Liquid boron: X-ray measurements and ab initio molecular dynamics simulations
David L. Price,
1
Ahmet Alatas,
2
Louis Hennet,
1
Noël Jakse,
3
Shankar Krishnan,
4
Alain Pasturel,
3
Irina Pozdnyakova,
1
Marie-Louise Saboungi,
5
Ayman Said,
2
Richard Scheunemann,
6
Walter Schirmacher,
7
and Harald Sinn
2,8
1
Centre de Recherche sur les Conditions Extrêmes et Matériaux: Haute Température et Irradiation, 45071 Orléans, France
2
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
3
Laboratoire de Physique et Modélisation des Milieux Condensées, 38042 Grenoble, France
4
KLA-Tencor, San Jose, California 95134, USA
5
Centre de Recherche sur la Matière Divisée, 45071 Orléans, France
6
Containerless Research, Inc., Evanston, Illinois 60201, USA
7
Department für Physik, E13, Technische Universität München, 85747 Garching, Germany
8
DESY, Notkestrasse 85, 22607 Hamburg, Germany
Received 1 March 2009; published 1 April 2009
We report results of a comprehensive study of liquid boron with x-ray measurements of the atomic structure
and dynamics coupled with ab initio molecular dynamics simulations. There is no evidence of survival into the
liquid of the icosahedral arrangements that characterize the crystal structures of boron but many atoms appear
to adopt a geometry corresponding to the pentagonal pyramids of the crystalline phases. Despite similarities in
the melting behavior of boron and silicon, there is little evidence of a significant structural shift with tempera-
ture that might suggest an eventual liquid-liquid phase transition. Relatively poor agreement with the observed
damping of the sound excitations is obtained with the simple form of mode-coupling theory that has proved
successful with other monatomic liquids, indicating that higher-order correlation functions arising from direc-
tional bonding and short-lived local structures are playing a crucial role. The large ratio of the high frequency
to the isothermal sound velocity indicates a much stronger viscoelastic stiffening than in other monatomic
liquids.
DOI: 10.1103/PhysRevB.79.134201 PACS numbers: 61.25.Mv, 62.60.+v, 64.70.Ja, 61.05.cp
I. INTRODUCTION
Renewed interest in the structure and dynamics of classi-
cal liquids has been stimulated by two recent developments:
the observation in both diffraction experiments
1
and numeri-
cal simulations
2–4
of first-order liquid-liquid phase transi-
tions LLPT between a high-density and low-density phase,
and the success of a relatively simple version of mode-
coupling theory MCT in explaining the dynamics of simple
liquids.
5,6
In both cases the details of the interatomic poten-
tial are important: the occurrence of a liquid-liquid transition
appears to require a potential with either two distinct short-
range repulsive distances
7
or a repulsive soft core
8
while the
MCT seems to work best if the potential can be approxi-
mated by a smoothed hard-sphere interaction.
6
Relatively little is known about liquid boron due in part to
its high melting point. The existence in the solid of
-rhombohedral and -rhombohedral crystal structures,
which can be regarded as high-density and low-density
phases,
9,10
suggests the possibility of high-density and low-
density phases in the liquid. Furthermore, the presence of
icosahedra and pentagonal pyramids in both solid phases im-
plies that two length scales are involved. The possibility of
their survival on melting—as has been found for complex
structural units in other semiconducting systems, for ex-
ample, NaSn Ref. 11 and CsPb Ref. 12—might be in-
voked to explain the unusual properties of the liquid. Boron
contracts on melting,
13
exhibits an increase—albeit
small—in the electrical conductivity,
14
and—as we shall
show—shows a considerable decrease in the longitudinal
sound velocity, properties similar to silicon and germanium
in which substantial evidence exists for an LLPT on extreme
supercooling.
2,15,16
Like Si and Ge, B is a semiconductor
under ambient conditions but transforms to a superconduct-
ing metal under pressure
17
and a recently discovered ionic
form at even higher pressure.
18
While the potential in the
solid is clearly far from a hard-sphere interaction, it is likely
to be more isotropic in the liquid, and the applicability of the
simple MCT approach cannot be ruled out a priori. In order
to address these questions we have made a comprehensive
study of liquid boron with x-ray measurements of the atomic
structure and dynamics coupled with ab initio molecular dy-
namics AIMD simulations, and relate these to the physical
and electrical properties of the liquid in cases where these are
known.
II. EXPERIMENTAL DETAILS
Crystalline boron exhibits a remarkable variety of struc-
tures, composed of icosahedra and pentagonal pyramids, and
characterized by large unit cells. The stable form at low tem-
perature is either the -rhombohedral
9
or a symmetry-broken
-rhombohedral
19
structure, and at high temperature the
rhombohedral. It melts into a stable liquid at 2360 10 K, a
temperature that is readily accessible with present-day levi-
tation techniques.
20
We measured its structure using a com-
bination of conical nozzle levitation, laser heating, and x-ray
diffraction XRD at the 12-ID-B beam line at the Advanced
Photon Source APS with an incident energy of 21 keV. The
experimental methods and data analysis procedures were
those used previously for liquid Al
2
O
3
,
21
Si,
22
and SiGe.
23
The present measurements were made on samples of 2.5 mm
PHYSICAL REVIEW B 79, 134201 2009
1098-0121/2009/7913/1342015 ©2009 The American Physical Society 134201-1