High-pressure twisting of tetrahedra and amorphization in -quartz
N. N. Ovsyuk* and S. V. Goryainov
Institute of Mineralogy and Petrology, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Received 30 July 1999
It is discovered that the major contribution to the distortions of the tetrahedra in the -quartz at high pressure
is their twisting. It is shown that just these twisting vibrational modes lead to instability resulting in amor-
phization of the structure. S0163-18299900745-6
Recently, a large number of computer simulations of the
-quartz structure at high pressures have been made.
1–6
Sig-
nificant distortions of SiO
4
tetrahedra should be taken into
account in these simulations when the relations between
various microscopic parameters become numerous and com-
plex. In this case, it is difficult to understand what sort of
structure transformations are responsible for the dominant
mechanisms of tetrahedral deformation. In order to clarify
these mechanisms, we propose a simple valence force model,
in which only two order parameters, most sensitive to pres-
sure, have been distinguished. The tilt angle of SiO
4
tetrahe-
dra is one of the two parameters, which was detected previ-
ously. It is commonly used to describe - phase transition
of quartz.
7
This angle is the main parameter of structure de-
formation at high pressure, and it is assumed to lead to in-
stability, resulting in amorphization.
8,9
We have found the
second parameter, carefully analyzing numerous parameters
of tetrahedral distortions, mentioned in the literature. We
have discovered that these parameters can be reduced to a
single parameter, i.e., the twist angle of tetrahedra. Earlier
this angle was not considered as the order parameter at high
pressures. The twist angle of tetrahedra can be defined as
deviation from a 90° angle between two opposite symmetri-
cal tetrahedron edges in -quartz. As a result, we have man-
aged to reveal some peculiarities, unnoticed in numerical cal-
culations, i.e., the tilt angle at high pressures tends to
saturation; the twist angle, on the other hand, starts to change
nonlinearly. Therefore this is the angle which is mainly re-
sponsible for structure instability. This information seems to
be important; despite a considerable quantity of experimental
observations and theoretical simulations of -quartz amor-
phization at high pressure,
1–12
there is no correct description
of the microscopic origin of the softening of the phonon
modes, which are responsible for the elastic instability for
reasons which are further discussed.
Earlier developed models aimed at explanation of high-
temperature anomalies
13–16
cannot be used for the descrip-
tion of the process of -quartz amorphization, as they do not
take into account essential tetrahedra distortions. The param-
eters, related to the least force constants and, consequently,
readily varying with pressure, play the main role in the pro-
posed valence force model of -quartz deformation in which
the tetrahedra distortions are taken into account. For ex-
ample, if we speak about the main force constants, we should
bear in mind that Si-O bond constant is significantly greater
than O-Si-O angles force constant. The latter is significantly
greater than Si-O-Si angle force constant. Therefore as the
key parameters in our model we use the tilt angle, which is
related to the Si-O-Si angle force constant and the twist
angle, which is responsible for the deformation inside the
tetrahedra and is related to the O-Si-O angles force constant.
For the full description of the quartz structure it is necessary
to introduce four more parameters, i.e., two symmetrical
O-Si-O angles and two lengths of Si-O bonds. According to
the experimental data, these four parameters at high pres-
sures slightly change with increasing pressure,
17
thus they
are considered to be constant. All the parameters are relative
and measured from the parameters of ideal -quartz when
Si-O distance is equal to 1.599 Å . The calculation on the
available experimental structural data
17
shows the tilt angle
at pressures higher than 3 GPa to be 100 times greater than
the four above-mentioned parameters. The twist angle , de-
scribing the tetrahedra distortion, is about ten times greater
than these four small parameters. Therefore we will describe
the tetrahedra distortions only using the twist angle.
Only one tilt angle is commonly used to construct an ana-
lytical deformation model of the quartz structure.
7,13
Now let
us consider the Gibbs potential, which takes into account
both the twist angle and the tilt angle:
G =3 K
0
- -
0
-
m
2
+3 K
s
2
+ P
+ P v ,
1
where v =( V -V
0
)/ V
0
is a relative change of the volume of
an elementary cell, is Si-O-Si angle, K
and K
s
are force
constants in GPa of Si-O-Si and O-Si-O angles, respec-
tively. Here we have neglected small nondiagonal force con-
stants. P
is the internal pressure, which isothermally trans-
fers -quartz structure into -quartz structure.
18
This
potential takes into account the tense state of the structure of
ideal -quartz. It is due to the fact that Si-O-Si angle, at
which deformation is lacking, should be
m
=147°, but ac-
tually, the corresponding angle in the ideal -quartz is
0
=155.6°. Using v and expansions into and parameters
we obtain the Gibbs potential, in which the variable part is as
follows:
G =K
2
/2+K
2
/2-g
1
+g
2
2
+g
4
4
, 2
where all the coefficients are the pressure linear functions.
The equilibrium values and for the minimum of this
potential are equal to
= -K
-2 g
1
g
2
/ K
/ 4 g
4
-2 g
2
2
/ K
1/2
, 3
PHYSICAL REVIEW B 1 DECEMBER 1999-I VOLUME 60, NUMBER 21
PRB 60 0163-1829/99/6021/144814/$15.00 14 481 ©1999 The American Physical Society