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 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 

scholarly journals Entropy of mixing of NaCd and AlMg molten alloys

1970 ◽  
Vol 9 (9) ◽  
pp. 25-28
Author(s):  
SK Chatterjee ◽  
LC Prasad ◽  
A Bhattarai
Keyword(s):  
Complex Formation ◽  
Hard Sphere ◽  
Pair Potential ◽  
Liquid Alloys ◽  
Sphere Diameter ◽  
Nearest Neighbour ◽  
Formation Model ◽  
Pseudopotential Theory ◽  
Entropy Of Mixing ◽  
Theory And Experiment

The complex formation model is used to explain the anomalous behaviour of entropy of mixing of NaCd and AlMg liquid alloys as a function of concentration.The interionic pair potential Φij(r) evaluated within the framework of pseudopotential theory which in turn is used to obtain the values of hard-sphere diameter of NaCd and AlMg liquid alloys. The hard-sphere diameter is used to evaluate the concentration dependent anamoly in entropy of mixing which occurs due to preferential ordering of unlike atoms as nearest neighbour on NaCd and AlMg liquid alloys, which could be simultaneously understood with the help of complex formation model. The computed value of Entropy of mixing (SM) from pseudopotential theory is positive at all concentration range except 0.8≤Ccd≤0.9 in NaCd liquid alloys. The disagreement between theory and experiment might be due to parameterisation of hard- sphere diameter of the complex (σ3) and Ψcomp. Key Words: Entropy of mixing; Pseudopotential theory; Hard-sphere diameter; Pair-Potential. DOI: http://dx.doi.org/10.3126/sw.v9i9.5513 SW 2011; 9(9): 25-28

scholarly journals Theoretical investigation of mixing properties of Sb-Sn binary liquid alloy at 905K

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 1-10
Author(s):  
H K Limbu ◽  
K K Mishra ◽  
A K Sah ◽  
I S Jha ◽  
D Adhikari
Keyword(s):  
Liquid Alloy ◽  
Nearest Neighbor ◽  
Regular Solution Model ◽  
Concentration Fluctuations ◽  
Heat Of Mixing ◽  
Entropy Of Mixing ◽  
Energy Of Mixing ◽  
Interchange Energy ◽  
Free Energy Of Mixing ◽  
Experimental Values

The thermodynamic, microscopic, surface and transport properties of Sb-Sn liquid alloy at 905K have been studied using regular solution model. In thermodynamic properties, free energy of mixing(GM) , activity(a), entropy of mixing(SM), heat of mixing (HM) have been studied. To understand structural behavior of the liquid alloys concentration fluctuations in the long wavelength limit i.e. (Scc(0)) and short range order parameter (α1) have been computed. Surface property is studied with the help of Butler’s model while transport property is computed from Moelwyn-Hughes equation. The theoretical and experimental values of thermodynamic and microscopic properties of Sb-Sn liquid alloy at 905K have been compared. In present work the value of interchange energy (w) is found to be negative suggesting that there is a tendency of unlike atoms pairing (i.e. Sb-Sn) as the nearest neighbor indicating the ordering behavior in Sb-Sn liquid alloy. The symmetric behavior of concentration fluctuations of the liquid alloy has been well explained by the model. The temperature dependence of interchange energy (w) has been found during the computation of entropy of mixing (SM) and heat of mixing (HM) of the liquid alloy.BIBECHANA 15 (2018) 1-10

Structural Properties of In1-xSnx at Different Concentrations and Temperatures

2016 ◽  
Vol 1141 ◽  
pp. 142-146
Author(s):  
C.H. Patel ◽  
Amit B. Patel ◽  
Nisarg K. Bhatt ◽  
P.N. Gajjar
Keyword(s):  
Structural Properties ◽  
Structure Factor ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Pair Potential ◽  
Effect Of Temperature ◽  
Sphere Diameter ◽  
Pseudopotential Theory ◽  
Structure Factors ◽  
Different Temperatures

