Lattice defects vacancies

The term surface of a metal usually means the top layer of atoms (ions). However, in this book the term surface means the top few (two or three) atomic layers of a metal. Surfaces can be divided into ideal and real. Ideal surfaces exhibit no lattice defects (vacancies, impurities, grain boundaries, dislocations, etc.). Real surfaces have all types of defects. For example, the density of metal surface atoms is about 10 and the density of dislocations is on the order of magnitude 10 cm . ... 

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. 

Theoretical explanations which have been advanced to account for the decrease in order occurring at the temperature of fusion of a crystalline solid include an increase in the amplitude of thermal vibrations so that the stabilizing forces of the crystal are overcome, and/or that there is a marked increase in the concentrations of lattice defects (vacancies) or dislocations. Within a few degrees of the melting point, the... 

Moreover, the resistivity is influenced by all kinds of lattice defects (vacancies, dislocations, grain boundaries, etc.) and impurities. 

Point lattice defects vacancies, interstitials,and substitutional elements... 

This is the first book devoted to the theoretical modelling of refractory carbides and nitrides and alloys based on them. It makes use of computational methods to calculate their spectroscopic, electric, magnetic, superconducting, thermodynamical and mechanical properties. Calculated results on the electronic band structure of ideal binary transition-metal carbides and nitrides are presented, and the influences of crystal lattice defects, vacancies and impurities are studied in detail. Data available on chemical bonding and the properties of multi-component carbide- and nitride-based alloys, as well as their surface electronic structure, are described, and compared with those of bulk crystals. 

Impurity atoms can form solid solutions in ceramic materials much as they do in metals. Solid solutions of both substitutional and interstitial types are possible. For an interstitial, the ionic radius of the impurity must be relatively small in comparison to the anion. Because there are both anions and cations, a substitutional impurity substitutes for the host ion to which it is most similar in an electrical sense If the impurity atom normally forms a cation in a ceramic material, it most probably will substitute for a host cation. For example, in sodium chloride, impurity Ca and ions would most likely substitute for Na and Cl ions, respectively. Schematic representations for cation and anion substitutional as well as interstitial impurities are shown in Figure 12.21. To achieve any appreciable sohd solubility of substituting impmity atoms, the ionic size and charge must be very nearly the same as those of one of the host ions. For an impurity ion having a charge different from that of the host ion for which it substitutes, the crystal must compensate for this difference in charge so that electroneutrality is maintained with the solid. One way this is accomplished is by the formation of lattice defects—vacancies or interstitials of both ion types, as discussed previously. 

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... 

The smallest imperfections in metal crystals are point defects, in particular vacant lattice sites (vacancies) and interstitial atoms. As illustrated in Fig. 20.21a, a vacancy occurs where an atom is missing from the crystal structure... 

Catalytic oxidations on the surface of oxidic materials usually proceed according to the Mars-Van Krevelen mechanism [P. Mars and D.W. van Krevelen, Chem. Eng. Sci. 3 (1954) 41], as illustrated in Fig. 9.17 for the case of CO oxidation. Instead of a surface reaction between CO and an adsorbed O atom, CO2 is formed by reaction between adsorbed CO and an O atom from the metal oxide lattice. The vacancy formed is filled in a separate reaction step, involving O2 activation, often on defect sites. 

We have shown that by stacking atoms or propagation units together, a solid with specific symmetry results. If we have done this properly, a perfect solid should result with no holes or defects in it. Yet, the 2nd law of thermod5mamics demands that a certain number of point defects (vacancies) appear in the lattice. It is impossible to obtain a solid without some sort of defects. A perfect solid would violate this law. The 2nd law states that zero entropy is only possible at absolute zero temperature. Since most solids exist at temperatures far from absolute zero, those that we encounter are defect-solids. It is natural to ask what the nature of these defects might be. 

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. 

It is possible for one or more lattice defects to associate with one another, that is, to cluster together. These are indicated by enclosing the components of such a cluster in parentheses. As an example, (VMVX) would represent a defect in which a vacancy on a metal site and a vacancy on a nonmetal site are associated as a vacancy pair. 

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. 

Introduction of defects (vacancies or interstitials) in a perfect lattice determines a variation in the free energy G of the lattice which may be written as ... 

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. 

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