It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

Free Energy of a Nonuniform System. I. Interfacial Free Energy

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

An overview of the state of art in ferroelectric thin films is presented. First, we review applications: microsystems' applications, applications in high frequency electronics, and memories based on ferroelectric materials. The second section deals with materials, structure (domains, in particular), and size effects. Properties of thin films that are important for applications are then addressed: polarization reversal and properties related to the reliability of ferroelectric memories, piezoelectric nonlinearity of ferroelectric films which is relevant to microsystems' applications, and permittivity and loss in ferroelectric films-important in all applications and essential in high frequency devices. In the context of properties we also discuss nanoscale probing of ferroelectrics. Finally, we comment on two important emerging topics: multiferroic materials and ferroelectric one-dimensional nanostructures. (c) 2006 American Institute of Physics.

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Ferroelectric thin films: Review of materials, properties, and applications

The entanglement concept in polymer rheology

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Domain wall nanoelectronics

It has been verified by means of the polarization microscope that rochelle salt in the ferroelectric state consists of many domains. The domain structure in an annealed crystal is caused by the electrostatic self energy. When the electric field along the $X$ direction is increased and then decreased gradually, successive positions of the domain wall produce a hysteresis loop, which proves the existence of a restoring force on the wall. This restoring force causes lag of charging, and its variation with time produces a fatigue effect. The propagation velocity of a domain wall is about 0.2 cm/sec for 100 v/cm. A group of domains parallel to the $b$ axis has been created artificially. When a stress ${Y}_{z}$ is applied, a set of domains inverts its polarization direction. $Z$-cut specimens of K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ cooled below the Curie temperature divide into many regions which appear to be domains. The phase transition in K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ propagates from only one nucleus.Theoretically it has been concluded that the domain wall energy of rochelle salt is $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{{P}_{0}}^{3}$ erg/${\mathrm{cm}}^{2}$ and the wall width $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}/{P}_{0}$ cm, where ${P}_{0}$ is the saturation polarization.

Domain Structure of Rochelle Salt and K H 2 P O 4

It has been tried to classify newly discovered ferroelectrics as well as old ones according to their Curie-Weiss constants. Results have suggested that the displacive type ferroelectrics are not necessarily oxide crystals, and have also shown that small Curie-Weiss constants are not very rare in new ferroelectrics. Classification of ferroelectrics by the transition entropy is misleading in some cases.

A Note on the Classification of Ferroelectrics

Domain Structure of Rochelle Salt

Horner et al's method of dielectric measurement at microwave region has been extended so that it can be applied for cylindrical specimens of arbitrary cross-sections with relatively high loss tangent and high permittivity. Small amount of Specimen is good enough for our method. As the first application of our method, dielectric constants of BaTiO 3 single crystal have been measured from room temperature to 170°C at a frequency of 3.3KMc/s. Above the Curie point, dielectric constants measured at 3.3KMc/s agree well with those measured at 24KMc/s by Benedict and Durand, while the loss tangents slightly above the Curie point are 0.01±0.007 in our case compared to 0.1 in the case of Benedict and Durand.

Measurement of Microwave Dielectric Constants of Ferroelectrics

Diffuse streaks of the X-ray diffraction fiber pattern of polyoxymethylene have been observed at room temperature They were found to be unobservable at -170°C, the lowest temperature in this study The existence of anisotropic diffuse streaks suggests that a special type of disorder exists in the crystal Intensity measurements of the Bragg reflections were carried out over the temperature range from -150°C to room temperature NMR measurements were also carried out Comparison of NMR and X-ray results lead to the conclusion that rotational or twisting thermal motion around the chain axis begins at above -110°C in the crystalline region; the fluctuation of the atomic position around the helical axis was estimated at about 14° at room temperature

Jiro Furuichi

Papers

Domain Structure of Rochelle Salt and K H 2 P O 4

A Note on the Classification of Ferroelectrics

Domain Structure of Rochelle Salt

Measurement of Microwave Dielectric Constants of Ferroelectrics

Thermal Motion of Polyoxymethylene in Crystalline Region. I