Simple Phase Representation: General Considerations

Concerning the (Pt) and Pt₃Al phases, there is disagreement on which particular model should be used. These phases are similar to (Ni) and Ni₃Al respectively. (Here, (Pt) and (Ni) denote combinations of four atoms of the elements in the four-compound sublattice formalism (CSF); arithmetically, Pt₄ and Ni₄ respectively.) One school of thought states that as all four phases are based on the f.c.c. lattice, then Ni₃Al, which can be viewed as an ordered f.c.c. phase, should be included as the f.c.c. phase in modelling (Pt) and Pt₃Al. On the other hand, another school of thought stipulates that, since (Pt) and Pt₃Al solidify separately, they should be modelled separately. The second school of thought would allow for Pt₃Cr and PtCr to be modelled as part of (Pt), since they form by ordering within the (Pt) phase field at lower temperatures. This might be considered as anomalous in that Pt₃Al would not be incorporated in the f.c.c. model, whereas Pt₃Cr would be. However, given that phases should be modelled in the same way only if they are likely to be contiguous, this would not be a problem unless Pt₃Al is likely to be contiguous with Pt₃Cr. At the moment, this is not likely. A similar argument can be made for Pt₃Al, which just like Ni₃Al, solidifies as a separate phase from (Pt), and is not formed within.

Another source of contention is that in the model being developed here, many parameters are needed to describe the phase. For the Ni-Al system, it could be argued that there are many data points and that the large number of parameters is justified. However, for Pt-Al, not only are there fewer data points, but there is also much greater uncertainty in the binary phase diagram regarding the reaction temperatures involving Pt₃Al, and even the type of ordering. Thus, a much simpler model is prescribed for the Pt₃Al phase, both because of a dearth of data (as compared with Ni₃Al), and also because the Pt₃Al and (Pt) phases solidify separately. All the information regarding ordering needs to be gathered before any incorporation into modelling is attempted. However, it must be noted that in the Dupin database (6), the Ni₃Al phase is modelled as ordered f.c.c., even though it solidifies separately. The latest database from Dupin (6) was used to draw the Ni-Al phase diagram, and the γ/γ′ boundary did not agree well with that in the experimental phase diagram, so it is questionable whether Dupin's complex modelling is really worthwhile.

It is best to adopt the most appropriate model for each phase in the system on the basis of its crystal structure and the available experimental data. Simple substitutional solid solutions can be modelled with two sublattices; one sublattice of sites of mixed occupancy (by the substituting elements) and one of interstitial sites. Ordered phases have a more complex crystallography in that atoms have preferential site occupancy. These phases are modelled with a more complex sublattice model comprising multiple sublattices with mixing of a number of different elements on each, depending on the crystallography. Although a multiple sublattice model is more complex than a simple two-sublattice model, it is easier to use the former to describe phases with a limited homogeneity range. In the extreme case, a stoichiometric phase is thus modelled with a single component on each sublattice. It is often useful to model an ordered phase along with its disordered ‘parent’ phase, for example b.c.c._B2 and b.c.c._A2, or f.c.c._L12 and f.c.c._A1, with a single Gibbs energy description enabling the ordering transition to be modelled. This modelling is quite complex, and whether such complications should be included depends on the application of the database.

There are databases being developed without such complex modelling and these are very useful. One example is the COST 531 lead-free solders database (7), comprising assessed thermodynamic data for binary and ternary systems based on eleven elements associated with lead-free solder materials. Thus, it might be questioned whether the current pgm database should be concerned with order/disorder reactions. The answer should be positive, of course, because the ordered Pt₃Al phase, which is an ordered f.c.c. phase, is the basis of the alloys. However, if there are too few experimental data available, modelling the Pt₃Al and f.c.c._A1 phase with a single Gibbs energy description will be difficult. If a model requiring many parameters is optimised with few data points, the parameters themselves become meaningless and the results are highly unlikely to be representative. Thus, in the current work, it was decided to model such ordered phases separately and then extend the database subsequently if there is both sufficient need and the experimental data become available. In this way, the database grows with the available experimental data, and at any time, the database is the optimum that can be achieved. Currently, the database is being developed so that the phase equilibria between the phases on solidification can be derived. As more work is done on developing the alloys for application, the order/disorder reactions will become increasingly important, especially for the Pt₃Al phase. A combination of Thermo-Calc^TM (8), Pandat (9) and MTDATA (10) software was used for the present work.

