Defect non-stoichiometric

Non-stoichiometric defects can occur by oxidation and reduction of the cations, by introduction of interstitials, or by loss of the anions. 

Non-stoichiometric Defects. These often occur in transition-metal compounds, especially oxides and sulfides, because of the ability of the metal to exist in more than one oxidation state. A well-known case is FeO which consists of a cep array of oxide ions with all octahedral holes filled by Fe2 + ions. In reality, however, some of these sites are vacant, while others—sufficient to maintain electroneutrality—contain Fe3 + ions. Thus the actual stoichiometry is commonly about Fe0 950. Another good example is TiO which can readily be obtained with compositions ranging from Ti0 740 to Tij 670 depending on the pressure of oxygen gas used in preparing the material. 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

Semiconducting Ceramics. Most oxide semiconductors are either doped to create extrinsic defects or annealed under conditions in which they become non stoichiometric. Although the resulting defects have been carefully studied in many oxides, the precise nature of the conduction is not well understood. Mobihty values associated with the various charge transport mechanisms are often low and difficult to measure. In consequence, reported conductivities are often at variance because the effects of variable impurities and past thermal history may overwhelm the dopant effects. 

A special mention is in order of high-resolution electron microscopy (HREM), a variant that permits columns of atoms normal to the specimen surface to be imaged the resolution is better than an atomic diameter, but the nature of the image is not safely interpretable without the use of computer simulation of images to check whether the assumed interpretation matches what is actually seen. Solid-state chemists studying complex, non-stoichiometric oxides found this image simulation approach essential for their work. The technique has proved immensely powerful, especially with respect to the many types of defect that are found in microstructures. 

As materials chemistry has developed, it has come to pay more and more attention to that archetypal concern of materials scientists, microstructure. That concern came in early when the defects inherent in non-stoichiometric oxides were studied by the Australian. I.S. Anderson and others (an early treatment was in a book edited by Rabenau 1970), but has become more pronounced recently in the rapidly growing emphasis on self-assembly of molecules or colloidal particles. This has not yet featured much in books on materials chemistry, but an excellent recent popular account of the broad field has a great deal to say on self-assembly (Ball 1997). The phenomenon of graphoepitaxy outlined in Section 10.5.1.1 is a minor example of what is meant by self-assembly. 

There are two basic questions which can be decided only by experiments. First, we must know whether the metal or the oxygen is present in excess, and second, we must know how the excess component is incorporated in the oxide lattice. In connection with the latter question we have to remember that a non-stoichiometric crystal remains electrically neutral (except in narrow regions near the surfaces), so that if the excess component is present in the crystal as ions, lattice defects with charges of opposite sign must necessarily be present also (see Figs. 1.77 and 1.78). The most important defect structures will be discussed in this section. 

Investigations based on equation (a) are indirect. Direct structural studies using diffraction techniques (X-ray or neutron), or electron microscopy, while they cannot detect the low concentrations of defects present in NiO or CoO are indispensible to the study of grossly non-stoichiometric oxides like FeO, TiOj, WOj etc., and particularly electron microscopes with a point-to-point resolution of about 0.2 nm are widely used. The first direct observation of a point defect (actually a complex of two interstitial metal atoms, and two oxygen atoms in Nb,2029) was made" using electron microscopy. 

A number of selenium and tellurium compounds of the presently discussed metals show a quite different behavior from the Fe-S system. Iron and selenium form two compounds FeSe with a broad stoichiometry range and FeSe2 with a much narrower composition field. Below 400 the non-stoichiometric Fei xSe exists by creation of iron vacancies and can have compositions lying between FeySes and Fe3Se4. At low temperatures there exist two phases an a (PbO type) and a f) (NiAs type) phase. The crystal sUiicture of the diselenide, FeSe2, is an orthorhombic, C18 (marcasite) type. In the Fe-Te system, the defect NiAs structure is found at a composition close to FeTei.s, as about one-third of the Fe atoms are missing. At compositions around FeTe the behavior is complex, and the f)-phase has the PbO structure (like FeSe) but with additional metal atoms (i.e., FeuTe). 

Point defects were mentioned in a prior chapter. We now need to determine how they aiffect the structure auid chemical reactivity of the solid state. We will begin by identifying the various defects which can arise in solids and later will show how they can be manipulated to obtain desirable properties not found in naturally formed solids. Since we have already defined solids as either homogeneous and heterogeneous, let us look first at the homogeneous t5 e of solid. We will first restrict our discussion to solids which are stoichiometric, and later will examine solids which can be classified as "non-stoichiometric", or having an excess of one or another of one of the building blocks of the solid. These occur in semi-conductors as well as other types of electronically or optically active solids. 

In a non-stoichiometric crystcd, the lattice may have either excess charge or excess cations and/or anions situated in the lattice. Consider the semiconductor, Ge. It is a homogeneous solid and is expected to contain excess charge. The defect reactions associated with the formation of p-type and n-type lattices are ... 

This presentation is presented for those who wish to examine the mathematics of both non-stoichiometric intrinsic- defect compounds and the ionization of defects in both stoichiometric and nonstoichiometric compounds as represented by ... 

We now proceed as we did for the stoichiometric case, namely to develop defect- concentration equations for the non-stoichiometric case. Consider the effect of Anti-Frenkel defect production. From Table 2-1, we get Kaf with its associated equation, kAF In Table 2-2, we use Kxi for X-interstitial sites. Combining these, we get ... 

In the non-stoichiometric case where ionization of defects is the norm, the mathematics become too complicated so that the equations are not solvable. However, we can use a thermodynamic method to obtain the results we want. We will present here the case of silver bromide whose use in photographic film highlights the use of defect chemistry for practical purposes. 

Point defects are only notionally zero dimensional. It is apparent that the atoms around a point defect must relax (move) in response to the defect, and as such the defect occupies a volume of crystal. Atomistic simulations have shown that such volumes of disturbed matrix can be considerable. Moreover, these calculations show that the clustering of point defects is of equal importance. These defect clusters can be small, amounting to a few defects only, or extended over many atoms in non-stoichiometric materials (Section 4.4). 

Non-stoichiometric compounds Mass action law treatment of defect equilibria... 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

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