₄超结构的组成对应于TaC _0.80，具有最高的熔化温度和硬度。