Network rigidity in GeSe2 glass at high pressure
Sytle M. Antao1*, Chris J. Benmore1, Baosheng Li2, Liping Wang2, Evgeny Bychkov3, and John B.
Parise2
1
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Mineral Physics Institute & Department of Geosciences, Stony Brook University, Stony Brook, NY 11794-2100,
USA
3
LPCA, UMR 8101 CNRS, Université du Littoral, 59140 Dunkerque, France
2
Gradual structural transitions in glasses, which
occur via continuous changes in density, are inherently
difficult to identify due to their disordered nature. Such
transitions may often be hidden in glass diffraction data
although they are important throughout the field of
materials science. Acoustic techniques, however, can be
applied to a variety of materials to identify phase
transitions (especially second order or higher) and obtain
elastic properties of solid bulk materials. While the
measured compressional velocities can be linked to
density changes in the glass, shear waves in glasses
provide an insight into network rigidity and this is
demonstrated most dramatically with the application of
pressure (P) [1].
State-of-the-art ultrasonic
interferometry offers direct measurements of sound
velocities, and hence, elastic properties. Large-volume
multi-anvil apparatus, with simultaneous P generation
and ultrasonic measurements, have been used to observe
the effect on shear (S) and compressional (P) -wave
Fig. 1 Dominant densification mechanisms in
velocities during the densification process in amorphous
GeSe2 up to pressures of 9.6 GPa. While S-waves are not
GeSe2 glass at high pressure.
readily transmitted through a liquid, they are sensitive to
network rigidity in a solid glass (or frozen liquid).
Equation-of-state measurements show a gradual
increase in the density of GeSe2 glass under P, up to 33 %
at 8.5 GPa [2]. Similarly, ab initio molecular dynamics
simulations predict gradual structural changes in GeSe2 glass with P, accompanied by a reduction in
chemical disorder up to 13 GPa [3]. Raman studies have indicated that a conversion of edge-to-corner
sharing tetrahedra is the dominant densification mechanism up to 3 GPa, beyond which the edge/corner
sharing ratio remains constant (Fig. 1) [4]. High-energy X-ray diffraction experiments up to 9.6 GPa have
shown that a gradual increase in average coordination number occurs with increasing P, and this process
is expected to dominate at P > 4 GPa. Furthermore, the conversion from tetrahedra to higher-order
polyhedra are accompanied by an elongation of the mean Ge-Se bond length, together with an increase in
extended-range order [5].
A minimum observed in the shear-wave velocity, associated anomalous behaviour in Poisson’s
ratio, and discontinuities in elastic moduli at 4 GPa are indicative of a gradual structural transition in the
glass (Fig. 2). This is attributed to a network rigidity minimum originating from a competition between
two densification mechanisms. At pressures up to 3 GPa, a conversion from edge-to-corner sharing
tetrahedra results in a more flexible network. This is contrasted by a gradual increase in coordination
number with P, which leads to an overall stiffening of the glass. On depressurization, both velocities
2
decrease irreversibly to ambient P due to permanent densification, and no minima is observed in VS. The
minimum observed in VS but not in VP suggests a different densification process in GeSe2 network glass
compared to that of SiO2. The main difference is attributed to the conversion of edge- to corner- sharing
tetrahedra in GeSe2 glass up to 3 GPa which reduces the degree of cross-linking in the network to a
minimum despite the continuous increase in density. The type of data from the current measurements
provide important information on interpreting changes in the macroscopic properties of glasses with
pressure when combined with structural data.
4.0
0.30
Poisson's ratio
VP/(km/s)
3.8
3.6
3.4
3.2
3.0
2.8
a
2.6
2
4
6
8
0.25
0.20
0.15
0.10
c
0.05
8
10
P/GPa
L
K
G
35
1.9
100
80
30
25
1.8
20
L
60
K
40
20
1.7
b
2
4
6
P/GPa
8
10
15
d
G
2
4
6
8
10
P/GPa
Fig. 2 Variations with pressure. a, VP, b, VS, c, Poisson’s ratio, and d,
elastic moduli. Solid symbols are data on pressurization and open
symbols are data on depressurization. Lines in a-c are polynomial fits
as guides to the eye. In d, linear trend lines are fit to the data above and
below 4 GPa (G = shear or rigidity modulus =  VS2; K = bulk modulus
4
= K =  ( VP2  VS2 ) ; and L = longitudinal modulus =  VP2). At 4.6
3
GPa, there are abrupt increases in K and L, whereas G shows a
significant slope change. These discontinuities in elastic moduli are
indicative of a second-order transition.
K or L/GPa
G/GPa
2.0
VS/(km/s)
6
4
2
10
P/GPa
3
ACKNOWLEDGEMENTS
This study was supported by NSF grants EAR-0510501 and DMR-0452444 to JBP, and
DoE/NNSA (DEFG5206NA26211) to BL. The experimental work was performed at X17B2 of the
National Synchrotron Light Source (NSLS), supported by the U.S. Department of Energy, Division of
Materials Sciences and Division of Chemical Sciences, under Contract No. DE-AC02-98CH10886. This
research was partially supported by COMPRES, the Consortium for Materials Properties Research in
Earth Sciences under NSF Cooperative Agreement EAR 01-35554.
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PUBLICATION
Antao, S.M., Benmore, C.J., Li, B., Wang, L., Bychkov, E., and Parise, J.B. (2008): Network rigidity in
GeSe2 glass at high pressure. Physical Review Letters, 100, 115501.
FOR MORE INFORMATION
Sytle M. Antao
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Email: sytle.antao@anl.gov