*3.3. Influence of Temperature*

The research results of the effect of temperature, T = 300 K, 400 K, 500 K, 600 K, 700 K, 900 K, 1100 K 1300 K, and 1500 K, on the structural characteristics are shown in Figure 6.

**Figure 6.** The structural characteristics as structural shape (**a**) of NiAu5324 alloy at T = 300 K; RDF (**b**) and structural unit number (**c**) at different T.

The results indicate at T = 300 K, NiAu5324 alloy has structural shape, r = 2.47 Å, g(r) = 6.51, 802 FCC, 811 HCP, 3711 Amor (Figure 6a). When increasing T from T = 300 K to T = 1500 K, r decreases from r = 2.47Å to r = 2.32 Å, g(r) changes from g(r) = 6.51 to g(r) = 4.62 (Figure 6b), FCC decreases rapidly from 802 FCC to 0.0 FCC, HCP decreases dramatically from 811 HCP to 0.0 HCP, Amor increases from 3711 HCP to 5324 HCP, at T = 700 K Amor state maximum increases (Figure 6c). This proves that with T < 700 K, NiAu alloy is in the crystalline state, T > 700 K, and NiAu alloy is in the liquid state, thereby, this is a crystallizing process between the crystallization and liquid states of NiAu alloy. The results of phase transition from crystalline state to a liquid state by type 1 phase transition theory, for each value of temperature (T), will correspond to a total energy value of the system (Etot). To confirm that, a study of the relationship between T and Etot was carried out and the obtained results are shown in Figure 7.

**Figure 7.** The structural shape of NiAu5324 alloy at temperatures 700 K (**a**), phase transition (**b**) of NiAu5324 alloy at different temperatures.

Increasing T from T = 300 K to T = 400 K, 500 K, 600 K, 700 K, 900 K, 1100 K, 1300 K, and 1500 K leads to l insignificant change range l = 7.34 nm to l = 7.35 nm and Etot increase from Etot = −446.0 eV to Etot = −430.2 eV, −424.3 eV, −418.2 eV, −415.6 eV, −405.5 eV, −394.2 eV, −383.1 eV, and −372.4 eV. In it, the structural shape of NiAu alloy at T = 700 K (Figure 7a) and an interrupting point at T = 600 K then corresponds with Etot = −418.2 eV observed at glass temperature (Tg), Tg = 600 K (Figure 7b). The results obtained show that, with T < 600 K, NiAu5324 alloy exists in the crystalline state and T > 600 K is in a liquid state, this result is completely consistent with the results obtained in on and are considered as the basis for future empirical research.

#### *3.4. Influence of Annealing Time*

The crystallization process of NiAu5324 alloy is carried out after the tempering period and shown in Figure 8, Table 4.

**Figure 8.** The crystallization process of NiAu5324 alloy after different annealing time (**a**), the shape of NiAu alloy at t1 = 50 ps (**b**), t2 = 150 ps (**c**), t3 = 250 ps (**d**).



The result shows that after incubation period, t = 50 ps, 150 ps, 250 ps, Etot decreases from Etot = −425 eV to Etot = −430 eV (Figure 8a), the structural shape at t1 = 50 ps (Figure 8b), t2 = 150 ps (Figure 8c), t3 = 250 ps (Figure 8d) corresponding with the link length, the height of the RDF Ni-Au varies greatly from r = 2.45 Å to r = 2.49 Å, g(r) = 5.26 to g(r) = 5.88 and structural unit number FCC increases from 0.0 FCC to 1463 FCC, HCP increases from 0.0 HCP to 368 HCP, and Amor decreases from 5324 Amor to 3493 Amor (Table 4). The results obtained show that NiAu5324 alloy at Tg = 600 K after the annealing time t = 250 ps, the crystallization process increases, proving that NiAu5324 alloy is easy to crystallize at the temperature Tg and results obtained are consistent with the results of the previous alloys such as AlNi [69], NiCu [71], FeNi [68,70].

When increasing heating rate, the temperature leads to r, g(r) decreases, l, Etot increase, FCC, HCP decrease and Amor increase and vice versa with increasing atomic number and the incubation time at Tg = 600 K. This is a very useful result for the process of implementing experimental results in the future.

#### **4. Conclusions**

After studying the effect of factors on the structure and crystallize process, we got the following results: The relationship between size (l) and atomic number (N) is determined according to the formula is l~N<sup>−</sup>1/3; the total energy of the system (−Etot) always depends on N by function, the result is consistent with results [67–75] when the glass temperature (Tg), Tg = 600 K. With NiAu5324, when increasing the heating rate from 4 × 1012 K/s to <sup>2</sup> × 1013 K/s, 4 × 1013 K/s, 2 × <sup>10</sup><sup>14</sup> K/s, and 4 × 1014 K/s leads to r decrease from r = 2.47 Å to r = 2.43 Å, and g(r) decrease from g(r) = 6.51 to g(r) = 6.05, corresponding to the change of g(r) and structural unit number. FCC, HCP, Amor FCC decreases from 802 FCC to 0.0 FCC, HCP decreases from 811 HCP to 13 HCP, Amor increases from 3711 Amor to 5311 Amor. When increasing atom number from NiAu2048 to NiAu2916, NiAu4000, NiAu5324, NiAu6912, first peak position (r) of RDF changes values from r = 2.49 Å to r = 2.45 Å, g(r) changes from g(r) = 6.43 to g(r) = 6.77, the structural unit number changes corresponding to FCC increases from 312 FCC to 1869 FCC, HCP increases from 308 HCP to 914 HCP, Amor increases from 1293 Amor to 4129 Amor. Similarly, with NiAu5324 when increasing T from T = 300 K to T = 1500 K, r decreases from r = 2.47 Å to r = 2.32 Å, g(r) changes in the range from g(r) = 6.51 to g(r) = 4.62, FCC decreases rapidly from 802 FCC to 0.0 FCC, HCP decreases rapidly from 811 HCP to 0.0 HCP, Amor increases from 3711 HCP to 5324 HCP, Amor state maximum increases. When increasing in annealing times at Tg = 600 K leads to the structural unit number FCC, HCP increases, Amor decreases. It indicates that the heating rate increase leads to the NiAu alloy change from crystallizing state to the amorphous state; increasing atomic number, annealing times leads to crystallization process increase; increasing temperature leads to process change from a crystallization state to a liquid state. This is a very essential factor and a basis for future empirical research.

**Author Contributions:** D.N.T.: conceptualization, methodology, validation, investigation, writing original draft preparation. V.C.L.: data curation. ¸S. ¸T.: writing—review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

