Stoichiometry small deviations from

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. " ... 

Small deviation from stoichiometry. I. Metal vacancies... 

Let us consider the compounds which show a small deviation from the stoichiometric composition and whose non-stoichiometry is derived from metal vacancies. The free energy of these compounds, which take the composition MX in the ideal or non-defect state, can be calculated by the method proposed by Libowitz. To readers who are well acquainted with the Fowler-Guggenheim style of statistical thermodynamics, the method here adopted may not be quite satisfactory however, the Libowitz method is understandable even to beginners who know only elementary thermodynamics and statistical mechanics. It goes without saying that the result calculated by the Libowitz method is essentially coincident with that calculated by the Fowler-Guggenheim method. 

The production of self-activated CaW04 is more difficult than that of MgW04. Small deviations from stoichiometry in the composition have a marked effect on the efficiency. Also, traces of Pb2 + shift the emission peak from 415 nm to 439 nm (0.0006 mol % Pb2+). To bind excess CaO in the production process, a small proportion of sulfate is used. The precipitated CaW04 is washed until chloride-free, dried,... 

Investigating HoNi2E>2C one has to consider that between Tn and Tc the magnetic and superconducting properties are quite sensitive to the details of the preparation procedure and to small deviations from the ideal stoichiometry (Wagner et al., 1999 Dertinger et al., 2001 Alleno et al., 2001 Behr and Loser, 2005 see also Sections 3.1 and 4.9.3). 

In compounds such as CdTe (26), CdS (23), PbS (5), or PbTe (7), the very small deviations from 1 to 1 stoichiometry result from lattice disorder arising from the presence, in small concentrations, of vacancies or interstitials. Thus, in CdTe it is believed that the predominant structural defects are Cd interstitials... 

The individual grains of samples with a pronounced orthorhombic distortion show striations or bands when viewed in an electron microscope (see figure 3). This is believed to be due to domain formation in one band the "b" axis of the unit cell is oriented 90° to the "b" axis of the adjacent band. Electron microscopy also shows that small deviations from stoichiometry result in an amorphous second phase forming in the grain boundaries. Because most of the phases in equilibrium with YBa2Cu307 are insulators, a grain boundary phase is probably an insulator. 

In order to detect small deviations from stoichiometric composition, physical properties such as electrical, magnetic, or optical characteristics provide us a valuable information. The measurements of physical properties described above are commonly used with many other systems where variations in stoichiometry appear in compounds as well as with rare earth oxides. 

The oxide scale shows only small deviations from stoichiometry and, hence, the ionic fluxes are independent of position within the scale. 

Kc,Ke, and are the instantaneous values at that place. Since all of these values may change with the position in the scale, it is necessary to integrate Equation (3.40) in order to define jc in terms of the scale thickness and the measurable metal chemical potentials at the metal-scale, and scale-gas, ix, interfaces. Eor phases with small deviations from stoichiometry, jc can be assumed to be independent of x. 

Since ZnO shows only small deviations from stoichiometry we can write Equation (3.54) ... 

No data are known on the dependence of partial vapor pressures on the composition of the solid phase, because of the small deviation from stoichiometry in Th02(s). 

Very small deviations from oxygen stoichiometry can change drastically the superconducting properties of the thallium cuprates without destroying the structure. This is the case of the thallium cuprates for which a spectacular effect of oxygen... 

An element or compound is polytypic if it exists in two or more layerlike crystal structures that differ in their layer-stacking sequences. Polytypes are nearly identical in structure and composition and polytypism is a special case of polymorphism the two-dimensional translations within the layers are essentially preserved, whereas the lattice spacing normal to the layers varies between polytypes and is indicative of the stacking period. There is increasing evidence that some polytypic structures are characterized either by small deviations from stoichiometry or by small amounts of impurities. " ... 

The glass s >strate is covered by a metallic film (Ag) which serves as a back contact. The heterojunction system is based on a CdS film (between lO and 30 ym thickness) which due to sulfur vacancies is n-type. On the top of the CdS film a Cu S film (x 2) is prepared which due to small deviations from stoichiometry is p-type. A highly transparent grid represents the front contact. The front glass plate through which the incoming radiation penetrates to the junction provides a hermetically sealed encapsulation which is required for long time stability. 

A general tendency similar to that of oxygen deficient oxides applies to metal deficient oxides in the oxide Mi-yO the metal vacancies are doubly charged at very small deviations from stoichiometry and tend to become singly charged with increasing nonstoichiometry. 

As regards the electron holes two limiting conditions may be considered At low concentrations of electron holes (small deviations from stoichiometry p we have... 

For small deviations from stoichiometry, i.e., the concentration of the electron... 

Electroneutrality Equations (5.47) and (5.49) hold for small deviations from stoichiometry, while Equations (5.48) and (5.50) hold for large deviations from stoichiometry. 

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