X-ray Debye-Waller factor measurements of solid3Heand4He

Abstract

X-ray synchrotron radiation was used to measure Debye-Waller factors of helium crystals for both 3 He and 4 He in both hcp and fcc phases. To our knowledge, there are no previous measurements for 3 He. The ranges studied for 3 He and 4 He crystals were 11.52-12.82 and 10.95-12.13 cm 3 , respectively, and 11.5-18.2 and 12.0-20.3 K. With small uncertainty, only a Gaussian dependence upon momentum transfer Q was found, and no anisotropy was detected in the hcp phase. Mean square atomic deviations, ͗u 2 ͘, and Lindemann ratios were obtained. Large Lindemann ratios confirm that these solids are highly anharmonic. The ͗u 2 ͘ values agree within an average 1% with computations of Draeger and Ceperley from path integral Monte Carlo methods including unusual extrapolations to the thermodynamic limit. Because the path-integral Monte Carlo ͑PIMC͒ computations exhibit a T 3 dependence for ͗u 2 ͘, which also depends upon molar volume, an empirical analysis was made of the present data as well as of published x-ray and neutron data on hcp 4 He. The volume dependencies are similar to those found from calorimetry, over a large volume range, and the temperature dependencies show similar systematic variations with molar volume both in x-ray data and PIMC results.

Supersolid Helium at High Pressure

“…X-ray diffraction studies measuring the zeropoint energy induced motions of the 4 He atoms from their lattice sites appear to confirm this expectation [13,28]. The declining supersolid fraction with pressure beyond 55 bar is also consistent with this expectation.…”

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].…”

Three-dimensional periodic complex structures in soft matter: investigation using scattering methods

“…Note that for bi-continuous cubic phases, expressions including the q vector direction dependence are available [15]. The values of ku 2 l have to be small and more precisely, by analogy with solid state theory, one can apply the Lindemann criterion for the melting of a solid, for which melting arises when ku 2 l/d ffi 0.120.2, where d is the typical interatomic distance [16]. For a mesophase, d can be replaced by the typical distance between particles.…”