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Lu et al. J Mater Inf 2022;2:11 I http://dx.doi.org/10.20517/jmi.2022.15 Page 5 of 18

Table 2. Crystallographic and model information of stable phases in Ni-Mo-Re system
Phase Pearson symbol Prototype Model
Liquid - - (Ni,Mo,Re) 1
fcc_A1 cF4 Cu (Ni,Mo,Re) 1(VA) 1
bcc_A2 cI2 W (Ni,Mo,Re) 1(VA) 3
hcp_A3 hP2 Mg (Ni,Mo,Re) 1(VA) 0.5
oP56 NiMo (Ni) 24(Ni,Mo,Re) 20(Mo) 12
Ni 3Mo oP8 Cu 3Ti (Ni,Mo) 3(Ni,Mo) 1
Ni 4Mo tI10 Ni 4Mo (Ni) 4(Mo) 1
tP30 CrFe (Ni,Mo,Re) 2(Ni,Mo,Re) 4(Ni,Mo,Re) 8
(Ni,Mo,Re) 8(Ni,Mo,Re) 8
cI58 -Mn (Ni,Mo,Re) 2(Ni,Mo,Re) 8(Ni,Mo,Re) 24
(Ni,Mo,Re) 24
bct tI56 Mo 3CoSi (Mo,Re) 9(Ni,Re) 4(Ni) 1

cell volume only, then to volume and cell shape, and finally simultaneously to volume, cell shape and atomic
position (i.e., full relaxation) in the present work. On this basis, a fast convergence speed can be achieved. To
check the symmetry preservation, the radial distribution functions were analyzed [64] .

In addition, VASP calculations were also performed to obtain the formation energies of all the end-members
of the and phases. The k-point meshes were 12 × 12 × 12 and 8 × 8 × 15, respectively. To facilitate
the calculations, the ZenGen script-tool [65] was adopted to conveniently generate input files for the VASP
calculations.

THERMODYNAMIC MODELS
In the Ni-Mo-Re system, the stable phases included in this assessment are liquid, fcc, bcc, hcp, , Ni 3Mo,
Ni 4Mo, , and the bct phase with a Mo 3CoSi structural prototype. Their crystal structure information and
the thermodynamic models are summarized in Table 2. The thermodynamic descriptions of the pure elements
Ni, Mo and Re were taken from the Scientific Group Thermodata Europe (SGTE) unary database (Version
5.0) [66] . All the phases were described by the sublattice model within CEF. Detailed mathematical expressions
are available in our previous work [67] .

Solution phases
The solution phases (including liquid, fcc, bcc and hcp) were treated as substitutional solutions and described
by a substitutional solution model with the Redlich-Kister polynomials [68] .

Normally, for the interaction parameter, a linear temperature dependence is sufficient, i.e., , + , + , .
In the present work, the measured excess heat capacity for the fcc phase of the Ni-Mo system is available, so a
( ) term was introduced to produce a constant excess heat capacity.
Intermetallic phases
In the present work, three intermetallic phases, i.e., , Ni 3Mo and Ni 4Mo, were considered for the Ni-Mo
system. The solubility of Re was ignored in both Ni 3Mo and Ni 4Mo due to the lack of experimental data.

The molar Gibbs energy of each intermetallic phase is described as:
( )
∑ ∑ ∑

= + ln + ; (1)

where is the site fraction of component i in the sublattice s, is the Gibbs free energy of the end member

I, R is the gas constant, as is the number of sites of sublattice s and corresponds to the molar excess