View source for Anomalous surface structure of liquid tin

Original entry: Hsin-I Lu, APPHY 225, Fall 2009

"Anomalous surface structure of liquid tin"

O.G. Shpyrko, A. Grigoriev, C. Steimer, P.S. Pershan, B. Lin, M. Meron, T. Graber, J. Gerbhardt, B.M. Ocko and M. Deutsch, Phys. Rev. B70, 224206(2004). 
==Summary==
The authors conducted X-Ray reflectivity measurement on liquid Sn surface. The appearance of quasi-Bragg peak indicated the existence of surface-induced layering. Physical origin of the quasi-Bragg diffraciton is from interference of X-Rays emitted from adjacent atomic layers. The quasi-Bragg peak at <math>q_z \approx</math> 2.2 Å <math>^{-1}</math> corresponds to an atomic layering of close-packed spheres with the <math>d \approx 2.8 </math> Å spacing of the atomic diameter of Sn. 

The authors observed a low-angle shoulder in additional to the main quasi-Bragg peak. This indicates the existence of a second length scale. From a model of high-density surface layer, i.e., smaller distance between the first two layers than the spacing of the subsequent layers, experimental data can be explained.
 
Although Surface-induced layering is also found in other liquid metals, such as Hg, Ga, and In.
High-surface layer is only found liquid Sn. 

==Soft Matter Keywords==
[[Liquid metal]], [[Surface-induced layering]], [[Capillary wave]], [[X-Ray reflectivity]]

==Soft Matter==
[[Image:Bragg.jpg|thumb|Fig. 1. Bragg diffraction [1]]]
*  X-ray Diffraction
X-ray diffraction is a typical way to measure structures of solids in condensed matter physics. When electromagnetic radiation with wavelength comparable to atomic spacings in solids are incident on crystalline sample, the scattered waves from adjacent atomic layers can form constructive interference when Bragg's law is satisfied [1]. 

<math>\;
2 d\sin\theta = n\lambda
</math>

where d is the interplanar distance; <math>\theta</math>, the scattering angle; and <math>\lambda</math>, wavelength of incident electromagnetic wave.

*  X-ray reflectivity measurement of surface layering
[[Image:x-Ray.jpg|thumb|Fig. 2: X-ray reflectivity measurement. <math>k_{in}</math> and <math>k_out</math> are
the wave vectors of the incident and detected x rays, respectively.]]

If there is surface layering occurring in liquid metal, X-ray diffraction should be able to detect the atomic spacing between layers, <math>d</math>.
Figure 2 shows the surface layering measurement of X-ray. X rays with a wavevector <math>k_{in}=2\pi/ \lambda</math>, where <math>\lambda</math>=0.729 Å is the x-ray wavelength, are incident on the horizontal liquid surface at an angle <math>\alpha</math>. The detector selects, in general, a ray with an outgoing wave
vector <math>k_{out}</math>. The reflectivity <math>R(q_z)</math> is the intensity ratio of these two rays, when the specular conditions <math>\alpha = \beta</math> and <math>\Delta \Theta = 0</math> are fulfilled. In this case the surface-normal momentum transfer is <math>q_z=(2 \pi / \lambda)</math>(sin<math>\alpha</math> + sin<math>\beta</math>). The signature of layering in the x-ray reflectivity curve is the appearance
of a quasi-Bragg peak at a wave vector transfer <math>q_z=2 \pi /d</math>.

[[Image:x-ray.jpg|thumb|Fig. 3: The measured x-ray specular reflectivity (points) of the surface of liquid Sn.]]
The x-ray specular reflectivity shown with circles in Fig. 3 is the difference between the specular signal recorded with an Oxford scintillation detector at <math>\alpha = \beta</math> and <math>\Delta \Theta = 0</math>. The quasi-Bragg peak at <math>q_z \approx 2.2</math> Å <math>^{-1}</math> corresponds to an atomic layering of close-packed spheres with the <math>d \approx</math>2.8 Å spacing of the atomic diameter of
Sn.
==References==
[1] http://en.wikipedia.org/wiki/Bragg_diffraction