Regular Associated Solution Model Research Articles

Thermo-Physical Properties of Al-Mg Alloy in Liquid State at Different Temperatures

Thermo-physical properties of Al-Mg alloys in molten state at 1073 K have been studied using thermodynamic modeling. Thermodynamic properties, such as free energy of mixing, heat of mixing, entropy of mixing, activities and structural properties, such as concentration fluctuation in long wavelength limit, Warren-Cowely short range order parameter have been studied at 1073 K, 1173 K, 1273 K and 1373 K on the basis of regular associated solution model. The surface properties such as surface concentrations and surface tension of the liquid alloys have been studied by using Butler’s model. A consistent set of model parameters have also been obtained by using optimization procedure based on statistical thermodynamics. Our analysis reveals that Al-Mg alloy is moderately interacting and it shows ordering nature at 1073 K. The nature of the alloys changes from ordering to segregating as the temperature increases.

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

Redlich−Kister (R−K) polynomials have been associated with the extended regular associated solution model to predict and explain the thermodynamic properties and structural properties of Al−Fe liquid alloy at 1873 K, 1973 K, 2073 K and 2173 K; 1873 K being its melting temperature. The thermodynamic properties, such as free energy of mixing and activities of free monomers ( and ) and structural properties, such as concentration fluctuation in long wave length limit, chemical short range order parameter and ratio of diffusion coefficients ( have been predicted at above stated temperatures. Renovated Butler model has been employed to predict the surface tension and surface segregation of the alloy at stated temperatures with the help of thermodynamic properties. Theoretical findings prevail that the tendency towards compound formation of the liquid alloy decreases with increase in its temperature beyond melting temperature. Eventually, its surface tension decreases and there is gradual exchange of atoms between the surface and bulk regions to maintain equilibrium at elevated temperatures. The liquid alloy under investigation thus shows ideal behaviours at higher temperatures. BIBECHANA 15 (2018) 60-69

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

<p>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 (a<sub>Tl</sub> and a<sub>Na</sub>) and free energy of mixing (G<sub>M</sub>) 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 (S<sub>CC</sub>(0)), short range order parameter (α<sub>1</sub>) and ratio of mutual to intrinsic diffusion coefficients (D<sub>M</sub>/D<sub>id</sub>) 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 (X<sup>S</sup><sub>Tl</sub> and X<sup>S</sup><sub>Na</sub>) and surface tension (σ) of the alloy at above mentioned temperatures.</p><p><strong>Journal of Nepal Physical Society</strong><em><br /></em>Volume 4, Issue 1, February 2017, Page: 101-110</p>

Thermodynamics of the Cu–Bi system determined by vapour pressure measurements

Application of Knudsen method for solid and liquid copper in the temperature range 1300–1725K, liquid bismuth in temperatures 769–1129K, and liquid Cu–Bi alloys in temperatures from 871 to 1469K, provided experimental data which made it possible to characterize thermodynamic properties of liquid and gaseous phase of Cu–Bi system. Standard enthalpies of copper and bismuth monomers sublimation and dissociation of bismuth dimer as well as parameters of Regular Associated Solution model (RAS), describing excess Gibbs energy of liquid phase of the examined system, were determined. The obtained model takes into account also presence of disturbances in vaporization of bismuth dimer from Cu–Bi alloys by introducing into the model a parameter which describes the evaporation coefficient of that particle.

Thermodynamic, structural, transport and surface properties of Pb-Tl liquid alloy

