Properties of Phase transitions of a Higher Order

The following is a thermodynamic analysis of a III order (and some aspects of a IV order) phase transition. Such a transition can occur in a superconductor if the normal state is a diamagnet. The equation for a phase boundary in an H-T (H is the magnetic field, T, the temperature) plane is derived. by considering two possible forms of the gradient energy, it is possible to construct a field theory which describes a III or a IV order transition and permits a study of thermal fluctuations and inhomogeneous order parameters.Comment: 13 pages, revtex, no figure

Defect driven flexo-chemical coupling in thin ferroelectric films

Using Landau-Ginzburg-Devonshire theory, we considered the impact of the flexoelectro-chemical coupling on the size effects inpolar properties and phase transitions of thin ferroelectric films with a layer of elastic defects. We investigated a typical case, when defects fill a thin layer below the top film surface with a constant concentration creating an additional gradient of elastic fields. The defective surface of the film is not covered with an electrode, but instead with an ultra-thin layer of ambient screening charges, characterized by a surface screening length. This geometry is typical for the scanning probe piezoelectric force microscopy. Obtained results revealed an unexpectedly strong effect of the joint action of Vegard stresses and flexoelectric effect (shortly flexo-chemical coupling) on the ferroelectric transition temperature, distribution of the spontaneous polarization and elastic fields, domain wall structure and period in thin PbTiO3 films containing a layer of elastic defects. A nontrivial result is the ferroelectricity persisting at film thicknesses below 4 nm, temperatures lower than 350 K and relatively high surface screening length (~0.1 nm). The origin of this phenomenon is the re-building of the domain structure in the film (namely the cross-over from c-domain stripes to a-type closure domains) when its thickness decreases below 4 nm, conditioned by the flexoelectric coupling and facilitated by negative Vegard effect. For positive Vegard effect, thicker films exhibit the appearance of pronounced maxima on the thickness dependence of the transition temperature, whose position and height can be controlled by the defect type and concentration. The revealed features may have important implications for miniaturization of ferroelectric-based devices.Comment: 25 pages, 9 figure

Theory of a Higher Order Phase Transition: Superconducting Transition in BKBO

We describe here the properties expected of a higher (with emphasis on the order fourth) order phase transition. The order is identified in the sense first noted by Ehrenfest, namely in terms of the temperature dependence of the ordered state free energy near the phase boundary. We have derived an equation for the phase boundary in terms of the discontinuities in thermodynamic observables, developed a Ginzburg-Landau free energy and studied the thermodynamic and magnetic properties. We also discuss the current status of experiments on $Ba_{0.6}K_{0.4}BiO_3$ and other $BiO_3$ based superconductors, the expectations for parameters and examine alternative explanations of the experimental results.Comment: 18 pages, no figure

Modeling of grain boundary dynamics using amplitude equations

We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both $\langle100\rangle$ and $\langle110\rangle$ coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations.Comment: 21 pages. We extended the discussion on the geometrical nonlinearities in Section

Perturbative calculation of the scaled factorial moments in second-order quark-hadron phase transition within the Ginzburg-Landau description

The scaled factorial moments $F_q$ are studied for a second-order quark-hadron phase transition within the Ginzburg-Landau description. The role played by the ground state of the system under low temperature is emphasized. After a local shift of the order parameter the fluctuations are around the ground state, and a perturbative calculation for $F_q$ can be carried out. Power scaling between $F_q$'s is shown, and a universal scaling exponent $\nu\simeq 1.75$ is given for the case with weak correlations and weak self-interactions.Comment: 12 pages in RevTeX, 12 eps figure