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ArticleName Partial-cluster model of viscosity of copper-aluminum melt
DOI 10.17580/tsm.2021.04.10
ArticleAuthor Malyshev V. P., Makasheva A. M.

Zh. Abishev Chemical-Metallurgical Institute, Karaganda, Kazakhstan:

V. P. Malyshev, Head of the Laboratory of Entropy-Information Analysis of Complex Physicochemical Systems, Doctor of Engineering Sciences, Professor, e-mail:
A. M. Malysheva, Employee of the Laboratory of Entropy-Information Analysis of Complex Physicochemical Systems, Doctor of Engineering Sciences, Professor, e-mail:


The adequacy of the developed partial-cluster viscosity model with respect to melts of metal alloys was verified using the well-studied copper-aluminum system, for which the state diagram and viscosity isotherms are known in a wide range of compositions. Based on the literature on the thermodynamics of mixing copper and aluminum melts, it was found that this shift is accompanied by heat generation due to the formation of intermetallic compounds in the melt. The destruction of these compounds requires appropriate heat consumption, therefore, it should be taken into account in the partial-cluster viscosity model as an additional thermal barrier to randomization. On this basis, a refined and more generalized form of the partial-cluster model with the expression of the randomization energy of the melt in the form of the algebraic sum of the randomization heat along the liquidus line and the heat of destruction of any intermetallic formations is proposed ΔHch = RTliq – ΔHmix. Application of the generalized partial-cluster model to copper-aluminum melts ensured the repetition of the extreme form of empirical isotherms, even with the appearance of excess viscosity in the calculated dependence. A more detailed analysis of the heat of mixing according to its covalent and metal components showed that the second of them is already randomized and only the covalent component should be taken into account, which should be randomized and should be included in the total randomization barrier in the form ΔHch = RTliq – ΔcovH. Taking this component into account allowed us to obtain a more adequate calculated dependence of the viscosity of the Cu – Al alloy at a temperature of 1100 оC with a correlation coefficient of 0.986, which can be considered as a priority result in the description of viscosity isotherms according to state diagrams. This result is due to the analytical determination of the fraction of clusters in the melt based on the distribution of clusters proposed by the authors according to the number of particles included in the framework of the concept of randomized particles developed by the authors, which is directly related to the Boltzmann’s distribution.

keywords Partial-cluster model, viscosity, Cu – Al alloy, randomization, distribution, thermal barrier, phase diagram, isotherm

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