Substitutional impurity defects

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

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... 

Because of the speeial atomie arrangement of the earbon atoms in a carbon nanotube, substitutional impurities are inhibited by the small size of the carbon atoms. Furthermore, the serew axis disloeation, the most eommon defeet found in bulk graphite, is inhibited by the monolayer strueture of the Cfj() nanotube. For these reasons, we expeet relatively few substitutional or struetural impurities in single-wall earbon nanotubes. Multi-wall carbon nanotubes frequently show bamboo-like defects associated with the termination of inner shells, and pentagon-heptagon (5 - 7) defects are also found frequently [7]. 

Figure 1 A dilute alloy system, showing a substitutional impurity, an interstitial impurity and an electromigration defect, and its reference system, the unperturbed host system. Some charge transfer effects are shown. Lattice distortion effects are omitted.

Additionally, we have Illustrated another type of defect that can arise within the homogeneous lattice of 3.1.2. (in addition to the vacancy and substitutional impurities that are bound to arise). This is called the "selfinterstitial". Note that it has a decisive effect on the structure at the defect. Since the atoms are all the same size, the self-interstitial introduces a line-defect in the overall structure. It should be evident that the line-defect introduces a difference in packing order since the close packing at the arrows has changed to cubic and then reverts to hexagonal in both lower and upper rows of atoms. 

A second kind of electronic defect involves the electron. Let us suppose that the second plane of the cubic lattice has a vacancy instead of a substitutional impurity of differing valency. This makes it possible for the lattice to capture and localize an extraneous electron at the vacancy site. This is shown in the following diagram. The captured electron then endows the solid structure with special optical properties since it ean absorb photon energy. The strueture thus becomes optically active. That is, it absorbs light within a well-defined band and is called a "color-center" since it imparts a specific color to the crystal. 

Phosphors are inorganic materials which convert incident radiant energy to visible light within a device. The device chosen can be a cathode-ray tube, i.e.- a television tube, or a fluorescent lamp. A phosphor consists of a matrix modified by an additive chosen so that it becomes optically active within the matrix, or compound. This is an example of a substitutional impurity in a lattice wherein the additive, usualty Ccdled an "activator", introduces a lattice defect that is optically active. However, the added impurity still follows all of the rules found for defects in a lattice, as shown by the following example. 

The topic of defects in semiconductors encompasses point, line, planar and volume defects. Point defects include those defects occupying, or sharing, a single lattice site these would include substitutional impurities... 

The Schottky defect population in the electrolyte is rather too low for practical purposes. To overcome this problem the Lil is sometimes doped with Cal2. The extra I- ions extend the Lil structure, and the Ca2+ ions form substitutional impurity defects on sites normally reserved for Li+ ions. The consequence of this is that each Ca2+ ion in Lil will form one cation vacancy over and above those present due to Schottky defects in order to maintain charge neutrality. This can be written... 

The disordered structure can be stabilized to room temperature by inclusion of substitutional impurities on the In sites. Thus the oxide formed when Ga is substituted for In, Ba2(ln1 xGaJt-)205+s to form Galn defects has a disordered cubic perovskite structure even at room temperature for values of x between 0.25 and 0.5, and the similar Ba2iln1 vCox)205+3 with Coin defects has a disordered cubic perovskite structure at room temperature when x lies between 0.2 and 0.8. The defects present in the In sites hinder oxygen ordering during the timescale over which the samples cool from the... 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

Appendix C contains the chemical formulae for the minerals used in this book. There are very few minerals that have the ideal crystalline structures discussed above. There are sufficient substitutional impurities, crystal defects, and distortions that make the CBPC structure significantly different from the models discussed above. Several well-established minerals exhibit these features, as are many of those listed in Appendix C. For example, Ca(UO2)2(PO4)2T0H2O is formed by the substitution of Ca in autunite by uranyl (UO2) ions, making the autunite a mineral of radioactive uranium. Similarly, (Ce,Th)P04 is formed by the substitution of the Ce in monazite by Th. Numerous minerals can be formed by substitutions and provide a researcher sufficient degree of freedom to synthesize very complex minerals to produce useful CBPCs. 

The simplest defect in a semiconductor is a substitutional impurity, such as was discussed in Section 6-E. There are also structural defects even in pure materials, such as vacant lattice sites, interstitial atoms, stacking faults (which were introduced at the end of Section 3-A) and dislocations (see, for example, Kittel, 1971, p. 669). They are always in small concentration but can be important in modifying conduction properties (doping is an example of this) or elastic properties (dislocations arc an example of this). 

Point Defects and Phase Diagrams. As will become more evident in subsequent parts of this chapter, substitutional impurities are one of the key types of point disorder. These defects correspond to foreign atoms that are taken into the lattice and which occupy sites normally reserved for the host atoms. For example, in the case of fee A1 some small fraction of the host lattice sites can be occupied by Cu... 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

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