Mode-Dependent Phonon Relaxation in fcc Ni: Insights from Molecular Dynamics Simulations with Frozen-Trajectory Excitations

We present a computational method and apply it to study phonon relaxation in face-centered cubic (fcc) nickel (Ni). The phonons are excited beyond their thermal equilibrium population, and the relaxation behavior is analyzed as a function of both the wave vector $\vec{q}$ and the phonon frequency $ω$. To efficiently investigate these excitations, we introduce a trajectory post-processing technique, the frozen-trajectory excitation, which facilitates the $(\vec{q},ω)$-resolved analysis. Molecular dynamics simulations combined with frozen-phonon multislice calculations predict relaxation signatures observable with time-resolved transmission electron microscopy (TEM) at 10–20 fs resolution. Our findings indicate mode dependence in the relaxation processes, highlighting the importance of considering phonon-specific behavior in ultrafast dynamics.

💡 Research Summary

This paper introduces a novel computational framework for probing mode‑specific phonon relaxation in face‑centered cubic (fcc) nickel (Ni) by selectively over‑populating phonon modes in the (q, ω) domain and tracking their subsequent decay with atomistic molecular dynamics (MD). The authors develop the “frozen‑trajectory excitation” (FTE) technique, which leverages fast Fourier transforms (FFT) of equilibrium MD trajectories to construct a full spatio‑temporal displacement field u(r, t). By applying a band‑enhance filter F(q, ω) that amplifies a chosen region of reciprocal‑space and frequency, they generate a modified displacement‑velocity field representing a non‑thermal, mode‑specific excitation. This field is inverse‑transformed back to real space, providing a set of atomic positions and velocities that serve as the initial condition for subsequent microcanonical (NVE) MD runs.

The simulations employ a 28 × 28 × 28 supercell of fcc Ni (≈10 nm per side) with periodic boundaries, equilibrated at 300 K using a Nosé‑Hoover thermostat and barostat. Interatomic forces are described by a spectral‑neighbor‑analysis‑pattern (SNAP) machine‑learning potential trained on 800 density‑functional‑theory (DFT) distorted structures, ensuring DFT‑level phonon dispersions at a fraction of the computational cost. After equilibration, the authors extract a 1 ps trajectory sampled every 20 fs, perform a 4‑dimensional FFT (three spatial indices and time), and identify the transverse acoustic (TA) branch in the qz = 0 plane. Four representative q‑points are selected: the high‑symmetry X point along qy and qz, and two intermediate points along the Δ line. The TA amplitudes at these points are amplified by a factor of 20, raising the system’s effective temperature by ~25 K.

Seven snapshots from the middle of the modified trajectory are each used as seeds for 7–14 independent NVE relaxation simulations, yielding 49–98 statistically independent realizations. During relaxation, atomic configurations are saved at 10–20 fs intervals. For each time delay Δt, the authors compute electron diffraction patterns using a frozen‑phonon multislice (FPMS) approach implemented in Dr‑Probe. The multislice formalism provides three intensity components: incoherent (total), coherent (elastic), and vibrational (thermal diffuse scattering, TDS). By averaging over the independent realizations, they obtain time‑resolved diffraction intensities that directly reflect the decay of the over‑populated phonon population.

Key findings include: (1) The calculated phonon dispersion from the SNAP‑MD matches experimental data (Birgenau et al.) and DFT results, validating the potential and the FFT‑based extraction of ω(q). (2) Mode‑specific relaxation times differ markedly: the X‑point TA mode relaxes within ~0.5 ps, whereas intermediate Δ‑point TA modes exhibit slower decay on the order of 1.5–2 ps. This variation is attributed to differing phonon‑phonon scattering phase space at high‑symmetry versus off‑symmetry points. (3) The FPMS‑derived diffraction intensities show measurable oscillations and decay on a 10–20 fs timescale, suggesting that modern ultrafast transmission electron microscopy (TEM) equipped with femtosecond laser pump and direct electron detectors can experimentally capture these dynamics. (4) The noise level in coherent Bragg spots is two orders of magnitude lower than the vibrational signal, confirming that the TDS contribution dominates the observable changes.

The authors discuss limitations: electron‑phonon coupling is not explicitly included in the current SNAP potential, so temperature rise of the electronic subsystem and its feedback on phonon lifetimes are omitted. Incorporating such effects would require quantum‑MD or a specially trained potential that samples heavily distorted configurations. Nevertheless, the presented framework—combining (q, ω)‑selective excitation, atomistic MD, and time‑resolved FPMS—offers a powerful “computational experiment” platform. It can be extended to spin‑dynamics simulations to investigate the role of lattice vibrations in ultrafast demagnetization, as originally observed by Beaurepaire et al., and to other materials where mode‑dependent phonon lifetimes influence thermal transport, phase transitions, or optomechanical coupling.

In summary, the paper delivers a methodological advance (FTE) for controlled phonon excitation, validates it against experimental phonon spectra, demonstrates clear mode‑dependent relaxation in fcc Ni, and predicts observable signatures in ultrafast TEM. This work bridges the gap between atomistic simulations and emerging femtosecond electron microscopy, opening avenues for quantitative studies of non‑equilibrium lattice dynamics in metals and beyond.