Modulated structures structure, example

There is little doubt that many materials that at present are described as containing ordered arrays of point or extended defects will be successfully described as notionally defect-free modulated structures. For example, the intergrowth Aurivillius phases, described as containing extended planar defects, have recently been described compactly as modulated structures. " The same formalism has been applied to hexagonal perovskite structures and superconducting copper oxides. Others will certainly follow. 

The continuous sinusoidal composition change that occurs during spinodal decomposition can be considered to be a modulation of the solid structure. It is now known that many structures employ modulation in response to compositional or crystallographic variations, and in such cases the material flexibly accommodates changes without recourse to defect populations. (Other modulations, in, for example, magnetic moments or electron spins, although important, will not be discussed here.)... 

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... 

Some of the earliest examples of modulated structures to be unraveled were the fluorite-related vernier structures. These structures occur in a number of anion-excess fluorite-related phases and use a modulation to accommodate composition variation. They can be illustrated by the orthorhombic phases formed when the oxyfluoride YOF reacts with small amounts of YF3 to give composition YOxF3 with x in the range 0.78-0.87, but similar phases occur in the Zr(N, O, F) system with x taking values of 2.12-2.25 and other systems in which the Zr is replaced by a variety of lanthanides. 

Electro-optical modulators are other examples whose efficiency is enhanced in the presence of ion-radicals. These devices are based on the sandwich-type electrode structures containing organic layers as the electron/hole-injecting layers at the interface between the electrode and the emitter layer. The presence of ion-radicals lowers the barrier height for the electron or hole injection. Anion-radicals (e.g., anion-radicals from 4,7-diphenyl-l,10-phenanthroline—Kido and Matsumoto 1998 from tetra (arylethynyl) cyclooctatetraenes—Lu et al. 2000 from bis (1-octylamino) perylene-3,4 9,10-bis (dicarboximide)s— Ahrens et al. 2006) or cation-radicals (e.g., cation-radicals from a-sexithienyl—Kurata et al. 1998 l,l-diphenyl-2-[phenyl-4-A/,A- /i(4 -methylphenyl)] ethylene— Umeda et al. 1990, 2000), all of them are electron or hole carriers. 

Despite intensive research, the structural arrangements of Rf-Rh diblock molecules in their solid sate and LC structures remain largely hypothetical as XRD patterns provide too small a number of reflections to prove unambiguously the proposed structures [66], The present state of knowledge in this field was recently reviewed by Krafft and Riess [66] and therefore will not be discussed in detail here. Only four representative examples of non-modulated lamellar structures are shown in Fig. 6a-d the two models on top were proposed for the LC1 (high temperature phase = HT) and LC2 (low temperature phase = LT) phases of CioH2i-CioF2i [102] and those shown in Fig. 6c,d were obtained by Monte-Carlo... 

The translation of mRNA to protein concludes the gene expression cascade and links the proteome to the genome. Consequently, control of translation can be a direct and effective means to modulate the proteome [21, 30, 31]. In addition to transcript interactions with protein regulators, translation is also modulated by structural features or regulatory sequences appearing within the mRNA molecules. The 7-methylguanylate triphosphate nucleotidyl caps at the 5 end, poly-A tails, uORFs, and IRESs are examples of structures that affect the rate and efficiency of translation in eukaryotes [21]. 

Whenever a crystal transforms (usually on cooling) to a lower symmetry structure in which a number of orientational variants are possible, transformation twins are an almost invariable consequence if the new phase is nucleated at several different places in the original structure. The formation of Dauphine twins at the jS-to-a transformation in quartz is a classic example, which has already been mentioned briefly in Section 8.6. We now consider the twins and modulated structures associated with the monoclinic-to-triclinic transformation in the K feldspars, KAlSisOg. 

Similar to modulated structures, symmetry of quasicrystals also can be described in space with more than three dimensions. For example, two-dimensional and three-dimensional quasiperiodicity can be described in five-and six-dimensional space, respectively, using 5x5 and 6x6 rotation matrices. Yet, the properties of these matrices (Eqs. 1.44 to 1.47) remain the same for both modulated structures and quasicrystals. 

IR-11.6.1 Introduction Several special problems of nomenclature for non-stoichiometric phases have arisen with the improvements in the precision with which their structures can be determined. Thus, there are references to homologous series, non-commensurate and semi-commensurate structures, Vernier structures, crystallographic shear phases, Wadsley defects, chemical twinned phases, infinitely adaptive phases and modulated structures. Many of the phases that fall into these classes have no observable composition ranges although they have complex structures and formulae an example is Mo17047. These phases, despite their complex formulae, are essentially stoichiometric and possession of a complex formula must not be taken as an indication of a non-stoichiometric compound (cf. Section IR-11.1.2). 

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