Impurity atoms interstitial

Moving from Nb to its more electron defident neighbor Zr creates a qualitatively new situation. The d elelctron concentration is too low to allow for the formation of the [MfiXg] duster. The number of electrons is even too low for the [M6X12] type duster. Unlike Nbjn, where the duster centers can be reversibly occujned by impurity atoms, interstitial atoms are a necessary requirement for the formation of the [ZreX,2] unit. All the [ZreQ,2] duster compounds which... 

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

Substitutional impurities replace one metal atom with another, while interstitial impurities occupy the spaces between metal atoms. Interstitial impurities create imperfections that play important roles in the properties of metals. For example, small amounts of impurities are deliberately added to iron to improve its mechanical... 

Interstitial 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. 

When normal sites in a crystal structure are replaced by impurity atoms, or vacancies, or interstitial atoms, the local electronic structure is disturbed and local electronic states are introduced. Now when a dislocation kink moves into such a site, its energy changes, not by a minute amount but by some significant amount. The resistance to further motion is best described as an increase in the local viscosity coefficient, remembering that plastic deformation is time dependent. A viscosity coefficient, q relates a rate d8/dt with a stress, x ... 

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... 

Internal boundaries are important in influencing the properties of single crystals in a number of ways. Impurities and other point defects, such as self-interstitials or vacancies, often congregate near to such interfaces. Moreover, because the regularity of the crystal structure is disrupted at the interface, unusual atom coordination can occur, allowing impurity atoms to be more readily accommodated. This in turn leads to differing, often enhanced, chemical reactivity, dissolution, and other physicochemical properties. 

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. 

These problems have of course different weights for the different metals. The high reactivity of the elements on the left-side of the Periodic Table is well-known. On this subject, relevant examples based on rare earth metals and their alloys and compounds are given in a paper by Gschneidner (1993) Metals, alloys and compounds high purities do make a difference The influence of impurity atoms, especially the interstitial elements, on some of the properties of pure rare earth metals and the stabilization of non-equilibrium structures of the metals are there discussed. The effects of impurities on intermetallic and non-metallic R compounds are also considered, including the composition and structure of line compounds, the nominal vs. true composition of a sample and/or of an intermediate phase, the stabilization of non-existent binary phases which correspond to real new ternary phases, etc. A few examples taken from the above-mentioned paper and reported here are especially relevant. They may be useful to highlight typical problems met in preparative intermetallic chemistry. 

The purities in mass%, declared by worldwide commercial suppliers, range from 99.9% for alkaline-earth metals and rare earths metals, to 99.999% for Al, Cr, Mn, Fe. .., to 99.9999 for Au, Ag, Pt. In certain cases, these values can be misleading since they refer to the metal contents, disregarding the non-metallic impurities contents (interstitial H, C, N, O, etc.). Moreover, the concentration is expressed in mass% and, for low atomic mass impurities, such as H or O, this can result in a much lower at.% purity value. The elements for special use, such as for spectrog-raphy, may require very high purities, which can be attained only by specialized laboratories. 

We are now in a position to calculate an atomically meaningful value for the coefficient Dq in Eq. (18.3). Consider two parallel planes in a lattice with impurity atoms located interstitially. The planes are a lattice constant a apart along the x-axis. Let there be n impurity atoms on one plane, with n + [a dn/dx) on the next. Since the... 

A unique situation exists in the case of diamonds, where the detailed spectroscopic descriptions of the centers are detected, but models are only proposed for a few of these. From more then 100 detected centers models are only determined for seven, mainly based on EPR interpretations. The model includes identification of the impurity, vacancy, interstitial atom, their aggregations and their crystallochemical position together with quantum-chemical and spectroscopic description. 

The simple cubic structme, sometimes called the rock salt structure because it is the structme of rock salt (NaCl), is not a close-packed structure (see Figure 1.20). In fact, it contains about 48% void space and as a result, it is not a very dense structure. The large space in the center of the SC structme is called an interstitial site, which is a vacant position between atoms that can be occupied by a small impurity atom or alloying element. In this case, the interstitial site is surrounded by eight atoms. All eight atoms in SC me equivalent and me located at the intersection of eight adjacent unit cells, so that there me 8 x (1/8) = 1 total atoms in the SC unit cell. Notice that... 

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 point defect is called an impurity. Impurities can occur in two ways as an interstitial impurity, in which an atom occupies an interstitial site (see Figures 1.21, 1.22, and 1.29) or when an impurity atom replaces an atom in the perfect lattice (see Figure 1.29). In the first instance, either the same atom as in the lattice, or an impurity atom, can occupy an interstitial site, causing considerable lattice strain as the atomic planes distort slightly to accommodate the misplaced atom. The amount of strain created depends on how large the atom is relative to lattice atoms. It... 

It is theoretically possible for cations to occupy anion sites, and vice versa. Kroger-Vink notation, then, dictates that an M atom on an X site be designated as Mx and that an X atom on an M site be designated as Xm- Recall that we can have defect clusters, such as a Frenkel defect. Defect clusters are enclosed in parentheses—for example, (VmVx) or (X Xm)—to indicate that the individual defects are associated with one another. Impurity atoms are also coded as to lattice position. If we introduce a metal impurity atom L into our compound MX, it might occupy a metal cation site, and is thus designated as Lm- Similarly, Sj is an S impurity atom on an interstitial site. 

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.

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. 

