Thermodynamics assessment of the Erbium-Ruthenium system by combining the Ab-initio and CALPHAD methods

In the present study, the erbium-ruthenium system was optimised using the CALPHAD approach. The thermodynamic properties and the phase diagram were evaluated. The enthalpies of formation of the intermetallic compounds for the binary system Er-Ru were calculated by ab- initio methods. The liquid phase was treated with the exponential model, while a solution model was applied to represent the HCP (Er, Ru) solid solution. The five intermetallic compounds Er₃Ru, Er₅Ru₂, Er₃Ru₂, ErRu₂, and Er₄₄Ru₂₅ were considered as stoichiometric compounds. The calculations are in good agreement with the phase diagram information and experimental thermodynamic values documented in the literature.本研究采用CALPHAD方法（Calculation of Phase Diagrams，相图计算法）对铒-钌二元体系进行了优化，对该体系的热力学性质与相图开展了评估。采用从头算（ab-initio）方法计算了Er-Ru二元体系金属间化合物的形成焓。液相采用指数模型进行描述，密排六方（Hexagonal Close-Packed，HCP）(Er, Ru)固溶体则通过溶液模型表征。本研究将Er₃Ru、Er₅Ru₂、Er₃Ru₂、ErRu₂及Er₄₄Ru₂₅这五种金属间化合物视为化学计量比化合物。计算结果与文献记载的相图信息及实验热力学数值具有良好的一致性。