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

2017 ◽  
Vol 22 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Ganesh Kumar Shrestha ◽  
Bijay Kumar Singh ◽  
Indu Shekhar Jha ◽  
Ishwar Koirala
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Energy Parameter ◽  
Concentration Fluctuations ◽  
Size Ratio ◽  
Liquid Alloys ◽  
Order Energy ◽  
Energy Of Mixing ◽  
Different Temperatures ◽  
Free Energy Of Mixing

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 (Scc(0)) at different temperatures in the entire range of concentration. Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, page: 25-33

scholarly journals A Theoretical study of thermodynamic properties of Cd-Bi liquid alloy

BIBECHANA ◽  
1970 ◽  
Vol 8 ◽  
pp. 90-95
Author(s):  
D Adhikari
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Liquid Alloy ◽  
Theoretical Study ◽  
Energy Parameter ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Good Agreement

Flory’s model has been used for the study of thermodynamic properties of Cd-Bi liquid alloys. Free energy of mixing, heat of mixing, entropy of mixing and activity of Cd have been determined. All of these computed quantities have been found to be in a good agreement with observed values.Keywords: Flory’s model; thermodynamic properties; Cd-Bi liquid alloy; weakly interacting system; interaction energy parameter  DOI: http://dx.doi.org/10.3126/bibechana.v8i0.5693  BIBECHANA 8 (2012) 90-95

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

Calculation on the Free Energy of Mixing of some Silane Systems

2011 ◽  
Vol 391-392 ◽  
pp. 1017-1021
Author(s):  
Ru Zhang ◽  
Yan Fen Wu ◽  
Ping Hu
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Activity Coefficients ◽  
Influence Factors ◽  
Critical Parameters ◽  
Model Parameters ◽  
Free Energies ◽  
Wilson Model ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Six binary silane systems were chosen to calculate the activity coefficients (γ) and free energies of mixing (ΔGm). These systems included: methyldichlorosilane + methyltrichlorosilane, methyldichlorosilane + methylvinyldichlorosilane, methyldichlorosilane + toluene, methyltrichlorosilane + methylvinyldichlorosilane, methyltrichlorosilane + toluene, methylvinyldichlorosilane + toluene. Based on the Antoine constants, critical parameters of the pure components and Wilson model parameters, γ and ΔGmwere calculated. The influence factors of these thermodynamic properties were also discussed.

scholarly journals Energetics and local order in In-based liquid alloys

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 60-71
Author(s):  
RP Koirala ◽  
BP Singh ◽  
IS Jha ◽  
D Adhikari
Keyword(s):  
Thermodynamic Properties ◽  
Local Order ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Association Model ◽  
Long Wavelength ◽  
Energy Of Mixing ◽  
Self Association ◽  
Free Energy Of Mixing ◽  
Solution Behaviour

A comparative study has been carried out to understand the concentration dependence of 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  and Warren-Cowley short range order parameter  of  In-based three liquid alloys (In-Pb , In-Tl and In-Zn) on the basis of self-association model. The analysis reveals that self-association model successfully explains the observed properties of the liquid alloys.  Positive deviation of the thermodynamic properties of the alloys from the Raoultian solution behaviour indicates that the alloys are weakly segregating in nature. The comparative assessment of the interaction energy and the microscopic properties suggests that the degree of segregation is greatest in In-Zn alloy and comparable in In-Pb and In-Tl alloys.BIBECHANA 13 (2016) 60-71

The statistical thermodynamics of multicomponent systems

1951 ◽  
Vol 205 (1081) ◽  
pp. 247-269 ◽  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Potential Energy ◽  
Multicomponent Systems ◽  
Reference Species ◽  
Two Phase ◽  
Energy Of Mixing ◽  
Volume Of Mixing ◽  
Two Component Systems ◽  
Free Energy Of Mixing

