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The Application of MTDATA to the Melting/Freezing Points of ITS-90 Metal Fixed-Points

The Application of MTDATA to the Melting/Freezing Points of ITS-90 Metal Fixed-Points. H Davies, D I Head, J Gray, P Quested Engineering and Process Control Division 23 November 2006. Contents. Thermodynamic modelling introduction Sn-X systems Data availability for Sn-X

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The Application of MTDATA to the Melting/Freezing Points of ITS-90 Metal Fixed-Points

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  1. The Application of MTDATA to the Melting/Freezing Points of ITS-90 Metal Fixed-Points H Davies, D I Head, J Gray, P Quested Engineering and Process Control Division 23 November 2006

  2. Contents • Thermodynamic modelling introduction • Sn-X systems • Data availability for Sn-X • Sn-X binary diagrams • Influence of X on Tm(Sn) • Real Sn compositions and simulations • Equilibrium or not ? • Al-X systems • Data availability for Al-X • Non-metals (C, N, O) • Al-X binary diagrams • Influence of X on Tm(Al) • Simulations on freezing of real “pure” Al compositions and doping experiments • A Virtual Measurement System for fixed points ? • Conclusions

  3. How a thermodynamic model works • The equilibrium state of a chemical system at a fixed temperature (T), pressure (P) and overall composition can be calculated by minimising its Gibbs energy (G) with respect to the amounts of individual species (unaries) that could possibly form, either as distinct phases or within solutions • Models for the variation of G with T and P for unaries and for the influence of interactions between unaries on G for solutions are needed in order to make such calculations possible G(T) = A + BT + CTlnT + DT2 + ET3 + F/T • More complex models describe the pressure dependence of G for unaries and the contribution made by magnetism, if appropriate • Other effects such as surface energy (small particles/droplets) and strain can in principle be taken into account

  4. Unary data for Sn • Sets of coefficients describing G(T,P) must be derived for chemical species in ALL phases (gas, liquid, different crystalline structures) in which they appear. The most stable phase at chemical equilibrium can then be predicted for a chosen T and P as the one with the lowest Gibbs energy

  5. Unary data for Sn • Just showing stable phases • Note diamond phase (grey tin) moving towards stability below room temperature

  6. Unary phase diagrams The phase rule: F = C + 2 - P relates the number of degrees of freedom in a system (F) to the number of components (C) and phases (P). For a one component system in which 3 phases (such as gas, liquid and solid) co-exist the number of degrees of freedom is zero - neither temperature nor pressure can be fixed arbitrarily.

  7. Binary data • The molar Gibbs energy of a solution phase (Gm) can be written: Gm(T,x) = Sj xjGj(T) + Gmag +RT Sj xjlnxj + EGm(T,x) • where R is the gas constant and Gj is the molar Gibbs energy of component j, present in solution with mole fraction xj. The four terms represent unary contributions, magnetic contributions, ideal entropy contributions and finally additional or excess contributions to the Gibbs energy of the phase resulting from interactions between components during mixing. The Redlich-Kister equation is widely used to model the excess Gibbs energy of mixing: EGm(T,x) = SjSk>j xj xk (0Ljk + 1Ljk(xj-xk) + 2Ljk(xj-xk)2 + 3Ljk(xj-xk)3 + …) • nLjk are coefficients determined to model the measured mixing properties of the phase in question as closely as possible. nLjk may be temperature dependent but anything more complex than a linear temperature dependence is unusual. Different powers of (xj-xk) in the Redlich-Kister equation allow asymmetry in the Gibbs energy of mixing to be modelled.

