Structural and Small-Angle Scattering Analysis on Melting of Gold Nanoparticle

Molecular Dynamics (MD) simulation was used for time evolution of melting dynamics on gold nanoparticle with thickness 8 nm. The systems are heated up from room temperature up to three times melting point in 10 ps to ensure that the system is melted and expanding. After t = 7 ps, the system is collapsed, hence pressure oscillation is vanished. Common Neighbor Analysis (CNA) along with wide angle scattering confirmed the melting state at the end of simulation. While small-angle scattering indicated the expansion of the system, it cannot precisely calculate system radius due to its small size.


Introduction
Nanoparticle structure and size need to be analyzed to understand the functionalities for applications.The structure will give properties in the sense that the applications will be in the context of mechanical, optical, and other potentiality.Gold as a functional material, in geometry of nanoparticle, is potentially applicable in biology and medicine [1].
In order to analyze its significance, thermodynamic analysis along with structure calculation will gives appropriate indicator of nanoparticle properties [2].Heat treatment can be done by transferring energy gradually [3] or by sudden energization [4].For higher energies, a system could have nonequilibrium phase change and suffer spallation as in the context of laser ablation.
To perform experiment in investigating phase transition every period of time is difficult to do.MD simulation offers the possibility to calculate the properties during phase transition and visualize it by means of atomistic point of view.In this article, we perform MD simulation in melting of gold nanoparticle and analyze its breaking structure through CNA, small-angle and wide angle scattering.

Method
The nanoparticle system was built in spherical shapes with diameter 8 nm and consists of 16,754 atoms using Large-scale atomic/molecular massively parallel simulator (LAMMPS) [5].The atoms interaction are represented by interatomic potential provided by Foiles [6].Inside the sphere, the atoms are composed in FCC(100) direction.
The nanoparticle was heated from 300 K up to 4,300 K in 10 ps.The final temperature, Tf = 4,300 K which is three times larger than melting temperature Tm = 1338 K [7], was chosen in order to mimic the melting state with condition that the geometry is broken.In the beginning, the system was relaxed at room temperature and 0 GPa.Local atomic temperature was analyzed based on method by Upadhyay and Urbassek [8].

Results and Discussion
The evolution of gold nanoparticles from solid state into melting state is shown in Figure 1.The perfect crystalline state at the beginning of the simulation is reflected through the uniform temperature of around 300 K. Figure 1 indicated that as the temperature increases, the system expands and melts at the end of simulation.We increase the temperature from room temperature up to 4300 K, which is three times larger than melting temperature of bulk gold.If the temperature is highly above boiling point then the system will rupture as in the case of laser ablation [4,8,16].Atoms are colored in temperature scale.
The pressure oscillation is following the shrink and expand characteristic as the temperature increases.After t = 7 ps, the system tears down and melts.Hence, the sphere geometry is rupture and nanoparticles are heading to liquid state.It effected the pressure oscillations where after t = 7 ps the oscillation vanished.CNA calculation on local crystal structure is shown in Figure 3.At the beginning of simulation, the total FCC percentage was 79.5 %.It is still considered a perfect crystalline state inside the nanoparticle.CNA accounted for the surface of sphere, which is not rectangular, hence 20.5 % of atoms is considered unknown structure [17].As time evolves, the FCC percentage is decreasing, and at the end of simulation there is no more FCC structure.Figure 4 shows the structure factor (S(Q)) of the system in the term of small-angle scattering and wide-angle (crystal structure).Small-angle scattering is employed to calculate the particle size in every time step.This perform of calculation is beneficial because we can compare it with particle size.It is stated in Fahdiran and Urbassek [4] that the first minimum of S(Q) value is correlated with radius of nanoparticle with R = 4.493/Q, where Q is scattering vector.For our case the first minimum occurred at Q = 0.2655 Å -1 and corresponded to radius of 16.93 Å.Our system has a diameter of 8 nm (80 Å), i.e. radius = 40 Å, hence the calculation does not show exact agreement.The cause of this is due to the size of the nanoparticle is not adequate for the calculation.In Fahdiran and Urbassek article, the radius of the nanoparticle is 50 V, where for the case of Aluminum 1 V = 2.602 Å, hence the radius is 130 Å.Our radius is smaller than the calculation that has been performed in the cited article.Despite the disagreement of our result with the equation, the minimum from t = 0 ps, 5 ps, and 8 ps is slightly shifted to the left which indicates that the system is expanding.
For larger scattering vector, the profile at t = 0 ps strongly suggest perfect crystalline state.As the system evolves, the peak of indicated crystal structure is merged and at the end of simulation shows that the system is melted.This was indicated by the fact that the value of S(Q) is equal to unity at larger scattering vector.

Conclusion
We performed MD simulation on melting dynamics of gold nanoparticle and analyzed it size by means of small-angle scattering analysis and corresponds it crystal structure through wide angle calculation.Temperature increase affected the pressure oscillation and as the system expands, it vanished.CNA calculation strongly suggests the melted state of the system at the end of simulation and confirmed through the wide angle profile.In this study, small-angle scattering profile help to indicate the expansion of the system while it is not adequate to calculate precisely the nanoparticle size during expansion due to the small size of the system.

Figure 2
indicated the evolution of temperature and pressure of gold nanoparticle with heating rate 400 K/ps.