2. 1 Day 3. Interfacial energies in high temperature systems George Kaptay Kaptay / Day 3 / 1 A 4-day short course See J94

3. 2 Interfacial energiesInterfacial forces Interfacial phenomena Complex phenomena Modeling algorithm Kaptay / Day 3 / 2

4. 3 Types of phases and interfaces to be modeled gasW(s) Al(l) NaCl(l) MgO(s) Si(s) AlN(s)TiC(s) Kaptay / Day 3 / 3

5. 4 Modeling interfacial energies The excess interfacial Gibbs energy: AB Kaptay / Day 3 / 4

6. 5 The excess interfacial enthalpy for the liquid/gas interface For liquid metals (structures surface – see Day 1 / 18):   (11-9)/11 = 0.182 Where the cohesion energy of the liquid metal (classic): Kaptay / Day 3 / 5 See J48

7. 6 The excess interfacial entropy for the liquid/gas interface From the LEED measurements [Somorjai et al]: Kaptay / Day 3 / 6 See J48

8. 7 The molar surface area of the liquid/gas interface For the {111} plane of the fcc crystal: f i = 0.906. For fcc crystals f b = 0.740 → f = 1.09. When an fcc crystal is melted, Δ m V = 1.06, → f = 1.06. Kaptay / Day 3 / 7 See J48

9. 8 Surface tension of pure liquid metals Kaptay / Day 3 / 8 Experimental points Calculated values See J48

10. 9 Surface tension of liquid metals / new age (1)   (11-9)/11 = 0.182 To correlate the calculated values: Kaptay / Day 3 / 9

11. 10 q 1 = 25.4 ± 1.2, q 2 = 0. Kaptay / Day 3 / 10From vaporization enthalpy From critical points

12. 11 Surface tension of liquid metals / new age (2) For the {111} plane of the fcc crystal: f i = 0.906. For fcc crystals f b = 0.740 → f = 1.09. For melted fcc crystals f b,fcc = 0.74/(1.12) = 0.66 → f =1.01 For melted bcc crystals f b,bcc = 0.68/(1.096) = 0.62 → f =0.97 For melted hcp crystals f b,hcp = 0.74/(1.086) = 0.68 → f =1.03 Average for melted fcc, bcc and hcp crystals: f = 1.00 ± 0.02 Kaptay / Day 3 / 11

13. 12 Surface tension of liquid metals / new age (3) Kaptay / Day 3 / 12

14. 13 Surface tension of liquid metals / new age (4) Kaptay / Day 3 / 13 q 1 = 25.4 ± 1.2, q 2 = 0.

15. 14 q 1 = 26.3 and q 2 = -2.62.10-4 molK/J Kaptay / Day 3 / 14

16. 15 T-coefficient of surface tension / new age (5) Kaptay / Day 3 / 15

17. 16 Kaptay / Day 3 / 16

18. 17 Kaptay / Day 3 / 17 The classic model for surface tension was improved by changing 2 things at the same time: i. the cohesion energy is made T-dependent through heat capacity (known for 130 years) ii. a new, ordering term is taken into account in the excess surface entropy (known for 30 years) General lesson : Models exist on almost everything. Majority of them can be improved. If you change only one thing in the model, usually you spoil it. You must be brave enough to change at least two (sometimes three), different things in the model to get it work again – in a better way.

19. 18 Surface structure of MX type molten salts Kaptay / Day 3 / 18 Bulk liquid of MX associates Vapour See P75

20. 19 Surface tension of MX molten salts Kaptay / Day 3 / 19 Experimental points Calculated values

21. 20 Surface tension of molten monoxides (MO) MOTKTK  v H kJ/mol V l cm 3 / mol  MO/g, mJ/m 2 model  MO/g, J/m 2 measured FeO1.650413.215.8 532  70550  50 MgO2523574.916.5 695  100700  100 CaO1823578.321.1 623  90650  100 SrO182347727.8 425  60 - BaO1823336.434.1 239  30250  50 Kaptay / Day 3 / 20

22. 21 Surface energy of solid metals Kaptay / Day 3 / 21

23. 22 Surface energy of solid metallic mono-carbides Kaptay / Day 3 / 22

24. 23 Surface energy of solid ionic mono-oxides Kaptay / Day 3 / 23

25. 24 Excess interfacial enthalpy of sA/lA interface The Kelvin equation for the critical radius of nucleation: The molar volume can be modeled as: At T  0 K, the solid nucleus will be stable from an atom, i.e. r cr  r A : Kaptay / Day 3 / 24 See J67

26. 25 Excess interfacial entropy of sA/lA interface From side of the solid there is not too much change in freedom: Liquid atoms will loose part of their freedom at the s/l interface. The entropy of melting: The excess interfacial entropy: Kaptay / Day 3 / 25

27. 26 Interfacial energy sA/lA Kaptay / Day 3 / 26

28. 27 Summary of interfacial energies of pure metals (example: Fe) Kaptay / Day 3 / 27

29. 28 Interfacial energy sA/lB There is an extra excess enthalpy term, connected with the interaction of A and B atoms across the interface: From the theory of regular solutions: Finally, the new excess enthalpy term: Kaptay / Day 3 / 28

30. 29 Interfacial energy sA/lB Zn/Sn (473 K), Ag/Pb (608 K), Cu/Pb (1193 és 1093 K), Fe/Cu (1373 K), Nb/Cu (1773 K), W/Cu (1773 K), Mo/Sn (1873 K), W/Sn (2273 K), Fe/Pb (1373 and 1193 K) and Fe/Ag (1373 K) Kaptay / Day 3 / 29

