Modulated crystal structure

Figure 4.35 Modulated crystal structures (a) crystal showing a displacive modulation of one set of atoms and (b) a crystal showing a compositional modulation of one set of atoms. (The change in the average chemical nature of the atom is represented by differing circle diameters.)...

Once Te-III was identified as incommensurate, subsequent analysis was conducted on the previously-collected powder-diffraction data using the formalism of 4D superspace [234], and the JANA2000 software for structure refinement [235]. The Rietveld refinement of the incommensurate Te-III diffraction profile is shown in Fig. 9, and the modulated structure is shown in Fig. 10. Tellurium was only the second element found to have a modulated crystal structure at high-pressure, the... 

P.M. de Wolff, The pseudo-symmetry of modulated crystal structures, Acta Cryst. A30, 777(1974). 

J. Appl. Crystallogr., 1996, 29, 301 303 Structure factor of modulated crystal structures by A. Yamamoto, Acta Crystallogr. Sect. A, 1982, 38, 87 92... 

Figure 8.21 Schematic representations of normal and modulated crystal structures and diffraction patterns (a) a normal superlattice, formed by the repetition of an anion substitution (b) part of the diffraction pattern of (a) (c) a crystal showing a displacive modulation of the anion positions (d) a crystal showing a compositional modulation of the anion conditions, (the change in the average chemical nature of the anion is represented by differing circle diameters) (e) part of the diffraction pattern from (c) or (d) (f) a modulation wave at an angle to the unmodulated component (g) part of the diffraction pattern from (f). Metal atoms are represented by shaded circles and non-metal atoms by open circles...

Modulated crystal structures are by no means a rarity. Since the Calaverite mineral, many other examples of modulated structures and more generally aperiodic crystals were and continue to be discovered. They occur in all types of... 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

Klemm, J.D., et al. Crystal structure of the Oct-1 POU domain bound to an octamer site DNA recognition with tethered DNA-binding modules. Cell 77 21-32, 1994. 

In general, these defect-free modulated structures can, to a first approximation, be divided into two parts. One part is a conventional structure that behaves like a normal crystal, but a second part exists that is modulated5 in one, two, or three dimensions. The fixed part of the structure might be, for example, the metal atoms, while the anions might be modulated in some fashion. The primary modulation might be in the position of the atoms, called a displacive modulation (Fig. 4.35a). Displacive modulations sometimes occur when a crystal structure is transforming from one... 

Bass, R. B., Strop, P., Barclay, M. and Rees, D. C. (2002). Crystal structure of Escherichia coli MscS, a voltage-modulated and mechanosensitive channel, Science, 298, 1582-1587. 

Emphasis to a similar approach has been given by Zvyagin (1993). He pointed out that many crystal structures can be represented as a composite of certain standard construction modules and various combinations, distributions and arrangements of these. The simplest example of a modular structure is the densest packing... 

Grune T, Brzeski J, Eberharter A, Clapier CR, Corona DF, Becker PB, Muller CW (2003) Crystal structure and functional analysis of a nucleosome recognition module of the remodeling factor ISWl. Mol Cell 12 449-460... 

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