*3.2. Effect of Atomic Number*

Similarly, with the influence of atomic numbers NiAu2048, NiAu2916, NiAu4000, NiAu5324, and NiAu6912 on structural characteristics, results are shown in Figure 4.

**Figure 4.** *Cont*.

**Figure 4.** The structural shape (**a1**,**b1**,**c1**,**d1**,**e1**), radial distribution function (RDF) (**a2**,**b2**,**c2**,**d2**,**e2**), structural unit number (**a3**,**b3**,**c3**,**d3**,**e3**) of NiAu alloy with different N.

The results indicate that NiAu2048 alloy at T = 300 K has structural shape and l = 7.34 nm, Etot = −173.85 eV (Figure 4(a1)), together with the radial distribution function, has r = 2.49 Å, g(r) = 6.47 (Figure 4(a2)), and the structural unit numbers are 312 FCC, 443 HCP, 1293 Amor (Figure 4(a3)). When increasing atoms number from NiAu2048 to NiAu2916, NiAu4000, NiAu5324, NiAu6912, then structural shape changes, size (l) increases from l = 7.34 nm to l = 10.89 nm, Etot decreases from Etot = −173.85 eV to Etot = −580.35 eV (Figure 4(b1,c1,d1,e1)); r changes from r = 2.49 Å to r = 2.45 Å, g(r) changes from g(r) = 6.43 to g(r) = 6.77 (Figure 4(b2,c2,d2,e2)); and the structural unit number change corresponding to FCC about from 312 FCC to 1869 FCC, HCP about from 308 HCP to 914 HCP, Amor increases from 1293 Amor to 4129 Amor (Figure 4(b3,c3,d3,e3)). The given result indicates that increasing N leads to l increase and Etot decrease. As a result, there is a relationship between l, N, and Etot, N. To confirm the defining relationships between size, atom number, and between Etot, atom number of NiAu alloy, the results are shown in Figure 5.

**Figure 5.** The relationship between characteristic quantities such as structures as dependence between l, N (**a**); −Etot,N(**b**) of the NiAu alloy with different N.

The given result shows that increasing N leads to l increase, and satisfy the formula: l = 18.021 − 138.153N<sup>−</sup>1/3, corresponding to l~N−1/3 (Figure 5a) and −Etot proportional to N (Figure 5b). The results are consistent with the results of crystallizing process temperature (Tm) proportional with N−1/3 [74,75] and size (l or D) proportional with N−1/3 [67–73]. This proves that increasing atom number leads to crystalline atoms number FCC, HCP increase, Amor decrease, size increase, the total energy of system decrease; and the relationship with l~N−1/3 is an important result for future experimental implementation.
