Forms of disorder

Diffraction is not limited to periodic structures [1]. Non-periodic imperfections such as defects or vibrations, as well as sample-size or domain effects, are inevitable in practice but do not cause much difSculty or can be taken into account when studying the ordered part of a structure. Some other forms of disorder can also be handled quite well in their own right, such as lattice-gas disorder in which a given site in the unit cell is randomly occupied with less than 100% probability. At surfaces, lattice-gas disorder is very connnon when atoms or molecules are adsorbed on a substrate. The local adsorption structure in the given site can be studied in detail. 

In this seetion we begin the diseussion with some basie thermodynamie eonsiderations whieh, as we hope, will show elearly why the efleets of surfaee heterogeneity make the study of surfaee phase transitions so diflieult. Then we shall eoneentrate mainly on the results of the reeent eomputer simulation studies of phase transitions in model systems exhibiting various forms of disorder. 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

Some forms of disorder common in adsorbed layers are islands of clustered adsorbates leaving patches of bare substrate domains in which different patches of the overlayer have identical structure but do not match at their junction because of an error in registry, i.e., an error in relative positioning parallel to the surface periodicity errors, in which individual adsorbates do not fit in the periodic arrangement of the surrounding... 

Generally, it is difficult to obtain experimental information about the exact form of disorder present on any actual surface much work remains to be done in this direction. 

Unless we are working in a tight-binding situation with a low coordination number, we believe that these values of V0jB and gc should be valid for all forms of disorder. What determines localization is the spread in the energies of atomic states—due to whatever cause for nearest neighbours this must be about 3B. It seems unlikely that localization can occur without a decrease in N(E an issue that is discussed further in Chapter 10. 

The factor 0.03 is deduced here for s-state and a half-filled band, and simple diagonal disorder (Fig. 1.17). We believe that it has much wider validity, and can be applied, at any rate in a theory of non-interacting electrons (as for instance in a semiconductor) to any form of disorder or for p- or d-states. Our confidence depends on the success of the scaling theory of Abrahams et al. (1979), which will be outlined in Section 13. 

In this review, we have argued that the metallicity is intimately connected to the presence of JTD. We could speculate that the population of many different JTD states at high temperatures introduces a form of disorder that could trigger a metal-insulator transition of the Anderson type. It reveals conversely that cooperation is required between JTD and the electronic motion to establish coherent band-like properties. The transition at 250 K in K4C60 shows that the nature of the distortion can change, a situation close to that of the fulleride salt. A similar transition in metallic compounds might be responsible for the de-stabilization of the metallic state. 

The crystal structure of [Bu N] jRe2Clg has been described. The molecules exhibit a subtle form of disorder such that 74 % of the Re—Re units are aligned in one direction with the remaining 26 % perpendicular to this direction. On the basis of this structural information it has been found possible to determine the polarization relative to the molecular axis of the absorption band at ca. 700 nm. The bond is found to be entirely Z polarized, which virtually assures its assignment to the 6 6 transition. The... 

Defining order in an amorphous solid is problematic at best. There are several qualitative concepts that can be used to describe disorder [7]. In figure A 1.3.28 a perfect crystal is illustrated. A simple form of disorder involves crystals containing more than one type of atom. Suppose one considers an alloy consisting of two different atoms (A and B). In an ordered crystal one might consider each A surrounded by B and vice versa. 

Many forms of disorder in a surface stmcture can be recognized in the LEED pattern. The main manifestations of disorder are broadening and streaking of diffraction spots and diffuse intensity between spots [1]. 

The commonest form of disorder among the B-site cations results in the B- and B -cations swapping positions, an example of antisite disorder. Antisite disorder is temperature sensitive and is often influenced by the preparation methods employed and the particle size of the product, with nanoparticles often having different surface ordering than bulk samples. These defects have consequences for the electronic and magnetic properties of the phase. 

The issue of order is central to data structures, but it is also the opposite of a basic mathematical notion, randomness. Currently, data encryption is a valued use of computation. The basic coding method involves creating a form of disorder approaching randomness to render files unintelligible... 

Consider an ideal case where the crystal exhibits none of the forms of disorder mentioned in the previous section. A given polymorph is then characterized by localization about an equilibrium point in phase space where the potential energy surface is concave. The relevant part of the energy... 

For patients with abnormal peroxisome biogenesis, the possibilities for treatment are very poor. Supplementation of docosahexaenoic acid is now being tested in patients with the milder forms of disorders of peroxisome biogenesis. 

Thermal analysis techniques have been applied to determine the decomposition of RHA and also to investigate the hydration characteristics of RHA-cement pastes exposed to different conditions. The reported results ofDTA, DSC, and TG of RHA-cement pastes show variations. The thermal curves of RHA from different sources are not comparable because of variation in their physico-chemical characteristics, the conditions under which the husk is heated, and other factors.Thermograms generally show endothermal and exothermal peaks. Those ashes formed at lower temperatures show an exothermal effect for the oxidation of the unbumed carbon. Endothermal effects at about lOO C denote the expulsion of water from the adsorbed surface. The oxidation reactions correspond to the loss of weight in TG. Some DSC results have been obtained for the ash obtained at 1200°C.[ The peaks in DSC (Fig. 22) were interpreted from XRD studies. An exothermic peak at 135°C is attributed to the transformation of the try dimite phase (T toT ) and four endothermal effects at 190,220,235, and 250°C represent the transformation of the low form of disordered cristabolite. The endothermic peak at 250°C is caused by a transformation of the well-crystallized form. 

In the literature a number of approaches have been taken to create a suitable starting structure. In general, some form of disorder is introduced, with the exception of two studies of DMPC which started from a crystal structure. This method has the disadvantage that it is doubtful that an equilibrated liquid-crystalline phase is reached within the simulation time. A careful method to build a bilayer consists of placing lipids taken from a library of structures, that agrees with observables... 

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