VOLUME 74, NUMBER 22 PHYSICAL REVIEW LETTERS 29 MAY 1995 X-Ray Reflectivity Measurements of Surface Layering in Liquid Mercury O. M. Magnussen and B. M. Ocko Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 M. J. Regan, K. Penanen, and P. S. Pershan Division of Applied Science and Department of Physics, Harvard University, Cambridge, Massachusetts 02138 M. Deutsch Department of Physics, Bar-Ilan University, Ramat-Gan 52100, Israel (Received 9 January 1995) The surface normal structure of the mercury liquid-vapor interface has been investigated by measuring the x-ray reflectivity out to a momentum transfer of q z  2.5 Å –1 . The results provide direct experimental proof of surface layering in liquid metals. The layer spacing is given by the atomic dimensions of the Hg atoms. The minimum layer width agrees well with the predictions of capillary wave theory; the layering amplitude decays into the bulk with a characteristic length of 3 –3.5 Å, which is close to the decay length of the bulk pair correlation function. PACS numbers: 61.10.–i, 61.25.Mv, 68.10.–m At the free surface of a liquid metal the density changes from a thin atomic vapor to a dense liquid over a distance of only a few atomic diameters [1]. This rapid vertical den- sity variation is accompanied by a similarly rapid change in the effective interatomic interaction potential. The inter- face density profile is therefore ideally suited to test the ex- tensive body of theoretical studies and simulations carried out over the last decades. Many of these studies predict layering at the surface to a depth of a few atomic diame- ters in several liquid metals [2–6], including mercury, in strong contrast to simple nonmetallic liquids where mono- tonic profiles have been observed [7,8]. Considerable progress towards angstrom-resolution de- termination of the structure of liquid metal surfaces has been achieved in recent years using x-ray reflectivity and grazing incidence x-ray diffraction techniques [9–13]. The reflectivity studies confirmed a relatively narrow in- terface region but were inconclusive with respect to sur- face layering due to their limited q z range. If layering indeed occurs, a Bragg-like peak should be observed at q z  2p a, where a is of the order of the molecular spac- ing. For liquid metals, where a  3 Å, this entails mea- surements out to $2 Å –1 . The best previous measure- ments, performed by Bosio et al. [10] on Hg with a labo- ratory x-ray source, extended only to q z  0.75 Å –1 and, hence, could not unambiguously resolve surface layering. Here we report an x-ray reflectivity study of the surface of liquid mercury extending to q z  2.5 Å –1 . The mea- surements were carried out at a wavelength l  1.227 Å using the Harvard-Brookhaven liquid surface diffractome- ter at beam line X22B of the National Synchrotron Light Source. The glass sample cell was composed of a lower compartment containing the sample through (60 mm 3 20 mm 3 7 mm) and an upper preparation compartment. After cleaning the cell with concentrated nitric acid and ultra pure water (Milli-Q), the sample compartment went through several cycles of hydrogen filling (zero grade pu- rity) and evacuation. Subsequently, pure Hg (8N bulk pu- rity) was filled in the upper vessel, degassed for 30 min, and finally dropped via a teflon needle valve into the glass trough up to a level several mm higher then the rim. Kept under hydrogen, the Hg surface is stable for more than 24 h, as verified by the high reproducibility of the mea- sured reflectivity curves. To minimize vibrational surface excitations the cell was mounted on an active vibration isolation table, which in turn was mounted on the spectrometer. For measurements in the range q z , 0.4 Å –1 the incident beam was collimated to a vertical angular divergence of 0.07 mrad and limited in height by a 0.05 mm slit 240 mm upstream of the sample to keep the footprint of the incident beam smaller than the sample size. For higher q z the slits were gradually opened to increase the reflected signal. The negligible increase in the divergence of the reflected beam, as compared to the incident beam, indicated a flat Hg surface and an efficient elimination of vibrational pickup from the environment by the isolation table. To obtain the specular reflectivity, intensity measure- ments were carried out along the specular axis 2u  0 ±  and by moving the detector by 2u  0.6 ± (i.e., several times the resolution width) out of the plane of reflection. Since the diffuse background depends only weakly on 2u, normalized by the incident beam intensity. Figure 1(a) shows the absolute reflectivity R of liquid mercury at room temperature (circles and plus signs) along with the theoretical reflectivity R f for a perfectly flat surface (solid line), calculated from the Fresnel law of optics. Also shown is a theoretical reflectivity for an interface broadened by the Hg atomic form factor and by thermally excited capillary waves (dotted line). The reflectivity falls from close to unity below the critical angle [14] to 3 3 10 28 at q z  22.3 Å –1 , yet it is always 4444 0031-9007 95 74(22) 4444(4)$06.00 © 1995 The American Physical Society