Material ferroelectric

Gq(T) being the free energy of the paraelectric state. For small deformations, m , the interaction potential between the ions, can be considered as harmortic  

The ferroelectric state is therefore stable for temperatures less than T. Let us note that everything takes place as though there was an apparent stiffness In the paraelectric phase, the frequency of one of the vibration modes of the lattice, referred to as soft mode  

Spontaneous polarization is the polarization that minimizes the free energy. For T = T, G = Gg, which shows the inadequacy of a Taylor expansion limited to the order. We must take into account the inharmonic contribution to the elastic energy, keeping only to even order terms, the polarizations and -P being equally 

Susceptibility therefore varies with temperature according to the Curie-Weiss 

It can also be proved that transition is of the second order. To explain a first order transition, as experimentally observed for barium titanate and several other oxides [XU 91], the free energy has to be expanded up to sixth order term. The previous relations still hold good on the condition of replacing T by T, (slightly lower than T ). 

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Smolyaninov I P, Zayats A V and Davis C C 1997 Near-field second-harmonic imaging of ferromagnetic and ferroelectric materials Opt. Lett. 22 1592-4... 

Oxygen Octahedra. An important group of ferroelectrics is that known as the perovskites. The perfect perovskite stmcture is a simple cubic one as shown in Figure 2, having the general formula ABO, where A is a monovalent or divalent metal such as Na, K, Rb, Ca, Sr, Ba, or Pb, and B is a tetra- or pentavalent cation such as Ti, Sn, Zr, Nb, Ta, or W. The first perovskite ferroelectric to be discovered was barium titanate [12047-27-7] and it is the most thoroughly investigated ferroelectric material (10). 

Ferroelectric Ceramic—Polymer Composites. The motivation for the development of composite ferroelectric materials arose from the need for a combination of desirable properties that often caimot be obtained in single-phase materials. For example, in an electromechanical transducer, the piezoelectric sensitivity might be maximized and the density minimized to obtain a good acoustic matching with water, and the transducer made mechanically flexible to conform to a curved surface (see COMPOSITE MATERIALS, CERAMiC-MATRix). 

Piezoelectric and Electrostrictive Device Applications. Devices made from ferroelectric materials utilizing their piezoelectric or electrostrictive properties range from gas igniters to ultrasonic cleaners (or welders) (72). 

Barium carbonate also reacts with titania to form barium titanate [12047-27-7] BaTiO, a ferroelectric material with a very high dielectric constant (see Ferroelectrics). Barium titanate is best manufactured as a single-phase composition by a soHd-state sintering technique. The asymmetrical perovskite stmcture of the titanate develops a potential difference when compressed in specific crystallographic directions, and vice versa. This material is most widely used for its strong piezoelectric characteristics in transducers for ultrasonic technical appHcations such as the emulsification of Hquids, mixing of powders and paints, and homogenization of milk, or in sonar devices (see Piezoelectrics Ultrasonics). 

Ferroelectrics. Ferroelectrics, materials that display a spontaneous polarization ia the abseace of an appHed electric field, also display pyroelectric and piezoelectric behavior. The distinguishing characteristic of ferroelectrics, however, is that the spontaneous polarization must be re-orientable with the appHcation of an electric field of a magnitude lower than the dielectric breakdown strength of the material. 

Ferroelectric Thin-Film Devices. Since 1989, the study of ferroelectric thin films has been an area of increasing growth. The compositions studied most extensively are in the PZT/PLZT family, although BaTiO, KNbO, and relaxor ferroelectric materials, such as PMN and PZN, have also been investigated. Solution deposition is the most frequentiy utilized fabrication process, because of the lower initial capital investment cost, ease of film fabrication, and the excellent dielectric and ferroelectric properties that result. 

Ferroelectrics. In the preceding section, positive-temperature-coefficient (PTC) ceramics were mentioned and it was remarked that they are made of a ferroelectric material. 

B01 F. Bauer, U.S. Patent, No. 4,611,260, Method and Device for Polarizing Ferroelectric Materials, September 9, 1986. 

