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Thermodynamics and thermophysical properties of liquid Fe-Cr alloys

Rada Novakovic National Research Council (CNR–IENI) Genoa, Italy. Thermodynamics and thermophysical properties of liquid Fe-Cr alloys. Mixing behaviour of liquid binary alloys: energetic & structural factors. Observable indicators: Phase diagrams.

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Thermodynamics and thermophysical properties of liquid Fe-Cr alloys

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

  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

  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

  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

  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

  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

  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

  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

  10. Subtracting Butler’s equ. for both components, and combining with and taking into account the bulk (surface) phase activity coefficients obtained byFowler_Guggenheim methodas and the  and xscan be calculated. The surface tension can be calculated inserting xs 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

  11. * 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 Surface tension calculations of binary systems

  12. * 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 Surface tension calculations of ternary systems

  13. Geometric models Kohler Toop Chou

  14. 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 Ti46Al46Nb8 (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

  15. 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

  16. 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

  17. 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

  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

  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

  20. Microscopic functions (B-T) & Thermodynamics For ideal solution the SCC(0) becomes The CSRO parameter and SCC(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

  21. Microscopic functions & local arrangements of atoms in the melt SCC(0)and CSRO parameter indicate chemical order & segregation (phase separation): SCC(0) – the nature of mixing CSRO parameter – thedegree of order Criteria for mixing behaviour 1. SCC(0) < SCC(0, id) presence of chemical order SCC(0) > SCC(0, id) segregation 2. -1 < CSRO < 0 ordering in the melt CSRO =-1complete ordering 0 < CSRO < 1 segregation CSRO =1phase 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

  22. 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

  23. The interdiffusion coefficient (Dm) can be given in terms of the SCC(0)by For “ideal” alloys, SCC(0)= SCC(0,id)= cAcB, then and finally combining the last two eqs. it is obtained, The criteria for mixing behaviour: SCC(0) > SCC (0, id)segregation Dm < Did SCC(0) < SCC (0, id)presence of chem. order Dm > Did 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. 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

  25. Viscosity Viscosity()of liquid alloys-the atomic level structure and interactions. The composition dependenceof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) negativedeviations (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!)

  26. In the framework of the QLT the viscosity, , is related to theSCC(0)and diffusionby: For a thermodynamically ideal mixture,SCC(0)=SCC(0,id)=c(1-c) previous equ. becomes: with and for the viscosity of pure components (Stokes-Einstein) Assuming 1 = 2 = =1, it is obtainedthe Stokes-Einstein type relation for diffusion and viscosity:

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

  28. Results of calculationsviscosity of some binary systems

  29. 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

  30. 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

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