Thermodynamic properties, such as free energy of mixing, heat of mixing, entropy of mixing, activities and the microscopic structural properties, such as concentration fluctuation in long-wavelength limit and chemical short-range order parameter of Pb-Tl liquid alloy at 773 K have been studied on the basis of regular associated solution model. We have estimated the mole fractions of the complex and the unassociated atoms assuming the existence of complex as energetically favoured in the liquid state. The compositional contributions of the heat of mixing of the species Pb and Tl and the heat of formation of the compound to the net enthalpy change have also been studied. The transport properties such as, viscosity and the ratio of mutual and intrinsic coefficients have been studied using different approaches. The surface concentration of Tl atoms has been computed and it has been employed to calculate the surface tension of Pb-Tl liquid alloy. Both the theoretical and the experimental values of the concentration fluctuation in long-wavelength limit are found to be less than the ideal value, revealing that the concerned system is hetero-coordinating in nature. The interaction energies are found to be temperature dependent and respective alloy is found to be weakly interacting system. BIBECHANA 13 (2016) 100-113

Thermodynamic and structural properties of Bi-based liquid alloys

Thermodynamic and microscopic structural properties of two Bi-based liquid alloys, such as In–Bi at 900K and Tl–Bi at 750K have been studied employing the regular associated solution model. We have estimated the mole fractions of the complexes and the free monomers assuming the existence of complexes In2Bi in In–Bi melt and TlBi in Tl–Bi melt. The thermodynamic properties have been studied by computing the Gibbs free energy of mixing, enthalpy of mixing, entropy of mixing and activities of the monomers. The compositional contributions of the heat associated with the formation of complexes and the heat of mixing of the monomers to the net enthalpy change has also been studied. The structural properties of the liquid alloys have been studied by computing concentration fluctuation in the long-wavelength limit, chemical short-range order parameter and the ratio of mutual to intrinsic diffusion coefficients. For both of the alloy systems, the theoretical as well as the experimental values of SCC(0) are found to be lower than the corresponding ideal values over the whole composition range, indicating the hetero-coordinating nature of Bi–In and Bi–Tl alloy melts. All the interaction energy parameters are found to be negative and temperature dependent, and both the alloy systems are found to be weakly interacting.

Segregating to ordering transformation in In–Sn melt

The regular associated solution model has been used to study the thermodynamic and microscopic structural properties of In-Sn liquid alloy at 700 K. We have assumed the existence of complex in the liquid mixture and estimated the mole fractions of the complexes and the unassociated monomers throughout the entire concentrations. The thermodynamic properties, such as the free energy of mixing (), the enthalpy of mixing (), the entropy of mixing () and the activities of the monomers ( and ), and the microscopic structural properties, such as concentration fluctuation in long-wavelength limit () and the Warren–Cowley short-range order parameter (), have been computed using concept of the determined mole fractions. The theoretical analysis suggests that the In–Sn system behaves as homo-coordinating nature in Sn-rich region and hetero-coordinating nature in In-rich region in the liquid state. The interaction energy parameters are found to be temperature-dependent and the In–Sn liquid alloy is found to be weakly interacting system.

Thermodynamic and structural behaviour of Tl-Na liquid alloy

In this work we intend to study the thermodynamic and microscopic structural properties of Tl-Na liquid alloy at 673 K on the basis of regular associated solution model. We have estimated the mole fractions of the complex and the free monomers assuming the complex TlNα as energetically favoured in the initial melt. In thermodynamic properties, we have computed free energy of mixing (GM), enthalpy of mixing (GM), entropy of mixing (SM) and activities of the monomers (αTl and αNα). The compositional contributions of the heat of mixing and the heat of formation of the complex to the net enthalpy change have also been studied. The microscopic structural properties of the alloy have been studied by computing concentration fluctuation in the long wavelength limit (SCC(O)), chemical short range order parameter (α1) and the ratio of mutual to intrinsic diffusion coefficients (DM/Did). Both the theoretical and the experimental values of SCC(O) are found to be less than the ideal values at all compositions which indicates the ordering nature of Tl-Na liquid alloy at 673 K. All the interaction energy parameters are found to be negative and temperature dependent. The liquid system is found to be moderately interacting.DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11784BIBECHANA 12 (2015) 20-29

