Mathematical modeling of electrical conductivity of melts with eutectic and monotectic interaction characteristics of components

The authors propose to use the generalized conductivity theory (GCT) for mathematical modeling of electrical conductivity of metallic melts with eutectic and monotectic interaction of components. The main GCT approaches are considered and analyzed: the method of transition to unit cell and the effective medium method, which allow describing the properties of heterogeneous liquid metallic systems. The paper presents a mathematical formulation of the problem of calculating the effective coefficients of electrical conductivity from the known values ​​of the specified parameters of the initial components and their concentrations. An example of calculating the specific electrical resistance of Pb-Bi melt with eutectic interaction of the components is given. The calculation was carried out using the method of transition to the elementary cell of Rayleigh: a model of a structure with interpenetrating components, a model of a structure with isolated inclusions; and the effective medium method. The results of calculations for these models are compared with experimental data on the specific electrical resistance of liquid Pb – Bi alloys in a wide range of temperatures and concentrations. All three approaches to estimating the specific electrical resistance of Pb – Bi melts showed the results close to the experimental data. The closest values ​​were demonstrated by the model of a structure with interpenetrating components, for which the standard deviation of the calculated values ​​from the experimental ones was less than 4 %. The authors substantiated that the use of GCT for calculating the effective coefficients of melts’ electrical conductivity is advisable at the initial stages of developing new metallic materials with specified properties, especially in cases where direct experiments are difficult. This approach allows for a significant reduction in time and financial costs of synthesizing samples and experimentally studying their physicochemical characteristics.

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