Problem Set - 3 MM 651 Thermodynamics of Materials

1. An empirical equation for the excess Gibbs energy of liquid Ag[1]-Cu[2] alloy is ΔGex = - R (2100 + 0.511 T) x1 x2. Derive the equations for Hex, Sex, μ1, μ2 and compute γ1 and γ2 at 1550 K and x2 = 0.5 2. The activity coefficient of Zn in liquid Zn – Cd alloy at 700 K is given by ln γzn = 0.875 X2

cd – 0.30 X3cd

Derive the expression for ln γcd on composition and calculate the Gibbs free energy of mixing for Xcd = 0.4 at 700 K. 3. CaO and MgO form solid solutions with limited solubility. Assuming that the solutes obey Henry’s law with γ°CaO = 12.88 and γ°MgO = 6.23, calculate the solubility of CaO in MgO and MgO in CaO. 4. Melts in the system Pb-Sn exhibit regular solution behaviour. At 473 °C, apb = 0.055 in a liquid solution of Xpb = 0.1. Calculate the value of the ao

L and find the activity of Sn in a liquid solution of Xsn = 0.5 at 500 °C. 5. The Gibbs free energy of mixing of a solid solution is given by

ΔGαmix = 10,600 X1 X2 + RT [X1 ln X1 + X2 ln X2]

Calculate the critical temperature Tc for phase separation. Calculate the spinoidal and the phase boundary at 0.7 Tc. 6. Ge-Si forms an isomorphous system with complete solid and liquid solutions. The melting points of Ge and Si are 1200 oC and 1680 oC respectively. At 1475 oC, the liquidus and solidus compositions are respectively, XSi = 0.32 and XSi = 0.665. Assuming the both the solid and liquid solutions are ideal solutions, estimate the values of heat of fusion of Ge and Si. 7. A (TmA= 1400 K) and B (TmB=1000 K) form a eutectic and their Heats of Fusion are 3200 and 2500 cals/mol respectively. At 1200 K, solubility of B in solid A, XB

S = 0.05 and in liquid XB

L = 0.40. At 600 K, the solubility of A in solid B is 0.07 and of B in solid A is 0.03. Find the activity coefficient of A and B at 600 K and of B in solid A at 1200 K. Assume the liquid to be an ideal solution. 8. The excess gibbs free energy for the Fe-Ni liquid solution is given by the expression

ΔGex = (-4100 + 0.8 T) x1 x2 J/mol. Calculate the values for Hex, Sex and compute γ1 and γ2 at 1800 K and x2 = 0.5 9. Two elements A and B (or 1 and 2) form complete solutions in both the solid [α] and liquid [L] phases. Two calculate the phase diagram, it is necessary to compare the Gibbs free energy of mixing of both the solutions. Assume that both the solutions are regular solutions. Formulate the equations for Gibbs free energy of mixing of both the solutions assuming that the reference state is {L,L}