Octahedral tilt

Woodward, P. (1997a). Octahedral tilting in perovskites I. Geometrical considerations. Acta Cryst. B53, 32-43. 

Aleksandrov K.S. and Barotolome J., Octahedral Tilt Phases in Perovskite-like Crystals with Slabs Containing an Even Number of Octahedral Layers, J. Phys. Condens. Matter., 6 (1994) pp.8219-8235. 

The rare earth titanates crystallize in an orthorhombically distorted form of the perovskite structure, commonly known as the GdFeOs type, found widely for other LnT03 materials and described in Pnma (Pbnm in earlier literature) (Figure 16). As the Ln + ions are too small for 12-fold coordination, the TOe octahedral tilt to accommodate a lower coordination number, which is near 9-fold. 

Howard CJ, Stokes HT (1998) Group-theoretical analysis of octahedral tilting in perovskites. Acta CiystallogrB54 782-789... 

Wadhawan VK (1982) Ferroelasticity and related properties of crystals. Phase Trans 3 3-103 Woodward PM (1997) Octahedral tilting in perovskites. I. Geometrical cortsideratiorts. Acta Crystahogr... 

Woodward PM (1997b) Octahedral tilting in perovskites II Stucuture-stabilizing forces. Acta Crystallogr B53 44-66... 

A second structural response which preserves the perfect (or nearly perfect) BX octahedral geometry is octahedral tilt or rotation. This response is mostly associated with A cations that are too small for the cuboctahedral cage site, and so the BX octahedra twist so as to effectively reduce the cavity dimensions, again allowing the structure to accommodate values of t less than 1. As with cation displacement, rotation also lowers the symmetry of the crystal (Section 1.7) and has a profound influence on the physical properties of these phases. 

The systematics of octahedral tilt in perovskites is given by H. Megaw above and ... 

The symmetry of ordered rock-salt A2(BB X) double perovskites, taking into account octahedral tilting, has been systematically derived via group theoretical analysis. If the stmcture is cubic, with a tilt system aVa , the space group is Ftriitn (225), the new axes run parallel to the simple cubic perovskite axes, and the lattice parameter is double the simple cubic lattice parameter a. Thus, in the case of Ba FeMoO, a=0.81865 nm Relatively small A cations usually lead to octahedral tilting, as... 

The oxyfluorides NbO F (a = 0.38854nm), TaO F (a=0.3896nm) and TiOF (a = 0.38102) are similar. In these cases the O and F atoms are placed at random over the oxygen sites. Both ReOj and NbOjF display octahedral tilting and a drop in symmetry when subjected to high pressure. 

Tungsten trioxide, WO3, is similar to ReOj, but the octahedra now exhibit cation displacement and octahedral tilting so that a variety of temperature-sensitive lower symmetry forms occur. Below -43°C the e-structure is monocUnic, with an a b c tilt system coupled with displacement of the W cations away from the centres of the octahedra. Between -43 and -tl7°C the 5-form has a triclinic structure with the... 

Although the microdomain description is adequate for many compounds, for some phases a more accurate picture is obtained if they are described in terms of two (or more) mutually interacting subsystems. The distribution of atom/vacancies, octahedral tilt, distortion or similar features may not follow a strict crystallographic repeat distance but may be modulated into a wave-like repetition, the wavelength of which is a function of composition, preparation conditions and so on. As an example, suppose that the unit cell for a perovskite has instead of octahedra with alternate tilts +

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Figure 2.19 Modulated structures, schematic (a) chain of unmodulated BO octahedra, with a repeat a (b) modulation of octahedral tilt angle cp, with modulation wavelength 3.57 (c) resultant octahedral tilt wave (exaggerated)...

Note that in some of these phases, the octahedra in the layers may be tilted in opposite directions in successive layers, similar to the octahedral tilts found in the ABXj perovskites (Chapter 1), a feature not emphasised in the figures. 

In practice, many phases are disordered and contain random or partly ordered wider or narrower bands of perovskite-like stracture corresponding to different n values. Non-stoichiometry is common for phases containing Co, Mn or Fe as the B-site cation. In addition, octahedral tilting and distortion are present in the perovs-kite slabs, and these both lower the symmetry of the structures and influence their physical properties. 

The symmetry consequences of octahedral tilting, rotation, distortion and cation ordering in KjNiF phases is dealt with by ... 

Perovskites are vital circuit elements for many electronic purposes, from simple capacitors to dielectric resonators used in mobile phones, satellite communications, TV broadcasting and so on. The dielectric properties of bulk perovskites arise from the presence of polarisable constituents in the crystal. These include cation displacements, octahedral tilting and distortions as well as any defects present, such as grain boundaries and various point defects. The relative permittivity is the basic parameter describing a dielectric. In a static electric field this is written as (Table 6.1) but in varying electric fields is replaced by the complex relative permittivity, - is", which is a function of the frequency of the apphed electric field. 

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