Stoichiometric Variations

The most important gaseous component is X2, as is the case in most oxides, halides, and sulfides. The stoichiometric variation will be linked to the partial pressure of the surrounding nonmetal atmosphere. The nonmetal component will be gained at high pressures and lost at low pressures. These options correspond to oxidation and reduction. 

Pure Cr203 is an intrinsic semiconductor with a band-gap of approximately 3.3 eV. Generally, Cr203 shows little stoichiometric variation. On doping with Ti02, Ti4+ ions substitute on Cr3+ sites in the structure. The conductivity of the doped solid is n-type and has a dependence upon oxygen partial pressure. The three... 

Stoichiometric variations in compositions of a material and of surface layers can be revealed by AEM. Because a relatively small amount of scattering occurs through a thin HRTEM specimen, X-rays are generated from a volume that is considerably less than in the case of electron microprobe analysis (EPMA). For quantitative microanalysis, a ratio method for thin crystals (57) is used, given by the equation ... 

Rutile and anatase are used in photocatalysis and as catalyst supports and we describe some important structural features later. The titanium-oxygen system plays a key role in understanding stoichiometric variations. The highest oxide, Ti02, is polymorphic and the four known crystal structures are rutile, anatase, brookite and a high-pressure form similar to a-Pb02. 

Crystal Self-Diffusion in Nonstoichiometric Materials. Nonstoichiometry of semiconductor oxides can be induced by the material s environment. For example, materials such as FeO (illustrated in Fig. 8.14), NiO, and CoO can be made metal-deficient (or O-rich) in oxidizing environments and Ti02 and Zr02 can be made O-deficient under reducing conditions. These induced stoichiometric variations cause large changes in point-defect concentrations and therefore affect diffusivities and electrical conductivities. 

Soon after the discovery of the RNi2B2C compounds (see Section 1.1) high-quality polycrystalline samples and even single crystals could be prepared, thus enabling significant studies at an early stage. Some properties, however, sensitively depend on small stoichiometric variations or on atomic disorder in the samples. In this section, we focus on this problem including a short overview on preparation techniques. Studies on the deposition and on basic properties of thin films will also be reported. 

Statistical thermodynamic treatments of defect populations have lead to an explanation of existence of grossly nonstoichio-metric crystals in terms of microdomains of ordered structure. The model considers that the nonstoichiometric matrix is made up of a mosaic of small regions of ordered defect-free structures, the microdomains. To account for stoichiometric variation, one can postulate that at least two microdomains with different compositions occur. However, compositional change might simply arise at the surface of the domain. For example, if there are compositionally identical microdomains, one of which is bounded by an anion surface and one by a cation surface, variation in the two populations can give rise to compositional variation. In a strict sense, as each microdomain is ordered, the concept of a defect is redundant, except for... 

The exact temperature of the phase transition in the experiments above is subject to some uncertainty, which we attribute to the stoichiometric variations in both the central atom of the counterion (P,As) and the type of the halide. The picture that emerges, however, is compatible with the full scope of experimental results a dynamic Jahn-Teller effect at high temperature, a structural phase transition in the 120-150 K range, and a distortion of the molecular ion in the low-temperature phase, arising from the positive synergy of the cooperative Jahn-Teller effect and the low symmetry of the environment. The static-to-dynamic transition does not coincide with the structural transition and its temperature depends on the detection method whereas ESR spectra are isotropic at room temperature, infrared lines are still split, indicating a distorted state on the time scale of the measurement. This... 

In conclusion, the temperature dependence of shift factors for the networks studied here do not follow the WLF equation, but rather an Arrhenius-type relationship. The apparent activation energies are independent of stoichiometric variation [as they are when is varied by changing prepolymer molecular weight (13)]. ... 

In addition, the deprotonation process allows additional stoichiometric variations depending on the stability of the protonated hydride complex MH2+, which may prefer either the classical or the nonclassical tautomeric form. In the latter case, the product may be unstable, depending on the reaction conditions, toward replacement of H2 by a solvent molecule, leading to the possible alternative stoichiometries of equations 26-28. 

Palatnik et al. (1971, 1975), Tu et al. (1972), Ahn and Shafer (1971), Ikesawa and Suzuki (1973), Mitani et al. (1975) and Mayr et al. (1979) have studied the dependence of the absorption spectra on the nature and the temperature of the substrate, the impurities and the lattice effects. Ahn and Shafer (1971) have shown that with increasing incorporation of iron in a EuS film, the optical absorption increases. From optical transmission and reflection spectrometry data and the first experiment on light scattering from acoustic spin waves, Mayr et al. (1979) have shown that it is possible to determine stoichiometric variations, lattice defects, oxide formation and magnetic homogeneity. 

In practice the stmctures are often complex when details are analysed, especially with respect to stoichiometric variations. In these cases, ordering of component atoms can skew the symmetry away from hexagonal or rhombohedral to orthorhombic or monoclinic. These forms are sensitive to pressure, temperature and composition, implying that complicated phase relationships are usual. In the descriptions that follow in this and the following section, these subtleties have largely been put to one side, and it has been assumed that the structures consist of ideal layer stacking. 

AGk, AH, AH thus obtained represent the stoichiometric variations of the Gibbs free energy, enthalpy and entropy, respectively, on the transfer of one mole of solute between the two phases in standard state. AG is the same for the hypothetical ideal state and the real state pro wded that the activity equals unity in both. However AHJ is different in the two cases and reference should be made to the hypothetical ideal state. Because the intermolecular attractions which determine AH are identical in the hypothetical (standard) and reference states, AH refers also to the modification of partial molar enthalpy between the reference states. The same conclusion holds true for the modification of molar heat capacities. A/Sk, like AGk, does not apply to the modification of partial molar entropy between reference states but refers to the hypothetical standard state described above. 

The stoichiometric variations of entropy and enthalpy are obtained by using the equations ... 

The stoichiometric variations of standard Gibbs free energies of vaporization of single solutes A G result from fugacities and molar volumes [26] ... 

Mechanical and thermo-mechanical properties These properties have been considered in reviews by Gibson and Harvey (1966), Vier (1975) and Eyring (1979). Such properties as thermal expansion, elastic properties and volume change accompanying stoichiometric variation have been considered. 

An attractive aspect of co-crystallisation in the synthesis of new API forms is the possibility of forming co-crystals containing identical constituents in different stoichiometric ratios.Mechanochemical methods provide a particularly simple procedure for constructing such stoichiometric variations by simply grinding different amounts of starting materials. This was first demonstrated for the model API caffeine upon co-crystallisation with acetic... 

The synthesis of stoichiometric variations was systematically investigated for co-crystals of the model API nicotinamide with various dicarboxylic acids. 

Table 8.1 Results" of screening for stoichiometric variations of nicotinamide co-crystals with dicarboxylic acids. ...

Stoichiometric change due to reaction of gas with a solid belongs to this class of transformation, such as the stoichiometric variation in cerium oxide under oxygen pressiue, which can be expressed as... 

Table 17.3. Comparison of the masses of the cell computed starting from the stoichiometric variation and those obtainedfrom the density and the cell parameters...

Fig. 22 PLE at Xem = 434 nm and PL spectra at Xex = 319 nm of undoped ZnS nanoparticles. Inset PL spectra of undcyed ZnS showing reduction in blue emission intensities with stoichiometric variations of X = [S VZn " ] (after Manzoor et al.. Ref [39]).

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