# Molecular Dynamics Study on the Crystallization Process of Cubic Cu-Au Alloy
## 3 Results and Discussion
### Factors Affecting the Structure and Crystallization Process of Cu-Au Alloy
#### 3.2.2 Temperature  
Similarly, the effect of temperature on the structural and crystallization of the considered alloy is shown in Figure 3.  
The result shows, with Cu-Au alloy at temperature (T), T = 300 K, heating rate of 4 \(\times\) 10\({}^{12}\) K/s and h = 3.0 fs has the length of link (r) as r\({}_{\rm Cu-Au}\) = 2.66 A, the height of RDF was g\({}_{\rm Cu-Au}\)(r) = 5.22, size (I), l = 8.36 nm, E\({}_{\rm tot}\) = \(-\)194 eV and structure units number was 537 FCC, 256 HCP, and 2123 Amor. Therefore, when the temperature (T) was increased from T = 300 K to T = 400, 550, 600, 700, 800, 1000, and 1500 K, it was found that the structural shape of the material at T = 300 K was such as that in Figure 3a, and the radial distribution function links Cu-Au has r\({}_{\rm Cu-Au}\) a change about r\({}_{\rm Cu-Au}\) = 2.66 A to r\({}_{\rm Cu-Au}\) = 2.62, 2.60, 2.58, 2.54, 2.54, 2.66, and 2.62 A, respectively, the height of RDF decreased from g\({}_{\rm Cu-Au}\)(r) = 5.22 to g\({}_{\rm Cu-Au}\)(r) = 4.81, 4.33, 4.33, 4.25, 3.84, 3.82, and 3.79, respectively, the material size increased from l = 8.36 nm to l = 8.45, 8.76, 8.87, 9.07, 9.20, 9.52, and 10.01 nm, respectively,  
Figure 3: The structural shape (**a**), radial distribution function (**b**), and number of structural units (c) of Cu–Au alloy at heating rate 4 \(\times\) 10\({}^{12}\) K/s, time per heating step h = 3.0 fs with different values of temperature. the total energy of the system increased from E\({}_{\rm tot}=-194\) eV to E\({}_{\rm tot}=-190\), \(-185\), \(-182\), \(-178\), \(-176\), \(-168\), and \(-154\) eV, respectively (Figure 3b), and the number of structural units changed: FCC decreased from 537 FCC to 339 FCC at T from T = 300 K to T = 400 K; HCP decreased from 256 HCP to 183 HCP at T from T = 300 K to T = 400 K; Amor increased from 2123 Amor to 2404 Amor at T from T = 300 K to T = 400 K (Figure 3c). Additionally, with T > 550 K, the Cu-Au alloy turns to liquid state. The obtained results show that when increasing the temperature, T, leads to the size, I, the total energy of the Etot system increased, the bond length, r, does not change significantly, and the height of the radial distribution function, g(r), decreased. The obtained results are completely consistent with previous publications with other alloys (as AlNi nano [67], NiCu nano and bulk [68,71], NiFe nano [69], and NiAu bulk [73]). Similarly, with the number of structural units FCC and HCP numbers decreased, Amor increased sharply, and there was a disappearance of the number of structural units at the temperature T = 550 K. The reason for this phenomenon was that size caused effects: when the temperature increased, the motion between atoms increased, and the interaction between atoms increased, combined with the phenomenon of thermal expansion leading to I, Etot increased, r has a negligible change, and g(r) decreased. To confirm that, we studied the relationship between temperature and total energy of the system to determine the phase transition of the material. The results are shown in Figure 4.  
The obtained results show that when T increased from T = 300 K to T = 400 K, 550 K, 600 K, 700 K, 800 K, 1000 K, and 1500 K, the size, I, has an insignificant change value in range from I = 8.36 nm to I = 10.01 nm, and E\({}_{\rm tot}\) increased from E\({}_{\rm tot}=-194\) eV to E\({}_{\rm tot}=-190\), \(-185\), \(-182\), \(-178\), \(-176\), \(-168\), and \(-154\) eV, respectively. In consequence, these results show that, with T < 550 K, Cu-Au alloy exists in the crystalline state and for T > 550 K was in a liquid state. Where, the structural shape of Cu-Au alloy at T = 550 K was amorphous. The intersection of the two lines of crystallization and the line in the liquid state is at a point, T = 550 K, which was called the crystallization point or the glass temperature (T\({}_{\rm g}\)), T\({}_{\rm g}\) = T = 550 K (Figure 4).