Surface structure of liquid Bi and Sn: An x-ray reflectivity study
P. S. Pershan,
1
S. E. Stoltz,
1
Oleg G. Shpyrko,
2
Moshe Deutsch,
3
Venkatachalapathy S. K. Balagurusamy,
1
Mati Meron,
4
Binhua Lin,
4
and Reinhard Streitel
1
1
Department of Physics and SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
2
Department of Physics, University of California–San Diego, San Diego, La Jolla, California 92093, USA
3
Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
4
CARS, University of Chicago, Chicago, Illinois 60637, USA
Received 10 November 2008; revised manuscript received 12 January 2009; published 13 March 2009
X-ray reflectivity measurements of the liquid Bi surface are presented and analyzed together with previous
liquid Sn results. Published measurements on liquid Ga, In, and K all exhibit a single strong maximum at a
wave-vector transfer of the order of the reciprocal of an atomic-diameter, due to surface-induced layering. In
contrast, both Sn and Bi exhibit—in addition—a weak broad peak at much smaller wave-vector transfers. This
feature is an unambiguous signature of an enhanced electron density in the near-surface region. Possible ways
of modeling this enhancement are presented. Once the different surface-roughening effects of thermal capillary
waves are accounted for, the surface structure factors of Sn and Bi are remarkably similar. The principal
difference between the two is that the depth of the layering below the surface is more than 40% larger for Bi
than for Sn. This is considerably larger than the ratio of their covalent radii which is only 10%. No
theoretical explanation can be offered at this time for the surface structure difference between Sn and Bi and
other elemental liquid metals studied to date: Ga, In, and K.
DOI: 10.1103/PhysRevB.79.115417 PACS numbers: 68.03.-g, 68.35.Ct, 61.25.Mv
I. INTRODUCTION
Slightly over 30 years ago, Rice and co-workers
1,2
pre-
dicted that the atoms at the free surface of a liquid metal
should be stratified to a depth of a few atomic diameters. The
physical basis of this prediction is the change across the free
surface between the conducting metallic liquid phase, in
which the interactions are dominated by columb/quantum ef-
fects involving the free-electron Fermi gas and the liquid of
positively charged ions, and the nonconducting vapor phase
dominated by van der Waals interactions. According to Rice
this change suppresses the short-distance fluctuations of the
surface and causes atomic layering similar to that occurring
at a hard wall.
3
The surface-induced layering phenomena that
were initially confirmed by x-ray reflectivity measurements
two decades later fell into two classes. For liquid Ga,
4
In,
5
and K Ref. 6, the atomic layering was well described by a
relatively simple distorted crystal model DCM that will be
described below.
7
The reflectivity for liquid Hg deviated
from this simple model and required a more complex one,
putting it into a class by itself. Results from a subsequent
experiment on liquid Sn seemed to display yet a third class
of surface structure, exhibiting a layer of enhanced density at
the vapor-liquid surface.
8
We have carried out x-ray reflectivity measurements on
the free surface of liquid Bi. These measurements show that
the layered surface is capped by a single atomic layer of a
density higher than that of the bulk. Thus, it appears that
both Bi and Sn exhibit a similar surface structure requiring
a relatively subtle deviation from the DCM that is different
from both that of Hg and the simple DCM of Ga, In, and K.
II. BACKGROUND
The kinematics of x-ray scattering from liquid surfaces
have been discussed in a number of recent papers.
8–10
X rays
of wavelength are incident on the x-y plane of the liquid
surface at an angle with respect to the surface plane. Scat-
tered radiation is detected at a reflectance angle with re-
spect to an x-y surface plane and azimuthal angle by a
scintillation detector with the resolution defined by a rectan-
gular slit of a horizontal width w and a vertical height h
placed in front of the detector at a distance L from the
sample. Measurements have been performed at Sector 15-ID
ChemMat-CARS of the Advanced Photon Source. For x
rays produced by an undulator beamline at a third generation
synchrotron source, the incident beam is essentially parallel,
monochromatic, and physically smaller than the detector slit.
For incident angles larger than four or five times the
critical angle
c
=
r
0
2
/ , where
is the electron den-
sity of the bulk liquid and r
0
is the classical radius of the
electron, the differential cross-section for scattering from a
liquid surface can be expressed as
6,11,12
d
d
2
q
xy
A
0
q
c
2q
z
4
|q
z
|
2
q
xy
q
max
2q
xy
2
. 1
In this expression, the three components of the wave-vector
transfer of a ray scattered into the center of the detector are
q
x
= 2/cos sin ,
q
y
= 2/cos cos - cos ,
q
z
= 2/sin + sin . 2
The first term in Eq. 1, A
0
q
c
/ 2q
z
4
, corresponds to the
scattering from an ideally flat and sharp surface i.e., no
roughness at which the electron density changes discontinu-
ously from the vacuum or vapor density 0 to
upon
crossing the x-y surface plane. A
0
is the cross-sectional area
PHYSICAL REVIEW B 79, 115417 2009
1098-0121/2009/7911/1154177 ©2009 The American Physical Society 115417-1