3.Microstructure and Phase Transitions

1. 3.Microstructure and Phase Transitions Definition of the Microstructure Definition

2. 3.Microstructure and Phase Transitions Definition of the Microstructure Change-over from 2D to 3D Definition

3. 3.Microstructure and Phase Transitions Types of Microstructure

4. 3.Microstructure and Phase Transitions Microstructural Evolution crystallization crystallization out of solutions solidification liquid-solid electrolytic deposition sublimation most important ! Example:casting gaseous-solid PVD,CVD

5. Erstarrungsgefüge Gussblock

6. 3.Microstructure and Phase Transitions Microstructure of cast iron Schematic illustration of the microstructure real microstructure Explanation

7. 3.Microstructure and Phase Transitions dendritic growth Ni-based superalloy Video Dendritic Solidification

8. 3.Microstructure and Phase Transitions Crystallites in a glass matrix

9. Verfahren zur…

10. z.B. reaktives Sputtern

12. 3.Microstructure and Phase Transitions Microstructural Evolution crystallization crystallization out of solutions solidification liquid-solid electrolytic deposition sublimation most important ! Example:casting gaseous-solid PVD,CVD

13. Galvanoforming Automobil-Armaturenbretter

14. 3.Microstructure and Phase Transitions Phase Diagrams (1) Characterization of external parameters, which describe the equilibrium state of a material intensive variables 1. pressure p 2. temperature T 3. chemical composition; concentration c or mol fraction x (single or multicomponent systems) components are the pure chemical elements which are required to form a material phases: areas of different properties which are separated by phase boundaries

15. 3.Microstructure and Phase Transitions Thermodynamic Aspects (1) What does thermodynamic equilibrium mean in regard to thermodynamics? Time limits to infinity t  !! But in reality: time t is not equal to infinity ! Thermodynamic functions of state (where T is temperature and S is entropy) - internal energy: U - enthalpy: H = U + p V - free energy: F = U - T S - free enthalpy: G = H - T S equilibrium is reached when the 2nd principle of themodynamics is satisfied: with H = U + p·V G = H - T·S = U + p·V -T·S

16. 3.Microstructure and Phase Transitions Thermodynamic Aspects (2) H = f(T) Hm« Hv Hm : melting enthalpy Hv : enthalpy of vaporization

17. 3.Microstructure and Phase Transitions Thermodynamic Aspects (3) The state of a material can be changed, when internal energy is added or removed ! The decisive criterion for equilibrium is the free enthalpy G (Gibbs-enthalpy): GGG = Gminimum for voluntary processes ! The thermodynamic equilibrium is determined by the minimum of the free enthalpy G when the temperature T and the pressure p are kept constant !! dG = 0 (T, p = const.) G < 0

18. 3.Microstructure and Phase Transitions Thermodynamic Aspects (4) The stability of phases and the Gibbs free enthalpy G Equilibrium

19. 3.Microstructure and Phase Transitions The Process of Nucleation (1) What do we need G for? Crystallization which happens through formation and growth of a nucleus Formation of a nucleus is related to a change in G ! (1) Gvolume is released during transition (2) Gsurface is consumed during formation of the boundary surface G = - Gvolume + Gsurface

20. 3.Microstructure and Phase Transitions The Process of Nucleation (3)

21. 3.Microstructure and Phase Transitions The Process of Nucleation (4) Deriving the critical radius of the nucleus: G = -Gvolume + Gsurface critical radius rc:

22. 3.Microstructure and Phase Transitions The Process of Nucleation (5) Deriving the critical radius of the nucleus: and (G=H-T·S) : interfacial energy gv: free formation enthalpy for the solid phase Hm: melting enthalpy Tm: melting temperature Example: Cu

23. 3.Microstructure and Phase Transitions Nucleus Growth (2)

24. 3.Microstructure and Phase Transitions Nucleus Growth (3) • Schnellere Anlagerung an vorhandene Keime => Kleinere krit Keimgröße

25. 3.Microstructure and Phase Transitions Nucleus Growth (4) The Shape of a Crystal Stages of displacement for a slowly growing (a) and a fast growing directions (b)

