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 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 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 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

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

scholarly journals Free Energy of Mixing of some Binary Liquid Alloys

2016 ◽  
Vol 3 (1) ◽  
pp. 97
Author(s):  
S.K. Chakrabarti ◽  
J.P. Yadav ◽  
S.M. Rafique
Keyword(s):  
Free Energy ◽  
Theoretical Work ◽  
Heat Of Mixing ◽  
Size Factor ◽  
Liquid Alloys ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Statistical Mechanical Model ◽  
Interchange Energy ◽  
Free Energy Of Mixing

<p>Binary liquid alloys often show interesting behaviour as regards their thermodynamic properties. The heat of mixing often bears a large negative value and the entropy of mixing an S-shape. The free energy of mixing becomes asymmetric around the equi-atomic composition especially in case of complex forming alloys. In the present theoretical work we have tried to compute the free energy of mixing of some binary alloys e.g. lithium-lead, potassium amalgam and magnesium-tin―all in liquid state near their respective melting points. All these alloys form strongly interacting systems. So, we have applied Flory’s model which is a statistical mechanical model considering the size factor of the constituent species of a binary liquid alloy. We have ignored the interaction between the complex and each ingredient within an alloy and amended the formula accordingly. In the light of observed activity of a metal within an alloy we have ascertained the interchange energy by the method of successive numerical approximations and then calculated the free energy of mixing according to the said model for different concentrations of the ingredients. Our results explain the observed anomaly in the free energy of mixing of the present liquid alloys.</p><p>Journal of Nepal Physical Society Vol.3(1) 2015: 97-101</p>

scholarly journals Free Energy of Mixing of the Binary Liquid Alloys of Sodium

2012 ◽  
Vol 3 ◽  
pp. 24-26
Author(s):  
S. K. Chakrabarti ◽  
J. Akhter ◽  
R. Sinha
Keyword(s):  
Free Energy ◽  
Liquid Alloy ◽  
Binary Alloys ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Liquid Alloys ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Interchange Energy ◽  
Free Energy Of Mixing

Sodium is a highly reactive alkali metal. Within a binary liquid alloy it generally forms complexes. Due to formation of such complexes the thermodynamic properties of the binary alloys of sodium often show anomaly-deviating maximally from that of the ideal alloys. In the present work we have confined our investigation into the free energy of mixing (GM) of two binary alloys of sodium in liquid phase-Na-Pb and Na-Hg-near the melting point. For this purpose we have used Flory’s model and started with the activity of sodium in the sodium-lead liquid alloy and that of mercury in the sodium amalgam at molten stage. By the method of successive approximations we have ascertained the value of interchange energy for each alloy in the light of the experimental values of activity and finally computed GM for different concentrations of the constituent species. Our computation explains the observed symmetry and anomaly in the free energy of mixing of the Na-Pb and Na-Hg liquid alloys respectively.The Himalayan PhysicsVol. 3, No. 32012Page : 24-26

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

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 100-113 ◽  
Author(s):  
SK Yadav ◽  
LN Jha ◽  
D Adhikari
Keyword(s):  
Liquid Alloy ◽  
Surface Concentration ◽  
Heat Of Formation ◽  
Concentration Fluctuation ◽  
Heat Of Mixing ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Experimental Values

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

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

scholarly journals Size Sensitive Transport Behavior of Liquid Metallic Mixtures

2015 ◽  
Vol 20 (2) ◽  
pp. 140-144
Author(s):  
Bhrigunandan Prasad Singh ◽  
Ishwar Koirala
Keyword(s):  
Size Effect ◽  
Transport Properties ◽  
Diffusion Coefficients ◽  
Liquid Alloys ◽  
Long Wavelength ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Gibb’S Free Energy ◽  
Limit Diffusion

We have used a formalism that connects thermodynamic and transport properties. The formalism has been used to calculate the Gibb’s free energy of mixing, concentration fluctuations in the long wavelength limit, diffusion coefficients and viscosity in Cu-Tl, Cu-Pb and Sn-Tl binary liquid alloys at 1573K, 1473K and 723K respectively with aid of size effect and no size effect. Our calculations show that appreciable size ratio has more effects on the transport properties as compared to thermodynamic properties of homo-coordinated liquid alloys Cu-Tl, Cu-Pb and Sn-Tl.Journal of Institute of Science and Technology, 2015, 20(2): 140-144  

scholarly journals Thermodynamic, structural, surface and transport properties of Zn-Cd liquid alloy at 800 K

BIBECHANA ◽  
2016 ◽  
Vol 14 ◽  
pp. 54-65 ◽  
Author(s):  
K K Mishra ◽  
H K Limbu ◽  
B Yadav ◽  
A K Khan ◽  
I S Jha ◽  
...  
Keyword(s):  
Wave Length ◽  
Heat Of Mixing ◽  
Size Factor ◽  
Mixing Properties ◽  
Binary Liquid ◽  
Long Wave ◽  
Energy Of Mixing ◽  
Alloy Increase ◽  
Structural Surface ◽  
Free Energy Of Mixing

The mixing thermodynamic and structural properties of Zn-Cd liquid at 800K has been studied using Flory’s model. To explain the mixing properties of binary liquid alloys, size factor (ф) and ordering energy (ω) are taken into account. Thermodynamic properties like free energy of mixing (GM), activity (a), Heat of mixing (HM) and entropy of mixing (SM) and the microscopic properties like concentration fluctuation in the long wave length limit (Scc(0)) and chemical short range order parameter (α1) have been calculated. Surface property has also been studied with the help of Buttler’s model. The viscosity of the melt has been computed from Kaptay equation and BBK models. Both the viscosity and surface tension of the alloy increase with addition of zinc- component. BIBECHANA 14 (2017) 54-65

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