Temperature dependences of surface tension, density and viscosity study of Sn-Ag-Cu with Bi additions using theoretical models

Abstract

Abstract In this work, the kohler, Muggianu,Toop and Hillert geometric models were used to calculate the surface tension, molar volume and density of the liquid Sn-Ag-Cu-Bi quaternary alloys along three selected sections xSn:xAg:xCu = 1:1:1, 1:1:2 and 1:2:1 in the temperature range of 923 K–1423 K. The choice of this temperature range was made on the basis of the calculation results of the liquidus line of the alloys belonging to the three sections. The same properties have been estimated for five selected Sn2.7Ag0.86Cu3.86Bi, Sn3.13Ag0.48Cu4.02Bi, Sn2.95Ag0.53Cu6.81Bi, Sn2.68Ag1.01Cu6.62Bi and Sn3.24Ag0.75Cu1.76Bi quaternary alloys between 623 K and 1123 K for comparison with the available experimental data. Moreover, the surface tension and density of these five alloys have also been calculated on the basis of Guggenheim and theoretical equation, respectively. In addition, the Seetharaman-sichen and Kaptay equations were extended to estimate the viscosity of SAC + Bi alloys. We also discussed the influence of Bismuth addition in liquid Sn-Ag-Cu-Bi. Estimated values show that Bi increases molar volume and density but decreases the surface tension and viscosity. On the other hand, the surface tensions diminish with the temperature for the all studied models, with the exception of some concentration of Bismuth; an inverse tendency is observed (dσ/dT) > 0. While, the density diminishes with increasing temperature for all alloys (dσ/dT) < 0. These models have been shown to be a great alternative for calculating the thermo-physical properties of quaternary systems.