Impurity atoms substitutional

Fig.l Atomic configuration of the model CU4O16A4 in the ab plane, where A is an impurity atom substituted for an 0 (oxygen) atom. 

Nb " (n-type) [40]. This behavior can be easily explained if we consider hematite to be a small polaron conductor with n- and p-type charge carriers assumed to be Fe and Fe" ", respectively. Then, if the impurity atoms substitute for a Fe irm in the crystal lattice, they would cause the creation of Fe (n-type) or Fe" " (p-type) to balance the lattice charge. By doping at sufficient levels, high carrier conductivities can be attained. For example, Zr" " was doped into single crystals to give donor densities on the order of 10 cm, conductivities aroimd 0.1 cm , and... 

For substitutional solid solutions, impurity atoms substitute for host atoms. Interstitial solid solutions form for relatively small impurity atoms that occupy interstitial sites among the host atoms. 

Addition of impurity atoms may result in the formation of substitutional or interstitial solid solutions. For substitutional, an impurity atom substitutes for that host atom to which it is most similar in an electrical sense. 

A second doping method is the substitution of an impurity atom with a different valence state for a carbon atom on the surface of a fullerene molecule. Because of the small carbon-carbon distance in fullerenes (1.44A), the only species that can be expected to substitute for a carbon atom in the cage is boron. There has also been some discussion of the possibility of nitrogen doping, which might be facilitated by the curvature of the fullerene shell. However, substitutional doping has not been widely used in practice [21]. 

Similar calculations were carried out for the single impurity systems, niobium in Cu, vanadium in Cu, cobalt in Cu, titanium in Cu and nickel in Cu. In each of these systems the scattering parameters for the impurity atom (Nb, V, Co, Ti or Ni) were obtained from a self consistent calculation of pure Nb, pure V, pure Co, pure Ti or pure Ni respectively, each one of the impurities assumed on an fee lattice with the pure Cu lattice constant. The intersection between the calculated variation of Q(A) versus A (for each impurity system) with the one describing the charge Qi versus the shift SVi according to eqn.(l) estimates the charge flow from or towards the impurity cell.The results are presented in Table 2 and are compared with those from Ref.lc. A similar approach was also found succesful for the case of a substitutional Cu impurity in a Ni host as shown in Table 2. 

Substitutional impurity atoms(both cation and anion)... 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

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... 

Color can also be induced into colorless crystals by the incorporation of impurity atoms. The mineral corundum, 01-AI2O3, is a colorless solid. Rubies are crystals of A1203 containing atomically dispersed traces of Cr203 impurity. The formula of the crystal can be written (CrvAli r)203. In the solid the Al3+ and Cr3+ cations randomly occupy sites between the oxygen ions, so that the Cr3+ cations are impurity substitutional, CrA1, defects. When x takes very small values close to 0.005, the crystal is colored a rich ruby red. 

The position of a defect that has been substituted for another atom in the structure is represented by a subscript that is the chemical symbol of the atom normally found at the site occupied by the defect impurity atom. The impurity is given its normal chemical symbol, and the site occupied is written as a subscript, using the chemical symbol for the atom that normally occupies the site. Thus, an Mg atom on a Ni site in NiO would be written as MgNi. The same nomenclature is used if an atom in a crystal occupies the wrong site. For example, antisite defects in GaN would be written as GaN and NGa. 

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. 

Eigure 1.29 Representation of interstitial and substitutional impurity atoms in a crystalline solid. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. 

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. 

Fig. 4.22 On the surface of a solid, there are a wide variety of atomic processes. A formation of a surface vacancy-adatom pair, or their recombination B association or dissociation of adatoms with an atomic cluster and cluster diffusion C diffusion of a surface vacancy, especially toward the lattice step D falling off a lattice step of an adatom E diffusion of a substitutional or interstitial impurity atom and its interaction with an adatom F diffusion of an adatom and its long range interactions with other adatoms G diffusion, dissociation and activation of a ledge atom H dissociation and activation of a kink atom into an adatom, a ledge atom, or an adatom on the layer above.

Experimental studies of adatom interactions focus on two quantities, namely the binding energy and the interatomic force, or the distance dependence of the potential energy. These are two different quantities, although in the past they have been occasionally mixed up in some studies. In many FIM studies where the term force is used, concern is in reality only with binding energy at a certain bond distance or a certain site. We will describe briefly here some FIM studies of adatom interactions with metallic substrates. In Section 4.2.5 adatom-adatom and adatom-substitutional impurity atom interactions will be discussed. 

Despite a possible wide significance of such a topic, there is only one reported study of adatom-substitutional impurity atom interaction, where the interaction of a W adatom with substitutional Re atoms in a W lattice is studied by using a W-3% Re alloy as the substrate.182 The planes used in FIM studies of adatom behavior are usually quite small containing only a few hundred atoms. Thus a plane of a W-3% Re alloy is likely to contain a few Re substitutional atoms. The perturbation to the overall electronic and elastic properties of the substrate lattice should still be relatively small. Therefore the interaction of a single substitutional impurity atom with a diffusing adatom can be investigated. 

The simplest lattice defects as far as FIM observations are concerned are point defects, such as vacancies, self-interstitials and substitutional as well as interstitial impurity atoms. Vacancies invariably show up as dark spots in the field ion images. Other point defects may appear as either bright image spots or vacancies in the image. Thus these defects can be identified from field ion images of high index planes where all the atoms in a plane are fully resolved. 

Extrinsic Crystal Self-Diffusion. Charged point defects can be induced to form in an ionic solid by the addition of substitutional cations or anions with charges that differ from those in the host crystal. Electrical neutrality demands that each addition results in the formation of defects of opposite charge that can contribute to the diffusivity or electronic conductivity. The addition of aliovalent solute (impurity) atoms to an initially pure ionic solid therefore creates extrinsic defects.10... 

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