Barium titanate crystal structure

Szostak et al 52 have made calculations of the /Miyperpolarizability of 2-nitroaniline and 2 nitrophenol and for their radical ions and suggest that the latter might have a role in the nonlinear optical response. A localized orbital model of the response of the barium titanate crystal has been developed by Khatib et al 253 Lacroix et al.254 have performed INDO calculations on crystal structures for a highly polarizable zwitterionic merocyanine dye. 

The dielectric constant of barium titanate, along [001] is about 200 and along [100] it is 4000 at room temperature.3 The spontaneous polarization at room temperature is 26 X 10-6 C./cm.2, and the value of the coercive field has been found to vary from 500 to 2000 volts/cm. The crystal structure of barium titanate at room temperature can be represented by a tetragonal unit cell with size of a0 = 3.992 A., and c0 = 4.036 A., but the symmetry becomes cubic above 120°C., at which temperature the crystals no longer exhibit ferroelectric properties. 

In different temperature ranges, barium titanate BaTi03 exists in several stable phases. Table 10.4.2 lists the crystal data and properties of the polymorphic forms 0fBaTiO3, and Fig. 10.4.2 shows their structures. 

Barium titanate, the first ceramic material in which ferroelectric behaviour was observed, is the ideal model for a discussion of the phenomenon from the point of view of crystal structure and microstructure see also [10] and [11]. 

FIG. 13.1. The crystal structures of barium titanate, BaTiOa (a) hexagonal, (b) cubic. 

In contrast, the nonlinearities in bulk materials are due to the response of electrons not associated with individual sites, as it occurs in metals or semiconductors. In these materials, the nonlinear response is caused by effects of band structure or other mechanisms that are determined by the electronic response of the bulk medium. The first nonlinear materials that were applied successfully in the fabrication of passive and active photonic devices were in fact ferroelectric inorganic crystals, such as the potassium dihydrogen phosphate (KDP) crystal or the lithium niobate (LiNbO,) [20-22]. In the present, potassium dihydrogen phosphate crystal is broadly used as a laser frequency doubler, while the lithium niobate is the main material for optical electrooptic modulators that operate in the near-infrared spectral range. Another ferroelectric inorganic crystal, barium titanate (BaTiOj), is currently used in phase-conjugation applications [23]. 

Although correlation between parameters is a function of the data structure and has nothing to do with deficiencies in the model, it has implications for both the choice of the model and the design of the experiment. EVANS described his experiences with the determination of the crystal structure of tetragonal barium titanate (BaTiOa). The problem was ample in that it involved only three atomic positional parameters (one for Ti and two for 0), plus nine thermal parameters. There was considerable interest in the details of the structure because of the ferroelectric properties of the material. The proposed model was essentially a simple cubic arrangement of atoms, but with Ti displaced slightly from the center of an octahedron. By ordinary x-ray standards, this distortion (which was expected to be on the order of 0.15 A) could be measured with a standard error of 0.01-0.02 A if... 

Barium titanate is of particular interest, since it shows remarkable ferroelectric behavior. The reason for this is understood in terms of the structure. Here the ion, Ba2+, is so large relative to the small ion, Ti4+, that the latter can literally rattle around in its octahedral hole. When an electric field is applied to a crystal of this material, it can be highly polarized because each of the Ti4+ ions is drawn over to one side of its octahedron thus causing an enormous electrical polarization of the crystal as a whole. 

Barium titanate is cubic with a perovskite structure. However, at room temperature (actually below the Curie temperature of 120°C) it is tetragonal with a spontaneous electric polarization in the direction of the c-axis (only the higher temperatures form is shown in Figure 7.2). In this ferroelectric condition a crystal of BaTiOs has a domain structure. 

Piezoelectricity links the fields of electricity and acoustics. Piezoelectric materials are key components in acoustic transducers such as microphones, loudspeakers, transmitters, burglar alarms and submarine detectors. The Curie brothers [7] in 1880 first observed the phenomenon in quartz crystals. Langevin [8] in 1916 first reported the application of piezoelectrics to acoustics. He used piezoelectric quartz crystals in an ultrasonic sending and detection system - a forerunner to present day sonar systems. Subsequently, other materials with piezoelectric properties were discovered. These included the crystal Rochelle salt [9], the ceramics lead barium titanate/zirconate (pzt) and barium titanate [10] and the polymer poly(vinylidene fluoride) [11]. Other polymers such as nylon 11 [12], poly(vinyl chloride) [13] and poly (vinyl fluoride) [14] exhibit piezoelectric behavior, but to a much smaller extent. Strain constants characterize the piezoelectric response. These relate a vector quantity, the electrical field, to a tensor quantity, the mechanical stress (or strain). In this convention, the film orientation direction is denoted by 1, the width by 2 and the thickness by 3. Thus, the piezoelectric strain constant dl3 refers to a polymer film held in the orientation direction with the electrical field applied parallel to the thickness or 3 direction. The requirements for observing piezoelectricity in materials are a non-symmetric unit cell and a net dipole movement in the structure. There are 32-point groups, but only 30 of these have non-symmetric unit cells and are therefore capable of exhibiting piezoelectricity. Further, only 10 out of these twenty point groups exhibit both piezoelectricity and pyroelectricity. The piezoelectric strain constant, d, is related to the piezoelectric stress coefficient, g, by... 

Yashima M, Hoshina T, Ishimura D et al (2005) Size effect on the crystal structure of barium titanate nanoparticles. J Appl Phys 98 014313... 

Titanates are double oxides of the form MeTiOa or Me2Ti04. Barium titanate BaTiOa and its solid solution crystals with other titanates are especially well-known. BaTiOs crystallizes in the perovskite structure. Its technical importance results from its ferroelectric and associated piezoelectric properties, its high dielectric constant at room temperature, and the interesting semiconducting properties which it exhibits when doped [13]. The remarkable temperature dependence of the electrical resistance of such doped material (the temperature coefficient can be metal-like) is used to advantage in control and circuit devices. 

Domain. In a ferroelectric or ferromagnetic crystal, e.g. barium titanate, a domain is a small area within which the polarization is uniform. If the crystal is exposed to a high electric or magnetic field, those domains in which the polarization is in a favourable direction will grow at the expense of other domains. A domain structure gives rise to hysteresis (q.v.). 

The only other commercially important grade of titanate pigment, besides those listed above, is barium nickel titanium yellow priderite. The name priderite, just as with spinel and rutile above, refers to the crystal structure of this compound. These... 

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