Cage diffusion in liquid mercury Yaspal S. Badyal Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Ubaldo Bafile Instituto di Fisica Applicata ‘‘Nello Carrara,’’Consiglio Nazionale delle Ricerche, Firenze, Italy Kunimasa Miyazaki Department of Chemistry and Chemical Biology, Harvard University, Massachusetts 02138, USA Ignatz M. de Schepper Interfaculty Reactor Institute, TU Delft, 2629 JB Delft, The Netherlands Wouter Montfrooij* University of Missouri, Columbia, Missouri 65211, USA Received 1 April 2003; published 31 December 2003 We present inelastic neutron scattering measurements on liquid mercury at room temperature for wave numbers q in the range 0.3 q 7.0 Å -1 . We find that the energy half width of the incoherent part of the dynamic structure factor S ( q , E ) is determined by a self-diffusion process. The half width of the coherent part of S ( q , E ) shows the characteristic behavior expected for a cage diffusion process. We also show that the response function at small wave numbers exhibits a quasielastic mode with a time scale characteristic of cage diffusion, however, its intensity is larger by an order of magnitude than what would be expected for cage diffusion. We speculate on a scenario in which the intensity of the cage diffusion mode at small wave numbers is amplified through a valence fluctuation mechanism. DOI: 10.1103/PhysRevE.68.061208 PACS numbers: 66.10.Cb, 05.60.-k, 61.25.Mv, 25.40.Fq I. INTRODUCTION The collective microscopic dynamics of dense hard- sphere fluids can be understood on the basis of cage diffu- sion. In this process, the particles with hard sphere diameter  hs , while all moving diffusively, find themselves locked up in a cage formed by their nearest neighbors. As a conse- quence, the coherent collective dynamic structure factor, S c ( q , E ) of the system becomes, as a function of wave num- ber q and energy E, very narrow in energy for wave numbers near q  hs 2  , i.e., near the peak in the static structure factor S ( q ). This narrowing is referred to as de Gennes nar- rowing of S c ( q , E ). It is believed that cage diffusion plays an important part in the dynamics of real fluids, such as noble gas fluids 1,2, concentrated colloidal suspensions 3,4, and liquid metals. Over the past decennia, the microscopic dynamics of liq- uid metals in particular have been the subject of intensive study by neutron scattering and x-ray investigations 5–17, and molecular dynamics simulations 6,18,19. Liquid metals pose a particularly interesting problem because of the long range of the interatomic potential. The extended hydrody- namics modes have been investigated in these systems, and the influence of the mode coupling mechanism on these modes 9,10, leading to long-time tails in the correlation functions. In here, we present results on the fast short-time decay mechanism of liquid mercury pertinent to cage diffu- sion. Recent neutron scattering experiments by Bove et al. 5 on liquid mercury at room temperature showed that the in- coherent part of the scattering function i.e., the dynamics of individual Hg atoms was characterized by two time scales: a slow time scale reflecting self-diffusion and a fast time scale reflecting cage diffusion. These two time scales were also present in molecular dynamics MD simulations carried out by the same group 6. However, their neutron scattering setup did not allow for a detailed investigation of the inco- herent dynamic response, as it was setup primarily to inves- tigate q dependence of the sound modes outside the hydro- dynamic regime. We report inelastic neutron scattering experiments on Hg at room temperature number density n =0.0408 Å -3 ) at a higher energy resolution, allowing us to investigate whether cage diffusion is indeed present in mercury, and determine the origin of the two time scales found previously 6. Our results show that, as expected, self-diffusion is the dominant dynamic process in Hg on long-time scales. On short-time scales, the decay of the self-correlation function is deter- mined by cage diffusion. This short-time scale is manifest in the neutron scattering response as a broad quasielastic line with an energy half width of 2 meV. The mode associated with this second time scale disappears from the spectra for q 1Å -1 , however, its intensity at the smallest q values is an order of magnitude larger than what could be expected from cage diffusion. We show that this mode cannot be viewed as an extension of the hydrodynamic Rayleigh mode to finite q values. Instead, we speculate that the intensity of the cage diffusion mode in the neutron scattering spectra at *Corresponding author. PHYSICAL REVIEW E 68, 061208 2003 1063-651X/2003/686/0612087/$20.00 ©2003 The American Physical Society 68 061208-1