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

Abstract

Atomic vibration amplitudes in dense fcc and hcp ${}^{4}\mathrm{He}$ crystals have been measured using synchrotron x rays from the dependence of integrated Bragg intensities up to wave vectors of $91{\mathrm{nm}}^{\ensuremath{-}1}.$ Observed raw Bragg x-ray integrated intensities cover an extraordinary range, greater than ${10}^{5},$ due to the combined effect of the Debye-Waller factor and electronic form factor. From analysis of these intensities mean-square atomic vibration amplitudes $〈{u}_{Q}^{2}〉$ and Lindemann ratios are determined. Path-integral Monte Carlo (PIMC) computations of Draeger and Ceperley, extrapolated to the thermodynamic limit, provide excellent agreement with these experimental results. For both present measurements and the PIMC results, one finds both a predominantly Gaussian distribution in $〈{u}_{Q}^{2}〉$ and an extraordinarily large Lindemann ratio. In contrast, these directly measured x-ray values are significantly larger than published values inferred from Born-von K\'arm\'an fitting to phonon dispersion measured by neutron scattering. Mildly anharmonic neon, which is fairly well described by self-consistent phonon theories, is contrasted with present results on fcc ${}^{4}\mathrm{He}$ at corresponding densities.