Equilibrium Batios

This equation is a result of considering the adsorption and desorption kinetics described in the equilibrium which establishes the Langmuir equation 9.31. Chen, et al. [68] have studied the adsorption kinetics of poly(acrylic add) onto BaTiOs from aqueous solution. Their results are given in Table 9.13. The adsorption kinetics are faster in the case of pH 10.5 because the n ative charge on the polymer attracts the positive charge on the BaTiOg surface. At pH 1.5 there is no charge on the polymer, thus diffusion to the surface is not enhanced. 

In Table 4 we report the structural parameters that define the equilibrium tetragonal structure for each Hamiltonian examined. In addition, we report the value of the spontaneous polarisation P calculated at both equilibrium and experimental structures of the two phases. Comparison with experiment [100, 102-104] enables us to identify the functional that best describes the fully distorted phase. As described in the previous sections, accurate results are achieved in the calculations only when the electronic, structural and dis-tortional properties of the material are reproduced simultaneously by the Hamiltonian under investigation. We have shown earher that each of these observables varies appreciably as a function of the mixing parameter in the hybrid F-BLYP series. The tetragonal phases of BaTiOs and KNbOs provide... 

Figure 10.6 Equilibrium total electrical conductivity (a) versus logao of BaTiOs. (a) Undoped, polyc7Stalline BaTi03 [10] (b) Acceptor (1.8mol% AI)-doped single c stalline BaTi03 [28] (c) Donor (1.0 mol% La)-doped polyc stalline BaTlOs [11].

Figure 10.23 Thermodynamic factors ( A ) for O (solid line) and Ti (dotted line) versus oxygen activity, as evaluated from the equilibrium defect structure of 1 mol% La-doped BaTiOs in Figure 10.17. Data from Ref [30].

CaTiOs and SrTiOs have empty n and a bands the bottom of the n band is located about 3.1 eV above the 0 2p valence band [1], They are dielectric insulators. A tolerance factor t < 1 in CaTiOs is accommodated by a cooperative rotation of the Ti06/2 octahedra about the cubic [110] axis to give an 0-orthorhombic c/a > a/2) distortion. At room temperature, SrTiOs is cubic with a t 1.0. On lowering the temperature, the larger thermal expansion of the Sr—O bond relative to the Ti—O bond reduces t and below 110 K, the structure accommodates a t < 1 by a cooperative rotation of the TiOg/2 octahedra about the cubic [001] axis to give tetragonal symmetry. In BaTiOs, the structure accommodates to a t > 1, which would stretch the Ti—O bond from its equilibrium value, either by the formation of a 6H polytype or... 

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). 

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