31. 30 Interfacial energy between two immiscible liquids Ga-Pb: D.Chatain, L.Martin-Garin, N.Eustathopoulos: J. chim.phys., 79 (1982) 569 Al-Bi: I.Kaban, W.Hoyer, M.Merkwitz: Z.Metallkunde, 94 (2003) p.831 Kaptay / Day 3 / 30

32. 31 Covalent ceramic / liquid metal interface The London dispersion forces connect the atoms across the interface: Kaptay / Day 3 / 31

33. 32 Ionic ceramic / liquid metal interface (1) The ion A induced dipole (in atom B) interaction with each other: The adhesion energy: The corrected adhesion for dipole induced dipole interaction:: Kaptay / Day 3 / 32 See J66

34. 33 Ionic ceramic / liquid metal interface (2) The corrected adhesion energy for ion the ionic moment of ion C: Points from for the liquid Cu / MgO, ZrO2, Al2O3, SiO2 systems Kaptay / Day 3 / 33

35. 34 Wettability of solid Fe by molten chlorides AC/Br C nm IC/IAIC/IA kk W AC/B mJ/m 2  AC/g mJ/m 2  B/AC/g fok MgCl 2 /Fe0,0744,890,3966,4138121 CaCl 2 /Fe0,1043,480,4485,0147115 BaCl 2 /Fe0,1382,620,48101,9169114 NaCl/Fe0,0981,850,52118,811488 KCl/Fe0,1331,360,55133,29970 Calculated data are confirmed experimentally by Vetiukov et al. Kaptay / Day 3 / 34

36. 35 Interfacial energy in liquid metal / molten salt systems T.Utigard, J.M.Toguri, T.Nakamura, Metall.Trans. B., 17B (1986) 339 NaF/Bi (1373 K), NaCl/Bi (1373 K), NaF/Pb (1273 K), NaCl/Pb (1173 K), NaF/Ag (1273 K), NaCl/Ag (1273 K), NaF/Cu (1373 K) and NaCl/Cu (1373 K) Kaptay / Day 3 / 35

37. 36 The surface excess (by definition): The Gibbs equation: +Gibbs-Duhem (for binaries): Kaptay / Day 3 / 36 Concentration dependence of  (Gibbs, 1878)

38. 37 Langmuir (1918) The equilibrium between bulk and surface phases: A* + B = A + B* For the infinitely diluted solution of B in A: a A = 1, a B =  B  x B Kaptay / Day 3 / 37

39. 38 Belton (1976) Integration at infinitely diluted solution of B: dlna B = dx B /x B. Kaptay / Day 3 / 38

40. 39 [??] At infinitely diluted solution of B: x B >1) A* + B = A + B* Kaptay / Day 3 / 39 Gibbs – Langmuir – Belton (1878 – 1976)

41. 40 Theoretical Concentration dependence of  Fe-O/g Kaptay / Day 3 / 40

42. 41 Theoretical concentration dependence of  Fe-S/g Kaptay / Day 3 / 41

43. 42 Additive extension to ternary Fe-O-S system Kaptay / Day 3 / 42 Experimental points Calculated values

44. 43 Taking into account the competition between O and S atoms for surface sites Kaptay / Day 3 / 43 Calculated values Experimental points

45. 44 On the Butler equation (1932) Compared to the Gibbs equation: i. it is easier to teach and to apply, but still ii. at equal assumptions it provides the same results. The surface activity coefficient as function of surface composition is to be modelled Kaptay / Day 3 / 44

46. 45 Modeling surface excess Gibbs energy The model is based on the ratio of broken bonds (  ): For liquid metals: Hoar, Melford, 1957:  Monma, Suto, 1961:  = 0.16 -0.20, Speiser, Poirier, Yeum, 1987 – 1989:  = 0.25, Tanaka, Iida, Hara, Hack, 1994 – 2000:  = 0.17, For molten salts: Tanaka et al.:  = 0.06, later -0.1 (!!??) Kaptay / Day 3 / 45

47. 46 The Butler equation, applied to associated liquids Experimental points: V.N.Eremenko, V.I.Nizhenko, N.I.Levi, B.B.Bogatirenko: Ukr. Him. Zh., 1962, vol.28, No.4, pp.500-505 Al-Ni Kaptay / Day 3 / 46

48. 47  A = 1 J/m 2,  B = 0.5 J/m 2, V A = 1 10 -5 m 3 /mol, V B = 2 10 -5 m 3 /mol,  = 20 kJ/mol. Then: T c = 1202.79 K. At T = 875.86 K, bulk separation at x B = 0.1 and x B = 0.9 Kaptay / Day 3 / 47 Surface phase separation in monotectic alloys (a) Partial surface tensions as function of surface content See J99

49. 48 Kaptay / Day 3 / 48 Surface phase separation in monotectic alloys (b) Partial surface tensions as function of surface content See J99

50. 49 Kaptay / Day 3 / 49 Surface phase separation in monotectic alloys (c) Partial surface tensions as function of surface content See J99

51. 50 Kaptay / Day 3 / 50 Surface phase separation in monotectic alloys (d) Partial surface tensions as function of surface content See J99

52. 51 Kaptay / Day 3 / 51 Surface phase separation in monotectic alloys (e) Partial surface tensions as function of surface content See J99

53. 52 Kaptay / Day 3 / 52 Surface phase separation in monotectic alloys (f) Surface composition as function of bulk composition See J99

54. 53 Kaptay / Day 3 / 53 Surface phase separation in monotectic alloys (g) Surface tension as function of bulk composition See J99

55. 54 Kaptay / Day 3 / 54 Surface phase separation in monotectic alloys (h) A phase diagram with a surface phase separation line See J99

56. 55 Kaptay / Day 3 / 55 Surface phase separation in monotectic alloys (i) T-coefficient of surface tension as function of bulk composition See J99

57. 56 Two shapes of welding pools Kaptay / Day 3 / 56

58. 57 Thank you for your attention