Role of Thermal Equilibrium Dynamics in Atomic Motion during Nonthermal Laser-Induced Melting

This study shows that initial atomic velocities as given by thermodynamics play an important role in the dynamics of phase transitions. We tracked the atomic motion during nonthermal laser-induced melting of InSb at different initial temperatures. The ultrafast atomic motion following bond breaking can in general be governed by two mechanisms: the random velocity of each atom at the time of bond breaking (inertial model), and the forces acting on the atoms after bond breaking. The melting dynamics was found to follow the inertial model over a wide temperature range.

Figure 1

Illustration of the dynamics of laser-induced melting of InSb when governed by thermal equilibrium dynamics. The simulation is based on initial velocities given by a classical molecular dynamics program package (LAMMPS). After laser excitation, the atoms move at a constant velocity. (a)–(d) show only 18 atoms for clarity. The atomic positions are shown for (a) $\text{time}=0\mathrm{fs}$ and $T=500\mathrm{K}$, (b) $\text{time}=0\mathrm{fs}$ and $T=70\mathrm{K}$, (c) $\text{time}=350\mathrm{fs}$ and $T=500\mathrm{K}$, and (d) $\text{time}=350\mathrm{fs}$ and $T=70\mathrm{K}$. The time-resolved x-ray scattering intensity for 500 (e) and for 70 K (f) are also shown. The full molecular movie is available online.

Figure 2

Schematic of the experimental setup. Because of the difference in incident angle between the laser and the x rays, sample positions T1 and T2 will be exposed at different time delays, converting the spatial extent of the sample (and detector image) into a time axis.

Figure 3

Single shot recordings showing the drop in scattered x-ray intensity during nonthermal melting of InSb for temperatures of 500, 150, and 70 K. 10–25 curves were recorded and evaluated for each temperature. The data have been smoothed with a 60 fs Gaussian window. The solid lines show the x-ray intensities calculated from Eqs. (1)–(5). For intensities below 30%, the noise gives rise to large errors in the calculated displacement. We have plotted these points with lower reliability in gray.

Figure 4

The disordering time was measured at different temperatures. The experimental results are the average of a number of measurements (as given in Table 1 for each temperature), and the error bars show the standard error. The black solid line shows the trend predicted by the inertial model [2]. The red dashed line shows the disordering times using the classical energy. The blue dot-dashed line indicates the temperature-independent result at the value predicted by Zijlstra et al. [5].

Figure 5

Atomic average displacement for temperatures of 500, 150, and 70 K, calculated using Eqs. (1)–(5) for the average of single-shot measurements. The number of shots for each temperature is given in Table 1. The atomic motion was tracked up to 1.2 Å, corresponding to a decrease in the initial x-ray intensity of the 111 Bragg reflection of 30%. For intensities below this level, the noise gives rise to large errors in the calculated displacement. We have plotted these points with lower reliability in gray. The solid lines are calculated from the initial velocity given by thermodynamic equilibrium dynamics at the respective temperature.