Building a Thermodynamic Database for Platinum-Based Superalloys: Part II
Building a Thermodynamic Database for Platinum-Based Superalloys: Part II
USE OF MODELS REQUIRING FEWER PARAMETERS
Work is being done at Mintek, the University of Leeds and the University of Bayreuth to build up a platinum-aluminium-chromium-ruthenium (Pt-Al-Cr-Ru) database for the prediction of phase diagrams for further alloy development by obtaining good thermodynamic descriptions of all of the possible phases in the system. Binary descriptions were combined, allowing extrapolation into the ternary systems, and experimental phase equilibrium data were compared with calculated results. Very good agreement was obtained for the Pt-Al-Ru system, as described in Part I of this series of papers (1). This paper (Part II) addresses the Pt-Cr-Ru system, with equally encouraging results. The final paper in the series (Part III, to be published in a future issue of Platinum Metals Review) will deal with work on the platinum-aluminium-chromium-nickel (Pt-Al-Cr-Ni) database at the University of Bayreuth. The Pt-Al-Cr-Ru and Pt-Al-Cr-Ni databases will eventually be merged.
Work has been ongoing in building a thermodynamic database for the prediction of phase equilibria in Pt-based superalloys (1–5). The alloys are being developed for high-temperature applications in aggressive environments. The database will aid the design of alloys by enabling the calculation of the composition and proportions of phases present in alloys of different compositions. Currently, the database contains the elements platinum, aluminium, chromium and ruthenium. This paper is a revised account of work presented at the conference: Southern African Institute of Mining and Metallurgy ‘Platinum Surges Ahead’ at Sun City, South Africa, from 8th to 12th October 2006 (5). Part I, describing initial results for the Pt-Al-Ru system from the compound energy formalism model, was published in the July 2007 issue of Platinum Metals Review (1).
For the Ru-Al system, very good agreement has been obtained between experimental phase equilibrium data and calculations based on a version of the compound energy formalism model (1). However, for the other binary and ternary systems, there are insufficient data to obtain good results by this method, since more phases are represented in each system. This paper (Part II) describes the different approach which was needed, with simpler representation to allow for sparse data.
Part III will complete the series by describing work 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.
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-CalcTM (8), Pandat (9) and MTDATA (10) software was used for the present work.
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).
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.
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).
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.
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.
- L. A. Cornish, R. Süss, A. Watson and S. N. Prins, Platinum Metals Rev., 2007, 51, (3), 104 LINK https://www.technology.matthey.com/article/51/3/104-115
- I. M. Wolff and P. J. Hill, Platinum Metals Rev., 2000, 44, (4), 158 LINK https://www.technology.matthey.com/article/44/4/158-166
- L. A. Cornish, J. Hohls, P. J. Hill, S. Prins, R. Süss and D. N. Compton, J. Min. Metall. Sect. B: Metall., 2002, 38, (3–4), 197 LINK http://www.jmm.tf.bor.ac.yu/contents3-4%2002.htm
- L. A. Cornish, R. Süss, L. H. Chown, S. Taylor, L. Glaner, A. Douglas and S. N. Prins, ‘Platinum-Based Alloys for High Temperature and Special Applications’, in “International Platinum Conference ‘Platinum Adding Value'”, Sun City, South Africa, 3rd–7th October, 2004, Symposium Series S38, The South African Institute of Mining and Metallurgy, Johannesburg, South Africa, 2004, pp. 329–336
- L. A. Cornish, R. Süss, A. Watson and S. N. Prins, ‘Building a Database for the Prediction of Phases in Pt-based Superalloys’, in “Second International Platinum Conference ‘Platinum Surges Ahead'”, Sun City, South Africa, 8th–12th October, 2006, Symposium Series S45, The Southern African Institute of Mining and Metallurgy, Johannesburg, South Africa, 2006, pp. 91–102; http://www.platinum.org.za/Pt2006/index.htm
- B. Sundman and N. Dupin, in:“XXIX JEEP: Journées d'Étude des Équilibres entre Phases”, Lyon Villeurbanne, France, 2nd–3rd April, 2003, F. Bosselet and C. Goutaudieret al., Journal de Physique IV – Proceedings, EDP Sciences, Les Ulis, France, 2006
