scholarly journals Entropy of Mixing of Liquid NaCd System

1970 ◽  
Vol 10 ◽  
pp. 105-107
Author(s):  
S. K. Chatterjee ◽  
L. C. Prasad ◽  
A. Bhattarai
Keyword(s):  
Solid Phase ◽  
Excess Free Energy ◽  
Liquid Alloys ◽  
Compound Formation ◽  
Mixing Properties ◽  
Entropy Of Mixing ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Statistical Mechanical ◽  
Free Energy Of Mixing

The observed asymmetric behaviour of mixing properties of NaCd liquid alloys, with smaller negative value for excess free energy of mixing (-4.4919KJ) has aroused our interest to undertake a theoretical investigation of this system.The existence of an intermetallic compound in the solid phase, which is manifested in the phase diagram,  may be one of the factors for the anomalous behaviour of property of mixing. A simple statistical mechanical theory based on complex formation model (the complex is formed by the preferential arrangement of A and B constituent atoms of the alloy AB ;( μA + νB = Aμ Bν) has been used to investigate the phenomena of compound formation in NaCd liquid alloys through the study of entropy of mixing through out the whole concentration range.Nepal Journal of Science and Technology Volume 10, 2009 December Page: 105-107 

Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

2014 ◽  
Vol 10 (6) ◽  
pp. 2843-2852
Author(s):  
Sujeet Kumar Chatterjee ◽  
Lokesh Chandra Prasad ◽  
Ajaya Bhattarai
Keyword(s):  
Nearest Neighbor ◽  
Effective Interaction ◽  
Pair Potential ◽  
Sphere Diameter ◽  
Compound Formation ◽  
Pseudopotential Theory ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Statistical Mechanical ◽  
Free Energy Of Mixing

The observed asymmetric behaviour of mixing of  NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has  aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na,  effective interaction between  Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming  concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

scholarly journals Theoretical assessment for the mixing properties of AlMg liquid alloys at 1073K

2021 ◽  
Vol 2070 (1) ◽  
pp. 012074
Author(s):  
Shayista Ahmad ◽  
M P Sah ◽  
R P Chaudhary ◽  
I S Jha ◽  
J Mandal
Keyword(s):  
Free Energy ◽  
Short Range ◽  
Short Range Order ◽  
Liquid Alloys ◽  
Mixing Properties ◽  
Long Wavelength ◽  
Entropy Of Mixing ◽  
Mixing Energy ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Abstract The alloying behavior of AlMg alloy in the liquid form at 1073 K has been theoretically investigated in the framework of four-parameter model which is based on Maclaurin series. The analytical expressions for thermodynamic functions such as excess free mixing energy, free mixing energy, enthalpy of mixing and entropy of mixing and microscopic functions such as concentration fluctuations at the long wavelength limit and Warren-Cowley chemical short range order parameter have been derived. These expressions have been used to compute the excess Gibbs free energy of mixing, Gibbs free energy of mixing, activity, enthalpy(heat) of mixing, excess entropy of mixing, entropy of mixing, concentration fluctuations in long wavelength limit and Warren-Cowley short range order parameters of AlMg liquid alloys at 1073 K. The investigation shows the excellent concurrence between the experimental and theoretical measurements of the mixing properties of AlMg liquid alloys at 1073 K. Interaction parameters of energy depends on temperature.

scholarly journals Heat of Mixing of some Binary Liquid Alloys

1970 ◽  
Vol 7 (7) ◽  
pp. 96-99
Author(s):  
BK Kanth ◽  
SK Chakrabarti
Keyword(s):  
Free Energy ◽  
Successive Approximation ◽  
Chemical Model ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Atomic Composition ◽  
Entropy Of Mixing ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

There are a large number of binary liquid alloys the thermodynamic properties of mixing of which are not symmetrical about the equi-atomic composition-deviating maximally from those of the ideal alloys. Here we have considered three such alloys-indium-sodium, cadmium-sodium and copper-tin-and tried to calculate their heat of mixing at different concentrations of the ingredients. The liquidus lines of these alloys reveal that the constituent species form complexes. So, we have considered a quasi-lattice chemical model for computation of the thermodynamic entities. It is a statistical model in which grand partition function is used assuming that the energy of a given nearest neighbour bond is different if it belongs to the complex than if it does not. For each alloy we have started with the expression for excess free energy of mixing according to this model and computed the free energy of mixing for different concentrations of the metals within it by deriving the value of interaction parameters through successive approximation method. Thereafter, the expression for excess entropy of mixing is taken into account and the entropy of mixing is computed for different concentrations after finding out the temperature derivative of interaction parameters by the method of successive approximation. Finally the heat of mixing is calculated from these free energy of mixing and entropy of mixing on using the standard thermodynamic relation. The results explain the observed asymmetry in the heat of mixing of the said binary liquid alloys around equi-atomic composition. Key words : Binary liquid alloy; Quasi-lattice chemical model; Heat of mixing DOI: 10.3126/sw.v7i7.3836 Scientific World Vol.7(7) 2009 pp.96-99

scholarly journals Chemical Ordering in Na-Pb and Na-Hg Binary Liquid Alloys

2017 ◽  
Author(s):  
Ayideji Akintunde Ajayi ◽  
Enoch Debayo Ogunmola
Keyword(s):  
Binary Alloy ◽  
Liquid Alloy ◽  
Energy Parameter ◽  
Liquid Alloys ◽  
Mixing Properties ◽  
Long Wavelength ◽  
Chemical Ordering ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Liquid Binary Alloy

