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Page 4 of 18 Lu et al. J Mater Inf 2022;2:11 I http://dx.doi.org/10.20517/jmi.2022.15

directly employed in the present work.

Ni­Mo­Re
SeveralexperimentalinvestigationshavebeencarriedoutonthephaseequilibriaoftheNi-Mo-Resystem [3,42,42–44] .
Their measured phase diagrams are quite different in terms of the number and homogeneity ranges of the
ternary intermetallic compounds.

The experimental data mainly considered in the present work are the phase equilibria of the Ni-Mo-Re system
[3]
at1473and1873K determinedbyYaqoobandJoubert utilizingEPMA andXRD.Theequilibriumannealing
treatments for the alloys were at 1873 K for 9 h and at 1473 K for 70 d. The crystal structure identification of
the ternary intermetallic compounds was carried out and two unknown ternary compounds were observed.
One phase has a body-centered tetragonal crystal structure with a structure prototype Mo 3CoSi (named as bct
in the present work) and the other has a modulated structure. The isothermal section measured by Yaqoob
[3]
and Joubert showed a large extension of the and phases and a limited extension of the phase. The long
annealing time and phase identification technique ensured the reliability of their work so that their result was
used in the present work.

The phase equilibria at 1425 K were determined by Borisov et al. and Slyusarenko et al. using equilibrated
alloys. The annealing time for the samples was 33.3 d [42,43] . The obtained isothermal section shows good
[3]
compatibility with the work of Yaqoob and Joubert , except that only one ternary intermetallic compound
was found. Borisov et al. and Slyusarenko et al. probably misinterpreted two phases as one single phase
without performing phase identification [42,43] . Generally, these experimental data are considered reliable data.

The isothermal sections proposed by Kodentsov et al. and Feng et al. show poor agreement with that from
Yaqoob and Joubert [3] and are therefore not utilized in the present assessment [41,44] .

The site occupancies of the Ni-Mo-Re phase were determined by Yaqoob et al. as a function of composition
in the ternary homogeneity domain, which were considered in the present work [45] .

Chekhovskoi et al. measured the CP of the NMR-75 alloy (75 wt.% Ni, 15 wt.% Mo and 10 wt.% Re) in a
temperature range of 300-1300 K. However, the results were not used in the present work since it was difficult
to reproduce if other data were to be considered simultaneously [45] .

FIRST­PRINCIPLES CALCULATIONS
First-principles calculations were performed using the Vienna ab initio simulation package (VASP) with plane-
wave basis sets [56] based on density functional theory (DFT) [57] . Projector augmented wave pseudopoten-
tials [58] were adopted to represent the valence electrons. GGA-PW91 [59] was adopted to describe the ex-
change and correlation effects. A large plane-wave cutoff energy of 400 eV was set for the plane-wave basis.
The Monkhorst-Pack scheme [60] was used to construct the k-point meshes for Brillouin zone sampling. The
spin-polarized calculations were performed with ferromagnetism set. The convergence criteria for electronic
self-consistency and ionic minimization were 10 and 10 eV/unit cell, respectively. After relaxation, a final
−4
−5
static calculation was conducted by employing the tetrahedron method with Blöchl corrections [61] .
For the bcc, fcc and hcp solid solutions, the SQS method [62,63] was adopted to generate disordered structures
for the VASP calculations. Supercells containing 16 atoms were constructed considering the configurations
A12B4 and A15B1, where “A” denotes Ni for fcc, Mo for bcc and Re for hcp. Note that possible unstable
structures, such as fcc Mo15Ni1, were not calculated since the full relaxation may not maintain the original
structures. The total number of k-points multiplied by the total number of atoms per unit cell was at least
7200 for fcc, 6336 for bcc and 8000 for hcp. Using VASP, the SQS supercells were first relaxed with respect to