Tantalum and niobium are added, in the form of carbides, to cemented carbide compositions used in the production of cutting tools. Pure oxides are widely used in the optical industiy as additives and deposits, and in organic synthesis processes as catalysts and promoters [12, 13]. Binary and more complex oxide compounds based on tantalum and niobium form a huge family of ferroelectric materials that have high Curie temperatures, high dielectric permittivity, and piezoelectric, pyroelectric and non-linear optical properties [14-17]. Compounds of this class are used in the production of energy transformers, quantum electronics, piezoelectrics, acoustics, and so on. Two of... 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

The main source of spontaneous polarization in crystals is the relative freedom of cations that fit loosely into the crystal s octahedral cavities. The number of degrees of freedom of the octahedrons affects the spontaneous polarization value and hence influences the crystal s ferroelectric properties. Abrahams and Keve [389] classified ferroelectric materials into three structural categories according to their atomic displacement mechanisms onedimensional, two-dimensional and three-dimensional. 

Yu. Xu, Ferroelectric materials and their applications, Elsevier Science Publishers B.V., North-Holland, Amsterdam, 1991. 

A.P. Leonov, S.Yu. Stephanovich, Preparation and application of ferroelectric materials, Nauka, Moscow, 1984, p. 21 (in Russian). 

Lead titanate (PbTi03) is a ferroelectric material with unusual pyroelectric and piezoelectric properties. It is deposited by MOCVD from ethyl titanate and lead vapor in oxygen and nitrogen at 500-800°C.[42]... 

Another ferroelectric material is bismuth titanate, (Bi4Ti30i2), which is deposited from triphenyl bismuth, Bi(C5H5)3, and titanium isopropoxide at low pressure (5 Torr) and at temperatures of 600-800°C.[43]... 

Ferroelectric materials are capable of being polarized in the presence of an electric field. They may exhibit considerable anomalies in one or more of their physical properties, including piezoelectric and pyroelectric coefficients, dielectric constant, and optoelectronic constant. In the latter case, the transmission of light through the material is affected by the electric field, which produces changes in refractive index and optical absorption coefficient. Varying the applied field changes the phase modulation. 

Important ferroelectric materials are those with piezoelectric characteristics. They are crystalline ceramics that exhibit expansion along one crystal axis and contraction along another when subjected to an electrical field. Conversely, compression generates an electrical voltage across the material. These materials have a large number of industrial applications. 

CVD-derived powders may prove very useful and profitable in the production of bulk ferroelectric materials which are produced by hot-pressing or sintering. These powders offer great uniformity, small particle size, and high reactivity (see Ch. 19). 

Holzer, F., Kopinke, F.D. and Roland, U. (2005) Influence of ferroelectric materials and catalysts on the performance of non-thermal plasma (NTP) for the removal of air pollutants, Plasma Chem. Plasma Processing 25, 595-611. 

Some perovskites are widely used as piezo-transducers, BaTi03 for example, and lead zirconate (PbZr03) which is a well-known ferroelectric material sensitive to stresses. Also, some perovskites are good pyro-transducers that is, heat causes electric polarization of them. 

Liquid Crystal Displays (LCD). Liquid crystal displays, once limited to small devices such as calculators, are now displacing color CRT (cathode ray tube) displays in commercial quantities. The ability to fabricate these display devices at high quality and at low cost is partially due to the wider spread use of photopolymer-based materials. Photopolymer technology is being used for the alignment of liquid crystal (LC) elements (49), the orientation of ferroelectric materials (50), the synthesis of LC polymers (57) and the manufacture of color filters for liquid crystal display applications (52). 

Since P must remain normal to z and n, the polarization vector forms a helix, where P is everywhere normal to the helix axis. While locally a macroscopic dipole is present, globally this polarization averages to zero due to the presence of the SmC helix. Such a structure is sometimes termed a helical antiferroelectric. But, even with a helix of infinite pitch (i.e., no helix), which can happen in the SmC phase, bulk samples of SmC material still are not ferroelectric. A ferroelectric material must possess at least two degenerate states, or orientations of the polarization, which exist in distinct free-energy wells, and which can be interconverted by application of an electric field. In the case of a bulk SmC material with infinite pitch, all orientations of the director on the tilt cone are degenerate. In this case the polarization would simply line up parallel to an applied field oriented along any axis in the smectic layer plane, with no wells or barriers (and no hysteresis) associated with the reorientation of the polarization. While interesting, such behavior is not that of a true ferroelectric. 

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

Ferroelectric effect, smart materials exhibiting, 22 709-710, 721t Ferroelectric LCDs, 15 115 Ferroelectric materials, 11 94—98. 

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