Probing the atomic dynamics of ultrafast melting with femtosecond electron diffraction

TL;DR

Ultrafast melting of copper under femtosecond laser excitation is probed with time-resolved MeV electron diffraction to capture atomic-scale structural changes on picosecond timescales. The study combines Debye-Waller analysis of lattice heating with two-temperature model simulations and TTM-MD atomistic simulations (Migdal G_ei) to quantify energy transfer from hot electrons to the lattice and to track the onset and progression of melting. The results show surface-initiated melting slightly below T_melt, followed by rapid homogeneous melting, and they reveal no lattice-collapse signature at the proposed superheating limit; the Migdal coupling provides the best agreement with observed lattice temperatures and melt kinetics. These findings constrain electron-phonon coupling strengths and provide a coherent picture of ultrafast melting in metals, with implications for laser-based processing and high-energy-density physics.

Abstract

Melting is an everyday phase transition that is determined by thermodynamic parameters like temperature and pressure. In contrast, ultrafast melting is governed by the microscopic response to a rapid energy input and, thus, can reveal the strength and dynamics of atomic bonds as well as the energy flow rate to the lattice. Accurately describing these processes remains challenging and requires detailed insights into transient states encountered. Here, we present data from femtosecond electron diffraction measurements that capture the structural evolution of copper during the ultrafast solid to liquid phase transformations. At absorbed energy densities 2 to 4 times the melting threshold, melting begins at the surface slightly below the nominal melting point followed by rapid homogeneous melting throughout the volume. Molecular dynamics simulations reproduce these observations and reveal a weak electron lattice energy transfer rate for the given experimental conditions. Both simulations and experiments show no indications of rapid lattice collapse when its temperature surpasses proposed limits of superheating, providing evidence that inherent dynamics limits the speed of disordering in ultrafast melting of metals.

Figures (5)

• Figure 1: Electron diffraction study of ultrafast melting of copper. (a) Schematics of the experimental setup. The copper targets were pumped by intense 130fs, 400nm laser pulses and the induced solid-liquid phase transitions were probed with time-resolved electron diffraction using 350fs pulses of 3.2MeV electrons. (b) Top panel: sequence of diffraction patterns obtained at selected times over the solid-liquid phase transition obtained for an energy density of 2.55MJkg. Bottom panel: snapshots of atomic configuration in a small subvolume as obtained by MD simulations to illustrate the transient atomic structures at corresponding time delays. Green spheres are atoms in the fcc phase, while grey spheres are non-fcc (liquid) atoms. (c) Radially averaged scattering intensity of the diffraction patterns shown in (b). The vertical black lines indicate the positions of diffraction peaks for fcc copper. For comparison, the intensity for only the unpumped Si$_3$N$_4$ substrate was included.
• Figure 2: Temporal evolution of the electron scattering signal. The upper panels are results for an energy density of 2.55MJkg, the lower panels are for 1.26MJkg. (a) and (d) Time-resolved result of the total scattering signal. (b) and (e) Evolution of the intensity of the decaying (220) peak (red spheres) and the rise of diffuse scattering signal at Q = 6.8 Å$^{-1}$ (black squares). Error bars represent one standard deviation (SD). The gray band represents the ground intensity level (mean value $\pm$ 1 SD) reached at late times. The vertical arrow marks the time of complete melting $\mathrm{\uptau_{melt}}$. To account for the relatively large time intervals at late times, we define $\mathrm{\uptau_{melt}}$ as half of the time interval (1 ps) preceding the drop in (220) intensity to the liquid scattering level. (c) and (f) Time-resolved width of the (111) peak (FWHM) to monitor the signal from liquid scattering developing during the melting process. The gray band represents the initial constant level of the (111) peak width (mean value $\pm$ 1 SD). The onset of changes in the width ($\mathrm{\uptau_{onset}}$) is marked by the vertical arrow.
• Figure 3: Determining the lattice heating. (a) Experimental data of the decay of normalized diffraction peaks, normalized to the (111) peak (discrete data points), in comparison with corresponding DWFs that are calculated from TTM simulation results (solid lines). In these TTM simulations, we adopted a temperature-dependent $G_{ei}$ from Migdal et al.migdal2016 (see Methods). (b) Negative logarithm of the normalized DWF (discrete data points) as a function of $Q_{hkl}^2-Q_{111}^2$, overlaid with linear fits (solid lines) to extract the mean displacement $\Delta \langle u^2\rangle (t)$. (c) Evolution of lattice temperature derived from the measured DWFs compared to TTM simulation results based on electron-ion coupling according to Lin et al.Lin2008 (black line), and Migdal et al.migdal2016 (red line). Data in all graphs are for $\epsilon$ = 2.55MJkg.
• Figure 4: Results of TTM-MD simulation. (a) Snapshots of atomic configurations for different times distributed over the melting transition. The top side of the slab is free to move while the bottom side is fixed to simulate the substrate. The atoms in the simulations are colored according to the surrounding atomic structure: green are atoms in a fcc lattice, grey are disordered (liquid) atoms. (b) Evolution of the fraction of fcc atoms (dash-dot line) and the average ion temperature (red solid line). The yellow band highlights fcc fractions ranging from 98% to 95% (onset of melting); the green band fractions from 5% to 2% (melt completion). The red squares with error bars label lattice temperatures from the electron diffraction measurements for comparison. The energy density considered here is 2.55MJkg. (c) Snapshots of atomic configurations after reaching the predicted superheating limit of 1.25 $T_{melt}$ for selected areas at the center of the slab. The time points for the snapshots are marked out with color-coded circles on the fcc fraction curve in (b).
• Figure 5: Energy density dependence of melting times for copper. The measured times for melt completion and onset are represented by red triangles and blue circles, respectively. Error bars represent one standard deviation of statistical uncertainties. The data are compared to results from TTM-MD simulations, with open squares indicating the energy densities that have been modeled. The green shaded area corresponds to times when the fraction of fcc atoms is between 5% and 2% (melt completion), the yellow shaded area for times with fcc fractions from 98% to 95% (onset of melting). The light blue line with open diamonds represent the times when the average ion temperature reaches $1.25\,T_{melt}$.