# 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
#### 3.2.3 Heat Annealing Time  
The effect of annealing time on the structure and crystallization process of Cu-Au alloy is shown in Figure 5.  
The obtained results show that, at the initial time without annealing, t1 = 0 ps, the energy of the material at temperature T = 300, 400, 550, 600, and 1000 K has the corresponding energy value E\({}_{\text{tot}}\) = \(-\)198, \(-\)196, \(-\)192, \(-\)190, and \(-\)182 eV, respectively. When the annealing time was increased from t1 = 0 ps to t2 = 60 ps (2 \(\times\) 10\({}^{4}\) MD steps), t3 = 120 ps (4 \(\times\) 10\({}^{4}\) MD steps), t4 = 300 ps (10 \(\times\) 10\({}^{4}\) MD steps), and t5 = 450 ps (15 \(\times\) 10\({}^{4}\) MD steps), the total energy of the material in the corresponding temperatures have variable values (Figure 5). When the temperatures T = 400, 600, and 1000 K, the values change are not significant. When T = 300 and 550 K, the energy of the material decreased rapidly from the point t1 = 0 ps to t2 = 60 ps, and after that gradually slows down from t2 = 60 ps to t3 = 120 ps, whereas from t3 to t4, t5 was almost constant. It follows that the material has a strong crystallization process at the temperature T = 550 K--namely, this was the phase transition of the material's crystallization with T\({}_{\text{g}}\) = 550 K. At temperatures T = 300 and 400 K, the crystallization process occurs slowly; finally, at T > 600 K, crystallization does not occur because this was the region where the material has changed to a liquid state. To confirm that, we examined the structure and crystallization process at each specific temperature and the results are shown in Figure 6.  
Figure 5: The relationship between the annealing time and the total energy of the system at temperatures T = 300, 400, 550, 600, and 1000 K.  
Figure 6: The structural shape (a**1,a2,a3,a4,a5**), radial distribution function (**b1,b2,b3,b4,b5**), and number of structural units (**c1,c2,c3,c4,c5**) of Cu–Au alloy at heating rate 4 \(\times\) 10\({}^{12}\) K/s, time per heating step h = 3.0 fs, and the values of temperature T = 300, 400, 550, 600, and 1000 K.  
The results show that Cu-Au alloy at temperature (T) T = 300 K with a calcination rate 4 \(\times\) 10\({}^{12}\) K/s, time per heating step (h), h = 3.0 fs at heat annealing time (t), t1 = 0 ps has the structure shown in Figure 6(a1), the radial distribution function with r\({}_{\rm Cu-Au}\) = 2.66 A, the height of the RDF was g\({}_{\rm Cu-Au}\)(r) = 5.22, size (l), l = 8.36 nm, E\({}_{\rm tot}\) = \(-\)198 eV, and the number of structural units was 537 FCC, 256 HCP, and 2123 Amor. When increasing the heat annealing time t from t1 = 0 ps to t2 = 60 ps, t3 = 120 ps, t4 = 300 ps, and t5 = 450 ps, the length link of Cu-Au decreased from r\({}_{\rm Cu-Au}\) = 2.66 A to r\({}_{\rm Cu-Au}\) = 2.66, 2.62, 2.64, and 2.66 A, respectively, the height of the RDF increased from g\({}_{\rm Cu-Au}\)(r) = 5.22 to g\({}_{\rm Cu-Au}\)(r) = 5.61, 6.15, 5.92, and 5.82, respectively, the material size decreased from l = 8.36 nm to l = 8.33, 8.33, and 8.32 nm, respectively, the total the energy of the system change decreased from E\({}_{\rm tot}\) = \(-\)198 eV to E\({}_{\rm tot}\) = \(-\)195, \(-\)195, and \(-\)195 eV, respectively, and the number of structural units changed: FCC increased from 537 FCC to 984, 942, 1010, and 1048 FCC, respectively, and HCP change increased from 256 HCP to 243, 262, 275, and 242 HCP, respectively, whereas for Amor it decreased from 2123 Amor to 1689, 1712, 1631, and 1631 Amor, respectively (Figure 6(b1,c1)).