Chromium-Platinum

Until experimental results show otherwise, the assessment of Oikawa et al. (11) will be used, extrapolated into the ternary, and will then be reoptimised with experimental values from the Pt-Cr-Ru system. The assessment of Oikawa et al. (11) is shown in Figure 1. However, it was necessary to derive Gibbs energy parameters for the metastable h.c.p. phase in the binary system. The metastable phase was initially allocated the same set of Gibbs energy values as for the f.c.c. phase, but the parameters were optimised using the ternary data (described below).

Platinum-Ruthenium

It was initially thought that the description of Pt-Ru in the Spencer database (12) version of Pt-Ru would be the same as that in the Scientific Group Thermodata Europe (SGTE) database (13). However, this was not so. The phase diagram from Spencer is a eutectic, with a maximum in (Pt) and ∼ 10°C between the maximum and eutectic temperature, whereas that from SGTE is peritectic, which is consistent with available literature (14, 15) and experimental work at Mintek.

Optimising with data from Hutchinson (14) gave a good fit and convincing coefficients. While plotting the free energy curves demonstrated that Ru had an unusual energy curve, it would be unwise to change this feature, because it originated from the Ru unary data, is set across the entire database, and represents a best-fit value for many systems. One solution to this anomaly would be to add an interaction parameter, but it must be remembered that there are too few data available. However, it was found that the most reasonable fit to the phase boundaries of the (Pt) + (Ru) two-phase field, where a few compositions had been measured experimentally, resulted in the appearance of a very shallow eutectic reaction. The phase diagram, optimised using WinPhaD and calculated using Pandat, is given in Figure 2, and may be compared with the experimental diagram in Figure 3.

Chromium-Ruthenium

This system contains two intermetallic compounds: Cr₂Ru (σ) and Cr₃Ru. The accepted models have three sublattices, so this format would be followed for the Cr-Ru system despite the fact that, especially given such limited data, it would be difficult to have mixing on all three sublattices – many end-members would be needed. It was therefore decided that Cr only would be located on one sublattice, and the remaining two would have mixing; this is normal practice. The current model of choice for the σ phase is 10:16:4 (where the notation shows the numbers of atoms on each of the three sublattices; the previous model was 8:18:4). The previous model featured in the Glatzel assessment (16), although with mixing on all three sublattices. Elements are usually mixed on many sublattices only where there is a very wide range of phase stability. In this case, there is a narrow phase stability range, so the degree of mixing needs to be reduced.

The approach used was to build up the system with the most simple phase diagram descriptions possible: thus Cr₂Ru (σ) and Cr₃Ru would be line compounds. The Ru and Cr unary data were derived from Kaufman (17). Since Kaufman's (17) reported reaction temperatures involving Cr₂Ru (σ) and Cr₃Ru were suspiciously convenient: ∼ 750, ∼ 800 and ∼ 1000°C, it was realised that there were problems with the system, and the rounded data are the best that were obtained from the literature (15). These had to be used, as there are no other data available. Attempts to measure the reaction temperatures by differential thermal analysis (DTA) were inconclusive (18). The phase diagram gave a very good fit, as shown in Figure 4, compared with the experimental diagram (Figure 5) (15).

Platinum-Chromium-Ruthenium

Experimental results of the A15 Cr₃Ru and Cr₃Pt phases were not conclusive in showing whether the phases are contiguous, despite two more samples of intermediate compositions between Cr₃Ru and Cr₃Pt being prepared at Mintek. These samples were annealed at ∼ 850°C, because if the phases are contiguous, they should meet at this temperature for the sample compositions chosen. Depending on how the phases extend into the ternary, the sublattice on which substitution is occurring can be determined. For Cr₃Ru, if Ru is constant, then Pt substitutes for Cr; and for Cr₃Pt, if Cr is constant, Ru substitutes for Pt. It must, however, be remembered that the original samples were not in equilibrium, and the latest samples were annealed for longer, to promote equilibrium.

