Lattice defects interstitials

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

One feature of oxides is drat, like all substances, they contain point defects which are most usually found on the cation lattice as interstitial ions, vacancies or ions with a higher charge than dre bulk of the cations, refened to as positive holes because their effect of oxygen partial pressure on dre electrical conductivity is dre opposite of that on free electron conductivity. The interstitial ions are usually considered to have a lower valency than the normal lattice ions, e.g. Zn+ interstitial ions in the zinc oxide ZnO structure. 

The lattice may be distorted because of several reasons as vacancies, interstitials, dislocations and impurities. These lattice defects cause the so-called impurity scattering which produces the term i ei. At low temperatures, i ei is the constant electronic thermal resistance typical of metals. 

So far, we have dealt with optically active centers based on dopant ions, which are generally introduced during crystal growth. Other typical optically active centers are associated with inhinsic lattice defects. These defects may be electrons or holes associated with vacancies or interstitials in ionic crystals, such as the alkali halide matrices. These centers are nsually called color centers, as they prodnce coloration in the perfect colorless crystals. 

Fig. 2-26. Localized electron levels of lattice defects and impurities in metal oxides Mi = interstitial metal ion Vm = metal ion vacancy V = oxide ion vacancy D = donor impurity A = acceptor impurity.

Lattice defects in ionic crystals are interstitial ions and ion vacancies. In crystalline sodium chloride NaCl a cation vacancy Vn - is formed by producing a surface cation NaJ, (Nal - NaJ + Vua ) this is called the Schottky defect. On the other hand, in crystalline silver chloride AgCl a pair of cation vacancy Va,. and interstitial cation Ag is formed, (Ag - Agj + ) this is called the Frenkel... 

Fig. 3-12. Lattice defects and ion levels of ionic compound AB (a) ionnation of a pair of ion vacancy and interstitial ion, (b) A ion levels in ionic crystals. Va = A ion vacancy A] = intoatitial A ion Oa. = A ion level = unitary A ion level at lattice sites ...

Fig. 3 -13. (a) A ion levels at the surface and in the interior of ionic compound AB, and (b) concentration profile of lattice defects in a surface space charge layer since the energy scales of occupied and vacant ion levels are opposite to each other, ion vacancies accumulate and interstitial ions deplete in the space charge layer giving excess A ions on the surface. 

Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

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. 

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 this case, the number of zinc ions in interstitial positions and the number of free electrons will be decreased by an increase in the partial pressure of oxygen. These disorder reactions result in a dependence of the electrical conductivity on the oxygen pressure. This effect is a well known phenomenon in the field of semiconductors (1). Complicated relations, however, will occur at lower temperatures, at which no equilibrium can be attained between the gas phase and the lattice defects in the whole... 

Another type of lattice defect for elements is interstitial atoms, in which an atom is transferred from a regular lattice point to an interstitial position, normally unoccupied by an atom. Consider a crystal which has N atoms sited on regular lattice points and N, atoms sited on interstitial lattice points (the number of interstitial lattice points is A, which is fixed by the crystal structure under consideration), by a similar calculation, the free energy increment from the ideal crystal is expressed as... 

The studies on Cu2 aO mentioned above concluded that CujO is a metal-deficient p-type semiconductor with cation vacancies. It was not established, however, which kinds of defects (Vcu, Vcu) were dominant and what the effect of Q (interstitial oxygen) was on non-stoichiometry. To clarify these points, Peterson and Wiley measured the diffusion coefficient, D, of Cu in Cu2 O, by use of "Cu as a tracer over the temperature range 700-1153 °C and for oxygen partial pressures, greater than 10 atm. It has been widely accepted that lattice defects play an important role in the diffusion of atoms or ions. Accordingly it can be expected that the measurement of D gives important information on the lattice defects. 

The effects of damage by ion implantation on the low-temperature diffusion of dopant can also be studied by implanting Si+ or Ge+ ions into predeposited layers in Si. Recently, Servidori et al. (58) studied the influence of lattice defects induced by Si+ implantation. Using triple crystal X-ray diffraction and TEM, they confirmed (1) that below the original amorphous surface-crystal interface, interstitial dislocation loops and interstitial clusters exist and (2) that epitaxial regrowth leaves a vacancy-rich region in the surface. 

Creation of intrinsic donors by lattice defects (for instance oxygen vacancies or metal atoms on interstitial lattice sites) or... 

The catalyst particle is usually a complex entity composed of a porous solid, serving as the support for one or more catalytically active phase(s). These may comprise clusters, thin surface mono- or multilayers, or small crystallites. The shape, size and orientation of clusters or crystallites, the extension and arrangement of different crystal faces together with macrodcfects such as steps, kinks, etc., are parameters describing the surface topography. The type of atoms and their mutual positions at the surface of the active phase or of the support, and the type, concentration and mutual positions of point defects (foreign atoms in lattice positions, interstitials, vacancies, dislocations, etc.) define the surface structure. 

This suggests the need to look critically at what is really known about the nature of lattice defects. Here Roth s paper on ferrous oxide (1960) (37), Fe0i87O, marks an important stage. Methods of diagnosing how nonstoichiometry arises—e.g., that ferrous oxide is cation-deficient, Fe O—strictly go no further than an enumeration of the number of atoms of each kind per unit cell. That the changes in unit cell contents signify a corresponding number of simple vacancies or interstitials is purely inferential and, as now appears, questionable. 

The ionic defects characteristic of the fluorite lattice are interstitial anions and anion vacancies, and the actinide dioxides provide examples. Thermodynamic data for the uranium oxides show wide ranges of nonstoichiometry at high temperatures and the formation of ordered compounds at low temperatures. Analogous ordered structures are found in the Pa-O system, but not in the Np-O or Pu-O systems. Nonstoichiometric compounds exist between Pu02 and Pu016 at high temperatures, but no intermediate compounds exist at room temperature. The interaction of defects with each other and with metallic ions in the lattice is discussed. 

The nonstoichiometry of the hydrides, therefore, must be attributed to lattice defects such as vacancies or interstitials. The reason for the large homogeneity ranges in these hydrides is the low interaction energy between defects. 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

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). 

Primary effects comprise recoil of the nucleus and excitation of the electron shell of the atom. The excitation may be due to recoil of the nucleus, change of atomic number Z or emission of electrons from the electron shell. Secondary effects and subsequent reactions depend on the chemical bonds and the state of matter. Chemical bonds may be broken by recoil or excitation. In gases and liquids mainly the bonds in the molecules are affected. The range of recoil atoms is relatively large in gases and relatively small in condensed phases (liquids and solids). Fragments of molecules are mobile in gases and liquids, whereas they may be immobilized in solids on interstitial sites or lattice defects and become mobile if the temperature is increased. 

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