Interstitial disorder

So far, the solids that we have studied have been ordered, in the sense that they possess perfect translational symmetry. However, this perfection is really an idealization and, in reality, an actual crystal can be expected to have some sort of disorder, which breaks the long-range periodicity of the lattice. There are a number of ways in which disorder can arise. For instance, interstitial disorder occurs when an impurity atom is placed in the vacant space between two substrate atoms, which remain at their original locations in the lattice. Another situation is that of structural disorder, where the substrate atoms move away from their positions on the perfect lattice. However, the situation of interest in this chapter is that of substitutional disorder. Here, a perfect lattice of one type of atoms (say, A) has some of its members randomly replaced by another type (B). The result is a structurally periodic lattice, but with the constituent atoms A and B randomly placed on the lattice sites. The relative numbers of A and B atoms can be represented by the concentrations ca and cB, with ca + cB = l. The randomness of this type of solid introduces a level of difficulty into the theory, that we have not yet encountered. 

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... 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

CoUision cascades (see Fig. 1) lead to a distribution of vacancies, interstitial atoms, and other types of lattice disorder in the region around the ion... 

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

Another example of the same building principle is found in the literature 89) for the /5-analogous dialcoholic spiro host 24, namely in its 1 1 inclusion compound with benzene (Fig. 26). The host molecules are bound into infinite zigzag chains by H-bonds and disordered benzene molecules appear interstitially placed between such chains. 

Ochratoxin A (OTA) is a my cotoxin produced by some species of Penicillium and Aspergillus. It is nephrotoxic to all animal species tested and the causal agent of mycotoxic porcine nephropathy (Krogh, 1978). It was previously associated with the human renal disorder, Balcan endemic nephropathy (BEN), and tumours of the urinary tract (Pfohl-Leszkowicz et al., 2002). Recently, another endemic kidney disease (Tunisian chronic interstitial nephropathy, CIN) was linked to OTA-contaminated food (Creppy, 1999 Wafa et al.,... 

Figure 9.2 Schematic representation of magnetic defects in a magnetic matrix (a) vacancy or nonmagnetic impurity, (b) self-interstitial, (c) magnetic Frenkel defect , (d) magnetic foreign substituent, and (e) magnetic foreign interstitial. The magnetic matrix can have ordered (as drawn) or disordered spins.

We now introduce a Fourier transform procedure analogous to that employed in the solution theory, s 62 For the purposes of the present section a more detailed specification of defect positions than that so far employed must be introduced. Thus, defects i and j are in unit cells l and m respectively, the origins of the unit cells being specified by vectors R and Rm relative to the origin of the space lattice. The vectors from the origin of the unit cell to the defects i and j, which occupy positions number x and y within the cell, will be denoted X 0 and X for example, the sodium chloride lattice is built from a unit cell containing one cation site (0, 0, 0) and one anion site (a/2, 0, 0), and the translation group is that of the face-centred-cubic lattice. However, if we wish to specify the interstitial sites of the lattice, e.g. for a discussion of Frenkel disorder, then we must add two interstitial sites to the basis at (a/4, a/4, a]4) and (3a/4, a/4, a/4). (Note that there are twice as many interstitial sites as anion-cation pairs but that all interstitial sites have an identical environment.) In our present notation the distance between defects i and j is... 

Restrictive disorders Interstitial thickening Hemorrhage Cellular infiltration Abnormal surfactant production... 

The above situation, in which Ag" ions are disordered over, and readily move between, a large number of interstitial sites contrasts with the... 

Intrinsic Frenkel disorder, in which some of the oxygens are displaced into normally unoccupied sites, is responsible for the oxide ion conduction in, for example, Zr2Gd207, Fig. 2.11. The interstitial oxygen concentration is rather low, however, and is responsible for the low value of the preexponential factor and for the rather low (by -Bi203 standards ) conductivity. 

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