ON THE Si-O-Si BOND ANGLE IN α- AND β -QUARTZ

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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 α- AND β -QUARTZ.

Journal de Physique Colloques, 1981, 42 (C6), pp.C6-752-C6-754. �10.1051/jphyscol:19816221�. �jpa-

00221305�

JOURNAL DE

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

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ILL GrenobZe, France

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** IFF-XFA JiiZich, F.R.

Abstract.- The structural change from a to @-quartz is accompa- nied 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 te- trahedraassuming that the tedrahedra stay undeformed at all temperatures.

The a-phase is produced out of the 6-phase by rotations of the tetra- hedra 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 ex- perimentally /3/, could be calculated in perfect agreement including the coupling of the secondary order parameter. But the temperature de- pendence 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

Quartz

Fig. 1: Lattice expansion.

model /5/ of rigid Si04 tetrahedra, in 6-quartz for the disordered structure; - - - -

for the ideal 8-phase* -- ^ex-

perimental data /6/.

'"0 100 200 300 LOO 500 600 700

TEMPERATURE

1

Apparently the lattice expands less than predicted from the model.

Note that the usual thermal expansion by anharmonicity is ndt con- sidered 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 tetrahe- dra 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 Si- 0-Si plane with a small restoring force.

Recently we discovered another strongly temperature dependent mode at the M points

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 calcu- lation 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 tempera- ture, this means that the BA has smaller amplitudes at higher tempera- ture. 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

DE

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 compo- nents 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

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 Si- atom. The speculation does not explain why the 6-phase has a slightly disordered structure /I I/ with a BA

150. lo rather than 153.1

. ^On

the other hand this increasing contribution of n-bond character ex- plains the fact that the tetrahedra shrink with increasing temperature because the n-bond tightens the Si-0 bond.

/1/ S.M. Shapiro, D.C. O'Shea and H.Z. Cumrnins; Phys. Rev. Lett. 19,

361 (1967)

/2/ J.F. Scott; Phys. Rev. Lett. 21, 907 (1968)

/3/ J.D. Axe and G. Shirane; Phys. Rev. e, 342 (1970)

/4/ R.A. Young; Air Force Office of Scientific Res. Rep. 2569 (1962) /5/ H. Grimm and B. Dorner; J. Phys. Chem. Solids 36, 407 (1975) /6/ C.A. Sorrell, H.U. Anderson and R.J. Ackermann; J. Appl. Cryst.

7, 468 (1974)

-

/7/ H-Boysen, B. Dorner, F. Frey and H. Grimm; J. Phys. C 13, 6127 (1 980)

/8/ T.H.K. Barron, C.C. Huang, and A. Pasternak; J. Phys. C 9 , ³⁹²⁵

(1976)

/9/ B. Dorner, H. G r i m and H. Rzany; J. Phys. C, 13, 6607 (1980) /lo/ D.W.J. Cruickshank; J. Chern. Soc. 1077, 5486 (1961)

/11/ A.F. Wright and M. Lehrnann; J. Solid St. Chem.