It should be noted that Waterstrat's Cr₃Pt phase (19) was more narrow (almost stoichiometric) and did not decompose at lower temperature (which is what was calculated at one stage in the present work). A likely model for this case (19) would be Cr on one sublattice and Pt + Cr on the other, but this depends on the atomic sizes. These can be measured in different ways (giving different results) and the most appropriate method should be used for the mode of bonding of the particular atom. Pt and Ru show similar covalent radii. This being so, they could sit on the same sublattice. However, it is recommended that other A15 phases be researched to see how they would best be modelled, especially for the composition ranges (i.e. the spread on both sides from mole fraction X = 0.25). For the representation of Cr₃Pt within the ternary (and higher-order phase diagrams), the model would be much simpler (and have fewer end members) if the lattice components could be described as (Cr, Cr) (Cr, Pt, Ru).

To model the ternary system, an interaction parameter, added to increase the phase extensions into the ternary, was determined for the h.c.p. phase. The projected liquidus surface, shown in Figure 6, is an improvement on the assessment by Glatzel et al. (16). However, the invariant reactions are still incorrect, because Figure 6 shows the liquidus surfaces for (Ru) and Cr₃Pt abutting, by contrast with the experimental results in Figure 7. Those for (Cr) and (Pt) should in fact abut, because of the (Pt) + (Cr) eutectic observed in the ternary samples (20, 21). However, the junction between the incorrect surfaces of primary solidification is smaller than was calculated previously (16), and agrees more closely with the experimental results.

The thermodynamic description of the ternary system was optimised using the experimental data of Zhao (22), as this set of data seemed to be more complete and self-consistent, and Mintek's data (20, 23) were affected by coring. The assessment module of MTDATA was used to perform the optimisation. During the optimisation process it was found that it was necessary to adjust only the Gibbs energy description of the metastable h.c.p. phase in the Cr-Pt binary in order to get a reasonable fit to the experimental phase diagram data for the f.c.c. and h.c.p. phase boundaries. No ternary interactions were required for these phases (24).

The experimental data for the A15 phase fitted reasonably well, although the fit was little improved by allowing the optimisation to give a Gibbs energy description for the metastable Pt₃Ru A15 phase. The A15 phase extends from the Cr-Pt edge as required but too far into the ternary. Also, the A15 phase field is not wide enough as it extends into the ternary. This feature is probably due to the fact that the phase is modelled with a very narrow homogeneity range in the Cr-Ru system. Better modelling of the A15 phase in the binary system would undoubtedly improve the overall modelling of this phase, but this would require further experimental study of its stability range. The fit to the experimental b.c.c. phase diagram data is, however, very good. The calculated phase diagram for 1200°C, showing the experimental data, is given in Figure 8. The fit with the experimental data from Süss et al. (23) is not so good, particularly with respect to the (Ru) h.c.p. phase boundary, but this could be due to coring effects. Again, this could be improved by a better description of the A15 phase. The calculated phase diagram for 1000°C is given in Figure 9.

Conclusion

The latest developments to the Pt-Al-Cr-Ru database have improved the agreement with the experimental phase diagrams, and especially with diffusion data. The models of the f.c.c., Cr₃Ru and Cr₂Ru (σ) phases were changed, and the new models were selected so that fewer parameters were necessary. However, the order/disorder reactions of the f.c.c. phases have yet to be modelled successfully, and before this can be realised more experimental data are needed. The A15 phase needs to be modelled in order to produce a wider phase range within the ternary. Once again, more experimental data are needed to confirm whether the A15 phases in the Cr-Pt and Cr-Ru systems are contiguous. More samples between the two binary phases had been manufactured, annealed at intermediate temperatures and analysed, but the results were not conclusive. Thus, future work on the database can only be undertaken once more experimental data have been acquired.

Work is in hand at the University of Bayreuth on the platinum-aluminium-chromium-nickel (Pt-Al-Cr-Ni) database, which is eventually to be merged with the Pt-Al-Cr-Ru database. Part III of this series of papers, to be published in a future issue of Platinum Metals Review, will describe this work.