1. Thermodynamics and thermophysical properties of liquid Fe-Cr alloys Thermodynamics and thermophysical properties of liquid Fe-Cr alloys Rada Novakovic National Research Council (CNR–IENI) Genoa, Italy

2. Mixing behaviour of liquid binary alloys: energetic & structural factors Observable indicators:  Phase diagrams.  Empirical factors – physical, chemical & structural properties of alloy constituents (liquid metals), melting points, volume, first shell coordination, radius size, valence difference, electronegativity difference...  Thermodynamic functions – heat capacity, enthalpy, activity, excess Gibbs energy.  Microscopic functions – concentration fluctuations in the long wavelength limit & CSRO (Warren-Cowley short range order) parameter. MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

3. What kind of input data are necessary for modelling? 1. Thermodynamic data on mixing: heat capacity; enthalpy; entropy; Gibbs energies (integral & excess). partial quantities: activities (or chem. potentials). 2. Phase diagram information type of alloy system: segregating or compound forming 3. Thermophysical data: molar volume, surface tension, viscosity of pure components. 4. Structural data: coordination number; neutron diffraction data to be transformed into the microscopic functions 5. Experimental data on Thermo-Physical properties of alloys: for a comparison with theoretical results MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

4. The Fe-Cr system MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

5. Thermodynamic data of the Fe-Cr liquid phase [11Xiong] An improved thermodynamic modeling of the Fe–Cr system down to zero kelvin coupled with key experiments [86Mas] The Fe-Cr phase diagram [76Hul;81AB;82HS;87AS] previous assessments of the p.d. [93BLee] The reassessment of the Fe-Cr phase diagram [93BLee] T=1873K: The optimised term of the excess Gibbs free energy; the enthalpy of mixing [84Bat]; the activities [80Mar;69Fru;69Gil;98Zai]. [06Vre] The presence of interm.  - phase [06Ter] The melting, the enthalpy of mixing, thermal diffusivity - by atomic simulations Comment: The Cr-Fe phase diagram can be considered as COMPLETE (although some measurements in the liquid phase are necessary). MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

6. Results of calculations  - phase energ. favoured ( AB )  Weak influence on the energetics of the Fe-Cr liquid phase. MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

7. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

8. SURFACE TENSION SURFACE TENSION MODELS  Binary systems  Ternary systems  Geometric models EXAMPLES: Fe-Cr, Al-Nb-Ti

9. Surface properties of liquid binary alloys: surface segregation & surface tension Butler(1932) published the paper proposing his well known equation: ( i = A, B), that gives the relation between the surface tension and thermodynamics of liquids in which the bulk and surface phases are in equilibrium. MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

10. and combining with and taking into account the bulk (surface) phase activity coefficients obtained by Fowler_Guggenheim method as and the  and x s can be calculated. The surface tension can be calculated inserting x s into the Butler’s equation. MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy Subtracting Butler’s equ. for both components,

11. Surface tension calculations of binary systems * Models based on Butler’s equation - Regular solution - Subregular solution - “Central” atom - Compound Formation Model (CFM) - Self Aggregating Model (SAM) An interface Liquid / Gas : & * Probabilistic Models Singh et al. Monolayer or Multilayers

12. Surface tension calculations of ternary systems * Models based on Butler’s equation - Regular solution - Subregular solution - “Central” Atom - Compound Formation Model (CFM) - Self Aggregating Model (SAM) An interface Liquid / Gas : & * Geometric Models (from thermodynamic calculations of mixing properties in the bulk) SYMMETRIC - Kohler; Colinet; Muggianu ASYMMETRIC - Toop; Bonnier; Hillert; GENERALIZED - Chou Monolayer

13. Geometric modelsKohlerToopChou

15. Iso-surface tension lines of liquid Al-Ti-Nb alloys calculated by the Butler equation for the regular solution model at 2073 K. The square symbol represents the composition location of the Ti 46 Al 46 Nb 8 (at.%) in the Gibbs triangle and the corresponding surface tension calculated value MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

16. Surface tension reference data of Cr MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

17. Surface tension reference data of Fe MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

18. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

19. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

20. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

21. Microscopic functions (B-T) & Thermodynamics For ideal solution the S CC (0) becomes The CSRO parameter and S CC (0) are related to each other by where Z is the coordination number. MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

22. Microscopic functions & local arrangements of atoms in the melt S CC (0) and CSRO parameter indicate chemical order & segregation (phase separation): S CC (0) – the nature of mixing CSRO parameter – the degree of order Criteria for mixing behaviour 1. S CC (0) < S CC (0, id) presence of chemical order S CC (0) > S CC (0, id) segregation 2. -1 < CSRO < 0 ordering in the melt CSRO = -1 complete ordering 0 < CSRO < 1 segregation CSRO = 1 phase separation MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

23. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

24. The interdiffusion coefficient (Dm) can be given in terms of the S CC (0) by For “ideal” alloys, S CC (0)= S CC (0,id)= c A c B, then and finally combining the last two eqs. it is obtained, The criteria for mixing behaviour: S CC (0) > S CC (0, id) segregation  D m < D id S CC (0) D id MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

25. Results of calculations MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

26. Viscosity Viscosity (  ) of liquid alloys - the atomic level structure and interactions. The composition dependence of  of liquid alloys in respect to the linear low (ideal mixture): - a linear variation (simple liquids, e.g. Ag-Au, Sn-Pb, Bi-Pb) - positive deviations (compound forming alloys,  H <<0) - negative deviations (segregating alloys,  H >>0). Sometimes the viscosity of binary liquid alloys exhibits “strange” behaviour (Bi-Ga, Bi-Cu, Ga-Hg..), i.e. the same behaviour as their thermodynamic functions (according to the theory should be opposite!)

27. In the framework of the QLT the viscosity, , is related to the S CC (0) and diffusion by: For a thermodynamically ideal mixture,S CC (0)=S CC (0,id)=c(1-c) previous equ. becomes: with and for the viscosity of pure components (Stokes-Einstein) Assuming 1 = 2 = =1, it is obtained the Stokes-Einstein type relation for diffusion and viscosity:

28. Recently, we proposed the following viscosity equation: where m i and  i (i=A,B) are parameters that can be calculated from the experimental data.

29. viscosity Results of calculations viscosity of some binary systems

30. Modelling of the interfacial properties of molten Pb / FeCr substrate system: Application of the Phase Field Method  Study of thermodynamics and thermophysical properties of the Fe-Cr, Fe-O, Pb-O, Fe-Cr-Pb, Fe-Cr- Pb-O systems  Model formulation and implementation  Collection of input parameters for the Pb-Fe and Pb-Cr systems  Simulations, analysis of model parameters and validation with experimental micrographs for the Pb-Fe and Pb-Cr systems  Extension of the model and implementation towards ternary system Pb-Fe-Cr  Collection of input parameters for the Pb-Fe-Cr system  Simulations for the interface between molten Pb / FeCr - substrate system  Comparison with experimental micrographs for Pb / Fe-Cr diffusion couples MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy

31. Thank you for your attention! MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,September 19-23, 2011, Lerici (SP), Italy MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”, September 19-23, 2011, Lerici (SP), Italy