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-XSn-X binary diagrams

Influence of X on Tm(Sn)Real Sn compositions and simulationsEquilibrium or not ?

• Al-X systemsData availability for Al-XNon-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

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

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

Unary data for Sn

• Just showing stable phases

• Note diamond phase (grey tin) moving towards stability below room temperature

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.

Binary data

• The molar Gibbs energy of a solution phase (Gm) can be written:

Gm(T,x) = j xjGj(T) + Gmag + RT j 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) = j k>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.

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

Sn-PbFull binary phase diagram

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

Sn-X systems

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

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

1000 ppb

20 ppb

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

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

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

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

20 ppb

1000 ppb

NRC Sn composition simulationPb impurity only considered

Tm – Tliq = 15 K

Tm – T50% liq = 25 K

NRC Sn composition simulationOnly 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

NRC Sn composition simulationAnalysed levels for Ag, Cu, Pb and Si + 50% of limits of detectionfor others

Tm – Tliq = 84 K

Tm – T50% liq = 147 K

NRC Sn composition simulationAnalysed levels for Ag, Cu, Pb and Si + 100% of limits of detectionfor others

Tm – Tliq = 142 K

Tm – T50% liq = 250 K

NRC Sn composition simulationIdeal liquid and BCT phase models

Tm – Tliq = 120 K

Tm – T50% liq = 214 K

NRC Sn composition simulationIdeal liquid and pure Sn BCT phase models – Raoults Law assumption

Tm – Tliq = 180 K

Tm – T50% liq = 352 K

Summary of NRC analysed Sn composition simulation

Composition (Tm – Tliq) / K (Tm – T50% liq) / K

Pb only 15 25

Analysed Cu, Ag, Si and Pb

24 44

Analysed excluding Si

15 25

Analysed + 50% detection limits

84 147

Analysed + 100% detection limits

142 250

Ideal liquid and BCT solid solution

120 214

Ideal liquid and pure BCT solid

180 352

Equilibrium v Non-equilibrium (Scheil)

• 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 ???

Sn with 10 ppm Pb

Pressure effects

• Pressure dependence of melting is handled naturally by MTDATA

• Pressures relate to hydrostatic heads of approximately 0 to 29 cm

Sn with 10 ppm PbPressure = 101.325 kPa + 10 kPa + 20 kPa

Al-X systems

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

Al-SiFull binary phase diagram

Al-NPartial binary phase diagram

Predicted nitrogen solubility in liquid Al near Tm is greater than the 1800 ppb impurity found in NRC analysis

Al-CPartial binary phase diagram

Predicted carbon solubility in liquid Al near Tm is approx. 0.3 ppb (w/w)

Al-N (20, 50, 100, 500 and 1000 ppb)

<<< 1000 ppb

20 ppb

500 ppb

NRC analysis: 1800 ppb

Al-Si (20, 50, 100, 500 and 1000 ppb)

1000 ppb

20 ppb

NRC analysis: 420 ppb

Al-Cu (20, 50, 100, 500 and 1000 ppb)

1000 ppb

20 ppb

NRC analysis: 230 ppb

Al-Fe (20, 50, 100, 500 and 1000 ppb)

1000 ppb

20 ppb

NRC analysis: 220 ppb

NRC Al composition simulationMg, Si, Ti, V, Cr, Mn, Fe, Ni, Cu, P and N impurities considered

Tm – Tliq = 2.8 mK

Tm – T50% liq = 5.5 mK

NRC Al composition simulation (no N)Mg, Si, Ti, V, Cr, Mn, Fe, Ni, Cu, P impurities considered

Tm – Tliq = 275 K

Tm – T50% liq = 810 K

Scheil simulation results

NRC Al composition simulationOnly N impurity considered

Tm – Tliq = 2.3 mK

Tm – T50% liq = 4.7 mK

Summary of NRC analysed Al composition simulations

Composition (Tm – Tliq) / K (Tm – T50% liq) / K

Full analysis considered

2800 5500

N excluded 275 810

Only Al-N

(1800 ppb N)

2300 4700

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

Impurity dependence of the aluminiumpoint

MTDATA equilibrium simulation

• 36 ppm of Ag impurity • 76 ppm of Ag impurity

Ag impurity J Ancsin, Metrologia 40 (2003) 36–41

Impurity dependence of the aluminiumpoint

MTDATA equilibrium simulation

• 18.4 ppm of Si impurity • 44.1 ppm of Si impurity

Si impurity J Ancsin, Metrologia 40 (2003) 36–41

Impurity dependence of the aluminiumpoint

MTDATA equilibrium simulation

• 2.8 ppm of Ti impurity • 7.0 ppm of Ti impurity

Ti impurity J Ancsin, Metrologia 40 (2003) 36–41

Experimental data show “wrong” curvature

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

11 mK abscissa range

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

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