A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from fractional coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.

VESTA: a three-dimensional visualization system for electronic and structural analysis

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

A large body of work has been reported in the last 5 years on the development of lead-free piezoceramics in the quest to replace lead–zirconate–titanate (PZT) as the main material for electromechanical devices such as actuators, sensors, and transducers. In specific but narrow application ranges the new materials appear adequate, but are not yet suited to replace PZT on a broader basis. In this paper, general guidelines for the development of lead-free piezoelectric ceramics are presented. Suitable chemical elements are selected first on the basis of cost and toxicity as well as ionic polarizability. Different crystal structures with these elements are then considered based on simple concepts, and a variety of phase diagrams are described with attractive morphotropic phase boundaries, yielding good piezoelectric properties. Finally, lessons from density functional theory are reviewed and used to adjust our understanding based on the simpler concepts. Equipped with these guidelines ranging from atom to phase diagram, the current development stage in lead-free piezoceramics is then critically assessed.

Perspective on the Development of Lead-free Piezoceramics

Statistical physics of vehicular traffic and some related systems

It has turned out that the applied electric field is a powerful tool to clarify the transition mechanism of relaxor ferroelectrics. Kutnjak et al. have disclosed the existence of the critical end point in the temperature–field phase diagrams of a typical relaxor material Pb(Mg1=3Nb2=3)O3– PbTiO3, 1) and Iwata et al. have presented detailed and semiquantitative analyses of such phase diagrams, based upon the Landau free energy, where they took into account the terms up to the sixth order in the polarization. However, the reality regarding the perovskite-type oxide ferroelectrics may be more complicated, as can be easily guessed from the monoclinic phase discovered in the vicinity of the morphotropic phase boundary in the PbTiO3–PbZrO3 system. It is well known that in the free energy expansion by the polarization the terms up to the eighth order are required to reproduce the monoclinic phase. Therefore, a doubt may be cast on the validity of our previous analysis. The phase transitions reproduced by the Landau free energy, where the expansion is terminated at the eighth order, have been discussed from time to time, but it seems that the critical end point has never been considered so far. Under this circumstance, it seems meaningful to discuss the critical end point in detail based on a simple Landau free energy expanded up to the eighth order. We write the free energy as

Comments on the Critical End Point in Relaxor Ferroelectrics under the Applied Field

The existence of conical points in the dispersion relation in some hexagonal system is group-theoretically discussed. Invariants, including the Lifshitz invariant and the domain wall invariant, are obtained for the representation responsible for the appearance of the conical point. The phase transitions into the incommensurate and commensurate phases induced by the instability of such representation are discussed.

Conical Points in the Dispersion Relation and Related Phase Transitions

Mitsui's local field model of phase transitions in Rochelle salt is reexamined. The region for β and β', Lorentz factors, which yield spontaneous polarization only in intermediate temperatures, is extended. The cases that Mitsui treated where β and β' are both positive are included as a part of the present result. It has turned out that the sum of β and β' must be positive in order that a ferroelectric phase should appear either at low temperature side or at some intermediate temperatures.

The Role of Lorentz Factors in Rochelle Salt

The structure of the 90°-wall in the tetragonal phase of BaTiO 3 -type ferroelectrics is studied on the basis of the Landau free energy. The wall thickness of the 90°-wall is found to be much thicker than the one for the 180°-wall.

The 90°-wall in the tetragonal phase of BaTiO3-type ferroelectrics

The field-induced phase transition between the rhombohedral and tetragonal phases was investigated in Pb(Zn1/3Nb2/3)O3–8%PbTiO3 by dielectric constant and electrostriction loop measurements. The temperature-electric-field phase diagram was clarified, and physical properties near the field-induced phase transition were discussed using the Landau-type free energy function.

Yoshihiro Ishibashi

Papers

Comments on the Critical End Point in Relaxor Ferroelectrics under the Applied Field

Conical Points in the Dispersion Relation and Related Phase Transitions

The Role of Lorentz Factors in Rochelle Salt

The 90°-wall in the tetragonal phase of BaTiO3-type ferroelectrics

Field-Induced Phase Transition between Tetragonal and Rhombohedral Phases in Pb(Zn1/3Nb2/3)O3–8%PbTiO3