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ArticleName Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state
DOI 10.17580/nfm.2023.01.08
ArticleAuthor Makasheva A. M., Malyshev V. P., Bekbayeva L. A.

Zh. Abishev Chemical and Metallurgical Institute, Kazakhstan, Karaganda1NPJSC “Abylkas Saginov Karaganda Technical University”, Kazakhstan, Karaganda2:

A. M. Makasheva*, Doctor of Technical Sciences, Professor, Head of Laboratory of Entropy and Information Analysis of Complex Physical and Chemical Systems1, 2, e-mail:


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

V. P. Malyshev, Doctor of Technical Sciences, Professor, Academician of the Kazakhstan National Academy of Natural Sciences, Chief Researcher of Laboratory of Entropy and Information Analysis of Complex Physical and Chemical Systems1, e-mail:


NPJSC “Abylkas Saginov Karaganda Technical University”, Kazakhstan, Karaganda:
L. A. Bekbayeva, Doctoral Student, e-mail:

*Correspondence author.


The relationship between the liquidus line and viscosity isotherms was established for the copper-tin system based on the partial-cluster model within the concept of chaotic particles. The equations of temperature dependences of dynamic viscosity for copper and tin melts, as well as for the partial-cluster model of Cu – Sn alloy at different temperatures are derived. The shapes of the liquidus line curves duplicate the viscosity isotherms from the calculated data, which use smoothed temperature dependences for pure metals Cu and Sn, as well as different thermal chaotization barriers during the transformation of the alloy to the liquid state. The cause of deviation from the regularity of the general features of the liquidus line and viscosity isotherms was found. It consists in the formation of associated complexes of the CuxSny type, which are statistically stable chemical groupings without separation into a separate phase. These complexes (clusters) are in dynamic equilibrium with the solution matrix, characterized by a disorderly distribution of atoms. The formation of such groups is accompanied by the release of heat. This is accounted for in the partial-cluster viscosity model as an additional thermal barrier to chaotization during cluster fracture with further heating of the melt. Consideration of the new component made it possible to obtain an adequate dependence of the viscosity of Cu – Sn alloy on its composition and the thermal barrier on the liquidus line at 1100 °С. Directions for further determination of the model with the purpose of its refinement and wide use in adapting it to experimental data on viscosity at high temperatures of melts from their state diagrams are outlined and verified.

keywords Viscosity, state diagram, liquidus, Cu – Sn alloy, partial-cluster model, liquid state

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Full content Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state