The partial structure factors for liquid alloy In1-xSnx have been computed at varying concentration and temperatures using pseudopotential theory. The structure factor S(q) and pair correlation function g (r) have been determined using the hard-sphere approximation. The temperature dependent hard-sphere diameter σ (T) is estimated using Vσ=Vminr+12kBT criterion from the computed pair potential. The modified empty-core local pseudopotential, which represents the orthogonalisation effect due to s-core states, is used for electron–ion interaction with proper screening function. The only potential parameter, the core radius, is determined at different temperatures from the knowledge of structure factor. Intrinsic temperature effects have been studied through dimensionless damping term (see formula in paper) in the pair potential. The effect of temperature and concentration on structure factors is discussed to shed light on bonding in technologically important alloy. This used pseudopotential proved successful in explaining the structural properties of non-crystalline alloys at higher temperatures.

scholarly journals Thermodynamic properties of liquid InNa alloys

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 165-174
Author(s):  
AK Mishra ◽  
M Milanarun
Keyword(s):  
Thermodynamic Properties ◽  
Theoretical Study ◽  
Stoichiometric Composition ◽  
Enthalpy Of Mixing ◽  
Mixing Enthalpy ◽  
Size Difference ◽  
Formation Model ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Free Energy Of Mixing

Concept of complex formation model has been applied to account for the thermodynamic properties of liquid InNa alloy. The theoretical study reveals that the intermetallic compound In3Na2 exists at stoichiometric composition. Our expressions reproduce successfully the asymmetric behaviour of free energy of mixing, enthalpy of mixing, s-type entropy of mixing, CSRO and phase separation in liquid In- Na alloy. It is found that Na atoms segregate on the surface. The study reveals that various factors such as size difference and electronegative factor are not sufficient to account for the asymmetry in the system. The low value of order energy suggests that In-Na is a weak interacting system DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7192 BIBECHANA 9 (2013) 165-174

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.

THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

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

Diffusion-Induced Grain Boundary Migration and Role of Defects

1993 ◽  
Vol 319 ◽  
Author(s):  
T.K. Chaki
Keyword(s):  
Free Energy ◽  
Grain Boundary ◽  
Boundary Migration ◽  
Solute Concentration ◽  
Grain Boundary Migration ◽  
Thermally Activated ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Liquid Film Migration ◽  
Lattice Diffusivity

AbstractA model is presented to explain various aspects of diffusion-induced grain boundary migration (DIGM). The driving energies of DIGM are identified as the free energy of mixing and the interface free energy, the former being predominant in most cases of DIGM. The grain boundary migrates due to thermally activated motion of atoms across the interface under the influence of the driving energies. An expression for the velocity of migration is derived. It is shown that this depends parabolically on the solute concentration, in agreement with experimental observations in the case of liquid film migration (LFM), which is analogous to DIGM. Furthermore, the velocity is proportional to lattice diffusivity ahead of the boundary. Recent results of enhancement of DIGM by ion bombardment is explained by radiation-enhanced lattice diffusivity due to introduction of point defects by the ions. The model also explains that diffusion-induced recrystallization (DIR) is due to a free energy decrease associated with the transformation from the amorphous phase in the grain boundary layer to the crystalline phase.

Dolomite Decomposition to (Ca,Mg)O Solid Solutions: An X-Ray Diffraction Study.Part II.

1984 ◽  
Vol 39 (10) ◽  
pp. 981-985 ◽  
Author(s):  
G. Spinolo ◽  
U. Anselmi Tamburini
Keyword(s):  
Free Energy ◽  
Low Temperatures ◽  
Particle Sizes ◽  
Diffusional Process ◽  
X Ray Diffraction ◽  
High Iron Content ◽  
X Ray ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Low Pressures

Abstract The full decomposition of dolomites with low and high iron content at low temperatures and low pressures is discussed with reference to the free energy of mixing of the ternary system Ca. Fe, Mg/O. The actual products of the primary step are a couple of rock salt structured oxides close to the spinodal compositions and with very small particle sizes. A subsequent diffusional process can produce large crystallites with equilibrium compositions, but it is effective only when either a low-iron dolomite is used as starting material or higher temperatures are employed.

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