Study of the lattice dynamics of hexagonal close-packed³He and⁴He using inelastic x-ray scattering

Abstract

We present the first measurement of the coherent dynamic structure factor S(Q, ω) of solid 3 He. At a density of 13.25(10) cm 3 mol −1 , we observed longitudinal phonons, using high-resolution inelastic x-ray scattering at momentum transfers 6 nm −1 < |Q| < 23 nm −1 . Their dispersion relation was determined along the c-axis in single crystals of hcp 3 He, and the spectra were described with a single-phonon model. For comparison, hcp 4 He at the same density was studied with the same technique. The comparison, including all available 4 He data from neutron scattering experiments, results in a phonon frequency ratio ω 3 /ω 4 of 1.11(5). Special attention is given to the scattering contribution due to multi-phonon excitations.

X-ray Debye-Waller factor measurements of solid3Heand4He

“…6,34 For x-rays, our 3 He values of ⌰ M seem to be roughly 15 K higher than those for 4 He. Using a simple mass-scaling factor of ͱ4/3 and a frequency scaling ប ϭk B ⌰ M at the same V, one sees that the 3 He and 4 He x-ray values are consistent with such scaling.…”

“…There is enough information from measurements to make such fits for hcp, fcc, and bcc 4 He crystals. 5 There are also measurements for hcp 3 He crystals, 6 but not enough for a fit. We emphasize that any such value of ͗u 2 ͘ generated in this manner neglects the unusual excitations present in helium crystals, unlike the direct ͗u 2 ͘ measurements presented here which include all contributions to atomic displacements.…”

Inelastic X-ray Scattering of a Transition-Metal Complex (FeCl4–): Vibrational Spectroscopy for All Normal Modes

“…Here we employ a third synchro tron method, inelastic x-ray scattering (IXS) 4 . IXS has pre viously been applied to pure elements such as carbon in dia mond or graphite 5 , binary solid state compounds such as MgB 2 , MgO, and SiC 6 , complex superconductors 4c , liquids as diverse as water or 3 He 7 , and even DNA and proteins 8 , but never to a metal coordination complex.…”

Atomic vibration amplitudes in fcc and hcp4Hethrough x-ray diffraction measurements

“…7 Inelastic measurements are vital in providing information on specific excitations when they can be identified, and such work has been extended to 3 He and to larger ranges of Q using x rays at meV resolution. 18 However, coherent ͑Bragg͒…”