Anomalous layering at the liquid Sn surface

X-ray reflectivity measurements on the free surface of liquid Sn are presented. They exhibit the high-angle peak, indicative of surface-induced layering, also found for other pure liquid metals (Hg, Ga, and In). However, a low-angle shoulder, not hitherto observed for any pure liquid metal, is also found, indicating the presence of a high-density surface layer. Fluorescence and resonant reflectivity measurements rule out the assignment of this layer to surface segregation of impurities. The reflectivity is modeled well by a 10% contraction of the spacing between the first and second atomic surface layers, relative to that of subsequent layers. Possible reasons for this are discussed.

Figure 1

Kinematics of the x-ray measurement. $k_{\mathit{\text{in}}}$ and $k_{\mathit{\text{out}}}$ are the wave vectors of the incident and detected x rays, respectively.

Figure 2

The measured x-ray specular reflectivity (points) of the surface of liquid Sn. The Fresnel reflectivity (solid line) of an ideally flat and abrupt surface and the reflectivity of an ideal surface roughened by thermally excited capillary waves (dashed line) are also shown.

Figure 3

Diffuse scattering off the liquid Sn surface measured at a fixed angle of incidence $\alpha =5.05°$ (open circles). The peak corresponds to the specular condition at $q_z=0.48{\mathrm{\AA }}^{-1}$. The line is the capillary wave theory predictions for surface tension $\gamma =560\mathrm{mN}∕\mathrm{m}$.

Figure 4

The structure factor (squared) of the Sn surface as derived from the measured reflectivity ${\mid \Phi \left(q_z\right)\mid }^2=R\left(q_z\right)∕\left[R_F\left(q_z\right)\mathrm{CW}\left(q_z\right)\right]$ (open circles). The dashed line is the theoretically expected ${\mid \Phi \left(q_z\right)\mid }^2$ of a simple layered density profile as found previously for Ga and In. The solid line is a fit to a model, discussed in the text, where the distance between the first and second layers is reduced by 10% relative to that of the subsequent layers.

Figure 5

Models for the intrinsic surface-normal electron density profiles of Sn for a simple, equally spaced layering model (dashed line), and for a model including a contraction of the spacing between the first and second layers by 10% (solid line). The models yield the reflectivities shown by the same lines in Fig. 2. The inset is a blow up of the first layer region.

Figure 6

Experimental setup used in the GI-XRF measurements: the synchrotron beam (a) is Bragg reflected from a monochromator (b) which directs it downwards at the liquid Sn sample located inside a UHV chamber (c). The specularly reflected beam (solid line) is blocked by a beam stop on the exit window (d) to minimize the background. The fluorescence from the sample’s surface (dotted lines) is detected off specularly by an energy-dispersive detector (e) located as close to the chamber as possible to maximize its solid angle of acceptance.

Figure 7

Raw (line) and background-subtracted (open circles) measured fluorescence from the surface of liquid Sn. The sharp lines are due to the $K$ emissions lines (Ref. 20) of $\mathrm{Fe}(E=6.4\mathrm{keV})$, $\mathrm{Nb}(E=16.6\mathrm{keV})$, $\mathrm{Mo}(E=17.5\mathrm{keV})$, and $\mathrm{Sn}(E=25.2\mathrm{keV})$.

Figure 8

(Top) Relative energy variation of the reflectivity off the liquid Sn surface at a fixed $q_z=0.3{\mathrm{\AA }}^{-1}$. The line is the theoretical prediction of the change in the reflectivity due to the variation of the dispersion correction $f^{\prime }\left(E\right)$ of the scattering factor near the edge, as calculated by the IFEFFIT program (Ref. 23). The open circles are the measured values. (Bottom) Measured energy variation of the intensity transmitted through an Sn foil (points). The $K$ edge of Sn at $E=29.20\mathrm{keV}$ shows up clearly in both measurements.

Figure 9

The structure factor (squared) of the Sn surface as derived from the measured reflectivity, at ($E=29.20\mathrm{keV}$, triangles), above ($E=29.22\mathrm{keV}$, circles), and below ($E=17\mathrm{keV}$, squares) the $K$ edge. The solid line is a fit to the density model featuring reduced interatomic spacing for the top layer by approximately 10%. The dashed line is calculated for a model with a high-density surface monolayer of an atomic species other than Sn. The inset shows the density profile of such a layer. For a discussion see the text.