Determination of the Dynamic Viscosity of Liquid Alloys from the Phase Diagram

Abstract

That viscosity and fluidity are equilibrium processes may be established on the basis of the Boltzmann distribution in terms of randomized particles. Specifically, the virtual presence of three classes of particles— with crystal mobility, liquid mobility, and vapor mobility—is assumed. Accordingly, the viscosity and fluidity of solutions—in particular, molten metallic alloys—may be considered in terms of the equilibrium contributions of each component to the total viscosity and fluidity, despite the kinetic interpretation of the usual expressions for these liquid properties. A linear additive equation for the viscosity is only possible for perfect solutions; for present purposes, that corresponds to alloys with unlimited mutual solubility of the components. Alloys with eutectics, chemical compounds, and other singularities in the phase diagram are characterized by viscosity equations that reproduce the shape of the liquidus curve over the whole range of alloy composition at different temperatures. Greater smoothness and closeness of the curves is observed at higher temperatures. These aspects of the temperature dependence of the viscosity may be explained on the basis of randomized particles and the visual cluster model of viscosity, with calculation of the proportions of the clusters that determine the alloy viscosity. Such viscosity is determined from a formula in which the thermal barrier to randomization is the thermal energy RTcr at the liquidus temperature, which is characterized by the temperature of melt crystallization Tcr, analogously to the melting point of the pure materials. On that basis, we propose a method of calculating the alloy viscosity from the phase diagram. From the temperature dependences of the viscosity of the pure components, the alloy viscosity may be determined from the proportion of clusters at any temperature above the liquidus curve and the viscosities of the pure components, taking account of the mole fraction of each component. The result is a trifactorial model of the viscosity of a liquid alloy. In this model, the variable is the thermal barrier RTcr to randomization, which determines the proportion of clusters both for pure materials (at RTcr = RTm) and for alloys. Overall, this model corresponds to the virtual cluster theory of viscosity and is consistent with the concept of randomized particles.