## 2 Method of Calculation  
Initially, we saw randomly atoms of Fe\({}_{\text{1-x-y}}\)Ni\({}_{\text{x}}\)Co\({}_{\text{y}}\) alloy with a ratio into a cube of size (l) determined, and it was applied the following formula (1):  
\[1=\sqrt[3]{\frac{\text{N}}{\rho}}\ =\sqrt[3]{\frac{\left(\text{m}_{\text{Fe}} \text{-}\text{n}_{\text{Fe}}\text{+}\text{m}_{\text{Ni}}\text{+}\text{m}_{ \text{Co}}\text{-}\text{n}_{\text{Co}}\right)}{\rho}} \tag{1}\]  
where: l, N, \(\rho\) is the size, the number of atoms, and the density of atoms, respectively, and m\({}_{\text{Fe}}\), n\({}_{\text{Fe}}\), and m\({}_{\text{Ni}}\), n\({}_{\text{Ni}}\), m\({}_{\text{Co}}\), n\({}_{\text{Co}}\) is molar mass atomic and number of atoms of Fe, Ni, Co metals, respectively. To study the structural features, phase transitions, and crystallization, we use Lammps open-source software [37; 53; 54] based on the molecular dynamics simulation (MD) method, suitable for periodic boundary conditions and Sutton-Chen embedded force field (2) [53; 54; 55; 56]:  
\[\text{F}_{\text{i}}(\rho)=A_{\text{i}}\text{E}_{\text{i}}^{\text{(l)}}\rho\ln \rho;\text{p}_{\text{i}}^{\text{a(l)}}(\text{R})=\text{e}^{-\text{b}^{*}},\ \text{b}^{*}=\beta_{\text{i}}^{\text{(l)}}\left(\frac{\text{R}}{\text{R}^{ \text{N}}-1}\right),\left(\ \overline{\text{p}}_{\text{i}}\ \right)^{2}=\sum\limits_{1=0}^{3}\text{t}_{\text{i}}^{\text{(l)}}\left(\rho_{ \text{i}}^{\text{(l)}}\right)^{2} \tag{2}\]This is a high-precision embedded interaction potential field for the study of structural characteristics for Fe, Ni, and Co single-component metals [19; 20; 57], and 2-component alloys [32; 47]. Considering interaction force fields [58; 59; 60; 61; 62; 63] from the physical system can be investigated comprehensively the energy, phase stability, hole formation, and surface binding energy. It is known that for the metal 1 ingredient (that always has the FCC structure stable, and electron density is associated at equilibrium with the value of 1), the derivative of the interaction function will be always 0 to maximize entropy. To perform the simulation, we use the parameters of Fe\({}_{1\text{-}x\text{-}y}\)Ni\({}_{x}\)Co\({}_{y}\) alloy (corresponding to the values of the component metals Fe, Ni, and Co in Tables 1-3 of references [56; 64]). First, we combined the process of running 2 \(\times\) 10\({}^{4}\) step recovery statistics of MD simulation at temperature (T), T = 4500 K so that the atoms are in the initial steady state. Then, it is decreased the temperature from T = 4500 K to T = 1300 K, 1100 K, 900 K, 800 K, 700 K, 600 K, 500 K, 400 K, and 300 K (to increase the crystallization state with 42 \(\times\) 10\({}^{4}\) MD steps, heating rate 4 \(\times\) 10\({}^{11}\) K/s, and a heating step of 1 fs). In this way, are studied the influence of Fe, Ni, and Co doping concentrations corresponding to alloys Fe\({}_{5}\)Ni\({}_{32}\)Co\({}_{63}\), Fe\({}_{33.4}\)Ni\({}_{33.3}\)Co\({}_{33.3}\), Fe\({}_{63}\)Ni\({}_{32}\)Co\({}_{5}\); associated with number of atoms (N), (N = 2916 atoms, 5324 atoms, 8788 atoms, 13,500 atoms of Fe\({}_{63}\)Ni\({}_{32}\)Co\({}_{5}\) alloy), and temperature (T), respectively. To study the structure characteristics quantities through structure shape, and size (I), the Radial Distribution Function (RDF) formula is applied (3) [65]:  
\[\text{g(r)}=\frac{\text{V}}{\text{N}^{2}}\left(\frac{\sum_{i}\text{n}_{\text{ i}}(\text{r})}{4\pi\text{r}^{2}\Delta\text{r}}\right) \tag{3}\]  
where: r, n\({}_{\text{i}}\)(r), V, N, and g(r) are the link length, the coordinates, the volume, the number of atoms, and the radial distribution function, respectively. Moreover, g(r) is noted as the density value of the maximum probability of finding the atoms at the first peak of the RDF [66]. To determine the diffusion mechanism of the atoms, we used the Mean Squared Distance (MSD) method (3) [67].