This paper describes a new statistical approach to the theory of multicomponent systems. A ‘conformal solution’ is defined as one satisfying the following conditions: (i) The mutual potential energy of a molecule of species L r and one of species L s at a distance ρ is given by the expression u rs (ρ) = f rs u 00 ( g rs ρ ), where u 00 is the mutual potential energy of two molecules of some reference species L 0 at a distance ρ , and f rs and g rs are constants depending only on the chemical nature of L r and L s . (ii) If L 0 is taken to be one of the components of the solution, then f rs and g rs are close to unity for every pair of components. (iii) The constant g rs equals ½( g rr + g ss ). From these assumptions it is possible to calculate rigorously the thermodynamic properties of a conformal solution in terms of those of the components and their interaction constants. The non-ideal free energy of mixing is given by the equation ∆* G = E 0 ƩƩ rs x r x s d rs , where E 0 equals RT minus the latent heat of vaporization of L 0 , x r is the mole fraction of L r and d rs denotes 2 f rs — f rr — f ss . This equation resembles that defining a regular solution, with the important difference that E 0 is a measurable function of T and p , which makes it possible to relate the free energy, entropy, heat and volume of mixing to the thermodynamic properties of the reference species; and the predicted relationships between these quantities agree well with available data on non-polar solutions. The theory makes no appeal to a lattice model or any other model of the liquid state, and can therefore be applied both to liquids and to imperfect gases, and to two-phase two-component systems near the critical point.

scholarly journals Thermodynamic Properties of InNa Liquid Alloy

1970 ◽  
Vol 6 (6) ◽  
pp. 16-18
Author(s):  
SK Chakrabarti ◽  
IS Jha ◽  
BP Singh
Keyword(s):  
Thermodynamic Properties ◽  
Liquid Alloy ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Atomic Composition ◽  
Binary Liquid ◽  
Scientific World ◽  
Energy Of Mixing ◽  
Large Asymmetry ◽  
Free Energy Of Mixing

The large asymmetry observed in the properties of mixing of indium-sodium liquid alloy is discussed on the basis of quasi-lattice chemical model. A special attention is given to the concentration dependence of free energy of mixing, entropy of mixing and heat of mixing. The results explain the observed asymmetry in the properties of mixing of InNa liquid alloys around equi-atomic composition. Key words: Complex forming alloys; Binary liquid alloys; Quasi-lattice model; Thermodynamic properties. DOI: 10.3126/sw.v6i6.2627 Scientific World, Vol. 6, No. 6, July 2008 16-18

scholarly journals Conformal solution model for the thermodynamic properties of antimonyindium liquid alloys

1970 ◽  
Vol 9 (9) ◽  
pp. 13-15 ◽  
Author(s):  
SK Chakrabarti ◽  
IS Jha ◽  
BK Jha ◽  
BP Singh
Keyword(s):  
Free Energy ◽  
Liquid Alloy ◽  
Concentration Fluctuations ◽  
Solution Model ◽  
Heat Of Mixing ◽  
Atomic Composition ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

In the present work we have considered the antimony-indium liquid alloy which shows anomaly as regards its heat of mixing and the concentration fluctuations in the long-wavelength limit. On the other hand, the free energy of mixing and the entropy of mixing are found to be symmetric about the equi-atomic composition. Such alloying behaviour has been tried to explain on the basis of conformal solution model. This is a statistical mechanical model based on the formation of complex within the liquid alloy. In this model besides the interaction between unlike atoms, that between each constituent element and the complex too is taken into account. In course of theoretical treatment the activity of antimony is also computed for different concentrations. Our results indicate that Sb-In alloys are thermodynamically most stable around the equi-atomic composition. Key words: Binary liquid alloy; Conformal solution model; Free energy of mixing; Activity; Heat of mixing; Entropy of mixing; Concentration fluctuations in the long-wavelength limit. DOI: http://dx.doi.org/10.3126/sw.v9i9.5510 SW 2011; 9(9): 13-15

Thermodynamic Properties of Liquid Binary Transition-Metal Alloys in the Bretonnet-Silbert Model

2007 ◽  
Vol 263 ◽  
pp. 105-110 ◽  
Author(s):  
N.E. Dubinin ◽  
L.D. Son ◽  
N.A. Vatolin
Keyword(s):  
Free Energy ◽  
Transition Metal ◽  
Thermodynamic Properties ◽  
Excess Entropy ◽  
Thermodynamic Perturbation Theory ◽  
Exchange Correlation ◽  
Transition Metal Alloys ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Model Pseudopotential

In the present study, we apply the Bretonnet-Silbert local model pseudopotential, which takes into account the s-d hybridization in interacting between ion and s-electron to calculate the thermodynamic properties of binary transition-metal liquid alloys. The Wills-Harrison approach is used to take into account the d-electron terms in the free energy. We use the simplest variant of the variational method of the thermodynamic perturbation theory (with the hard-sphere reference system), the Vashishta-Singwi exchange-correlation function, and the Lorenz form of the density of d-electron states. The free energy of mixing, internal energy of mixing, and excess entropy of mixing are calculated for a Fe-Co liquid alloy at different compositions near the melting temperature. The agreement with the experimental data is quite satisfactory.

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