- A. Watson, A. Dinsdale, A. Kroupa, J. Vízdal, J. Vrestal and A. Zemanová, “The COST 531 Lead-free Solders Thermodynamic Database”, Proceedings of the 61st Annual ABM Congress, Rio de Janeiro, Brazil, 24th–27th July, 2006
- B. Sundman, B. Jansson and J.-O. Andersson, CALPHAD, 1985, 9, (2), 153 LINK http://dx.doi.org/10.1016/0364-5916(85)90021-5
- S.-L. Chen, S. Daniel, F. Zhang, Y. A. Chang, X.-Y. Yan, F.-Y. Xie, R. Schmid-Fetzer and W. A. Oates, CALPHAD, 2002, 26, (2), 175 LINK http://dx.doi.org/10.1016/S0364-5916(02)00034-2
- R. H. Davies, A. T. Dinsdale, J. A. Gisby, J. A. J. Robinson and S. M. Martin, CALPHAD, 2002, 26, (2), 229 LINK http://dx.doi.org/10.1016/S0364-5916(02)00036-6
- K. Oikawa, G. W. Qin, T. Ikeshoji, O. Kitakami, Y. Shimada, K. Ishida and K. Fukamichi, J. Magn. Magn. Mater., 2001, 236, (1–2), 220 and references therein LINK http://dx.doi.org/10.1016/S0304-8853(00)00520-5
- P. J. Spencer, The Noble Metal Alloy (NOBL) Database, The Spencer Group, Trumansburg, U.S.A., 1996 LINK http://www.spencergroupintl.com/
- A. T. Dinsdale, CALPHAD, 1991, 15, (4), 317 LINK http://dx.doi.org/10.1016/0364-5916(91)90030-N
- J. M. Hutchinson, Platinum Metals Rev., 1972, 16, (3), 88 LINK https://www.technology.matthey.com/article/16/3/88-90
- “Binary Alloy Phase Diagrams”, 2nd Edn., eds.T. B. Massalski, H. Okamoto, P. R. Subramanian and L. Kacprzak, in3 volumes, ASM International, Ohio, U.S.A., 1990
- U. Glatzel and S. N. Prins, ‘Thermodynamic Assessments of the Pt-Cr and Cr-Ru Systems with an Extrapolation into the Pt-Cr-Ru System’, in “CALPHAD XXXII: Program and Abstracts”, Quebec, Canada, 25th–30th May, 2003, p. 118seeC. K. Pollard, CALPHAD, 2004, 28, (3), 241 LINK http://dx.doi.org/10.1016/j.calphad.2004.10.004
- L. Kaufman and H. Bernstein, “Computer Calculation of Phase Diagrams, with Special Reference to Refractory Metals”, Academic Press, New York and London, 1970, p. 60
- R. Süss and L. A. Cornish, ‘Possible Changes to the Cr-Pt Binary Phase Diagram’, inProc. Microsc. Soc. south. Afr., Vol. 35, Kwazulu-Natal, 5th–7th December, 2005, p. 9
- R. M. Waterstrat, J. Less Common Met., 1981, 80, (1), P31 LINK http://dx.doi.org/10.1016/0022-5088(81)90164-8
- R. Süss, L. A. Cornish and M. J. Witcomb, J. Alloys Compd., 2006, 416, (1–2), 80 LINK http://dx.doi.org/10.1016/j.jallcom.2005.07.070
- R. Süss, U. Glatzel, S. N. Prins and L. A. Cornish, ‘A Comparison of Calculated and Experimental Liquidus Surfaces for the Pt-Cr-Ru System’, in Second International Conference of the African Materials Research Society, University of the Witwatersrand, Johannesburg, 8th–11th December, 2003, pp. 141–142
- J.-C. Zhao, J. Mater. Sci., 2004, 39, (12), 3913 LINK http://dx.doi.org/10.1023/B:JMSC.0000031472.25241.c5
- R. Süss, L. A. Cornish and M. J. Witcomb, ‘Investigation of Isothermal Sections at 1000 and 600°C in the Pt-Cr-Ru System’, J. Alloys Compd., in press LINK http://dx.doi.org/10.1016/j.jallcom.2007.03.063
- A. Watson, L. A. Cornish and R. Süss, Rare Met., 2006, 25, (5), 597 LINK http://dx.doi.org/10.1016/S1001-0521(06)60106-X
Financial assistance from the South African Department of Science and Technology (DST); the Platinum Development Initiative (PDI: Anglo Platinum, Impala Platinum and Lonmin); DST/NRF Centre of Excellence in Strong Materials; and Engineering and Physical Sciences Research Council (EPSRC) Platform Grant GR/R95798 is gratefully acknowledged. The authors would like to thank CompuTherm LLC, Wisconsin, U.S.A., and the National Physical Laboratory (NPL), Teddington, U.K., for the provision of the WinPhaD, Pandat and MTDATA software. This paper is published with the permission of Mintek and the Southern African Institute of Mining and Metallurgy.
Dr Andy Watson is a Senior Research Fellow in the Institute for Materials Research at the University of Leeds. He has worked in experimental and computational thermodynamics for many years and has interests in lead-free solders and intermetallic phases as well as pgm alloys.
Rainer Süss is Section Head of the Advanced Metals Group in the Advanced Metals Division at Mintek, as well as the co-ordinator of the Strong Metallic Alloys Focus Area in the DST/NRF Centre of Excellence for Strong Materials. His research interests include phase diagrams, platinum alloys and jewellery alloys.
Lesley Cornish is the Director of the DST/NRF Centre of Excellence in Strong Materials and an Honorary Professor at the University of the Witwatersrand, South Africa. She is associated with Mintek. Her research interests include phase diagrams, platinum alloys and intermetallic compounds.