ON THE Si-O-Si BOND ANGLE IN α- AND β
-QUARTZ
B. Dorner, H. Boysen, F. Frey, H. Grimm
To cite this version:
B. Dorner, H. Boysen, F. Frey, H. Grimm. ON THE Si-O-Si BOND ANGLE IN αAND β -QUARTZ. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-752-C6-754.
<10.1051/jphyscol:19816221>. <jpa-00221305>
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Submitted on 1 Jan 1981
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JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment au no 12, Tome 42, decembre 1981
page
C6-752
ON THE Si-0-Si BOND ANGLE IN a- AND 6-QUARTZ
B. Dorner
, H.
Boysen
* , F.
Frey
*
and H. Grimm
**
ILL GrenobZe, France
"~nst.f. KristaZZographie, Univ. Miinchen, F.R.G.
JiiZich, F.R. G.
**IFF-XFA
Abstract.- The structural change from a to @-quartz is accompanied by an enlargement of the Si-0-Si bond angle with increasing
temperature. At the same time the Si04 tetrahedra shrink. The
speculative explanation is that with increasing temperature the
electron density on the Si atom adopts some d-type components.
The soft mode at r and another strongly temperature dependent
mode at M reflect the structural changes.
Quartz undergoes a structural phase transition of first order at 5 7 3 O ~
from a trigonal a-phase to the hexagonal 6-phase. The I'-point soft mode
in a-quartz and its temperature dependence was observed by Raman
scattering /1,2/. An eigenvector determination f3/ confirmed that the
mode at 6.25 THz at room temperature has the displacements as expected
from the strubtural change /4/ for the soft mode.
Grimm and Dorner /5/ conceived a model of regular rigid SiO4 tetrahedraassuming that the tedrahedra stay undeformed at all temperatures.
The a-phase is produced out of the 6-phase by rotations of the tetrahedra around two-fold axes which are parallel to the hexagonal plane.
The tilt angle 6 can be interpreted as the order parameter. The order
parameter connected to a first order hase transformation
was fitted to the structural data /4/. Here To is the temperature at
which the phase tranformation occurs. At T = Tc the coefficient of the
quadratic term in a Landau expansion of the free energy goes to zero.
6,is the step in the order parameter which appears at To. There are
two parameters to be fitted:bo = 7.3O and To - Tc = loOc. This model
is very successful as it describes the structural parameters, one for
Si and three for 0, versus temperature very well. The components of
the eisenvector of the soft mode at room temperature as determined experimentally /3/, could be calculated in perfect agreement including
the coupling of the secondary order parameter. But the temperature dependence of the lattice constants a and c /6/ differs strongly from the
predictions of the model, see Fig. 1.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816221
Z
2
1.03
Quartz
Fig. 1: Lattice expansion.
model /5/ of rigid Si04
tetrahedra,in 6-quartz for the
disordered structure; - - - for the ideal 8-phase*
experimental data /6/.
--
'"0
100
200
300
LOO
500
TEMPERATURE
600
[OC
700
1
Apparently the lattice expands less than predicted from the model.
Note that the usual thermal expansion by anharmonicity is ndt considered by the model. As the structure is built up by corner connected
tetrahedra, the only possible conclusion is that the tetrahedra shrink
with increasing temperature. Obviously the deformation of the tetrahedra is anisotropic and much stronger for components contributing to c.
Another important feature is the bond angle (BA) Si-0-Si being
143.6~ at room temperature and having a maximum possible within the
quartz structure, with 153.1° in the ideal B-structure. The soft mode
in the @-phaseloverdamped at all accessible temperatures /3/, has an
eigenvector which leaves the tetrahedra rigid and does not vary the BA.
This means that adjacent tetrahedra move only perpendicular to the Si0-Si plane with a small restoring force.
Recently we discovered another strongly temperature dependent mode
at the M points / 7 / . It softens from 3.61 THz at room temperature to
0.82 THz in the @-phase. An eigenvector determination revealed that
this mode in 6-quartz leaves the Si04 tetrahedra rigid and does not
bend the BA just like the real soft mode.
Model calculations /8/ included this bond angle force (essentially
a three body force) by a central force between Si-Si atoms. A calculation of the temperature dependence for the soft mode and for the mode
at the M-point /8/ was performed by using the force constants as fitted
at room temperature /9/ and inserting atomic positions corresponding
to the structure at each temperature. The calculated modes soften with
increasing temperature. An inspection of the calculated eigenvectors
showed that the Si-Si displacement got smaller with increasing temperature, this means that the BA has smaller amplitudes at higher temperature. Only in the B-phase the two modes do not bend the BA in the
Si-0-Si plane.
Very probably the Si-0-Si bonds play a dominant role in the struc-
C6-754
JOURNAL DE PHYSIQUE
tural changes of quartz. It has been suggested /lo/ that the electron
density on the Si atom may change with temperature such that from the
basic sp3 hybridisation some density becomes d-type. The d-type components would built n-bonds to the oxygen p-electrons leading to a 180°
BA while the sp3 hybridisation would produce a-bonds leading to a BA
near 900 if the structure would allow. This, speculation explains why the
BA increases to a maximum with temperature. The maximum (extremum) of
the BA is connected to a higher symmetric phase. Thus there has to
appear a phase transformation and as it is a displacive one, we expect
a soft mode. The driving mechanism is the electron density on the Siatom. The speculation does not explain why the 6-phase has a slightly
0
On
disordered structure /I I/ with a BA = 150. lo rather than 153.1
the other hand this increasing contribution of n-bond character explains the fact that the tetrahedra shrink with increasing temperature
because the n-bond tightens the Si-0 bond.
.
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