Time-resolved diffraction profiles and atomic dynamics in short-pulse laser-induced structural transformations: Molecular dynamics study

The diffraction profiles and density correlation functions are calculated for transient atomic configurations generated in molecular dynamics simulations of a $20\mathrm{nm}$ Au film irradiated with $200\mathrm{fs}$ laser pulses of different intensity. The results of the calculations provide an opportunity to directly relate the detailed information on the atomic-level structural rearrangements available from the simulations to the diffraction spectra measured in time-resolved x-ray and electron diffraction experiments. Three processes are found to be responsible for the evolution of the diffraction profiles. During the first several picoseconds after the laser excitation, the decrease of the intensity of the diffraction peaks is largely due to the increasing amplitude of thermal atomic vibrations and can be well described by the Debye-Waller factor. The effect of thermoelastic deformation of the film prior to melting is reflected in shifts and splittings of the diffraction peaks, providing an opportunity for experimental probing of the ultrafast deformations. Finally, the onset of the melting process results in complete disappearance of the crystalline diffraction peaks. The homogeneous nucleation of a large number of liquid regions throughout the film is found to be more effective in reducing long-range correlations in atomic positions and diminishing the diffraction peaks as compared to the heterogeneous melting by melting front propagation. For the same fraction of atoms retaining the local crystalline environment, the diffraction peaks are more pronounced in heterogeneous melting. A detailed analysis of the real space correlations in atomic positions is also performed and the atomic-level picture behind the experimentally observed fast disappearance of the correlation peak corresponding to the second nearest neighbors in the fcc lattice during the laser heating and melting processes is revealed.

Figure 1

(Color online) The effect of the finite size of the MD system on the calculated structure functions. Elimination of spurious ripples induced by the truncation of the pair density function at $R_{\max }=100\mathrm{\AA }$ by introduction of the damping function $W\left(r\right)$ in Eq. (9) is illustrated in (a), where the results are shown for a $20.46\times 20.46\times 20.46{\mathrm{nm}}^3$ fcc Au system equilibrated at $300\mathrm{K}$. Solid (black) and dashed (red) lines show the results of the calculations performed with and without $W\left(r\right)$, respectively. Structure functions calculated using Eq. (9), with the damping function, for systems of four different sizes in the lateral directions are shown in (b).

Figure 2

(Color online) The time scales of the melting process in a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at different absorbed fluences. Semilogarithmic plots of the time required to melt certain fractions of the film are shown in (a). Each curve corresponds to a particular fraction of the remaining crystal phase as a function of the absorbed fluence. For example, the (red) curve with squares corresponds to the time after laser excitation when 90% of the atoms in the film belong to the crystal phase. The decrease of the fraction of the crystal phase with time is shown for each simulation in (b). The atoms in the crystal phase are distinguished from the ones in the liquid phase based on the local order parameter (Ref. 19).

Figure 3

(Color online) Contour plots of the lattice temperature (a) and pressure (b) for a simulation of laser melting of a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$. Solid and dashed lines show the beginning and the end of the melting process. Laser pulse is directed along the $Y$ axes, from the top of the contour plots. The stepwise shape of the contour plot boundaries is related to the discretization of the mesh over which average temperature and pressure values are calculated.

Figure 4

(Color online) Snapshots (a) and structure functions (b) of atomic configurations during the melting process in a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$. Atoms are colored according to the local order parameter $\varphi$—blue atoms have local crystalline surroundings, red atoms belong to the liquid phase. In (a), the laser pulse is directed from the right to the left sides of the snapshots. In (b), curves are shifted vertically with respect to each other in order to better show the changes in the structure function. Zero time corresponds to a perfect fcc crystal at $300\mathrm{K}$ just before the laser irradiation.

Figure 5

(Color online) Snapshots (a) and structure functions (b) of atomic configurations during the melting process in a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $55\mathrm{J}∕{\mathrm{m}}^2$. Atoms are colored according to the local order parameter $\varphi$—blue atoms have local crystalline surroundings, red atoms belong to the liquid phase. In (a), the laser pulse is directed from the right to the left sides of the snapshots. In (b), curves are shifted vertically with respect to each other in order to better show the changes in the structure function. Zero time corresponds to a perfect fcc crystal at $300\mathrm{K}$ just before the laser irradiation.

Figure 6

(Color online) Snapshots (a) and structure functions (b) of atomic configurations during the melting process in a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $45\mathrm{J}∕{\mathrm{m}}^2$. Atoms are colored according to the local order parameter $\varphi$—blue atoms have local crystalline surroundings, red atoms belong to the liquid phase. In (a), the laser pulse is directed from the right to the left sides of the snapshots. In (b), curves are shifted vertically with respect to each other in order to better show the changes in the structure function.

Figure 7

(Color online) Structure functions of atomic configurations generated by uniform uniaxial deformation of a $20\mathrm{nm}$ Au fcc film in the direction normal to the free (001) surfaces. The values of the deformation are indicated in the figure. Temperature of the film is $300\mathrm{K}$. Curves are shifted vertically with respect to each other in order to better show the changes in the structure function. Structure peaks are identified by Miller indices.

Figure 8

(Color online) Normalized height of the (111), (220), and (311) peaks as a function of time after irradiation of a $20\mathrm{nm}$ Au film with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$. All peak heights are normalized to their values at $0\mathrm{ps}$ $(T=300\mathrm{K})$. Dotted lines are calculated through the Debye-Waller factor up to the temperature of $1.25T_m$, which corresponds to the limit of crystal stability. The values of the average temperature of the film at different times after the laser pulse are shown in the additional top $x$ axis.

Figure 9

(Color online) Reduced pair distribution function $G\left(r\right)$ computed for atomic configurations obtained in a simulation of a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$ at times of (a) 0, (b) 11–14, and (c) 14 and $40\mathrm{ps}$.

Figure 10

(Color online) Radial distribution function $R\left(r\right)$ computed for atomic configurations obtained in a simulation of a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$ at times of 0, 10, and $20\mathrm{ps}$. Coordination number $N_c$ for the first coordination shell at $\sim 2.89\mathrm{\AA }$ can be obtained by integration of $R\left(r\right)$ between the two local minima on either side of the first peak.

Figure 11

(Color online) Decomposed radial distribution function $R\left(r\right)$ of (a) first, (b) second, and (c) third coordination shells computed for atomic configurations obtained in a simulation of a $20\mathrm{nm}$ Au film irradiated with a $200\mathrm{fs}$ laser pulse at an absorbed fluence of $180\mathrm{J}∕{\mathrm{m}}^2$ at times of 0, 10, 14, and $20\mathrm{ps}$. The peaks are calculated for atoms that belong to the corresponding coordination shells at the time of $0\mathrm{ps}$. The data for the three coordination shells and their sum at $10\mathrm{ps}$ are shown in (d).

Figure 12

(Color online) Structure functions calculated for atomic configurations obtained in a simulation of a $20\mathrm{nm}$ Al film irradiated with a $120\mathrm{fs}$ laser pulse at an absorbed fluence of $84\mathrm{J}∕{\mathrm{m}}^2$ at times of (a) 0, (b) 1, (c) 2, and (d) $3\mathrm{ps}$. Insets show the corresponding snapshots of the atomic configurations, with the direction of the laser pulse shown in (a). Atoms are colored according to the local order parameter (blue atoms have local crystalline surroundings; red atoms belong to the liquid phase). The irradiation conditions are the same as in the experiment reported in Ref. 11 (incident fluence of $700\mathrm{J}∕{\mathrm{m}}^2$, reflectivity of 88%).