BaTiO crystal structure

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

BaTiOs crystallizes in the perovskite structure. This structure may be described as a barium-oxygen face-centered cubic lattice, with barium ions occupying the corners of the unit cell, oxide ions occupying the face-centers, and titanium ions occupying the centers of the unit cells, (a) If titanium is described as occupying holes in the Ba-O lattice, what type of hole does it occupy (b) What fraction of the holes of this type does it occupy (c) Suggest a reason why it occupies those holes of this type but not the other holes of the same type ... 

Look up the radii of Ti", Ba, and listed in App. 3A, and making use of Pauling s size criteria, choose the most suitable cage for each cation. Based on your results, choose the appropriate composite crystal structure and draw the unit cell of BaTiO. How many atoms of each element are there in each unit cell ... 

Megaw, Helen Dick died in 2002 aged 94. She reported the crystal structure of BaTiOs in Nature 155, 484 (1945). She spent most of her academic career in Cambridge. 

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. 

In the present composite, since BaTiOs structure extends in the poling direction whereas AI2O3 matrix maintains its crystal structure and orientation, even after poling the residual stress would be generated in AI2O3 matrix. In the pervious work , residual stresses were observed in the same composite as the present study. 

Fig. 1.7 Crystal structure of BaTiOs using Ewald method and local density of charge...

The value of of the BaTiO, ceramics is lower than that reported for BaTiOj single crystal [9] (along [100] =4 000). This may be due to the structural and compositional variances. Meanwhile, the size of crystalline particle may affect the dielectric constant , that is, when the particle size is lower than certain value, the constant will decrease with the decrease of the size. In addition to those mentioned above, porosity and the existence of low dielectric constant affect the non-ferroelectric layers at the metal-ferroelectric interface and the grain boundaries. 

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

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. 

Fig. 5.19). The input barium titanyl oxalate powder has specific surface area 1 m /g. Therefore, the coefficient of refining rox/rut reaches 10 0 times on oxalate decomposition. Using more dispersed oxalate, however, is not reasonable due to the small particles coalescence on heating, and therefore, the oxalate grinding has almost no effect on the end of the BaTiOs synthesis. The morphology of nanoparticles depends on the gas release rate during the decay of oxalate, and hence the heating rate determines density of nucleation and nuclei coalescence probability. In addition, the increase in heating rate leads to a change in the mechanism of oxalate oxidation as described above. Structurally barium titanyl oxalate crystal transforms to the microreactor - particles of resin-like phase, size and activity of which can be flexibly controlled by the heating rate. The general view of the reactor is shown in Fig. 5.20.

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