Oxides lattice parameter

Fig. 5.10. MIGS density of states at the interface no and MIGS damping length Ip, for energies at the gap centre, as a function of the oxide ionicity (ec — f a)/P, for two crystal structures (NaCl full lines ZnS dashed lines). The anion level position 6a is taken at 6 eV above the bottom of the metal conduction band and the oxide lattice parameter is a = 5 A (after Bordier and Noguera, 1991).

An indirect estimate of surface tension may be obtained from the change in lattice parameters of small crystals such as magnesium oxide and sodium chloride owing to surface tensional compression [121] however, these may represent nonequilibrium surface stress rather than surface tension [68]. Surface stresses may produce wrinkling in harder materials [122]. 

Powder XR diffraction spectra confirm that all materials are single phase solid solutions with a cubic fluorite structure. Even when 10 mol% of the cations is substituted with dopant the original structure is retained. We used Kim s formula (28) and the corresponding ion radii (29) to estimate the concentration of dopant in the cerium oxide lattice. The calculated lattice parameters show that less dopant is present in the bulk than expected. As no other phases are present in the spectrum, we expect dopant-enriched crystal surfaces, and possibly some interstitial dopant cations. However, this kind of surface enrichment cannot be determined by XR diffraction owing to the lower ordering at the surface. 

The physical origin of this structural flexibility of the FeO overlayer is still unclear, the more so since no clear trend is observable in the sequence of lattice parameters of the coincidence structures. The FeO(l 11) phase forming up to coverages of 2-3 ML is clearly stabilized by the interactions with the Pt substrate since FeO is thermodynamically metastable with respect to the higher iron oxides [106,114], FeO has the rock salt structure and the (111) plane yields a polar surface with a high surface energy [115], which requires stabilization by internal reconstruction or external compensation. The structural relaxation observed in the form of the reduced Fe—O... 

Figure 1 shows the powder X-ray diffraction (XRD) pattern of the as-prepared Li(Nio.4Coo.2Mno.4)02 material. All of the peaks could be indexed based on the a-NaFeC>2 structure (R 3 m). The lattice parameters in hexagonal setting obtained by the least square method were a=2.868A and c=14.25A. Since no second-phase diffraction peaks were observed from the surface-coated materials and it is unlikely that the A1 ions were incorporated into the lattice at the low heat-treatment temperature (300°C), it is considered that the particle surface was coated with amorphous aluminum oxide. 

It has been noted that the conductivity and activation energy can be correlated with the ionic radius of the dopant ions, with a minimum in activation energy occurring for those dopants whose radius most closely matches that of Ce4+. Kilner et al. [83] suggested that it would be more appropriate to evaluate the relative ion mismatch of dopant and host by comparing the cubic lattice parameter of the relevant rare-earth oxide. Kim [84] extended this approach by a systematic analysis of the effect of dopant ionic radius upon the relevant host lattice and gave the following empirical relation between the lattice constant of doped-ceria solid solutions and the ionic radius of the dopants. 

Figure 5.8. Lanthanide Ln203 oxides (cubic cI80-Mn2O3 type, on the left side) and Pb alloys (LnPb3, cubic cP4-type, on the right). The trends of the lattice parameter and of the heat of formation are shown (see the text and notice the characteristic behaviour of Eu and Yb). A schematic representation of the energy difference between the divalent and trivalent states of an ytterbium compound is shown. Apromff represents the promotion energy from di- to trivalent Yb metal, A,//11, and Ar/Ynl are the formation enthalpies of a compound in the two cases in which there is no valence change on passing from the metal to the compound the same valence state (II or III) is maintained.

NMR properties, 33 213, 274 in NMR studies of zeolites, 33 254-264 in sheet silicate studies, 33 342-345 -magnesium oxide catalyst, lattice parameter, 35 75... 

Lateral polymerization model, 30 169-170 Lattice oxygen, 27 191, 32 118-121 chemical nature of, 27 195, 196 role of, 27 191-195 Lattice parameters, Cn/ZnO, 31 247 Layer lattice silicates, catalysts, 39 303-326 catalyst solution immobilization, 39 319-324 2-6-di-fert-butylphenoI liquid-phase oxidation on Cu -TSM, 39 322-324 propylene gas-phase oxidation on Cu Pd -TSM, 39 320-322 materials, 39 305-307 metal ion-exchanged fluorotetrasilicic mica, 39 306-308... 

It has been reported that the value of the cubic lattice parameter, which is directly related to the average oxidation state of the manganese, is critical to obtain effective cycling. The lattice parameter should preferably be 8.23A or less, and such values are associated with lithium-rich materials, Lii+Mriz-jOi, where the average manganese oxidation state is 3.58 or higher this value minimizes dissolution of manganese and also the impact of the... 

Figure 12. Correlation of the lattice parameter of the spinel Lii+JV[n2-/)4 with (a) the lithium content, (b) manganese oxidation state, and (c) capacity loss of the cell over the first 120 cycles, after ref 157.

Table 1.21 MEG values of lattice energy and lattice parameter for varions oxides, compared with experimental values. Source of data Mackrod and Stewart (1979). C/ is expressed in kJ/mole (in A) corresponds to the cell edge for cnbic snbstances, whereas it is the lattice parameter in the a plane for AI2O3, Fe203, and Ga203 and it is the lattice parameter parallel to the sixfold axis of the hexagonal unit cell in mtiles CaTi03 and BaTi03.

The rapid developments in the microelectronics industry over the last three decades have motivated extensive studies in thin-film semiconductor materials and their implementation in electronic and optoelectronic devices. Semiconductor devices are made by depositing thin single-crystal layers of semiconductor material on the surface of single-crystal substrates. For instance, a common method of manufacturing an MOS (metal-oxide semiconductor) transistor involves the steps of forming a silicon nitride film on a central portion of a P-type silicon substrate. When the film and substrate lattice parameters differ by more than a trivial amount (1 to 2%), the mismatch can be accommodated by elastic strain in the layer as it grows. This is the basis of strained layer heteroepitaxy. 

Direct experimental determinations of these quantities do not exist. The nearest approach seems to be in some observations made by Nicolson (26) in his work on surface tension. He found that when he made magnesium oxide particles by burning magnesium in air, their lattice constants were the same as those of the bulk material. When the crystals were made by the decomposition of magnesium carbonate in vacuo, the expected change in lattice parameter took place due to the surface tension. These negative results obtained in the first method of preparation were attributed to the presence of gases adsorbed from the air. 

The lattice parameters for the polymorphic MaOs obtained by various investigators are compared in Table 4. The different polymorphic forms show characteristic M—0 streaching frequencies in the infrared between 500 and 600 cm i. These M—O frequencies were found (75) to vary linearly with the lattice parameter a of the oxides. 

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