Stoichiometry departure from

Another source of departure from stoichiometry occurs when cations are reduced, as for example in tire reduction of zinc oxide to yield an oxygen-defective oxide. The zinc atoms which are formed in tlris process dissolve in the lattice, Zn+ ions entering interstitial sites and the coiTesponding number of electrons being released from these dissolved atoms in much the same manner as was found when phosphorus was dissolved in the Group IV semiconductors. The Kroger-Viirk representation of dris reduction is... 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

The most studied non-stoichiometric system in actinide CaF2-structured compounds is the An-0 system all actinide dioxides (with the exception of Th02) present large departures from stoichiometry. Since uranium and plutonium dioxides (and their solid solutions) are employed as fuels in nuclear reactors, a very large effort has been dedicated to the study of their physical and physico-chemical properties. All these properties are affected by the oxygen composition of the compound. 

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. 

In the case of coneentrated solutions of defects, i.e. large departures from stoichiometry, a fundamental fact in encountered AHimer and ASconf are strongly correlated, i.e. 

Finally, lida et al. and Rigo et al. have shown that an anomaly reported at 12 K is due to a small departure from stoichiometry. 

However, structural chemistry in oxides with large departures from stoichiometry cannot be solely explained by point defects. Defects cannot remain isolated and interactions between them begin to occur. Our discussion therefore begins with a general description of the fundamental knowledge about nonstoichiometry in oxides. Understanding such disorder and the complex defect... 

In a related application, polyelectrolyte microgels based on crosslinked cationic poly(allyl amine) and anionic polyfmethacrylic acid-co-epoxypropyl methacrylate) were studied by potentiometry, conductometry and turbidimetry [349]. In their neutralized (salt) form, the microgels fully complexed with linear polyelectrolytes (poly(acrylic acid), poly(acrylic acid-co-acrylamide), and polystyrene sulfonate)) as if the gels were themselves linear. However, if an acid/base reaction occurs between the linear polymers and the gels, it appears that only the surfaces of the gels form complexes. Previous work has addressed the fundamental characteristics of these complexes [350, 351] and has shown preferential complexation of cationic polyelectrolytes with crosslinked car-boxymethyl cellulose versus linear CMC [350], The departure from the 1 1 stoichiometry with the non-neutralized microgels may be due to the collapsed nature of these networks which prevents penetration of water soluble polyelectrolyte. 

If the nonmetallic element plays such a crucial role in interatomic bonding, one would expect the elastic modulus and hardness to be sensitive to departures from stoichiometry. The available data regarding the dependence of carbon content on the elastic modulus of the transition... 

With a known mineral, as determined by electron diffraction or other technique (such as X-ray diffraction), determination of the stoichiometry and structural formula can be a suitable test for analytical precision of thin-film elemental analyses. This simple test follows the practice commonly employed for electron microprobe data in which the accuracy (and completeness) of an analysis is judged by the departure from stoichiometry calculated for a given mineral. Thus, thin-film analyses of olivines, pyroxenes, garnets, feldspars and many other common rock-forming minerals can be examined for internal consistency via a calculation of structural formulae. 

If the temperature dependence of the electronic conductivity of a semiconductor is to be accounted for, it is necessary to analyse how the density of charge carriers and their mobilities each depend upon T (see Eq. (2.25)). In the first place attention will be confined to the density n of electrons in the conduction band and the density p of holes in the valence band. When the intrinsic properties of the crystal are under consideration, rather than effects arising from impurities or, in the case of compounds, from departures from stoichiometry, the corresponding conductivity is referred to as intrinsic conductivity . The approach to the calculation of n and p in this instance is as follows. 

The nitrides and carbides of titanium and zirconium and the carbide of hafnium are extremely hard substances, resembling metals both in appearance and in electrical conductivity. Their formulae approach AxBh but some departure from stoichiometry is possible. Each of these refractory substances has the sodium chloride structure, described alternately (p. 190) as cubic close-packed arrays of metal atoms with the small nonmetal atoms in the octahedral holes. Note, however, that the parent metals themselves do not have cubic close-packed structures. Thus, the older view of such nitrides and carbides as lattices of the parent metals that are expanded to accommodate nitrogen or carbon atoms in the holes (interstices) is not admissible. The nature of the bonding in such refractory nitrides and carbides appears to be linked to the nature of bonding in metals in general, an important and interesting topic, but best pursued in more advanced works. 

Within the last 30 years there has developed a lively interest in the electronic properties of solids, many of which depend upon the existence of lattice defects and departures from stoichiometry. 

In the case of normal heptane it is immediately observed that there is something wrong stoichiometrically - whereas the moles of propane and butane produced are nearly equivalent, there is a substantial discrepancy between the moles of methane and hexane as well as between the moles of ethane and pentane. It is inevitable that the first step is to check the analysis - any departure from stoichiometry is initially inconceivable. But the analysis is correct and this is where the interdisciplinary forces must come to the rescue - ability to understand what is happening on the surface and what is the effect of the composition of the surface upon the series of reactions that must take place. What is happening has been very aptly named by Professor Burwell as organometallie Zoo . This is shown in figure 1. It is the intermediate formation of butyl and propyl carbonium ions on the surface which can then react with adjacent heptyl carbonium ions to produce C and carbonium ions. These can then split to... 

The departure from the 1 1 reaction stoichiometry in the xenon-rhodium hexafluoride system is less than for the platinum system. This is surprising in view of the greater instability and chemical reactivity of the rhodium fluoride. Ruthenium hexafluoride, which is less reactive than rhodium hexafluoride, has been reported [7] to react non-stoichiometrically with xenon. Perhaps the use of small quantities of rhodium fluoride favored the 1 1 addition. There is as yet no evidence for the oxidation state of rhodium in the adduct, although the formulation Xe -1- [RhFe] would, as in the corresponding platinum case, appear to be energetically more favorable than Xe +[RhF6] . 

Te temperature of transition to superconducting state 6 index expressing departure from stoichiometry... 

The explanation depends on the existence of more than one oxidation state for the metal. In wiistite, iron can exist in either the -f2 or the -f3 oxidation state. Suppose a solid were to begin at the hypothetical composition of Fei.ooOi.oo, with iron entirely in the +2 oxidation state. For every two Fe ions introduced, three Fe ions must be removed to maintain overall charge neutrality. The total number of moles of iron is then less than that in the ideal FeO stoichiometry. The departure from the nominal stoichiometry can be far more extreme than that found... 

Some metals form extensive series of oxides such as Ti 02n 1 or Mo 03 1 with structures related to simple oxides MO2 or MO3. Many transition-metal oxides show departures from stoichiometry leading to semiconductivity and others have interesting magnetic and electrical properties which have been much studied in recent years. We shall illustrate some of these features of oxides by dealing in some detail with selected metal-oxygen systems and by noting peculiarities of certain oxides. 

---