Phonon Lifetimes throughout the Brillouin Zone at Elevated Temperatures from Experiment and Ab Initio

We obtain phonon lifetimes in aluminium by inelastic neutron scattering experiments, by ab initio molecular dynamics, and by perturbation theory. At elevated temperatures significant discrepancies are found between experiment and perturbation theory, which disappear when using molecular dynamics due to the inclusion of full anharmonicity and the correct treatment of the multiphonon background. We show that multiple-site interactions are small and that local pairwise anharmonicity dominates phonon-phonon interactions, which permits an efficient computation of phonon lifetimes.

Figure 1

Inelastic neutron spectra (circles) along with theoretical spectral densities according to perturbation theory (blue lines), one-phonon MD [dashed red lines—Eq. (1)] and $N$-phonon MD spectral densities [solid red lines—Eq. (3)] of Al at 900 K. The chosen spectra are representative for the cases where either PT is adequate (left panel: $\mathbf{q}=(0.25,0,0)$ with dominant transversal contribution), where it severely underestimates anharmonic broadening (middle panel: $\mathsf{L}$ point with dominant transversal contribution), or where the $N$-phonon background appreciably affects the resulting spectrum (right panel: $\mathsf{X}$ point with longitudinal polarization). Note that the theoretical spectra have been convolved with the experimental resolution as detailed in the Supplemental Material [29], corresponding to Gaussian kernels with FWHMs of 0.37, 0.22, and 0.34 THz in the left, middle, and right panels, respectively.

Figure 2

Experimental phonon linewidths $\mathrm{\Gamma }$ for Al (gray symbols) in comparison to perturbation theory (PT) using the third-order force constant tensors (blue lines) and results from DFT MD (GGA) in $3\times 3\times 3$ and $4\times 4\times 4$ fcc supercells [red symbols—Eq. (1)]. Here (a) shows the $\mathbf{q}$ dependence at 900 K for all branches and (b) the temperature dependence for selected $\mathbf{q}$ points, where in addition the linewidths according to TU-TILD [35] (green crosses) and LA [3] (green diamonds) are shown. The temperature variation in PT is due to both the (trivial) scaling with $T$ as well as a quasiharmonic interpolation of the force constants evaluated at 300 K and 900 K.

Figure 3

Root-mean-squared forces in units of meV/Å acting on a given atom at 900 K for DFT (red) and LA (blue) according to Taylor expansion of the potential up to quartic order, grouped into terms according to relative coordinations of participating atoms.