Barium titanate spontaneous polarization

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. 

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. 

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.

Ferroelectric behaviour is limited to certain materials and to particular temperature ranges for a given material. As shown for barium titanate in Section 2.7.3, Fig. 2.40(c), they have a Curie point Tc, i.e. a temperature at which the spontaneous polarization falls to zero and above which the properties change to those of a paraelectric (i.e. a normal dielectric). A few ferroelectrics, notably Rochelle Salt (sodium potassium tartrate tetrahydrate (NaKC406.4H20)) which was the material in which ferroelectric behaviour was first recognized by J. Yalasek in 1920, also have lower transitions below which ferroelectric properties disappear. 

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. 

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. 

Barium titanate (BaTi03> is one of the most thoroughly studied and most widely used piezoelectric materials. Just below the Curie temperature (120°C), the vector of the spontaneous polarization points in the [0011 direction... 

Usually, the value of the spontaneous polarization P, depends on the temperature. Figure 22-4 shows the temperature dependence of the spontaneous polarization in barium titanate (BaTiOs) crystal. As temperature changes, a variation of the charge density can be observed on those surfaces of the sample which are perpendicular to the unique polar axis in a crystal without twins, or in a poled polycrystalline solid (ceramic) with oriented grains. The phenomenon, where the spontaneous polarization changes with temperature, is called pyroelectric effect . All ferroelectric materials exhibit pyroelectric effect. 

In a previous paper [17] we have shown experimentally that uncharged laminate PET-PMMA/BaTSO>-PET exhibits piezoelectric properties. This laminated system of three-layered structure of different materials fulfills the heterogeneity condition moreover, the charges can be stored at the interfaces of the layers as a result of the equilibrium triboelectiic electrification and some effects caused by partially oriented PET films (mechanism C). However, we note that even PMMA/BaTIO, composite as inlemai layer of the laminate shows piezoelectricity to some extent, due to the spontaneous polariation of barium titanate particles (mechanism B). and the dipole polarization of PMMA (medi-anism D). 

Barium strontilun titanate - (Ba, Sr)Ti03 Ferroelectrics spontaneous polarization that can be switched with an electric field. They have a structural phase transition at a temperatiu-e (Curie temperature (TJ) at which permittivity has a strong anomaly. For example, lead zirconate titanate - Pb(Zr, Ti)Os, barium titanate - BaTiOs... 

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