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

Abstract

Atomic vibration amplitudes in dense fcc and hcp 4 He crystals have been measured using synchrotron x rays from the dependence of integrated Bragg intensities up to wave vectors of 91 nm Ϫ1 . 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 ͑PIMC͒ 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 measuredx-ray values are significantly larger than published values inferred from Born-von Kármán fitting to phonon dispersion measured by neutron scattering. Mildly anharmonic neon, which is fairly well described by selfconsistent phonon theories, is contrasted with present results on fcc 4 He at corresponding densities.

Compressibility of solid helium

“…For helium, in particular, this method has predicted kinetic-energy values [19] and Debye-Waller factors [31] in good agreement with data derived from experiments [32,33]. PIMC simulations have been also employed to study the isotopic shift in the helium melting curve [20,21].…”

Correlations and anharmonic effects in solid helium

“…To this end, the measured DebyeWaller factor must be recalculated. Experimental data for FCCP structures at low temperatures can be found in [10], and for BCC and FCC phases at comparatively high temperatures and pressures, they can be found in [4,11]. Results of calculations of the Lindeman parameter demonstrated that at low temperatures and relatively low pressures, values of the first-order correlation terms are comparable with those of the sixth-order anharmonisms.…”

“…The reason is that high amplitudes of particle oscillations in these crystals gives rise to radically new effects observed in it [3,4]. In addition, these crystals are very promising for investigations of solid-liquid phase transitions [5].…”

“…The given parameter can be obtained from experimental data on neutron scattering [1, 3] or diffraction of synchrotron radiation by a crystal [4]. To this end, the measured DebyeWaller factor must be recalculated.…”

“…In the middle 50s of the last century, the possibility appeared to investigate macroscopic systems of 3 He atoms. As a result, many works nowadays are devoted to binary 4 He and 3 He mixtures [8]. All this has led to a sharp increase in the number of articles devoted to quantum crystals.…”