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Non-statistical thermodynamic optimization: an extravagance or a useful tool?

Non-statistical thermodynamic optimization: an extravagance or a useful tool? . Cong (Leo) Dai. Outline. Thermodynamic modeling CALPHAD method Principles and examples Advantages and deficiencies Kantorovich idea Conclusions and future efforts. Thermodynamic modeling. B. C. A.

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Non-statistical thermodynamic optimization: an extravagance or a useful tool?

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  1. Non-statistical thermodynamic optimization: an extravagance or a useful tool? Cong (Leo) Dai

  2. Outline • Thermodynamic modeling • CALPHAD method • Principles and examples • Advantages and deficiencies • Kantorovich idea • Conclusions and future efforts

  3. Thermodynamic modeling B C A PhasSage, www.factsage.com PhasSage; http://honghua66.en.ecplaza.net; Solutionizing Heat Treatment Furnace (27982050)

  4. Analytical descriptions of the Gibbs energies of stoichiometric compounds and solutions Publications including tables of thermochemical data Databases A program minimizing the Gibbs energy of a system Thermo-Calc FactSage Pandat MALT2 What is needed to use thermodynamic modeling? Reliability of the analytical representations of the Gibbs energies?

  5. Phase diagrams of the Fe–Nb system TCFE2 database TCFE6 database A B

  6. Constructing the Gibbs energies

  7. CALPHAD technique is not unique • Step 1: a model The coin is a disc • Step 2: identify unknown model’s parameters Radius r, thickness h, density r ; they all must be positive • Step 3: collect all available experimental data r, h, d, l, a, V, m, r • Step 4: solve an optimization problem

  8. Finding r, h and r Non-linear least squares problem with linear constraints

  9. Almost the same happens in CALPHAD • Experimental data • Enthalpies of mixing at 1150°C • (Ag)+L / L liquidus temperatures • L / L+(Cu) liquidus temperatures • Chemical potential of Cu in (Ag) • Chemical potential of Ag in (Cu)

  10. Building the Gibbs energies of the phases A traditional CALPHAD method rests on a statistical foundation

  11. Statistical description of data • Measurement is non-repeated • Measurement is insufficient • Measurement errors are affected by random errors and systematical errors

  12. Kantorovich idea(1962) Instead of minimizing the sum of squared derivations, simultaneous inequalities should be used, which can be solved by linear programming methods. Kantorovich, L.V. Sib. Mat. Zh., 1962, vol.3, No.5, p. 701.

  13. Interval data • All possible outcomes of an experiment belong to a finite interval! • Any value in the same interval data is equally acceptable!

  14. Non-statistical approach • Error analysis • Postulate a model • Solve inequalities

  15. Data from Kawakami Reach the required temperature Remove the porcelain tube Measure the temperature variation Kawakami, M.: Sci. Rep. Res. Inst. Tohoku Univ. 7 (1930) 351.

  16. Mixing Enthalpy of liquid Mg-Ag alloys A B Kawakami, M.: Sci. Rep. Res. Inst. Tohoku Univ. 7 (1930) 351.

  17. Mixing Enthalpy of liquid Mg-Ag alloys No feasible region.

  18. Data from Gran Heat the furnace Hold at a predetermined temperature Quenched in an Argon-stream Analyzed by ICP-AES analysis (Inductively Coupled Plasma-Atomic Emission Spectrometry) J. Gran et al./ CALPHAD 36 (2012 89-93)

  19. Activity of Mg in liquid Mg-Ag alloys J. Gran et al./ CALPHAD 36 (2012 89-93)

  20. Activity of Mg in liquid Mg-Ag alloys No feasible region. Comparison Future work!

  21. Conclusions • CALPHAD technique is successful but not always satisfactory. • A non-statistical approach is established and applied to thermodynamic optimization.

  22. Future efforts • Comparisons in liquid Mg-Ag alloys. • Rules of assigning interval data. • Non-statistical approach applies to other interesting thermodynamic assessments.

  23. Acknowledgements Supervisor: - Dr. Dmitri Malakhov Thanks for your attention!

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