A simple model has been used to investigate the nature of chemical order in Na-Pb and Na-Hg liquid binary alloy at 700K and 673K respectively. The energy parameter obtained from the model was used to calculate the concentration dependent mixing properties such as Gibb’s free energy of mixing, Concentration fluctuations in the long wavelength limit and the Warren-Cowley chemical short range order parameter. Results obtained showed that both alloys are hetero-coordinated throughout the entire concentration and there is tendency for segregation and demixing to take place in the liquid alloys. We observed that Na-Hg liquid alloy is more strongly interacting binary alloy and chemically ordered than Na-Pb liquid alloy.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

Quasi-Chemical Model for Liquid Li-Cd Alloys

1989 ◽  
Vol 44 (6) ◽  
pp. 529-532
Author(s):  
L. C. Prasad ◽  
R. N. Singh
Keyword(s):  
Order Parameter ◽  
Short Range ◽  
Short Range Order ◽  
Chemical Model ◽  
Liquid Alloys ◽  
Range Order Parameter ◽  
Long Wavelength ◽  
Pairwise Interactions ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The quasi-chemical model based on pairwise interactions is used to study the concentration dependent thermodynamic properties of Li-Cd liquid alloys. Special attention is given to the concentration-concentration correlation function in the long wavelength limit [Scc(0)] and the chemical short-range order parameter (CSRO). The activity, free energy of mixing, Scc(0) and CSRO are computed as functions of temperature and concentration.

scholarly journals Viscosity of liquid Na-K alloy

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 135-144 ◽  
Author(s):  
R. P. Koirala ◽  
B. P. Singh ◽  
I. S. Jha ◽  
D. Adhikari
Keyword(s):  
Experimental Data ◽  
Atmospheric Pressure ◽  
Composition Dependence ◽  
Dynamic Behaviour ◽  
Enthalpy Of Mixing ◽  
Mixing Properties ◽  
Energy Of Mixing ◽  
Using Data ◽  
Free Energy Of Mixing ◽  
Theoretical Assessment

The present work reports a theoretical assessment of the composition dependence of mixing properties of liquid Na-K alloy at 384K at fixed pressure, most likely, at the atmospheric pressure. In this work we have estimated the interaction energy in the alloy at the mentioned temperature on the basis of quasi-chemical approximation for regular alloy and employed it to work out basic thermodynamic properties of mixing such as free energy of mixing, entropy of mixing and enthalpy of mixing as function of composition of the alloy. To understand the dynamic behaviour in the liquid Na-K alloy, we have carried out theoretical investigation of viscosity under consideration of Moelwyn-Hughes equation by using data for enthalpy of mixing obtained from quasi-chemical approximation. Due to scanty of experimental data on viscosity of Na-K alloy at 384K, we have performed computation of viscosity also from Kaptay equation for comparison. The calculations have shown that there is a good match between theoretically computed thermodynamic functions and the available corresponding experimental data. The sets of viscosity values obtained against composition from the two equations show deviations from the ideality and themselves are reasonably comparable to each other.DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11797BIBECHANA 12 (2015) 128-137

scholarly journals Thermodynamic and structural properties of Mg-Tl liquid alloy

BIBECHANA ◽  
2012 ◽  
Vol 8 ◽  
pp. 81-89 ◽  
Author(s):  
BP Singh ◽  
D Adhikari ◽  
IS Jha ◽  
BC Kumar ◽  
SK Chaudhary ◽  
...  
Keyword(s):  
Short Range ◽  
Enthalpy Of Mixing ◽  
Mixing Enthalpy ◽  
Mixing Properties ◽  
Long Wavelength ◽  
Energy Of Mixing ◽  
Chemical Complex ◽  
Free Energy Of Mixing ◽  
Associated Solution Model ◽  
Associated Solution

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

scholarly journals Theoretical investigations on temperature dependence of thermodynamic properties and concentration fluctuations of In-Tl binary liquid alloys by optimization method

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 11-23
Author(s):  
G K Shrestha ◽  
I S Jha ◽  
B K Singh
Keyword(s):  
Free Energy ◽  
Liquid Alloy ◽  
Entire Range ◽  
Excess Free Energy ◽  
Concentration Fluctuations ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Different Temperatures ◽  
Free Energy Of Mixing ◽  
Best Fit

The thermodynamic properties, i.e. free energy of mixing (GM), heat of mixing (HM), entropy of mixing (SM) and activity (ai) of the component i (i , and structural property i.e. concentration fluctuations in long wave-length limit [Scc(0)] of In-Tl binary liquid alloy at a specified temperature have been investigated in the framework of quasi-lattice model on assuming the coupled effect of size ratio and entropic (or energetic) as well as enthalpic effect. These properties of In-Tl liquid alloy at 723 K have been computed theoretically by estimating the best fit value of order energy parameter (W) and size ratio () over the entire range of concentration in order to match their experimental values. The best fit value of  W at 723 K has been used to determine the values of W at different temperatures with the help of temperature derivative of W which are then used for the optimization procedure in order to calculate the corresponding values of excess free energy of mixing, partial excess free energy of mixing and activity of the components involved in the alloy at different temperatures. These parameters have been used to investigate the concentration fluctuations in long wavelength limit {Scc(0)} of In-Tl binary liquid alloy at different temperatures over the entire range of concentration which have been used to predict the various other structural properties like excess stability function (EXS), diffusion coefficient ratio (Dm/Did), short range order parameter (α1) at different temperatures.BIBECHANA 15 (2018) 11-23

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