THEORETICAL STUDY OF THERMODYNAMIC PROPERTIES OF Cu-Pb LIQUID ALLOYS AT DIFFERENT TEMPERATURE BY OPTIMIZATION METHOD

Abstract

A theoretical assessment on thermodynamic properties and concentration fluctuations of Cu-Pb liquid alloys at a specified temperature has been made by using the fitted values for size ratio ( ) and order energy parameter (W) of the alloys in Quasi-Lattice Theory where the combined effect of size ratio, entropic and enthalpic effect is considered. The order energy parameter (W) of the alloys is temperature dependent and its value at the required temperature has been determined by using the value of order energy parameter at the given temperature and temperature derivative of order energy parameter ( ). The values of W at different temperatures have been used to determine the free energy of mixing of the alloys at different temperatures which are then used for the optimization procedure in order to calculate the corresponding values of partial excess free energy of mixing and activity of the constituents involved in the alloy at different temperatures. These parameters have been used to predict the concentration fluctuations in long wavelength limit (S cc (0)) at different temperatures in the entire range of concentration.Keywords: Optimization procedure, Order energy parameter, Partial excess free energy of mixing, Size ratio, Liquid alloys. INTRODUCTIONInvestigations on the thermodynamic and structural properties of the alloys in liquid state are very essential to study the alloying behavior of the alloys. In order to achieve this goal, metal physicists, chemists and metallurgists have been working on several models (Flory, 1942;Alonso & March, 1982; Bhatia & Singh, 1989;Prasad et al., 1989;Young, 1992;Akinlade et al., 2000;Adhikari et al., 2010;Jha et al., 2014; Singh et al., 2014a Singh et al., , 2014b to understand the mixing properties of binary liquid alloys for preparing desired alloys. Copper being one of the most useful metals in our life because of its extraordinary corrosion resistance property is widely used in our daily-life mostly as a pure metal. Since it is a little soft metal, its hardness can be increased by making its alloys which have huge commercial applications because of their good electrical and mechanical properties along with high corrosion resistance. Though there

Thermophysical properties of metallic melts and their effects on solidification related processes

“…The Cu-Pb phase diagram data [25][26][27][28][29][30][31][32][33], positive enthalpy of mixing [33,48] as well as the activity datasets [49,50] suggest endothermic mixing behaviour of these alloys, that is substantiated by a monotectic type phase diagram of the Cu-Pb system [25,[30][31][32]. The abovementioned properties datasets were used to calculate the interaction energy parameter, which resulted as 𝑖𝑖 = 1.66 𝑘𝑘 𝐵𝐵 𝑇𝑇, in agreement with the corresponding data reported in [34]. In the framework of SAM [24,41,51], using the phase diagram data [28-30], the interaction energy term 𝑖𝑖, the enthalpy of mixing [48], Cu [49] and Pb [50] activities, the thermodynamic properties of mixing were calculated for T = 1373 K (Figure 1).…”

“…Large positive interaction energies indicate complete demixing in this system and the presence of the two liquid phases in the phase-separated region with Pb-content within 18-67 at % below the critical solution temperature of 1280 K. Above that temperature, the homogeneous liquid phase exists. The enthalpy of mixing, Cu and Pb activities measured at temperature of 1473 K and together with the data on the Gibbs free energy of mixing [33] were taken to calculate the temperature dependent interaction energy, thermodynamic and structural functions of liquid Cu-Pb alloys [34]. On the other side, the calculations of the surface properties of Cu-Pb melts for T=1373 K were reported in [19].…”

Thermophysical Properties of Fe-Si and Cu-Pb Melts and Their Effects on Solidification Related Processes

“…Large positive interaction energies indicate complete demixing in this system and the presence of the two liquid phases in the phase-separated region with Pb-content within 18-67 at % below the critical solution temperature of 1280 K. Above that temperature, the homogeneous liquid phase exists. The enthalpy of mixing, Cu and Pb activities measured at temperature of 1473 K and together with the data on the Gibbs free energy of mixing [33] were taken to calculate the temperature dependent interaction energy and thermodynamic and structural functions of liquid Cu-Pb alloys [34]. On the other side, the calculations of the surface properties of Cu-Pb melts for T = 1373 K were reported in [19].…”

Comparison of Thermo-physical Properties of Mg-Ga and Mg-Pb Alloys at 1000 K

“…The alloys in the molten state are studied in metallurgy and industry for high-temperature application as well. Hence the mixing behavior of elements of the alloys at high temperatures was considered a prime concern to all metal physicists, metallurgists, and chemists (Shrestha et al, 2017). The Redlich-Kister (R-K) equation (Redlich & Kister, 1948) is considered an important tool to understand the thermodynamic property like excess Gibbs free energy of binary molten alloy at high temperatures.…”