Calculations from First Principles (Ab Initio)

Part II of this series of papers (2) described a simplified approach to the calculation of phase diagrams, for cases where use of the compound energy formalism model (1) is inappropriate due to the sparseness of experimental data.

At the University of Bayreuth, a different approach has been used to compensate for sparse data, using ab initio calculations to determine the enthalpy of formation of intermetallic compounds. These calculations, which are complex and time consuming, are based on density functional theory, as described by Kohn and Sham (8). The power of the technique derives from the fact that the thermodynamic results are often difficult to determine experimentally. The results can be used directly in a thermodynamic description of the alloy systems (9). The VASP program (10) has been used here to calculate the enthalpies of formation of the ordered compounds. At this stage, no magnetic contribution has been incorporated in the calculations, since there is some discrepancy in the experimental observations: for the L1₂-ordered CrPt₃ Kussmann et al. (11) observed ferromagnetic behaviour, whereas Pickard et al. (12) observed ferrimagnetic behaviour. The total enthalpies of the pure elements were compared with those obtained by Wang et al. (13), with very good agreement.

Resulting Chromium-Platinum Phase Diagram

The calculated phase diagram after thermo-dynamic optimisation is given in Figure 1 (7), and shows very good agreement with experimental data. The modelled eutectic temperatures agree, within the stated experimental errors, with the results of Venkatraman and Neumann (14) (derived on the basis of Massalski (15)), rather than those of Oikawa et al. (16). The ordering reaction still needs to be modelled correctly, and a later version of the Cr-Pt phase diagram shows promise (17). The small phase region of the L1₂ CrPt₃ phase at low temperatures may be a result of not yet having taken the magnetic properties into account. Since all the Gibbs energies have now been modelled, it is possible to calculate further thermodynamic data. Figure 2 shows a comparison between the calculated and experimental chemical activities (18, 20). Using ab initio calculations in the thermodynamic model has predicted the presence of L1₂ Cr₃Pt at low temperatures. This suggests that the platinum-rich side of the phase diagram should be examined further, probably using the diagram from Zhao (17).

Platinum-Aluminium-Chromium-Nickel

Thermodynamic assessment of the Cr-Pt system has already shown that many regions of the binary phase diagram are relatively unknown. The ab initio calculations used here show that a stable L1₂ Cr₃Pt structure is achieved. Greenfield and Beck (21) discovered a stable L1₂ structure at 63 at.% Cr, although it is not shown in experimental phase diagrams (14). More experimental work using rigorous X-ray diffraction techniques needs to be done to substantiate the L1₂ and L1₀ phase regions. A database for the Pt-Al-Cr-Ni system will be created. Many experiments on the Pt-rich side of the Pt-Al-Cr-Ni system have already been performed (22). The addition of nickel increases the curvature of the γ' solvus, as shown in Figure 3 (23).

Conclusions

The principal aim of the ongoing work at the University of Bayreuth is to describe the platinum-rich side of the Pt-Al-Cr-Ni system. It has been demonstrated that ab initio calculations can provide helpful information on the formation of phases to compensate for sparse experimental data on the alloy system. It is hoped that, in the long term, the Bayreuth database can be merged with the Pt-Al-Cr-Ru database, which is being developed by Mintek and the University of Leeds (see Part II of this series of papers (2)).