Using first-principles alloy theory, we perform a systematic study of the Co-Cu phase diagram. Calculations are carried out for ferromagnetic and paramagnetic ${\mathrm{Co}}_{1-x}{\mathrm{Cu}}_x$ solid solutions with face-centered-cubic (fcc) crystal structure. We find that the equilibrium volumes and magnetic states are crucial for a quantitative description of the thermodynamics of the Co-Cu system at temperatures up to 1400 K. In particular, the paramagnetic state of Cu-rich alloys with persisting local magnetic moments is shown to be responsible for the solubility of a small amount of Co in fcc Cu whereas the excess entropy in the ferromagnetic Co-rich region critically depends on the adopted lattice parameters. None of the common local or semilocal density functional theory approximations have the necessary accuracy for the lattice parameters when compared to the experimental data. The predicted ab initio Co-Cu phase diagram is in good agreement with the measurements and CALPHAD data, making it possible to gain a deep insight into the various contributions to the Gibbs free energy. The present study provides an atomic-level description of the thermodynamic quantities controlling the limited mutual solubility of Co and Cu and highlights the importance of high-temperature magnetism.

中文翻译：

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根据第一性原理对Co-Cu相图的严格评估

使用第一性原理合金理论，我们对Co-Cu相图进行了系统的研究。对铁磁和顺磁进行计算${\mathrm{有限公司}}_{\mathrm{1个}-X}{铜}_X$具有面心立方（fcc）晶体结构的固溶体。我们发现平衡体积和磁态对于定量描述Co-Cu系统在高达1400 K的温度下的热力学至关重要。特别是，具有持久局部磁矩的富Cu合金的顺磁态显示为造成少量Co在fcc Cu中的溶解性的原因，而铁磁富Co区域中的过量熵主要取决于所采用的晶格参数。当与实验数据进行比较时，没有一个通用的局部或半局部密度泛函理论近似值对晶格参数具有必要的精度。预测的从头算Co-Cu相图与测量值和CALPHAD数据高度吻合，可以深入了解对吉布斯自由能的各种贡献。本研究提供了控制Co和Cu的有限互溶性的热力学量的原子级描述，并强调了高温磁性的重要性。