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

Dielectric properties of (1-x)Pb(Sc1/2Ta1/2)O3(PST)–xPbZrO3 (PZ) (0 0.7, the permittivity er' exhibits a peak at the phase transition temperature Tc. With increasing x, the peak value decreased and Tt shifted towards the higher temperature region. The phase below Tc was confirmed to be ferroelectric by observation of P-E hysteresis loops. Phase transformation from the relaxor to the ferroelectric state occurred at x=0.7. For x>0.8, a steplike anomaly appeared at Tt below Tc. With increasing x, Tt shifted towards the higher temperature region. There was a structural change characterized by the splitting of the structure-sensitive maximum of the (200) reflection of XRD patterns, similar to orthorhombic PZ, around x=0.8. Two morphotropic phase boundaries were found: one between the pseudocubic and rhombohedral phases with erm' of 15000 at 100 kHz was at x=0.7, and the other between the rhombohedral and orthorhombic phases was at x=0.8.

Dielectric Properties of Solid Solutions (1-x)Pb(Sc1/2Ta1/2)O3–xPbZrO3 (0 < x < 1)

The dispersion relation in the hexagonal lattice is studied based on a simple model with the emphasis placed on the energy level crossing. By assuming the interactions between the nearest neighbors and second nearest neighbors, the analytical expression of the dispersion relation is shown. The level crossing at the Brillouin zone boundary is found to be due to the existence of the partial translation in the crystal structure. The appearance of the conical point crossing at the reciprocal lattice point k = (1/3, 1/3, 0) (the K-point) is reviewed from the group theoretical viewpoint.

Dispersion Relations near the Conical Point in Some Hexagonal Lattices

Microscopic Observations of Phase Transitions in CsPbCl3

Landau Theory of Phase Transition in Pyridinium Tetrafluoroborate Crystal

The third-order nonlinear susceptibility χ 3 in the paraelectric phase of finite ferroelectrics is theoretically studied on the basis of the Tilley–Zeks model. Using exact polarization profiles under an applied field, exact expressions of χ 3 can be derived. It has turned out that χ 3 in finite systems diverges as (α-α c ) -4 similarly to that in infinite systems, where α and α c represent the temperature and transition temperature, respectively.

Yoshihiro Ishibashi

Papers

Dielectric Properties of Solid Solutions (1-x)Pb(Sc1/2Ta1/2)O3–xPbZrO3 (0 < x < 1)

Dispersion Relations near the Conical Point in Some Hexagonal Lattices

Microscopic Observations of Phase Transitions in CsPbCl3

Landau Theory of Phase Transition in Pyridinium Tetrafluoroborate Crystal

Exact Expressions of Third-Order Nonlinear Susceptibility in Finite Ferroelectric Systems Based on the Tilley-Zeks Model