Work Assignment 2
Critical Review on
Thermodynamic Properties of Solid Solutions in the System Ag2S – Ag2Se
Ram Pyar Singh (13106027)
Department of Materials Science and Engineering,
IIT Kanpur, Kanpur, 208016, India
This paper is about the calculation of standard thermodynamic properties of the four solid solutions in the phase diagram of Ag2S – Ag2Se. They calculated these properties using the model of regular and subregular solutions. The four solid solutions are: a restricted fcc solid solution (γ- Ag2S-Ag2S1-xSe (x<0.3)), a complete bcc solid solution (β- Ag2S – Ag2Se), monoclinic solid solution (α) from Ag2S to Ag2S0.4Se0.6, and a orthorhombic solid ...view middle of the document...
At the high temperature the system is described by phase diagrams with a common minimum point on solidus and liquidus curves. In this region the standard thermodynamic properties are evaluated by using subregular solution model. While at low temperature region where there are two continuous solid solutions (monoclinic and orthorhombic) with a miscibility gap, the standard thermodynamic properties are evaluated by using both models of regular and subregular solutions.
Symmetric solid solution model:
The Gibbs free energy of one mole of binary solid solution Ag2(S, Se) at the pressure of 1 bar and temperature T can be calculated by following equation:
GT° (X1, X2) = Gmix + X1G1°+ X2G2°,
Where x1, x2 are atomic fraction of sulfur and selenium in solid solutions.
GT° (X1, X2) is the standard Gibbs free energy of solid solution Ag2SX1SeX2.
Gmix is Gibbs free energy of mixing,
G1° and G2°are the standard Gibbs free energies of the Ag2S and Ag2Se respectively.
The Gibbs free energy of mixing can be calculated by the equation:
Gmix = Gideal + Gxs
Where Gideal is free energy of mixing of ideal solutions which is given by,
Gideal = RT (X1lnX1 + X2lnX2)
Gxs is the excess molar Gibbs free energy of mixing which is given by,
Gxs = (a + bX2) X1X2
here a and b are constants which have no physical significance.
Also Gxs can be given by X1G̅1xs + X2G̅2xs, where G̅1xs and G̅2xs are partial molar excess Gibbs free energy of solution components.
G̅1xs = aX22 + b X22(X2 – X1)
G̅2xs = aX12 + 2b X12X2
The standard entropies of the solid solution Ag2SX1SeX2 can be calculated by the equation:
ST° (X1, X2) = Smix + X1S1°+ X2S2°
Where S1° and S2° are standard entropy of Ag2S and Ag2Se respectively.
Smix is the entropy of mixing of the solid solution which is given by,
Smix = Sideal + Sxs,
Sideal is entroy of mixing of ideal solution and can be given by:
Sideal = ¬¬¬-R (X1lnX1 + X2lnX2)
Sxs is the excess entropy of mixing and can be given by the equation which determines the temperature dependence of Gibbs free energy of mixing of solid solutions at constant Pressure and composition.
Sxs = - (Gxs /T)P, comp.
The molar excess heat of mixing of the solid solution Ag2SX1SeX2 can be calculated by the equation:
ΔHm = Gxs + TSxs
The specific heat capacity can be calculated by following equation
Cp = a1 +a2T +…………
As the standard Gibbs free energy of solid solution Ag2(S, Se) is linearly dependent on Temperature, T. So the second derivative of Cp w.r.t temperature is zero, then the heat capacity of the solid solution is expressed as linear combination of heat capacity of Ag2S and Ag2Se with their mole fractions in solution,
Cp0 (Ag2(S, Se)) = X1 Cp0 (Ag2S) + X2 Cp0 (Ag2Se)
a1 (Ag2(S, Se)) = X1 a1 (Ag2S) +X2 a1 (Ag2Se)
a2 (Ag2(S, Se)) = X1 a1 (Ag2S) +X2 a1 (Ag2Se)
Molar Volumes of solid solutions Ag2(S, Se) can be calculated using Retgers’s rule on the basis molar volumes of the Ag2S and Ag2S: