Larger deviations from stoichiometry

Non-stoichiometric oxides with high levels of disorder may adopt two modes of stabilization aggregation or elimination of point defects. Point defect aggregates forming clusters are examples of the former and extended defect structures like crystallographic shear-plane structures are examples of the latter. 

In a non-stoichiometric oxide of the type Mi jO (where M is a metal), the association of the vacancy and the positive hole, or M + ion, can form the simplest cluster complex for Fei , 0. X-ray and neutron diffraction measurements (Roth 1960) suggested that some Fe + ions are in tetrahedral sites (flgure 1.11(a)). An 

Anion-deficient fluorite oxides are also present, for example, U02- c, Ce02-x The presence of anion vacancies in reduced fluorites has been confirmed by diffraction studies. In reduced ceria for example, some well-ordered phases has been reported (Sharma et al 1999). The defective compounds show very high anion mobilities and are useful as conductors and as catalytic materials as will be described later. However, the structures of many anion-deficient fluorite oxides remain unknown because of the shear complexity of the disordered phases. There are, therefore, many opportunities for EM studies to obtain a better understanding of the defect structures and properties of these complex materials which are used in catalysis. 

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Let us consider a crystal similar to that discussed in Sections 1,3.3 and 1.3.4, which, in this case, shows a larger deviation from stoichiometry. It is appropriate to assume that there are no interstitial atoms in this case, because the Frenkel type defect has a tendency to decrease deviation. Consider a crystal in which M occupies sites in N lattice points and X occupies sites in N lattice points. It is necessary to take the vacancy-vacancy interaction energy into consideration, because the concentration of vacancies is higher. The method of calculation of free energy (enthalpy) related to is shown in Fig. 1.12. The total free energy of the crystal may be written... 

When the compound has a larger deviation from stoichiometry,... 

Eirst introduced in the late 1970s [1-5], electrodeposition is a low-cost, large-area semiconductor growth technique of thin films for applications in macroelectronic devices such as solar panels and large-area displays. Chalcogenide compounds (sulfides, selenides, and tellurides) afford larger deviations from stoichiometry without... 

Metal sulfides normally show a much larger deviation from stoichiometry than metal oxides. This is very clearly reflected in a high metal defect concentration of the strlfide lattice, resirlting in high values for the self-diffusion coefficient of the metal species. There are exceptions such as MnS, M0S2, and WS2, where the deviation from stoichiometry is srrraller or in the same order as for oxides. 

Transition elements, for which variable valency is energetically feasible, frequently show non-stoichiometric behaviour (variable composition) in their oxides, sulfides and related binary compounds. For small deviations from stoichiometry a thermodynamic approach is instructive, but for larger deviations structural considerations supervene, and the possibility of thermodynamically unstable but kinetically isolable phases must be considered. These ideas will be expanded in the following paragraphs but more detailed treatment must be sought elsewhere. " ... 

Uranium forms a trihydride which does not deviate from stoichiometry to any measurable degree at room temperature, but does so to a significant degree at elevated temperatures (29). For example, at 650° C., the deviation is larger than 5% to give UH2>84. The relation between lattice defects and nonstoichiometry in this compound is discussed below. 

CujS exhibits mixed conductivity, with Oqj+ 0.2 S/cm at 420°C. The electronic condnctivity is contributed by electrons and holes. For CujS eqniUbrated with copper, = 0.16 S/cm. As the mobility of the electrons is expected to be at least an order of magnitude larger than that of the ions, we conclude that n, p A/ . Yokota also fotmd that this class ( n, p A/ ) fits the experimental data. However, for T < 100°C, Allen and Bnhks find that the class /r = A/j fits their experimental data on CujS. This indicates that at elevated temperatnies thermally excited ionic defects dominate. However, thermal excitation of defect pairs is not effective at low temperatures T < 100°C), and one kind of ionic defect (copper vacancies) is formed by deviation from stoichiometry being accompartied by electronic defects (holes). Mixed condnctivity is observed also in Cuj xSe. Direct measurement of p and (n < p) shows that p N. Copper phosphates with the NASICON or allrrarrdite type stmcture exhibit mixed condnctivity with a wide range of ratios 0/0. ... 

In many cases, the layer growth can be described by a parabolic rate law x = kpt, where x is the scale thickness at time t and kp is the parabolic rate constant. This law may be derived from Wagner s theory of metal oxidation. The parabolic rate corrstants contain diffusion coefficients which are related to the concentration of the defects responsible for material transport through the layer. In fact, the higher the deviation from stoichiometry, the larger the diffusion coefficient and, consequently, the faster the oxidation rate of a metal at a given temperature. 

Larger etch pit densities of VCo.88 than of VCo,s3 form the subgrain boundaries characterized by the presence of substructure such as antiphase boundaries due to the formation of an ordered compound (150). The hardness of NbC decreases with carbon content and the hardness anisotropy of NbCo.8 is less pronounced than that of NbCo.9 (Fig. 11), which would be due to (a) deviation from stoichiometry of the crystal and (b) ordering of carbon vacancies. A high-resolution electron microscopy (HRFM) study gives very detailed information about defect order... 

The effect of compositional ratio of TiC on the evaporation rate of the films on the Mo substrate was examined by heating for 40 min in the temperature range 1873-2273 K in a vacuum of 5 X 10" torr. The compositional ratio, x = C/Ti, was determined from the EPMA measurement. The results are shown in Fig. 13, where TiC films on graphites formed by the CVD process were taken as a reference. The weight loss of the films became larger with deviation of the compositional ratio from stoichiometry. From X-ray photoelectron spectroscopy (XPS), the existence of free Ti was recognized in the films whose composition deviated from stoichiometry. 

There has been one report on the preparation of californium hydrides [235]. The hydrides were prepared by reaction of californium metal with hydrogen at elevated temperatures. It was believed that the stoichiometries were close to that for the dihydride (CfHj+The products exhibited fee structures with an average lattice parameter of Oo = 0.5285 nm, which is slightly larger than expected for the compound based on extrapolations of parameters for preceding actinide dihydrides. This larger parameter and the inability to prepare a trihydride of californium were believed to reflect a tendency for californium to be divalent In the lanthanide-hydrogen system, the hydrides of divalent europium and ytterbium metals deviate from the behavior of the other lanthanide hydrides [149]. 

The simplest argument that TmS is trivalent, TmSe intermediate valent and TmTe divalent under normal conditions comes from comparing the lattice constants of the lanthanide sulfides, selenides and tcllurides as shown in fig. 58 (after Bucher et al. 1975). The lanthanide contraction is the cause for the general trend in the curves and the standard divalent Sm, Eu and Yb ions with their larger ionic radius are the obvious deviations. TmTe lies on the divalent curve, TmS on the trivalent one and TmSe is intermediate and by linear interpolation between a hypothetical divalent and trivalent TmSe one obtains a valency of 2.75. The figure also shows that SmS, in this case by pressure or trivalent rare earth doping, can be intermediate valent, TmSe, in this case by stoichiometry variation, can become trivalent and TmTe, in this case by pressure, oxidation and stoichiometry variation, can become intermediate valent. 

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