Study of pressure-induced amorphization of minerals by low-frequency Raman and Fourier transform spectroscopies |
||
We have investigated the proper monoclinic-triclinic
ferroelastic phase transition (FPT) in Sr-anorthite (Sr,Ca)Al2Si2O8
which may be viewed as an intermediate stage of amorphization. We have
tried to clarify the most general reason for elastic instability of the
crystals. It appears that for these low-symmetric phase transitions there
are still no analytical solutions in literature. According to the Landay
theory of the phase transitions, it is postulated that the coefficient at
quadratic member of the expansion is zero at the critical value of the
external variable parameter, i.e., the cause of the soft mode occurrence
is not explained. As a result, it was not possible to obtain a correct
physical description of the FPT. In order to clarify these mechanisms, we
propose a simple valence force model, in which it is shown that the
mechanism causing the occurrence of the soft mode is the earlier neglected
linear-quadratic coupling of static symmetric and dynamic asymmetric
components of the strain tensor. The surprising thing was that only the
"kinematic" anharmonicity leads, if all other anharmonicities are
neglected, to decreasing with pressure of the sound velocity
corresponding to the soft mode. This anharmonic contribution occurs due
to a nonlinear relation between the curvilinear space of q-coordinates of
interatomic separation and x-space of the Cartesian atomic displacements,
when the hydrostatic pressure is applied to a ferroelastic. We have also
obtained the equation with whose help we can for the first time predict
the phase transition pressure if the initial elastic moduli are known.
We also have made lattice dynamics calculations of the
soft modes, causing phase transitions in natrolite
Na16[Al16Si24O80]16H2O using the valence force field model. According to
the calculations in the interatomic potentials model, natrolite should
become amorphous at 5 Gpa. We have investigated the dynamic and static
mechanisms of the pressure-induced amorphization of the number of frame
minerals. We have obtained the equation which can describe the
amorphization. We have also revealed some universal laws of the
amorphization mechanisms. It turned out that berlinite, quartz and
natrolite behave like anorthite at transition from different symmetry
phases to the triclinic one. According to the Landay theory of the phase
transitions, it is postulated that the coefficient at quadratic member of
the expansion is zero at the critical value of the external variable
parameter, i.e., it is not explained in detail. It is assumed, that this
coefficient is coupled with the elastic constants. What actually happens
is that this coefficient is the product of the elastic-constant matrix and
the kinematic coefficients matrix, which are responsible for the behaviour
of normal modes of a crystal. On the basis of the analysis made, using the
"ball-and-perfect springs" model, we come to a conclusion, that the basic
mechanism causing the proper phase transitions in some crystals is the
"kinematic" anharmonicity. This anharmonicity is coupled with the
transition from the natural curvilinear atomic q-coordinates (interatomic
bonds and angles between them) to the Cartesian coordinates of the atomic
displacements. The coincidence between our equation and experiment has
appeared to be unexpected, since this means, that predominantly
"kinematic" anharmonicity brings about a decrease of the sound velocity
with pressure, when all other anharmonicities are neglected. We believe
that it is possible to obtain similar equations for the phase transitions
in other crystals if we use combinations of the elastic moduli, expressing
the elastic stability conditions to be appropriate for the transitions in
these crystals as well as the mechanism of the softening of the shift
moduli considered in the present work. This mechanism is based on the fact
that each shift modulus linearly falls with pressure, which is in line
with the "kinematic" anharmonicity. We have investigated the dynamic and static mechanisms of
the amorphization of the number of frame minerals induced by
external pressure and also by cation exchange. It has been found that the
internal stress tensor, generated by the cation exchange, is of a more
complicated nature than the tensor of the external stress. This difference
comes from a specific coupling of the substituting cations with local,
microscopic displacements of the neighbouring atoms inside the unit cell.
It becomes evident why in a number of experiments a significant difference
in the action of internal and external pressures on the crystal structure
is observed and, also, why the internal pressure causes the greater
anisotropy than the external one. We have obtained the equation which can
describe the amorphization. We have also revealed some universal laws of the
amorphization mechanisms. We have shown, that transition in the
amorphous phase of the anorthite, berlinite, quartz and natrolite is
described by the common equation, which we have received considering the
microscopic model of the phase transition. On the basis of the analysis
made, using the "ball-and-perfect springs" model, we come to a conclusion,
that the basic mechanism causing the proper phase transitions in some
crystals is the "kinematic" anharmonicity. This anharmonicity is coupled
with the transition from the natural curvilinear atomic q-coordinates
(interatomic bonds and angles between them) to the Cartesian coordinates
of the atomic displacements. We believe that it is possible to obtain
similar equations for the phase transitions in other crystals if we use
combinations of the elastic moduli, expressing the elastic stability
conditions to be appropriate for the transitions in these crystals as well
as the mechanism of the softening of the shift moduli considered in the
present work.
|