  8. Binary Gibbs energies • Phase equilibria are determined by the relationship between Gibbs energies of phases • Temperature is 505.078 K therefore BCT and LIQUID phase Gibbs energies are identical at pure Sn • As Pb concentration increases the Gibbs energy of the FCC phase becomes lower (green line) until eventually the Pb rich FCC solid solution phase precipitates. This is reflected in the phase diagram on the next slide

  9. Sn-Pb Full binary phase diagram

  10. Where do the solute distribution coefficients come from? • Explicit distribution coefficients are not used in the calculations • They can however be deduced from the underlying thermodynamic data • Sections of phase diagrams up to 3 wt% solute and associated calculated distribution coefficients are shown to right

  11. Sn-X systems

  12. Data availability for Sn-X(impurity elements having thermodynamic data for interaction with Sn are underlined – MTSOL, MTSOLDERS, COST531) • Analysed and found above detection limits by NRC using glow discharge mass spectrometry (08-09-2005) • C, N, O, Na, Al, Si, S, Cl, Tl, Cu, Ag, Pb • Metallic elements not found but with high (> 50 ppb) detection limits • Co, In, Sb • Set of elements indicated from analysis and available for thermodynamic modelling • Ag, Al, Cu, In, Ni (as analogue for Co), Pb, Sb, Si • Full set of elements available for thermodynamic modelling • Ag, Al, Au, Bi, Cu, Ge, In, Ni, Pb, Pd, Sb, Si, Zn

  13. Sn-Ag (20, 50, 100, 500 and 1000 ppb) 1000 ppb 20 ppb

  14. Sn-Al (20, 50, 100, 500 and 1000 ppb)

  15. Sn-Cu (20, 50, 100, 500 and 1000 ppb)

  16. Sn-Pb (20, 50, 100, 500 and 1000 ppb)

  17. Sn-Sb (20, 50, 100, 500 and 1000 ppb) 20 ppb 1000 ppb

  18. NRC Sn composition simulation Pb impurity only considered Tm – Tliq = 15 K Tm – T50% liq = 25 K

  19. NRC Sn composition simulation Only analysed levels for Ag, Cu, Pb and Si considered Tm – Tliq = 24 K Tm – T50% liq = 44 K If Si is excluded these values become 15 and 25 K

  20. NRC Sn composition simulation Analysed levels for Ag, Cu, Pb and Si + 50% of limits of detection for others Tm – Tliq = 84 K Tm – T50% liq = 147 K

  21. NRC Sn composition simulation Analysed levels for Ag, Cu, Pb and Si + 100% of limits of detection for others Tm – Tliq = 142 K Tm – T50% liq = 250 K

  22. NRC Sn composition simulation Ideal liquid and BCT phase models Tm – Tliq = 120 K Tm – T50% liq = 214 K

  23. NRC Sn composition simulation Ideal liquid and pure Sn BCT phase models – Raoults Law assumption Tm – Tliq = 180 K Tm – T50% liq = 352 K

  24. Summary of NRC analysed Sn composition simulation

  25. Equilibrium v Non-equilibrium (Scheil) Sn with 10 ppm Pb • MTDATA can do limiting case non-equilibrium solidification simulation by assuming rapid diffusion in liquid and none in solid • Scheil solidification shows significant lowering of temperature at higher solid fractions • Equilibrium and Scheil are bounds to “true” behaviour ???

  26. Pressure effects Sn with 10 ppm Pb Pressure = 101.325 kPa + 10 kPa + 20 kPa • Pressure dependence of melting is handled naturally by MTDATA • Pressures relate to hydrostatic heads of approximately 0 to 29 cm

  27. Al-X systems

  28. Data availability for Al-X(impurity elements having thermodynamic data for interaction with Al are underlined –MTAL, MTSOL) • Analysed and found above detection limits by NRC using glow discharge mass spectrometry (08-09-2005) • C, N, O, Mg, Si, P, S, Cl, Ti, V, Cr, Mn, Fe, Ni, Cu • Metallic elements with high (> 50 ppb) detection limits • Au • Set of elements indicated from analysis and available for thermodynamic modelling C, N, Mg, Si, P, Ti, V, Cr, Mn, Fe, Ni, Cu • Full set of elements available for thermodynamic modelling • Ag, C, Ca, Ce, Cr, Cu, Fe, Ga, Ge, Hg, In, Li, Mg, Mn, Mo, N, Nb, Nd, Ni, P, Pb, Sb, Si, Sn, Ta, Ti, V, W, Y, Zn, Zr

  29. Al-Si Full binary phase diagram

  30. Al-N Partial binary phase diagram Predicted nitrogen solubility in liquid Al near Tm is greater than the 1800 ppb impurity found in NRC analysis

