Point defect properties

The addition of a third element to an ordered binary alloy can modify considerably the point-defect properties for example, the behavior of FeCo-2% V is very complex, because vanadium forms a resonant virtual bound state at the Fermi level, the partial filling of which depends strongly on the state of order (Riviire et al., 1983b). Solutes (specifically Mn, Re, and Ti) have also been shown to have complicated effects in CoAl (Fleischer, 1993). 

Up to now, the main progress in simulating point-defect properties in intermetallic compounds has been made by semiempirical methods. The first detailed papers in this sense concern the A15-structure superconductors (Moseev et al., 1983, 1986 Welch et al., 1984). Although these authors used very simplified pair potentials, qualitative results were obtained, which are discussed in more detail in Section 9.1. 

The best results have been obtained by embedded-atom-type methods, applied first with good success to many metallurgical properties of pure metals surface energy, point-defect properties (see for example Foiles et al., 1986 Chapter 4 by Voter in this volume). In these methods, the energy of each atom is computed from the energy F,(p,) needed to embed it in the local-electron density pi provided by the other atoms of the alloy (approximated by the superposition of atomic-electron densities Pj=Hj, /Pj(Ry)), plus an additional electrostatic short-range core-core repulsion y Rij) = Zj(Rf)Zj(Rjj)/Rjj. The total energy is then written as... 

A very detailed work was published recently on CuTi and CuTij body-centered tetragonal structure alloys (Shoemaker et al., 1991), unfortunately systems with no experimental information on point-defect properties. In both compounds, the removal of a Cu or Ti atom results in a vacant Cu site, with an adjacent Ti -u antisite defect in the latter case. Interstitials have complicated structures of the crowdion type, on a Cu (111) row, which involves seven Cu for six sites (CuTi case) or five Cu for four sites (CuTi2 case) and the creation of two or three antisite defects in the respective cases of Cu or Ti displacements. 

Some good papers have been published recently. Unfortunately the corresponding experimental data are most often lacking. The point-defect properties calculated from the electronic structure will have to be integrated in a proper thermodynamic theory. Such knowledge will also allow study in important fields that are practically unexplored up to now in intermetallic compounds point defect-impurity interaction, point defect-dislocation interaction, and consequences on the mechanical properties, etc. Considerable work is still required. 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

The microstmcture and imperfection content of coatings produced by atomistic deposition processes can be varied over a very wide range to produce stmctures and properties similar to or totally different from bulk processed materials. In the latter case, the deposited materials may have high intrinsic stress, high point-defect concentration, extremely fine grain size, oriented microstmcture, metastable phases, incorporated impurities, and macro-and microporosity. AH of these may affect the physical, chemical, and mechanical properties of the coating. 

The physical properties of tellurium are generally anistropic. This is so for compressibility, thermal expansion, reflectivity, infrared absorption, and electronic transport. Owing to its weak lateral atomic bonds, crystal imperfections readily occur in single crystals as dislocations and point defects. 

Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

The catalytic properties of the shock-modified rutile whose defect properties have been reported in previous sections of this chapter have been studied in a flow reactor used to measure the oxidation of CO by Williams and coworkers [82G01, 86L01]. As shown in Fig. 7.7 the effect of shock activation is substantial. Whereas the unshocked material displays such low activity that an effect could only be observed at the elevated temperature of 400 °C, the shock-modified powder shows substantially enhanced catalytic activity with the extent of the effect depending on the shock pressure. After a short-time transient is annealed out, the activity is persistent for about 8 h. Although the source of the surface defects that cause the activity is not identified, the known annealing behavior of the point defects indicates that they are not responsible for the effect. 

Changes in the atomic correlations are enabled by atomic jumps between neighbouring lattice sites. In metals and their substitutional solutions point defects are responsible for these diffusion processes. Ordering kinetics can therefore yield information about properties of the point defects which are involved in the ordering process. 

We will be considering primarily inorganic solids but must keep in mind that the same principles also apply to organic solids. Therefore, we intend to examine the nature of point defects in terms of their thermodynamics, equilibria and the energy required for their formation. It will be seen that point defects follow the same physical chemistry laws that apply to inorgcuiic compounds and physical properties in general. 

Point defects were mentioned in a prior chapter. We now need to determine how they aiffect the structure auid chemical reactivity of the solid state. We will begin by identifying the various defects which can arise in solids and later will show how they can be manipulated to obtain desirable properties not found in naturally formed solids. Since we have already defined solids as either homogeneous and heterogeneous, let us look first at the homogeneous t5 e of solid. We will first restrict our discussion to solids which are stoichiometric, and later will examine solids which can be classified as "non-stoichiometric", or having an excess of one or another of one of the building blocks of the solid. These occur in semi-conductors as well as other types of electronically or optically active solids. 

Note that "b" in this diagram is the same as that in 3.1.8. Because edge and volume defects propagate throughout the lattice, they affect the physical properties of the solid, whereas it is the point defects that affect the chemical properties of the solid. These latter properties include electrical and resistive, optical and reactivity properties of solids. Thus, we can now classify directs in solids as ... 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

We have observed large variations in the sorption capacities of zeolite samples characterized by (ID) channel systems, as for instance AFI (AIPO4-5 zeolite) and MTW (ZSM-12 zeolite) architectural framework types. Indeed, for such unconnected micropore networks, point defects or chemisorbed impurities can annihilate a huge number of sorption sites. Detailed analysis, by neutron diffraction of the structural properties of the sorbed phase / host zeolite system, has pointed out clear evidence of closed porosity existence. Percentage of such an enclosed porosity has been determined. 

There is now an extensive and rapidly growing theoretical literature on the nature of hydrogen or muonium defects in silicon and to some extent in other semiconductors (Van de Walle, 1991 DeLeo, 1991). Much of this has dealt with isolated hydrogen or muonium where the most frequent comparisons have been with the muon hyperfine parameters, at least qualitatively, and other features of the muonium centers that can be inferred from /rSR experiments. Isolated interstitial hydrogen or muonium is certainly one of the simplest point defects conceivable. Hence explaining the existence and properties of the two drastically different forms of muonium observed in silicon and several other semiconductors has been a particular challenge to current theoretical methods. 

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

The importance of point defects in a crystal cannot be overstated. They can change the physical properties of a solid significantly. To introduce the range of changes possible, Sections 1.3-1.6 outline some of the physical properties that are influenced in this way. 

The unique electronic properties of semiconductor devices arise at the regions where p-typc and ra-typc materials ate in close proximity, as in p-n junctions. Typical impurity levels ate about 0.0001 at %, and their inclusion and distribution need to be very strictly controlled during preparation. Without these deliberately introduced point defects, semiconductor devices of the type now commonly available would not be possible. 

Point defects can have a profound effect upon the optical properties of solids. The most important of these in everyday life is color,3 and the transformation of transparent ionic solids into richly colored materials by F centers, described below, provided one of the first demonstrations of the existence of point defects in solids. 

These examples indicate that it is necessary to keep the possible effect of point defects on bulk and mechanical properties in mind. Although less definitive than electronic and optical properties, they may make the difference in the success or failure of device operation. 

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

Intrinsic point defects are always present in a crystal as an inescapable property of the solid. For this to be so the intrinsic defect must be stable from a thermodynamic point of view. In this chapter the consequences of this thermodynamic aspect will be considered in more detail. 

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