Barium titanate lattice

Barium titanate is usually produced by the soHd-state reaction of barium carbonate and titanium dioxide. Dielectric and pie2oelectric properties of BaTiO can be affected by stoichiometry, micro stmcture, and additive ions that can enter into soHd solution. In the perovskite lattice, substitutions of Pb ", Sr ", Ca ", and Cd " can be made for part of the barium ions, maintaining the ferroelectric characteristics. Similarly, the TP" ion can partially be replaced with Sn +, Zr +, Ce +, and Th +. The possibihties for forming solution alloys in all these stmctures offer a range of compositions, which present a... 

A wide array of ferroelectric, piezoelectric and pyroelectric materials have titanium, zirconium and zinc metal cations as part of their elemental composition Many electrical materials based on titanium oxide (titanates) and zirconium oxide (zirconates) are known to have structures based on perovskite-type oxide lattices Barium titanate, BaTiOs and a diverse compositional range of PZT materials (lead zirconate titanates, Pb Zr Tij-yOs) and PLZT materials (lead lanthanum zirconate titanates, PbxLai-xZryTii-yOs) are among these perovskite-type electrical materials. 

A ferroelectric model material is barium titanate BaTi03. On cooling from high temperatures, the permittivity increases up to values well above 10,000 at the phase transition temperature Tc. The inverse susceptibility as well as the dielectric permittivity follows a Curie-Weiss law x1 f 1 oc (T — O). The appearance of the spontaneous polarization is accompanied with a spontaneous (tetragonal) lattice distortion. 

The phase transition in barium titanate is of first order, and as a result, there is a discontinuity in the polarization, lattice constant, and many other properties, as becomes clear in Figure 1.7. It is also clear in the figure that there are three phase transitions in barium titanate having the following sequence upon cooling rhombohedral, orthorhombic, tetragonal and cubic. 

Figure 1.7 Various properties of barium titanate as a function of temperature. Anisotropic properties are shown with respect to the lattice direction, (a) Lattice constants, (b) spontaneous polarization Ps and (c) relative permittivity er.

Lattice dynamics in bulk perovskite oxide ferroelectrics has been investigated for several decades using neutron scattering [71-77], far infrared spectroscopy [78-83], and Raman scattering. Raman spectroscopy is one of the most powerful analytical techniques for studying the lattice vibrations and other elementary excitations in solids providing important information about the stmcture, composition, strain, defects, and phase transitions. This technique was successfully applied to many ferroelectric materials, such as bulk perovskite oxides barium titanate (BaTiOs), strontium titanate (SrTiOs), lead titanate (PbTiOs) [84-88], and others. 

NaKC4H40e 4H2O), monopotassium dihydrophosphate (KH2PO4), or barium titanate (BaTiOs). At sufficiently high temperatures ferroelectrics show normal dielectric behavior. However, below a certain critical temperamre (so called. Curie temperature), even a small electric field causes a large polarization, which is preserved even if the external field is switched off. This means that below the Curie point ferroelectric materials show spontaneous polarization. The phase transition at the Curie temperature is related to the change of the lattice symmetry of the sample. 

In order to establish the model of intergranular impedance for doped barium titanate, it is important to notice that miorostructure properties of BaTiOj based materials, expressed in their grain boundary contacts, are of basic importance for electric properties of these materials. The barrier character of the grain boundaries is especially pronounced for doped BaTiOs materials which are used as PTC resistors. Basically two types of dopants can be introduced into BaTiOs large ions of valence 3+ and higher, can be incorporated into Ba positions, while the small ions of valence 5+ and higher, can be incorporated into the Ti sublattice [9-11], Usually, the extent of the solid solution of a dopant ion in a host structure depends on the site where the dopant ion is incorporated into the host structure, the compensation mechanism and the solid solubility limit [12], For the rare-earth-ion incorporation into the BaTiOs lattice, the BaTiOs defect chemistry mainly depends on the lattice site where the ion is incorporated [13], It has been shown that the three-valent ions incorporated at the Ba -sites act as donors, which extra donor charge is compensated by ionized Ti vacancies (V -), the three-valent ions... 

Cowley RA (1977) Structural phase transitions. In Balkanski M (ed) Proceedings of the international conference on lattice dynamics. Flammarion Sciences, Paris, p 625 Devonshire AF (1949) Theory of barium titanate - part 1. Phil Mag 40 Serie 7(309) 1040-1063 Devonshire AF (1951) Theory of barium titanate - part 11. Phil Mag 42 Serie 7(333) 1065-1079 Ehrenfest P (1933) Phase changes in the ordinary and extended sense classified according to the eorresponding singularities of the thermodynamic potential. Proc Acad Sci Amsterdam 36 153-157... 

Much later, it was found that barium titanates with a large surplus of Ti02 in the lattice, such as BaTi409 and Ba2Ti9O20, have good properties as microwave... 

Since anything that will affect the crystal lattice of barium titanate will alter its dielectric properties, it is important that impurities (SiOj, AI2O3, etc.) be controlled and maintained at comparatively low levels, not only in the as-received material but also throughout subsequent processing operations. Barium titanate is produced by solid-state reaction of BaC03 -I- Ti02 or precipitation from an intermediate such as the oxalate. 

In another example, at temperatures >393 K, barium titanate has the perovskite structure, which is simple cubic with all of the symmetry elements of the cubic lattice, so its point group is Oh or m3m. As the temperature is reduced to its Curie temperature, the lattice contracts and the oxygen ions on the faces of the cube squeeze the titanium ion in the center of the cube so that it is displaced in one direction while the oxygen ions are displaced in the opposite direction, destroying the inversion symmetry as well as the mirror symmetry about the central plane and the rotational symmetry about several of... 

Ferroelectric domains have also been observed by electron microscopy, in barium titanate as the domain forms, the lattice constant changes, giving a contrast difference between domains. Moreover, the electron beam can charge the surface and switch domains, making switching processes apparent. 

MacNevin and Ogle (87) investigated the effects of impurities on the photochromism of barium and calcium titanates as shown in Table V. Pure samples of barium and calcium titanate were not photochromic and doping with Ag+1, Cu+2, Sb+3, Sn+4, Zn+4, and Co+2 produced no enhancement of photochromism. However, increases in the concentrations of impurities such as Fe+3, Zn+2, Sb+5, and V+6 promote photochromic activity. MacNevin and Ogle concluded that the photochromism in these systems depends on the insertion into the lattice of an impurity ion having, (a) an ionic radius near that of Ti+4, and (b) an oxidation number other than 4 to make electron transfer possible. 

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