26. 3.Microstructure and Phase Transitions Nucleus Growth (5) - The Shape of a Crystal Hexagonales Prisma {10.0} und {11.0} bei Calcit Rhomboeder {h0.1} und {0k.1}

27. 3.Microstructure and Phase Transitions Phase Diagrams - Unitary System (Pure Metal) P T

28. 3.Microstructure and Phase Transitions Phase Diagrams (3) Gibbs´ phase rule • The number of components K is related to the number of phases P and of the degrees of freedom F by the Gibbs´ phase rule: • or, if one degree of freedom (e.g. pressure p) is kept constant • Examples (for a one component system  K = 1): • - at a triple point P = 3, which yields F = 1 + 2 – 3 = 0 • within a phase field P = 1 and so, F = 1 + 2 – 1 = 2 • on a boundary line P = 2, which yields F = 1 + 2 – 2 = 1 F = K – P + 2 F = K – P + 1

29. 3.Microstructure and Phase Transitions Phase Diagrams - Unitary System (with Multiple Phases) Characteristics Unitary system with 3 solid phases ,  and  including melted and gaseous phase P Multiple triple points ! T

30. 3.Microstructure and Phase Transitions Systems with Complete Insolubility in the Liquid and Solid Phase

31. How to understand the phase diagramof complete solubility ? 3.Microstructure and Phase Transitions

32. 3.Microstructure and Phase Transitions Systems with Complete Solubility in the Liquid and Solid Phase

33. Tx 2nd step: draw a line at the temperature Tx  tie line (conode) 3rd step: the tie line is divided into two parts: a corresponds to the amount of (liquid) phase b corresponds to the amount of the (solid) phase C b a 3.Microstructure and Phase Transitions How to Determine the Relative Ratios of Different Phases  the Lever Rule (A) T (l) 1st step: draw a line at the nominal concentration C (l)+(s) (s) c(B)

34. Tx with: a = c(s) – C and b = C – c(l) while a + b = c(s) – c(l)is the length of the tie line which corresponds to the total amount of alloy in the system C c(l) c(s) b a 3.Microstructure and Phase Transitions How to Determine the Relative Ratios of Different Phases  the Lever Rule (A) T Remember mechanics? (l) (l)+(s) (s) c(B)

35. Tx C b a 3.Microstructure and Phase Transitions How to Determine the Relative Ratios of Different Phases  the Lever Rule (A) T Now we are able to write down the lever rule: (l) (l)+(s)  relative ratio of the solid phase (s) c(B) c(l) c(s)  relative ratio of the liquid phase

36. 3.Microstructure and Phase Transitions Example:Ag-Au

37. Stand Vorlesung

38. 3.Microstructure and Phase Transitions Systems with Solubility in the Liquid Phase and Insolubility in the Solid Phase

39. 3.Microstructure and Phase Transitions Example:Bi-Cd

40. 3.Microstructure and Phase Transitions Thermodynamics of the eutectic phase diagram

41. 3.Microstructure and Phase Transitions How to Understand the Evolution of Eutectic Systems

42. 3.Microstructure and Phase Transitions Systems with Solubility in the Liquid phase and Limited Solubility in the Solid Phase (1) eutectic system

43. 3.Microstructure and Phase Transitions Example:Ag-Cu

44. 3.Microstructure and Phase Transitions How to Understand the Evolution of Peritectic Systems Peritectic Reaction

45. 3.Microstructure and Phase Transitions Systems with Solubility in the Liquid Phase and Limited Solubility in the Solid Phase (2) peritectic system Peritectic Reaction

46. Example:Pt-Re Peritectic Reaction

47. Thermodynamics of phase diagrams with intermetallic phases 3.Microstructure and Phase Transitions

48. 3.Microstructure and Phase Transitions Phase Diagrams (4) transition from binary to ternary systems ternary binary Phase spaces Phase transition areas Phase areas Phase transition curves Examples

49. 3.Microstructure and Phase Transitions Phase Diagrams - Multicomponent Systems Ternary Systems (2) Examples

50. 3.Microstructure and Phase Transitions Phase Diagrams - Multicomponent Systems Ternary Systems (1) Examples