  31. Al-C Partial binary phase diagram Predicted carbon solubility in liquid Al near Tm is approx. 0.3 ppb (w/w)

  32. Al-N (20, 50, 100, 500 and 1000 ppb) <<< 1000 ppb NRC analysis: 1800 ppb 500 ppb 20 ppb

  33. Al-Si (20, 50, 100, 500 and 1000 ppb) NRC analysis: 420 ppb 1000 ppb 20 ppb

  34. Al-Cu (20, 50, 100, 500 and 1000 ppb) NRC analysis: 230 ppb 1000 ppb 20 ppb

  35. Al-Fe (20, 50, 100, 500 and 1000 ppb) NRC analysis: 220 ppb 1000 ppb 20 ppb

  36. NRC Al composition simulation Mg, Si, Ti, V, Cr, Mn, Fe, Ni, Cu, P and N impurities considered Tm – Tliq = 2.8 mK Tm – T50% liq = 5.5 mK

  37. NRC Al composition simulation (no N) Mg, Si, Ti, V, Cr, Mn, Fe, Ni, Cu, P impurities considered Scheil simulation results Tm – Tliq = 275 K Tm – T50% liq = 810 K

  38. NRC Al composition simulation Only N impurity considered Tm – Tliq = 2.3 mK Tm – T50% liq = 4.7 mK

  39. Summary of NRC analysed Al composition simulations

  40. Impurity dependence of the aluminiumpointJ Ancsin, Metrologia 40 (2003) 36–41 • Al-X systems in NRC study based on 99.9999 wt% Al + precise impurity additions • Adiabatic calorimeter used to allow fraction melted to be quantified • X = Ag, Zn, Cu, Fe, In, Si, Ti, Mn, Cd, Sb, Ca, and Ni • MTDATA equilibrium calculations carried out for Ag, Si and Ti

  41. Impurity dependence of the aluminiumpointMTDATA equilibrium simulation • Ag impurity  J Ancsin, Metrologia 40 (2003) 36–41 • 36 ppm of Ag impurity • 76 ppm of Ag impurity

  42. Impurity dependence of the aluminiumpointMTDATA equilibrium simulation • Si impurity  J Ancsin, Metrologia 40 (2003) 36–41 • 18.4 ppm of Si impurity • 44.1 ppm of Si impurity

  43. Impurity dependence of the aluminiumpointMTDATA equilibrium simulation • Ti impurity  J Ancsin, Metrologia 40 (2003) 36–41 • 2.8 ppm of Ti impurity • 7.0 ppm of Ti impurity Experimental data show “wrong” curvature

  44. NPL Virtual Measurement system for Al alloys v1.0 (2005 NRC analysis for Mg-Si-Fe-Cu) Analysis / ppb (w/w) Mg 160 Si 420 Fe 220 Cu 230 45 mK abscissa range Note: The current release of this software was designed for commercial Al-alloys and not modified to handle ultra pure metals over very small temperature ranges 11 mK abscissa range

  45. Conclusions • General • Equilibrium thermodynamic and limiting case non-equilibrium (Scheil) simulations can help in (a) extrapolating non-constant freezing “plateaux” to true liquidus temperatures and (b) estimating deviations of observed liquidus temperature from true pure element melting point • Thermodynamic data availability • Much more data available for Al-X than for Sn-X (commercial Al-alloys v solders) • Chemical analysis issues • The effect of non-metals such as nitrogen is important for Al • Uncertainty in sample analysis in terms of the measured concentrations or the chemical state of the elements is a significant problem possibly introducing more uncertainty than thermodynamic modelling assumptions (eg real solutions v ideal) • Simulations • Results of Scheil simulations only start to deviate from equilibrium above 70% solid • Non-equilibrium modelling should be better at determining the liquidus temperature from sub-liquidus experimental data near the end of solidification • With the high carbon levels, indicated by the analysis and use of graphite crucibles, the phase Al4C3 should always be present • AlN and Al2O3 should also be present in solids with AlN dissolving significantly in liquid Al • Equilibrium simulations are in close agreements with NRC doping experiments for Ag and Si. Odd curvature of NRC Ti experimental results cannot be explained

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