On Using Thermo-Calc

1. On Using Thermo-Calc Sourav Das, Researcher, Product Research Group, Research and Development Division, Tata Steel

2. What is thermodynamics??? Science of flow of heat. • It is universal. We can find it in both organic (mitochondria, • ATP etc) and inorganic (black holes, mechanical systems, • chemical reactions) objects. • 2. It is based on macroscopic properties of matter. • 3. Entirely empirical.

3. Zeroth law : Defines temperature, T. If A and C are both in thermal equilibrium with a third body B, then they are also in thermal equilibrium with each other. 1st law : Defines energy, U Energy can be transformed (changed from one form to another), but can not created or destroyed. 2nd law : Defines entropy, S The entropy of an isolated system which is not in equilibrium will tend to increase with time. 3rd law : Gives a numerical value to the entropy As a system approaches to absolute zero, all the processes cease and the entropy of the system approaches a minimum value

5. Internal Energy, U A A A ΔU = q – w q or dU = dq – dw, where, dw = PdV if P = constant

6. Enthalpy, H V H = U + PV

7. Specific heat capacities Heat absorbed per unit change in temperature (dq/dT). Since, dq = dU + dw = dU + PdV (at constant pressure) dH = d(U + PV) = dU + d(PV) = dU + PdV + VdP = (dq – PdV) + (PdV + VdP) = dq + VdP Specific heat at constant volume So, specific heat at constant volume, CV = Cp = , at constant pressure H = U + PV

8. assuming CP is constant When the reaction A + B = C will be possible? ΔH = Hfinal – Hinitial = -ve But, why is it only possible? Why will it not necessarily happen?

9. Entropy, S For a reversible process, or P P/2 Why the reaction will happen in the direction of the arrow? Why not in the opposite direction? So, even if ΔH = 0, a reaction may spontaneously happen if the ΔS > 0 Entropy is a capacity property. Different entropies can be added together S1 + S2 + S3 = S4 15/01/2011

10. Entropy, S (again) P P/2 Possible arrangement, W = very very large Possible arrangement, W = 1, Probability of getting all the n mlecules at one side = 4 / [n(n-1)] How does Entropy fit with the probability picture? Through Boltzman’s law: S = k ln(w)

11. Gibbs Free Energy, G G = H – TS or ΔG = ΔH - TΔS Note: This is probably the most important parameter in all thermodynamical calculations

12. Equilibrium

13. Allotropic Transition in Pure Iron D. R. Gaskell, Thermodynamics of Materials

14. Mechanical Mixture free energy of mechanical mixture G* Gibbs free energy per mole x 1-x A B Concentration x of B

15. Solution free energy of mechanical mixture G* Gibbs free energy per mole G{x} free energy of solution A B x Concentration x of B

16. Chemical potential

17. Chemical potential Gibbs free energy per mole G{x} A B x Composition

18. Conditions: • Under standard conditions (T = 298 K and P = 101.3 kPa) • Without intermolecular interactions • Natural isotope composition of elements

19. Equilibrium between two solutions ,

20. Equilibrium between two solutions (contd……..) T = T1 (constant) Gibbs free energy per mole  α wt% C

21. Equilibrium between two solutions (contd……..) Gibbs free energy per mole T = T2 (constant), T2 >T1 α  Xα Xα wt% C

22. Equilibrium between two solutions (contd……..) T = T3 (constant), T3 > T2 Gibbs free energy per mole α  wt% C

23. Phase diagram between two phases T = T3 γ Temperature γ + α T = T2 α T = T1 C

24. Phase diagram among three phases  M2 M1 α α α α +   +  M     

25. We have considered: 1. Ideal solution (random distribution of solute atoms) and no change in binding energy when we mix the atoms together 2. Binary solution 1. In regular solution, there will be excess free energy of mixing and there may be liking or disliking among the atoms (back up slide for enthalpy of mixing) 2. There can be 8-10 elements in a commercial alloy

26. For a reversible process, or assuming CP is constant Heat capacity is a function of: 1. vibration of atoms 2. magnetic property of the atoms 3. Electronic heat capacity due to electronic configuration 4. Curling up of molecules etc etc……….

27. CP = b1 + b2T + b3T2 + b4/T2

28. Gibbs free energy per mole α  Xα Xα wt% C

30. References: 1. Introduction to the Thermodynamics of Materials, 3rd edition, D. R. Gaskell 2. Online available course materials from Georgia State University, USA 3. http://en.wikipedia.org 4. Classroom video lectures on Thermodynamics from MIT, USA 5. Class room video lectures from University of Cambridge, UK 6. Online course material from University of Texas at Austin, USA 7. Thermodynamics in Materials Science, International Edition1993, R. T. DeHoff 8. An Introduction to Metallurgy, 2nd edition, A. H. Cottrell 9. Chemical Thermodynamics of Materials, C. H. P. Lupis

31. Thank you for kind attention

32. Free energy of mixing If we consider an ideal solution, the entropy of mixing will be: If we consider a regular solution, there will be always a change in bond energy and there will be excess free energy