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Supporting Online Material www.sciencemag.org/cgi/content/full/299/5615/2045/ DC1 Materials and Methods Figs. S1 to S7 9 December 2002; accepted 20 February 2003 Microscopic Dynamics of Liquid Aluminum Oxide H. Sinn, 1 B. Glorieux, 2 L. Hennet, 3 A. Alatas, 1 M. Hu, 1 E. E. Alp, 1 F. J. Bermejo, 4 D. L. Price, 3 M.-L. Saboungi 5 * Collective excitations have been observed in liquid aluminum oxide at high temperatures by combining a containerless sample environment with inelastic x-ray scattering. The excitation spectra show a well-defined triplet peak struc- ture at lower wave vectors Q (1 to 6 nanometers -1 ) and a single quasi-elastic peak at higher Q. The high-Q spectra are well described by kinetic theory. The low-Q spectra require a frequency-dependent viscosity and provide previously unknown experimental constraints on the behavior of liquids at the interface between atomistic and continuum theory. The dynamics of liquids are reasonably well understood in two regimes of length scale: in the continuum limit (length scale  interparticle distance), where hydrody- namic theory can be applied, and in the short-wavelength regime (length scale  interparticle distance), where kinetic theory can be extended to liquid densities. The intermediate region, corresponding to a small but finite number of interparticle dis- tances, remains a challenge for modern sta- tistical physics (1–3). The dynamics of ion- ic liquids such as molten salts provide a potentially rich field for coupling experi- ments and theory because two classes of fluctuations, density and charge, can be observed by inelastic neutron scattering and light scattering measurements. Howev- er, the kinematic restrictions of neutron scattering make it impossible to reach acoustic modes over a certain range of wave vector Q, and the high-temperature regime is inaccessible by light scattering because the inelastic signal is obscured by the black-body radiation. The recently de- veloped high-resolution inelastic x-ray scattering (IXS) technique goes beyond these limitations as evidenced by results obtained on liquid metals, water, and or- ganic liquids (4 ). Here, we apply IXS to an oxide melt whose electrical transport properties classify it as a molten salt (5, 6 ). Aluminum oxide was chosen because many of its physical properties and structure have been determined in the mol- ten and supercooled states (7–9). The measure- ments were performed in a containerless envi- ronment. Alumina spheres 3 to 4 mm in diam- eter were suspended in an oxygen gas jet and heated with a 270-W CO 2 laser beam to tem- peratures between 2300 and 3100 K. Care- fully adjusted gas flow through a conical nozzle maintained the levitated sample at a position stable within 20 m above the plane of the top edge of the nozzle, allow- ing a clear path for the incident and dif- fracted x-ray beams. The temperature was measured by a pyrometer directed at the point illuminated by the x-ray beam (10). The IXS measurements were carried out at the 3ID-C beamline at the Advanced Pho- ton Source, with an inline monochromator consisting of two nested channel-cut crys- tals and a back scattering analyzer setup in the horizontal scattering plane 6 m from the 1 Advanced Photon Source, Argonne National Labora- tory, Argonne, IL 60439, USA. 2 Institut de Science et de Ge ´nie des Materiaux et Proce ´de ´s, 66100 Perpignan Cedex, France. 3 Centre de Recherche sur les Mate ´riaux a ` Hauts Tempe ´ratures, Centre National de la Re- cherche Scientifique (CNRS), 45071 Orleans Cedex 2, France. 4 Consejo Superior de Investigaciones Cientı ´fi- cas, Department of Electricity and Electronics, Univer- sity of the Basque Country, 48080 Bilbao, Spain. 5 Centre de Recherche sur la Matie `re Divise ´e, CNRS, University of Orleans, 45071 Orleans Cedex 2, France. *To whom correspondence should be addressed. E- mail: mls@cnrs-orleans.fr Fig. 1. Inelastic x-ray scattering spectra, I(Q, ), for liquid Al 2 O 3 at the six lowest wave vectors measured and a temperature of 2323 K. The fits of Eq. 3 are shown as solid lines, and the equivalent functions with the resolution function deconvo- luted are shown as dotted lines. The resolution function is shown hatched. cts, counts. R EPORTS www.sciencemag.org SCIENCE VOL 299 28 MARCH 2003 2047