新一代溶液几何模型中的关键参数——偏差函数的性质

Properties of Similarity Coefficient in New Generation Geometric Model

溶液几何模型是计算多元系溶液、熔体性质的有力工具。几何模型经过发展,已经积累了丰富的计算方法。经过总结和创新,发展出了新一代几何模型。首先提供了溶液几何模型的简明计算图式。通过Sb-Ga二元合金熔体体系与Cu2S-FeS-Ni3S2三元熔融硫化物体系性质计算,分别指出了传统溶液几何模型中对称模型与非对称模型各自的理论缺陷。证明了新一代几何模型在理论上优于传统几何模型。并结合二元完全互溶体系热力学性质之间的关系,分析了新一代溶液几何模型引入的重要参数,针对偏差函数在新一代几何模型中的意义进行了探讨。通过计算与实例明确提出偏差函数的正定性与对称性两个重要性质,并将偏差函数性质数学化。提出了研究热力学函数之间关系的新思路,为几何模型的进一步发展做好必要的理论准备。

With the development of the geometrical models, the new general solution model proposed by Chou has pres- ented its advantages on the prediction of solution properties. Compendious calculation roadmap of geometrical models was given. In the present paper, comparisons between traditional geometrical models and new general solution model were per- formed by evaluating the properties of Sb-Ga molten alloy system and CuzS-FeS-Ni3Sz sulfur melting system. The calcula- tion results showed the defects of symmetrical and asymmetrical models respectively, and also proved the self-consistency of the new generation model. Furthermore, from the viewpoint of mathematics, the key parameter of the new generational model, deviation function, was discussed by functional analysis. Positive definiteness and symmetrical characteristic of the deviation function of ternary properties were examined. The superiorities of the new general solution model were verified both in practical and theoretical aspects. Meanwhile, the current study also provided a new way to discuss the thermody- namics functions from the perspectives of functional analysis in mathematics.