Solid-state cells 596 INDEX

The second choice is a simpler solution. According to Sarko and Muggli,66 all 39 observed reflections in the Valonia X-ray pattern are indexable by a two-chain triclinic unit cell with a = 9.41, b =8.15 and c = 10.34 A, a = 90°, 3 = 57.5°, and y = 96.2°. Ramie cellulose, on the other hand, is completely consistent with the two-chain monoclinic unit cell. Also, there are significant differences between their high-resolution solid-state l3C NMR spectra, indicating that Valonia and ramie celluloses, the two most crystalline forms, reflect two distinct families of biosynthesis. On this basis, the Valonia triclinic and the ramie monoclinic forms are classified69 as Ia and Ip, respectively. It has been shown from a systematic analysis of the NMR spectra by these authors, and from electron-dif-... 

This edition of the Fuel Cell Handbook is more comprehensive than previous versions in that it includes several changes. First, calculation examples for fuel cells are included for the wide variety of possible applications. This includes transportation and auxiliary power applications for the first time. In addition, the handbook includes a separate section on alkaline fuel cells. The intermediate temperature solid-state fuel cell section is being developed. In this edition, hybrids are also included as a separate section for the first time. Hybrids are some of the most efficient power plants ever conceived and are actually being demonstrated. Finally, an updated list of fuel cell URLs is included in the Appendix and an updated index assists the reader in locating specific information quickly. 

Alumina is a material that has been studied extensively [6,19,20]. Its y-form is characterized as a tetragonally distorted defect spinel lattice, with a unit cell composed of 32 oxygen atoms and 21 A aluminum atoms. There are 2-/i vacant cation positions per unit cell. Among the 2116 aluminum atoms in the unit cell are a significant number of octahedral, as well as tetrahedral, sites. For the y-form, one can consider an idealized surface to be composed of two low-index defect-spinel crystal planes, specifically the (110) and (100) planes [19]. The presence of these planes implies that there is a mixture of octahedral and tetrahedral aluminum sites exposed on the surface. Recent solid-state NMR experiments have observed these sites indirectly [21] and suggest that the surface can also be described by (110) and (111) planes. In general, however, it is best to consider the surface of y-alumina as being composed of the (110), (100), and (111) planes. 

In this Seventh Edition of the Fuel Cell Handbook, we have discussed the Solid State Energy Conversion Alliance Program (SECA) activities. In addition, individual fuel cell technologies and other supporting materials have been updated. Finally, an updated index assists the reader in locating specific information quickly. 

The arrangement of helices in the solid and liquid crystalline states of poly(a-phenylethyl isocyanide) were determined by X-ray and electron diffraction. Well-defined diffraction patterns were obtained from oriented films using selected area electron diffraction. Intermolecular and intramolecular patterns were calculated from the five Debye-Scherrer rings. All the reflections were indexed in terms of a pseudo-hexagonal triclinic unit cell, with... 

We call this Pt(100) surface reconstructed. Surface reconstruction is defined as the state of the clean surface when its LEED pattern indicates the presence of a surface unit mesh different from the bulklike (1 x 1) unit mesh that is expected from the projection of the bulk X-ray unit cell. Conversely, an unreconstructed surface has a surface structure and a so-called (1 x 1) diffraction pattern that is expected from the projection of the X-ray unit cell for that particular surface. Such a definition of surface reconstruction does not tell us anything about possible changes in the interlayer distances between the first and the second layers of atoms at the surface. Contraction or expansion in the direction perpendicular to the surface can take place without changing the (1 x 1) two-dimensional surface unit cell size or orientation. Indeed, several low Miller index surfaces of clean monatomic and diatomic solids exhibit unreconstructed surfaces, but the surface structure also exhibits contraction or expansion perpendicular to the surface plane in the first layer of atoms (9b). 

Just as was found in the discussion prior to eqn (4.75), the set of allowed q vectors is restricted because of the condition that the crystal is periodic. Indeed, because of this restriction, the q vectors are of the form = lirmi/Na, qy = 2nm.2lNa and q, = Inm /Na, where mi, m2 and m3 take only integer values. We have thus reduced our original problem which demanded the diagonalization of a 3 A X 3 A matrix to a problem in which we diagonalize a 3 x 3 matrix A times, where q adopts A different values and labels the different vibrational states. Here we have trimmed our analysis down such that we consider only the case in which there is one atom per unit cell. Aside from index gymnastics, the extension to more atoms in each cell is relatively uneventful. Note also that the present discussion parallels, even in the details, that already given in the context of the electronic structure of periodic solids in chap. 4. 

The local MP2 electron-correlation method for nonconducting crystals [109] is an extension to crystalline solids of the local correlation MP2 method for molecules (see Sect. 5.1.5), starting from a local representation of the occupied and virtual HF subspaces. The localized HF crystalline orbitals of the occupied states are provided in the LCAO approximation by the CRYSTAL program [23] and based on a Boys localization criterion. The localization technique was considered in Sect. 3.3.3. The label im of the occupied localized Wannier functions (LWF) Wim = Wj(r — Rm) includes the type of LWF and translation vector Rm, indicating the primitive unit cell, in which the LWF is centered (m = 0 for the reference cell). The index i runs from 1 to A i, the number of filled electron bands used for the localization procedure the correlation calculation is restricted usually to valence bands LWFs. The latter are expressed as a linear combination of the Gaussian-type atomic orbitals (AOs) Xfiif Rn) = Xfin numbered by index = 1,..., M M is the number of AOs in the reference cell) and the cell n translation vector... 

In the previous section we introduced k = /cibi + K2I32 + /csbs as a convenient index to label the wavefunctions. Here we will show that this index actually has physical meaning. Consider that the crystal is composed of Nj unit cells in the direction of vector aj (j = 1, 2, 3), where we think of the values of Nj as macro-scopically large. N = A iA 2A 3 is equal to the total number of unit cells in the crystal (of order Avogadro s number, 6.023 x 10 ). We need to specify the proper boundary conditions for the single-particle states within this crystal. Consistent with the idea that we are dealing with an infinite solid, we can choose periodic boundary conditions, also known as the Born-von Karman boundary conditions,... 

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