Thermo-physical properties of Al–Fe melt

The thermodynamic properties, such as free energy of mixing, heat of mixing, entropy of mixing, activity and microscopic properties, such as concentration fluctuation in long wavelength limit, chemical short range order parameter, ratio of mutual and intrinsic diffusion coefficients of Al–Fe in liquid state at 1873 K have been studied on the basis of regular associated solution model. The complex Al3Fe is supposed to be energetically favoured in the liquid solution which is evident from the phase diagram of Al–Fe alloys. Thus the liquid mixture is treated as the ternary solution of complex and unassociated components. The concentrations of the complex Al3Fe and unassociated atoms have also been estimated. The concentration fluctuation in long wavelength limit is less than ideal values in whole range of concentration indicating that the system is ordered at all compositions. Our theoretical analysis suggests that the melt is strongly interacting hetero-coordinating system. The interaction energy parameters...

Segregation in Fe-Pd melt at 1873 K

The thermodynamic and structural properties of Fe-Pd liquid alloys at 1873 K have been computed using regular associated solution model. To compute these functions we have estimated the mole fractions of the complex assuming the existence of FePd3 complex in the melt. The thermodynamic properties such as free energy of mixing (GM), heat of mixing (HM), entropy of mixing (SM) and activity (a) of the melt have been estimated. To understand the microscopic structural properties, we have estimated the concentration fluctuation in long wavelength limit (Scc(0)) and the Warren-Cowley short range parameter (α1). The free energy of mixing was found to be negative at all compositions. But the heat of mixing and the entropy of mixing are found to be positive at all compositions. The equilibrium constant (K) is found be less than negative. The interaction energy parameters (w12, w13 and w23) are all found to be positive and temperature dependent. The theoretical estimation of the concentration fluctuation in long wavelength limit (SCC (0)) is found to be greater than the ideal values throughout the whole range. The theoretical analysis suggests that the Fe-Pd liquid alloy at 1873 K near the melting point is segregating (homo-coordinating) system. The Warren-Cowley short range order parameter is found to be positive which too suggest the homocoordinating (segregating) nature of the system at all compositions. The theoretical analysis also suggests that the Fe-Pd liquid alloy near melting point is weakly interacting system. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10386 BIBECHANA 11(1) (2014) 86-93

Determination and modeling of the thermodynamic properties of liquid calcium–antimony alloys

The thermodynamic properties of Ca–Sb alloys were determined by emf measurements in a cell configured as Ca(s)|CaF2|Ca–Sb over the temperature range 550–830°C. Activity coefficients of Ca and Sb, enthalpy, Gibbs free energy, and entropy of mixing of Ca–Sb alloys were calculated for xCa<0.55. To explain the connection between short-range order of liquid Ca–Sb alloys and the strong deviation from ideality in the thermodynamic properties, two thermodynamic models were invoked and reconciled: the regular associated solution model, assuming the presence of a CaSb2 associate, and the molecular interaction volume model (MIVM). For the first time, the MIVM was used successfully to model the activity coefficients of a system with high-melting intermetallics, reducing the number of fitting parameters necessary from 5 (regular associated model) to 2 (MIVM). From the interaction parameters optimized by fitting at 800°C, the activity coefficient of Ca was predicted at 650°C, with an average error of less than 0.6% in the emf value.

Thermodynamic and structural properties of Mg-Tl liquid alloy

The concentration dependent asymmetry in mixing properties of Mg-Tl liquid alloys at 923 K has been investigated on the basis of regular associated solution model. The concentration of ApB type complex in a regular associated solution of Mg and Tl have been determined. We have then used the concentration of complex to calculate the free energy of mixing, enthalpy of mixing, entropy of mixing, activity, concentration fluctuations in long wavelength limit SCC(0) and the Warren Cowley short-range parameter 1 α .The analysis suggests that heterocoordination leading to the formation of chemical complex Mg2Tl is likely to exist in the melt. The analysis reveals that there is a tendency of unlike atom pairing (Mg-Tl) in Mg-Tl alloy whole range of concentration.Keywords: Mg-Tl alloy; microscopic structure; pairwise interaction energy; chemical short range orderDOI: http://dx.doi.org/10.3126/bibechana.v8i0.5692BIBECHANA 8 (2012) 81-89

