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Page 8 of 18 Lu et al. J Mater Inf 2022;2:11 I http://dx.doi.org/10.20517/jmi.2022.15

withaCNof14isoccupiedbyintermediateandlargeatoms(CoandMo, respectively)andthesitewithaCNof
15 contains large atoms (Mo). Based on the observed XRD pattern and EPMA-determined composition of the
[2]
phase, Yaqoob removed the intermediate size Re from the site with a CN of 10 and placed it on the site with a
CN of 15 along with Mo. Therefore, the bct phase was described using a 3SL model of (Mo,Re) 9(Ni,Re) 4(Ni) 1.
The first sublattice combines the sites with CNs of 14 and 15, the second sublattice groups the sites with a CN
of 12 and the third is the site with a CN of 10.

The Gibbs free energy of bct is expressed by Eq. (1) and one of its end-members I is described by:
∑
= + + (7)

[2]
where the parameter a was fixed to the DFT data calculated by Yaqoob . The parameter b, corresponding to
the entropy of formation of the end-members, was assessed together with the excess Gibbs energy based on
phase equilibrium data.

RESULTS AND DISCUSSION
Forsolutionphases, inthefirststep, theatermsfortheinteractionparameterswereassessedusingtheSQSand
measuredenthalpy. Inthesecondstep, thebtermsrepresentingtheinfluenceoftemperatureontheinteraction
parameters were assessed based on the phase diagram and activity data.

For intermetallics, the enthalpy terms for the end-members were fixed to the VASP calculated data, while
the entropy terms of the end-members were assessed based on the phase diagram data. As a final step, all
parameters may be adjusted slightly to fit the experimental data better.

The thermodynamic parameters for phases in the present work are listed in Appendix II. A full database for
the Ni-Mo-Re ternary system is provided in the supplementary material.

Ni­Mo system
In general, the assessment of Zhou et al. is not as satisfactory as that of Yaqoob et al. [32,33] . Therefore, only the
results of Yaqoob et al. are compared with the present work in the following discussion. Figure 2 shows the
calculated phase diagram compared with experimental data [8–17] , as well as the previous assessment [33] . The
experimental data that were not mentioned by Yaqoob et al. are colored. It is difficult to fit the homogeneity
domain of the phase and the fcc solvus in equilibrium with the Ni 4Mo phase at low temperatures. The
results of Zhou et al. show good agreement for these phase equilibria but the cost is the poor agreement with
the measured of the Ni 4Mo phase [32] . The present assessed phase diagram is similar to that of Yaqoob et al.,
except for the homogeneity range of the phase and the related invariant reaction temperature [33] . However,
the main improvements of the present work were on the thermodynamic properties, as discussed below.

Figure 3A shows the enthalpy of mixing for the liquid phase. Chistyakov et al. and Sudavtsova measured
the enthalpy of mixing of liquid using calorimetry at 1823 and 1874 K, respectively [18,19] . The experimental
results from Sudavtsova are lower than those from Chistyakov et al. [18,19] . It is difficult to estimate which one is
better. In the present assessment, Sudavtsova’s results were found to be too negative that the bcc liquidus would
be higher than the experimental data when the temperatures for invariant reactions were fixed. Moreover,
considering that the experimental procedure of Chistyakov et al. was more detailedly described than that by
Sudavtsova, the results from Chistyakov et al. were adopted in the present work [18] .

Figure 3B shows the assessed enthalpies of mixing for solution phases at 298 K compared with the SQS
data [32,33] . As noted above, the SQS calculations were performed only for stable structures in the present