Theoretical Modeling to Predict the Thermodynamic, Structural, Surface and Transport Properties of the Liquid Tl−Na Alloys at different Temperatures

Abstract

Theoretical modeling equations are developed by extending regular associated solution model to predict the thermodynamic and structural properties of the liquid Tl−Na alloys at higher temperatures. The thermodynamic properties have been predicted by computing activities of unassociated monomers ( and ) and free energy of mixing ( ) at temperatures 673 K, 773 K, 873 K and 973 K. The structural properties have been predicted by computing concentration fluctuation in long wavelength limit ( ), short range order parameter ( ) and ratio of mutual to intrinsic diffusion coefficients ( ) at aforementioned temperatures. These properties have been then correlated with the modified Butler's model to predict the surface properties, such as surface concentrations of free monomers ( and ) and surface tension ( ) of the alloy at above mentioned temperatures.

Mixing properties of Ni-Al liquid alloy at different temperatures

“…forming tendency at elevated temperatures. The theoretical findings of this work are in accordance with that of others [3,29,[37][38][39]40].…”

Modeling equations to predict the mixing behaviours of Al−Fe liquid alloy at different temperatures

“…The terms ω 12 , ω 13 and ω 23 represent the pairwise interaction energies for the species A, B; A, A μ B and B, A μ B respectively. ω 12 and ω 13 in terms with activity coefficients at infinite dilution (γ 1 0 , 1=A and γ 2 0 , 2=B) can be correlated as follows [11,15] …”

“…The surface properties of Al−Fe liquid alloy at 1873 K have been computed using Equation (12a) in the framework of Renovated Butler model. The molar surface areas of the components of the liquid alloy (λ i ; i = A = Al and B = Fe) are calculated from Equations (12b) and (12c) by putting f = 1.06 [14,15,23]. The molar volume (V i 0 ) of the pure component is estimated from the ratio of its atomic mass to density (m/ρ).…”

“…We have computed the mixing behaviors of the alloy at 1873 K, 1973 K, 2073 K and 2173 K, 1873 K being its melting temperature. The parameters ω 12 , ω 13 and ω 23 in the preferred model are assumed to be temperature dependent only and they are computed using the following relations [15,23] d[ω i,j (T)] x p = (∂ω i,j / ∂T)dT and ω i,j (T k ) = ω i,j (T) + (∂ω i,j / ∂T)dT (13) where i , j = 1, 2 and 3 for i ≠ j, x p is the bulk mole fraction of A or B such that p = 1 or 2 and dT = T k − T; T (=1873 K) is the melting temperature and T k (=1973 K, 2073 K and 2173 K) are the temperature of interests for the alloy.…”

Thermodynamic, structural, surface and transport properties of Au-Ni liquid alloy at 1150 K

“…The surface properties and the viscosity of the liquid alloys are the direct consequences of their thermodynamic properties. Hence the surface properties, such as surface tension ( ) and the extent of surface segregation ( ) of the system were computed using Butler's model [30][31][32][33][34]. The viscosity ( ) of the system was computed on the basis of Kaptay [34,35] and Budai-Benko-Kaptay (BBK) [36] models.…”