In most semiconductors, there are, in addition to the allowed energy levels for electrons in the conduction and filled bands of the ideal crystal, discrete levels with energies in the forbidden gap which correspond to electrons localized at impurity atoms or imperfections. In zinc oxide, such levels arise when there are excess zinc atoms located interstitially in the lattice. At very low temperatures the interstitial zinc is in the form of neutral atoms. However, the ionization energy of the interstitial atoms in the crystal is small and at room temperature most are singly ionized, their electrons being thermally excited into the conduction band. These electrons give rise to the observed A-type conductivity. 

Defects which have extent of only about an atomic diameter also exist in crystals—the point defects. Vacant lattice sites may occur—vacancies. Extra atoms—interstitials—may be inserted between regular crystal atoms. Atoms of the wrong chemical species—impurities—also may be present. 

On the basis of thermodynamic considerations, some of the lattice sites in the crystal are vacant, and the number of vacant lattice sites generally is a function of temperature. The movement of a lattice atom into an adjacent vacant site is called vacancy diffusion. In addition to occupying lattice sites, atoms can reside in interstitial sites, the spaces between the lattice sites. These interstitial atoms can readily move to adjacent interstitial sites without displacing the lattice atoms. This process is called interstitial diffusion. The interstitial atoms may be impurity atoms or atoms of the host lattice, but in either case, interstitial atoms are generally present only in very dilute amounts. However, these atoms can be highly mobile, and in certain cases, interstitial diffusion is the dominant diffusion mechanism. 

The appearance impurity atom C in alloy increases its configurational energy Ec by the value p (chemical potential) and energy ET of thermal fluctuations by the value v (phonon potential). We shall examine the distribution of C atoms in potential field, determined by energy uy - p - v, where Uy is the energy of C atom in interstitial site ij. Numbers i, j indicate the number of A atoms in the sites nearest to interstitial site correspondingly of first and second type. 

Various kinds of packing defects exist in the ionic crystals of NaCl type. A pair of cation and anion may be shifted from their stable positions toward the surface of the crystal, thus leaving behind a pair of vacancies. This is called the Schottky defect. The cation may leave its stable position and enter into an interstitial site. The formation of an interstitial cation and a vacancy is called the Frenkel defect. In addition to these two common kinds of defects, the presence of impurity atoms, atoms of varied valence, vacancies, and/or interstitial atoms is also possible. Some other important defects are discussed below. 

Generally speaking most of the shallow impurity levels which we shall encounter are based on substitution by an impurity atom for one of the host atoms. An atom must also occupy an interstitial site to be a shallow impurity. In fact, interstitial lithium in silicon has been reported to act as a shallow donor level. All of the impurities associated with shallow impurity levels are not always located at the substitutional sites, but a part of the impurities are at interstitial sites. Indeed, about 90% of group-VA elements and boron implanted into Si almost certainly take up substitutional sites i.e., they replace atoms of the host lattice, but the remaining atoms of 10% are at interstitial sites. About 30% of the implanted atoms of group-IIIA elements except boron are located at either a substitutional site or an interstitial site, and the other 40% atoms exist at unspecified sites in Si [3]. The location of the impurity atoms in the semiconductors substitutional, interstitial, or other site, is a matter of considerable concern to us, because the electric property depends on whether they are at the substitutional, interstitial, or other sites. The number of possible impurity configurations is doubled when we consider even substitutional impurities in a compound semiconductor such as ZnO and gallium arsenide instead of an elemental semiconductor such as Si [4],... 

The situation with II-VI semiconductors such as ZnO is similar to the situation with the elemental and the III-V semiconductors in respect of the location of the impurity atoms and their influences on the electric property. It is reported in ZnO that P, As, or S atom replaces either Zn or O site, and a part of them are also located at an interstitial site, as well as at a substitutional site [2,5-7], The effect of a few kind of impurities such as group-IIIA and -VA elements on the electric property of ZnO was extensively studied, especially when the impurity atoms were located at a substitutional site. The effects of the greater part of elements in the periodic table on the electric property of ZnO are, however, not well understood yet. The purpose of the present study is to calculate energy levels of the impurity atoms from Li to Bi in the periodic table, to clarify the effect of impurity atoms on the electric property of ZnO. In the present paper, we consider double possible configuration of the impurity atoms in ZnO an atom substitutes the cation lattice site, while another atom also substitutes the anion sublattice site. The calculations of the electronic structure are performed by the discrete-variational (DV)-Xa method using the program code SCAT [8,9],... 

It has been seen in the previous section that the ratio of the onsite electron-electron Coulomb repulsion and the one-electron bandwidth is a critical parameter. The Mott-Hubbard insulating state is observed when U > W, that is, with narrow-band systems like transition metal compounds. Disorder is another condition that localizes charge carriers. In crystalline solids, there are several possible types of disorder. One kind arises from the random placement of impurity atoms in lattice sites or interstitial sites. The term Anderson localization is applied to systems in which the charge carriers are localized by this type of disorder. Anderson localization is important in a wide range of materials, from phosphorus-doped silicon to the perovskite oxide strontium-doped lanthanum vanadate, Lai cSr t V03. 

Point defects occur where an atom is missing, or is replaced by an impurity atom or is in an irregular place in the structural lattice. Point defects include selfinterstitial atoms and interstitial impurity atoms in a random arrangement. 

Ordinary ions. The removed electron is a valency electron. These ordinary ions may originate from atoms situated normally arranged on the lattice. The formation of an ordinary ion gives rise to a charge defect in the valency band, more commonly termed positive hole. If the electron is removed from an atom corresponding to an impurity level (impurity or interstitial atoms), an acceptor level is produced. 

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