Constitutional vacancies

The constitutional vacancy concentration in this case is given by... 

There are certain unusual types of defects in metal systems that are noteworthy. It has been found (Taylor Doyle, 1972) that in NiAl alloys A1 atoms on the Al-rich side do not substitute on the Ni sublattice instead there are vacancies in the Ni sites. For example, at 55 at.% Al, 18% of Ni sites are vacant while the A1 sites are filled. Such vacancies determined by composition are referred to as constitutional vacancies. Other alloys have since been found to exhibit such vacancies, typical of these being NiGa and CoGA. Another rather curious aspect of defects is the formation of void lattices when metals such as Mo are irradiated with neutrons or more massive projectiles (Gleiter, 1983). Void lattices arise from agglomeration of vacancies and are akin to superlattices. Typically, neighbouring voids in Mo are separated by 200 A. An explanation for the stability of void lattices on the basis of the continuum theory of elasticity has been proposed (Stoneham, 1971 Tewary Bullough, 1972). 

The T TiAl phase has an LIq ordered face-centered tetragonal structure (Ref 1-3), which has a wide range (49 to 66 at.% Al) of temperature-dependent stabihty (Ref 1). At the equiatomic TLAl composition, the c/a ratio is 1.02 tetragonality increases up to c/a = 1.03 with increasing aluminum concentration (Ref 4-6). Within the compositional range specified at ofif-stoichiometric compositions, excess titanium or aluminum atoms occupy antisites without creating constitutional vacancies (Ref 7). The y-TLAl phase apparently remains ordered up to its melting point of approximately 1450 °C (2640 °F). 

On the other hand, in some intermetallic compounds that permit off-stoichiometry (see Section 3.2), one finds structural ( constitutional ) vacancies, even at low temperatures the concentration of such defects may be important (sevoal percent) and in some cases the defects order. 

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. 

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. 

When a sibcon crystal is doped with atoms of elements having a valence of less than four, eg, boron or gallium (valence = 3), only three of the four covalent bonds of the adjacent sibcon atoms are occupied. The vacancy at an unoccupied covalent bond constitutes a hole. Dopants that contribute holes, which in turn act like positive charge carriers, are acceptor dopants and the resulting crystal is -type (positive) sibcon (Fig. Id). 

At T=OK, the criterion of minimum energy dictates that only one defect, the constitutional defect, is present. In NiAl for example this is the Ni antisite (Cab) in Ni-rich alloys, and the Ni vacancy (Cva) in Al-rich alloys [6]. The constitutional defects will be the dominant ones at high temperatures. The criterion that the A antisite should be the constitutional defect in A-rich alloys is ... 

On the other side of stoichiometry, we know from experiment that the constitutional defect in NiAl is the vacancy, so we can assume that Cva dominatej he defect populations. In this case we obtain the solution ... 

Figure 5.10. Defects consisting of oxygen vacancies constitute adsorption sites on a Ti02 (110) surface. Note how CO binds with its lone-pair electrons on a Ti ion (a Lewis acid site). O2 dissociating on a defect furnishes an O atom that locally repairs the defect. CO2 may adsorb by coordinating to an O atom, thus forming a carbonate group. [Figure adapted from W. Gopel, C. Rocher and R. Feierabend, Phys. Rev. B 28 (1983) 3427.]...

It is usually assumed that the dominant defect species responsible for nonstoichiometry is constituted by oxygen vacancies (rather than metal interstitials). This assumption can be justified on the basis of X-ray and neutron diffraction and density measurements . ... 

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. 

However, in order to perform intracrystalline chemical reactions that affect the components and not just the SE s, empty lattice sites (vacancies) constituting a complete... 

Let us re-examine the notion of a point defect in this context. If a molecular subgroup of a molecule is imperfect, this damaged molecule constitutes a point defect in the crystal, although the defect has no immediate influence on the molecule s translational mobility. Point defects that induce (translational) motion are vacancies or interstitials. We can infer from the form of the Lenard-Jones potential that vacan-... 

Until now, we have considered an infinite lattice, but a real material has limited dimensions, that is, n n2, n3 has boundaries. However, an infinite array of unit cells is a good approximation for regions relatively far from the surface, which constitutes the major part of the whole material [5], At this point, it is necessary to recognize that a real crystal has imperfections, such as vacancies, dislocations, and grain boundaries. 

Considering now oxide layer 1, there will be no decomposition of that layer required since it is in contact with the parent metal. Thus (dLj /dt)- = 0. Also, we neglect the possibility of a cation vacancy current J(jcv) due to unannihilated vacancies which diffuse into the parent metal instead of annihilating with metal atoms in the parent metal at the metal-oxide interface. Such would constitute a loss of potential oxide formation for layer 1. Another consideration is the positive contribution to the growth rate of layer 1 due to the decomposition of layer 2, so that we can write... 

This ignores the possibility of any oxygen solution current t/ ,°xy) into the parent metal, which, in terms of the equivalent anion vacancy current, °xv), would constitute a loss... 

C Hagemark and Toren [61] measured the Zn-Ziii+ ,0 phase boundary by an electro-chemical method and by Hall and conductivity measurements assuming that excess zinc constitutes a shallow donor in ZnO. New measurements of Tomlins et al. [62] suggest that Hagemark and Toren actually measured the phase boundary Zn-ZnOi-j, i.e., the concentration of oxygen vacancies. Recently, Lott et al. [63] measured the excess zinc in the vapor phase directly by optical absorption. Their results are shown in Fig. 1.6. 

Von Baumbach and Wagner [4] argued that the zinc interstitial is more probable because of the smaller ionic radius of the Zn++ ion (74 pm) compared with the oxygen ion (138 pm). What could not be decided for decades was the question whether the oxygen vacancy or the zinc interstitial constitutes the donor [5], see Sect. 2.1.1.1. 

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