Structural and energetic anomaly in liquid Na–Sn alloys

The alloying behaviour of Na–Sn liquid alloys at 773K has been studied by using regular associated solution model. This model has been utilized to determine the complex concentration in a regular associated solution of Na and Sn. We have then used the complex concentration to calculate the free energy of mixing (GM), enthalpy of mixing (HM), entropy of mixing (SM), concentration fluctuations in long wavelength limit (SCC(0)), the Warren Crowley short-range parameter (α1) and ratio of mutual and intrinsic diffusion coefficients (DM/Did). The analysis suggests that heterocoordination leading to the formation of complex Na3Sn is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature and the alloys are more ordered towards intermediate region.

Anomaly in mixing properties of lithium–magnesium liquid alloy

The concentration dependent asymmetry in mixing properties of LiMg liquid alloys at 1000 K has been investigated on the basis of regular associated solution model. The analysis suggests that heterocoordination leading to the formation of chemical complex Li2Mg is likely to exist in the melt.

Concentration Fluctuation in Long Wavelength Limit in Liquid Magnesium Alloy

The microscopic structure of MgSn liquid alloy at 1073K has been studied by using regular associated solution model. For this we have calculated the concentration fluctuation in long wave length limit [SCC(0)] and chemical short range order parameter (α1) of liquid MgSn alloy at 1073 K.Keywords: Binary Alloy; Complex; Chemical order; Microscopic FunctionThe Himalayan Physics Vol.2, No.2, May, 2011Page: 47-49Uploaded Date: 1 August, 2011

Energy Disorder in Liquid Fe-Si Alloy

The observed asymmetry in the properties of mixing of Fe-Si alloy in molten state is successfully explained on the basis of regular associated solution model. We have determined the free energy of mixing, heat of mixing and entropy of mixing of Fe-Si alloys in molten state at 1873 K. The analysis suggests that heterocoordination leading to the formation of complex Fe 2Si is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature.Keywords: Liquid alloy; Clusters; Thermodynamic propertiesThe Himalayan Physics Vol.1, No.1, May, 2010Page: 37-40Uploaded Date: 28 July, 2011

Chemical ordering and thermodynamic properties of HgNa liquid alloys

We have studied the thermodynamic properties and microscopic structures of HgNa liquid alloy at 673K on the basis of regular associated solution model. The concentrations of ApB type complex in a regular associated solution of Hg and Na have been determined. We have then used the concentration of complex to calculate the free energy of mixing, enthalpy of mixing, entropy of mixing, activity, concentration fluctuations in long wavelength limit SCC(0) and the Warren–Cowley short-range parameter α1. The analysis suggests that heterocoordination leading to the formation of complex Hg4Na is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Hg-rich region.

Disorder in liquid Cu–Pd alloys

The disorder in thermodynamic and microscopic structure of liquid Cu–Pd alloy at 1350 K has been studied using regular associated solution model. For this, we have calculated free energy of mixing (GM ), activity (a), concentration fluctuation in long wavelength limit [SCC (0)] and chemical short-range order parameter (α 1) of liquid Cu–Pd alloy at 1350 K. The energetic and structural asymmetry of liquid Cu–Pd alloys has been successfully explained on the basis of regular associated solution model.

Alloying Behaviour of CuPd Liquid Alloy

The mixing properties of CuPd alloy in molten state at 1350 K have been studied by assuming strong interaction between Cu and Pd atoms. Regular associated solution model has been used for the study. The asymmetry in integral excess free energy of mixing, heat of mixing and entropy of mixing has been well explained.

Concentration Dependence of Thermodynamic Properties of NaPb Liquid Alloy

We have determined integral excess free energy of mixing, heat of mixing and entropy of mixing of NaPb alloys in molten state at 700 K. The observed asymmetry in the properties of mixing of NaPb alloy in molten state is successfully explained on the basis of regular associated solution model. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature.