Reflection thermal diffuse x-ray scattering for quantitative determination of phonon dispersion relations
Synchrotron reflection x-ray thermal diffuse scattering (TDS) measurements, rather than previously reported transmission TDS, are carried out at room temperature and analyzed using a formalism based upon second-order interatomic force constants and long-range Coulomb interactions to obtain quantitative determinations of MgO phonon dispersion relations ℏ ωj (q), phonon densities of states g (ℏ ω ), and isochoric temperature-dependent vibrational heat capacities cv(T ) . We use MgO as a model system for investigating reflection TDS due to its harmonic behavior as well as its mechanical and dynamic stability. Resulting phonon dispersion relations and densities of states are found to be in good agreement with independent reports from inelastic neutron and x-ray scattering experiments. Temperature-dependent isochoric heat capacities cv(T ) , computed within the harmonic approximation from ℏ ωj (q) values, increase with temperature from 0.4 ×10-4eV /atom K at 100 K to 1.4 ×10-4eV /atom K at 200 K and 1.9 ×10-4eV /atom K at 300 K, in excellent agreement with isobaric heat capacity values cp(T ) between 4 and 300 K. We anticipate that the experimental approach developed here will be valuable for determining vibrational properties of heteroepitaxial thin films since the use of grazing-incidence (θ ≲θc , where θc is the density-dependent critical angle) allows selective tuning of x-ray penetration depths to ≲10 nm .