Coherent Dynamic Structure Factor of Liquid Lithium by Inelastic X-Ray Scattering

Abstract

We present high resolution inelastic x-ray scattering measurements of the coherent dynamic structure factor S͑Q, v͒ of liquid lithium at momentum transfers 0.36 # Q # 5 Å 21 . The determined S͑Q, v͒ agrees much better with molecular dynamic simulations using the neutral pseudo-atom potential rather than the empty core potential. We observe a positive dispersion in the sound velocity confirming that in liquid lithium the longitudinal dynamics reaches a solid-like response at high frequencies.[S0031-9007 (97)02529-5] PACS numbers: 61.25.Mv, 61.10.Eq, 61.20.Ne Recently, Canales et al. [1] calculated the dynamic structure factor of liquid lithium by means of molecular dynamic (MD) simulations using two different pair potentials: the empty core potential derived by Ashcroft [2]and an ab initio calculation for a pair potential deduced from the neutral pseudoatom method (NPA potential) [3]. Although the shapes of these two potentials are quite different, most of the calculated structural and thermodynamic properties are very similar [1]. Significant differences are observed in the calculations of the coherent part of the dynamic structure factor.Inelastic neutron experiments on the dynamic structure factor of liquid 7 Li were performed by de Jong et al. [4]. However, these measurements yielded no decision which of the two pair potential approaches is the more favorable. The reason is that an essential part of the coherent structure factor-the Brillouin modes-could not be observed at small momentum transfers Q. Because of the momentum-energy relation for a classical particle there exists a maximum energy transfer v at a momentum transfer Q, which is determined by the flight velocity of the incident neutron. In the neutron experiment mentioned above the Brillouin excitations were not detectable for Q , 1.2 Å 21 . Moreover, the high fraction of incoherent scattering at small Q and the uncertainties in the incoherent cross section of 7 Li makes it difficult to extract the coherent part from the experimental data.In contrast, these limitations do not appear in an inelastic x-ray scattering experiment with sufficient high energy resolution. At energy transfers of about a few meV the observed intensity originates dominantly from coherent scattering. The energy-momentum relation of the photon allows an almost unlimited energy transfer at any accessible momentum transfer [5,6].Previous experiments on liquid lithium were performed at the synchrotron laboratory HASYLAB in Hamburg [7,8]. The experiments reported here were carried out during the commissioning phase of the inelastic x-ray scattering beamline (ID16) at the European Synchrotron Facility (ESRF) in Grenoble. The x-ray radiation, coming from an undulator, was monochromized by a combination of a cryogenically cooled heat load monochromator and a silicon backscattering monochromator [Si(7,7,7) with E 13.8 keV]. The analyzer, a two dimensional focusing array of silicon crystals, is positioned at a 2.5 m distance from the sample in backscattering geometry. Details of the back...

How Well Do We Know Atomic Motions of Simple Liquids?

“…l approach the Q ! 0 hydrodynamic realm in a way reminiscent of that followed by other alkali metals [3] showing a large amount of positive anomalous dispersion. Our data approach a linear dispersion given by the high-frequency sound velocity c 1 3=…”

“…Within 1:6 A ÿ1 Q 1:8 A ÿ1 the separation of both contributions is again facilitated by a large difference in linewidth. For 1:1 A ÿ1 Q 1:3 A ÿ1 both contributions show comparable linewidths and the separation is done relying on the mode-coupling prescription [3,7]. It predicts a quasielastic spectrum with linewidth !…”

“…dynamic structure factor. Its intensity often shows, in addition to well-defined excitation peaks [3], zero-frequency (quasielastic) components due to spacedependent flow motions. These are known to be highly entangled since the diffusing particle can move to a new position only if it has been left vacant before, and therefore a significant correlation between the moving particle and its surroundings surely exists.…”

“…Such intricacies force the analysis of experimental S Q; ! [3] to rely upon a number of simplifying assumptions. Its inelastic component S inel Q; !…”

Evidence of short-time dynamical correlations in simple liquids

“…On the other hand, the resolution demand is particularly severe in this case, and the scattered intensity rapidly decreases on increasing the atomic number of the sample. This complementarity of IXS and INS allowed to improve the comprehension of the microscopic dynamics in alkali metals through a number of experiments performed in the last decade [17][18][19][20][21][22][23][24].…”