Narrow Results

In this paper, the surface tension, molar volume and density of liquid Ag–Cu–Sn alloys have been calculated using Kohler, Muggianu, Toop, and Hillert models. In addition, the surface tension and viscosity of the Ag–Cu–Sn ternary alloys at different temperatures have been predicted on the basis of Guggenheim and Seetharaman–Sichen equations, respectively. The results show that density and viscosity decrease with increasing tin and increasing temperature for the all studied models. While the surface tension shows a different tendency, especially for the Kohler and Muggianu symmetric models. On the other hand, the molar volume increases with increase of temperature and tin compositions. The calculated values of surface tension and density of Ag–Cu–Sn alloys are compared with the available experimental values and a good agreement was observed.

In this paper, some geometrical models such as Kohler, Muggianu, Toop, and Hillert have been used to estimate the molar volume of Au–Bi–Sn ternary systems based on the data of sub-binary systems over a wide temperature range (673–973K). The density of Au–Bi–Sn alloys was calculated from the calculated molar volume and using theoretical equation along three cross-sections $x_{\mathrm{\text{Au}}}$/$x_{\mathrm{\text{Bi}}}=1$/2, 1/1 and 2/1. In addition, the viscosity of Au–Bi–Sn alloys was calculated by using Seetharaman–Sichen equation over a wide temperature range (673–1273K). The density of these alloys show linear dependence on temperature for all investigated compositions, while the molar volumes increase with increasing temperature and Sn compositions. The results show, as a function of temperature, that the increase in concentration of tin influences the viscosity of the Au–Bi–Sn alloys. The calculated values of density of Au–Bi–Sn alloys are compared with the experimental values reported in the literature, and a good agreement was observed.

Some physicochemical properties such as surface tension, molar volume, density and viscosity of liquid Sn–Ag–Cu alloys have been calculated using Kohler, Muggianu, Toop and Hillert geometrical models along three cross-sections namely $x_{\mathrm{\text{Ag}}}$/$x_{\mathrm{\text{Cu}}}=1∕2$, 1/1 and 2/1. Indeed, Guggenheim, Kozlov–Romanov–Petrov and Kaptay equations have also been extended to estimate the surface tension and viscosity based on the thermodynamic data of the investigated system over wide temperature ranges of 823–1123K and 773–1173K, respectively. The results show that the three investigated properties, surface tension, density and viscosity, decrease with increasing tin for all studied models. On the other hand, a different behavior of these properties as a function of the temperature was noted. This evolution depends on the composition of the studied alloys.

On the contrary, the molar volume increases with increase of temperature and tin compositions. It should be noted that the surface tension, density and molar volume show a linear dependence on temperature for all the investigated compositions. For viscosity, a curvilinear dependence has been observed. The calculated surface tensions and densities were compared with those reported experimentally for Sn–Ag–Cu alloys along the cross-section $x_{\mathrm{\text{Ag}}}$/$x_{\mathrm{\text{Cu}}}=$1/1.