Transition pathways connecting crystals and quasicrystals

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz–Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

Quasi-exact description of the γ-unstable shape phase transition

The equation of the [Formula: see text]-unstable Bohr Hamiltonian, with particular forms of the sextic potential in the [Formula: see text] shape variable, is exactly solved for a finite number of states. The shape of the quasi-exactly solvable potential is then defined by the number of exactly determined states. The effect of exact solvability order on the spectral characteristics of the model is closely investigated, especially, concerning the critical point of the phase transition from spherical to deformed shapes. The energy spectra and the [Formula: see text] transition probabilities, up to a scaling factor, depend only on a single-free parameter, while for the critical point, parameter-free results are available. Several numerical applications are done for nuclei undergoing a [Formula: see text]-unstable shape phase transition in order to identify critical nuclei based on the most suitable exact solvability order.

Кинетика зарождения жидкой фазы в растянутом ГЦК-кристалле: молекулярно-динамическое моделирование

The kinetics of a spontaneous formation of liquid phase in a stretched (superheated) Lennard-Jones fcc crystal is studied. Molecular dynamics experiments are used to determine the main parameters of the nucleation process: nucleation frequency J , diffusion coefficient of nuclei D _*, nonequilibrium Zel’dovich factor Z , and critical nucleus size R _*. The calculations are performed at negative pressures from the endpoint of the melting line and at positive pressures that are higher by a factor of eight than the critical pressure. The simulation results are compared to the classical homogeneous nucleation theory. It is found that the theory qualitatively correctly reproduces the dynamics of developing the process. The theory and the simulation demonstrate good quantitative agreement for the transition rate of the liquid phase nucleus through the critical size, but there is large difference in the numbers of critical nuclei in the unit volume of the metastable phase. In the case of significant superheatings and negative pressures, the contribution of the energy of elastic stresses to the moving force of the phase transformation is small and it can be neglected in a first approximation. The mismatch between the theory and the simulation results can be eliminated taking that the surface free energy of a curved “crystal–liquid droplet” interface is smaller than that of a plane interface by 30–35%.