scholarly journals Thermodynamic Prediction of the Free Energy of Mixing and Activities of some Goldbased Binary Liquid Alloys

2020 ◽  
Vol 9 (1) ◽  
pp. 11-16
Author(s):  
Y.A. Odusote ◽  
A.I Popoola
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Reasonable Agreement ◽  
Liquid Alloys ◽  
Approximation Model ◽  
Binary Liquid ◽  
Thermodynamic Prediction ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Experimental Values

The free energy of mixing and activities of gold in selected six Au-based binary liquid Au-Cu, Au-Zn, Au-Pb, Au-Ni, Au-Sn and Al-Au alloys at different working temperatures have been studied using the quasi-chemical approximation model (QCAM). The predicted free enegry of mixing and activities results were compared with available experimental values. The predicted results are in reasonable agreement with reported experimental data and confirms that the model is reliable and, thus should serve as an alternative for the prediction of thermodynamic properties of binary liquid alloys. Keywords: free energy of mixing, activities, Au, Binary liquid alloys, concentration

scholarly journals Activity of Mercury in its Amalgams at Molten Stage

1970 ◽  
Vol 8 (8) ◽  
pp. 56-58
Author(s):  
SK Chakrabarti ◽  
BK Jha ◽  
IS Jha
Keyword(s):  
Free Energy ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Size Factor ◽  
Thermodynamic Relation ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Interchange Energy ◽  
Free Energy Of Mixing ◽  
Experimental Values

In the present work we have considered two molten amalgams e.g. sodium amalgam and potassium amalgam. Efforts are made to compute the activity of mercury therein by applying Flory's model. This statistical mechanical model is based on the size factor of the ingredients of a binary liquid alloy. In case of each of the amalgams we have started with the expression for the free energy of mixing (GM) according to this model. After knowing the ratio of the atomic volumes of the constituent species of an amalgam the prime task becomes the determination of the interchange energy (ω) between them. For this purpose the experimental values of GM for different concentrations of the ingredients of the amalgam are collected. From these known values ω has been computed by using the expression for GM. A suitable value of ω is chosen from the set of values so obtained. Putting this value of ω the free energy of mixing is calculated for several concentrations and then compared with its observed values. Accordingly, a modified value of ω has been considered and the calculations are repeated. In this way by the method of successive approximations we have ascertained the value of the interchange energy. Thereafter, with the help of standard thermodynamic relation activity has been computed. The results explain the observed anomaly of the activity of mercury in the present molten amalgams. Keywords: Binary liquid alloys; Flory's model; Amalgams; Activity of mercury. DOI: 10.3126/sw.v8i8.3850 Scientific World Vol.8(8) 2010 pp.56-58

scholarly journals Free energy of mixing and activity of indium-tin alloy

BIBECHANA ◽  
1970 ◽  
Vol 7 ◽  
pp. 26-29 ◽  
Author(s):  
IS Jha ◽  
Arun K Khan ◽  
BC Kumar
Keyword(s):  
Free Energy ◽  
Thermodynamic Parameters ◽  
Liquid Alloy ◽  
Reasonable Agreement ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Experimental Values

Flory's model has been used to calculate the free energy of mixing and activity of In in InSn liquid alloy at 700 K. The values of these thermodynamic parameters obtained from this model are compared with corresponding experimental values. The computed values are in reasonable agreement with the observed values. Keywords: Flory's model; Activity; Indium-tin alloy DOI: 10.3126/bibechana.v7i0.4040BIBECHANA 7 (2011) 26-29

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 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 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 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 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 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

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