Point Defects, Microdomains and Modulated Phases

This feature is frequently observed in brownmillerites and related phases (Sections 2.4.2, 2.4.3 and 2.4.5). Non-stoichiometric SrCoO can lose oxygen readily. In the range SrCoOj j rCoOjj, it appears to normal X-ray diffraction to be cubic, but electron microscopy shows it to consist of microdomains of brown-millerite-type material. 

Another exanple of this type of microstructure is provided by the relaxor ferroelectrics related to PbMgj Nb Oj. These have a structure described as consisting of polar nanoregions, coherently intergrown within the crystal matrix and sensitive to temperature (Section 6.7). Similarly, the oxide Sm, 8,5Ba3 is nominally 

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 + p and -rp so that the repetition along the chain is equal to the pseudocubic parameter (Eigure 2.19a), a single wave-like modulation imposed such that the octahedral tilt 

The wave-like modulations are generally described with reference to the reciprocal lattice of the phase rather than the direct unit cell. The modulation wave is specified in terms of a wave vector q, which is defined in terms of the reciprocal lattice vectors a, b or c. The diffraction pattern of the phase will now show a set of reflections corresponding to the subcell plus superlattice reflections due to the modulation. In cases with a single modulation wave, the indices are described, not by conventional Miller indices but by a four-index extension, so that each reflection is indexed as ha + kb + lc +mq. The value of q is obtained directly from the diffraction pattern. When there are two distinct modulations, the diffraction pattern reflections must be indexed on a five-index system ha +kb +lc +mq +mq, and for the system with modulation in three independent directs a six index notation is needed (also see Section 3.2.2). 

The (1 -xlBiFeOj-xLaFeOj system shows a one-dimensional modulated structure over the composition range x=0.19-0.3 at 1075°C. The basic unit cell of this 

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