48 Anomalous Dynamical Narrowing in Liquid Se We have observed strong narrowing in the inelastic X-ray scattering (IXS) spectra of liquid (l-) Se at the momentum transfer Q between 12 and 15 nm -1 [1]. Typically, in simple monatomic liquids, narrowing is observed at the first structure factor maximum, in this case, about 19 nm -1 . However, we see it at a somewhat lower Q . This is probably related to the covalent nature of the liquid. Se forms two-fold coordinated linear chain molecules, where atoms are covalently bonded. Crystalline Se with a trigonal form is stable at ambient conditions and it consists of helical chains, while metastable monoclinic forms consist of Se 8 ring molecules. When Se is melted, its two-fold coordinated chain structure is largely preserved and l-Se consists of disordered long chains where segments with a helical chain-like configuration (a) and ring-like one (b) are randomly distributed (see Fig. 1). We measured the dynamic structure factor S(Q,E) , where E is the energy transfer, using a high-resolution IXS spectrometer at beamline BL35XU . The energy of the incident beam was 21.747 keV and the spectrometer resolution depending on the analyzer crystals was 1.5 - 1.8 meV in the present experimental setup. The Se sample of 99.999 % purity and 0.04 mm in thickness was mounted in a single-crystal sapphire cell. IXS spectra of l-Se at 523 K were measured from 1.8 to 42 nm -1 over 40 meV. Figure 2 shows the overall features of the S(Q,E) of l-Se at 523 K. The energy integrals of S(Q,E) become the static structure factor S(Q) , which agrees well with that obtained from neutron scattering (NS) [2] as shown in Fig. 3(a). S(Q,0) , shown in Fig. 2, has a sharp first peak at 15 nm -1 , which is a little smaller than the first S(Q) maximum. That is, the S(Q,E) observed is very narrow at around 15 nm -1 . The spectra were analyzed using a model function consisting of several Gaussians to deconvolute S(Q,E) from the spectrometer resolution. Then we calculated the normalized second frequency moment of S(Q,E) , ω 0 ( Q ) , from the deconvoluted model function. Figure 3(b) shows the E-Q dispersion relation of ω 0 ( Q ) deduced from S(Q,E) (triangles). The triangles reasonably follow the solid line in Fig. 3(b) that is calculated using the sum rule, ω 0 2 ( Q ) = k B TQ 2 / (mS(Q)) , where m is a particle mass and S(Q) is obtained from NS [2]. More exactly, however, the triangles deviate below the solid line at the Q between 12 and 15 nm -1 . This discrepancy can be explained if we assume the Q dependence of m . Figure 3(c) shows the effective mass deduced from ω 0 ( Q ) . The mass as large as 2 - 3 atoms just pinpoints the Q where the strong narrowing occurs. The distance corresponding to the Q is close to the fourth-nearest- neighbor distance, and it is crucial to distinguish between helical chain-like and ring-like segments in 0 1 2 3 4 0 1 2 3 4 (a) (b) Fig. 1. Schematic illustration of helical chain-like (a) and ring-like (b) segments along a disordered chain. E (meV) S(Q, E) Q (nm -1 ) Fig. 2. Three-dimensional plots of S(Q,E) of liquid Se at 523 K. 49 M. Inui*, S. Hosokawa and K. Matsuda Faculty of Integrated Arts and Sciences, Hiroshima University *E-mail: inui@mls.ias.hiroshima-u.ac.jp References [1] M. Inui, S. Hosokawa, K. Matsuda, S. Tsutsui and A.Q.R. Baron - in preparation. [2] K. Maruyama et al. : J. Phys. Soc. Jpn. 74 (2005) 3213. the disordered chain as shown in Fig. 1. Thus, the large effective mass hints that the segments cooperatively move like a rigid molecule under the propagation of longitudinal waves with the corresponding Q . This must be the origin of the present narrowing. 0 0 0 2 4 6 0 1 2 3 10 20 30 40 Q (nm -1 ) 1 m eff (atom) S (Q) (a) (b) (c) Fig. 3. (a) The energy integral of S(Q,E) (open triangles) is plotted after being properly normalized. Also shown is the S(Q) obtained from neutron scattering (solid line). (b) E-Q dispersion relation of ω 0 (Q) obtained from S(Q,E) (open triangles) and sum rule (solid line). (c) Q dependence of effective mass.
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