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.