THE INFLUENCE OF MECHANICAL STRESSES ON INCOMMENSURATE SUPERSTRUCTURES OF THIN-LAYER CRYSTALS

Abstract

The study of the influence of mechanical stresses on the incommensurate (IC) superstructure of fine-layer ferroelectric and ferroelastic crystals was performed

Phase portraits for crystals [N(CH₃)₄]₂MeCl₄ of the group А₂ВХ₄, with even n were constructed. If the symmetry of a potential energy is described by a even number n, then this crystal have a spontaneous polarization.

The construction of phase portraits was carried out in the Python software environment using the scipy library.

It was established that mechanical stresses lead to the deformation of the superstructure, the blocking of its appearance, and the appearance of commensurate long-periodic phases.

Simultaneous influence of both superficial and mechanical energy on the IC of the superstructure for ferroelectric (n = 4) and ferroelastic (n = 3) was considered. It arises if the value of the surface energy is commensurate with the energy of the incommensurate superstructure. Small values of mechanical stress lead to the deformation of the IC superstructure, which leads to the localization of the wave vector of the incommensurability on the higher order commensurate values. Further increase in the magnitude of mechanical stress leads to the appearance of chaos and blocking the IC modulation. Such an effect of the mechanical stress on the superconducting state is characteristic of both ferroelectric and ferroelastic crystals.

In the work it was assumed that in the near-surface layer, the surface energy is greater than the energy of the incommensurate superstructure, which causes its absence in the near-surface layer, and the origin of the latter when it passes into the bulk part of the crystal. When the linear dimensions of the crystal are reduced, the effect of the surface defective layer will increase as a result of the reduction of the bulk part of the crystal. When the energy of an incommensurate superstructure becomes equal to the surface energy in a thin-layer (or micro-sized) crystal, the transition from the inhomogeneous state to a homogeneous state was observed.

It was established that the influence of surface energy on an incommensurate superstructure in a limited-sized crystal reduces the spatial region of its existence, and also was reducing the number of existing harmonics of oscillations of the superstructure. Consequently, this is the main feature of the difference in the influence of surface energy on the IC structure, in relation to other external factors.

Key words: incommensurate superstructures, phase portraits, surface energy.