Mechanisms of phase transitions in a hexagonal model with 1q and 3q incommensurate phases.

Abstract

A hexagonal three-dimensional model of particles with displacive degrees of freedom and interacting via a potential energy with harmonic and anharmonic third- and fourth-order terms has been studied by the molecular-dynamics technique. The phase diagram of the mdoel exhibits normal, k=0 commensurate, one-dimensional (1q) and three-dimensional (3q) incommensurate phases. The 3q phase can be visualized as a sequence of columns, oriented along the unique hexagonal axis. The columns, in turn, form a hexagonal discommensuration lattice. At higher temperature the 3q incommensurate phase is more stable than the 1q phase. The simulation has shown that (i) the 1q\ensuremath{\rightarrow}k=0 phase transition is driven by the antistripples, which are topological defects of the stripe discommensuration lattice. (ii) During the 3q\ensuremath{\rightarrow}k=0 phase transition the columns are eliminated. The first eliminations occur at random places, the next ones rather close to already annihilated columns. (iii) The 1q\ensuremath{\rightarrow}3q phase transition, which keeps the modulation wavelength, is driven by anisotropic antistripples nucleated equidistantly on the discommensuration planes of the 1q phase. The 3q phase which appears may contain deperiodization (dislocation) loops, formed on the hexagonal discommensuration lattice. (iv) In the 3q\ensuremath{\rightarrow}1q phase transition, without a change of the modulation wavelength, the columns of 3q phase merge to each other to form a stripe of discommensuration plane. (v) The mechanism of the 3q\ensuremath{\rightarrow}3q' phase transition, with a change of modulation wavelength, involves three types of deperiodization loops.