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

as well as their equilibria with other phases, it is necessary to develop a reliable thermodynamic database to
predict phase equilibria and transformations in Ni-based superalloys, starting from ternaries, such as Ni-Mo-
Re.

The phase diagram and thermodynamics of the Ni-Mo-Re ternary system were studied by Yaqoob and Jou-
[4]
bert [2,3] andtheenthalpiesofformationofcompoundswerecalculatedbyCrivello bymeansoffirst-principles
calculations. A new phase with a modulated phase structure was reported and named as the ’ phase by
[5]
Yaqoob et al. . The average structure of this phase is the phase, existing in the binary Mo-Re system and
extending to the ternary Ni-Mo-Re system. Further structural characterization of this compound could not
be completed because of the poor quality of the sample. Yaqoob [2] treated the phase as a line compound,
(Mo,Re) 2(Ni) 1, without considering its structural relationship with the phase and ignoring the experimen-
tally determined solubility range of Ni from ∼26 to ∼33 at.%. There exist other limitations in the assessment by
[2]
Yaqoob regarding the subsystems, the extension of the binary phase in the ternary system and the liquidus
projection.

The present work aims to obtain a set of self-consistent thermodynamic parameters of the Ni-Mo-Re system
withmoreinputsfromfirst-principlescalculations. ThebinarysystemsNi-MoandMo-Rearerevisedtoobtain
a better agreement with the experimental data. By combining the thermodynamic description of the Ni-Re
system reported by Yaqoob and Joubert [6] with the updated Ni-Mo and Mo-Re systems, the reassessment of
the Ni-Mo-Re ternary system is carried out.

LITERATURE REVIEW
All available experimental studies [3,7–46] are summarized in Table 1.

Ni­Mo
TheNi-Mosystemhasbeenextensivelyinvestigatedbyexperiments [3,7–33] andthermodynamicmodeling [32,33,47–49] .
Duetothelackofexperimentalandfirst-principlescalculatedthermodynamicdata, earlierthermodynamicas-
sessments [47,48] are less reliable considering the formation enthalpies of some intermetallic compounds. Mor-
ishita et al. treated the phase as a stoichiometric compound, which is inconsistent with the homogeneity
domain of 4 at.% [49] . With the aid of first-principles calculations (some of the data were calculated by Wang
et al.), Zhou et al. obtained a set of thermodynamic parameters of the Ni-Mo system by the CALPHAD
method [31,32] . However, overfitting with too many parameters to the phase diagram at low temperatures led
to a much larger heat capacity ( ) deviation from the experimental data [20,22] . Later, Yaqoob et al. reviewed
the experimental information critically and reassessed the Ni-Mo system [33] . The number of parameters was
reduced significantly compared with those of Zhou et al. [32] . However, the modeling of Yaqoob et al. can
be further improved considering the following issues: (1) the enthalpy of mixing of the liquid phase is not in
agreement with the experimental data [18,19] ; (2) the enthalpy of formation of the phase at high temperature
is lower than the experimental data [20,21] ; (3) for the fcc phase, the SQS calculated enthalpy, the experimental
Gibbs energy of mixing and the at high temperature cannot be reproduced and (4) the magnetic properties
of the fcc phase were ignored.

Mo­Re
Thermodynamic assessments of the Mo-Re system have been published by many authors [50–53] . Mathieu et al.
reviewed all the previous work and performed reassessments aided by first-principles calculations [53] . A full
five-sublattice (5SL) model and various simplified sublattice models of the phase were considered. Com-
pared with the previous assessments, the thermodynamic properties calculated by Mathieu et al. show better
agreement with the first-principles calculation data [53] . However, the homogeneity range of the phase at
1473 K calculated by Mathieu et al. (as well as other previous assessments) was very narrow. This is in contrast