Lattice beams

Castellated and lattice beams provide a service zone within the structural depth ... 

Lattice beams are desirable, if possible, due to their light weight. Where internals are stainless steel to prevent or minimize corrosion, they will also reduce cost. Unlike solid or built-up beams, the top and bottom members of a lattice beam have distinct functions. The bottom chord is the tension only member. The top chord is a compression only member. This is for beams above the line of support. For beams below the line of support, the reverse would be true. 

In a lattice beam, flie top chord is a compression member and must be capable of supporting a column axial load without buckling. A T-type compression member is... 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Figure Bl.21.3. Direct lattices (at left) and corresponding reciprocal lattices (at right) of a series of connnonly occurring two-dimensional superlattices. Black circles correspond to the ideal (1 x 1) surface structure, while grey circles represent adatoms in the direct lattice (arbitrarily placed in hollow positions) and open diamonds represent fractional-order beams m the reciprocal space. Unit cells in direct space and in reciprocal space are outlined.

The diffraction of low-energy electrons (and any other particles, like x-rays and neutrons) is governed by the translational syimnetry of the surface, i.e. the surface lattice. In particular, the directions of emergence of the diffracted beams are detemiined by conservation of the linear momentum parallel to the surface, bk,. Here k... 

One of the spots in such a diffraction pattern represents the specularly reflected beam, usually labelled (00). Each other spot corresponds to another reciprocal-lattice vector = ha + kb and is thus labelled (hk), witli integer h and k. 

Figure C2.3.12. Two-dimensional neutron scattering by EOggPO gEOgg (Pluronic F88) micellar solution under shear witli (a) tlie sample shear axis parallel to tlie beam, and (b) tlie sample rotated 35° around tlie vertical axis. Reflections for several of tlie Miller indices expected for a bee lattice are annotated. Reproduced by pennission from figure 4 of [84]-...

Epitaxial crystal growth methods such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have advanced to the point that active regions of essentially arbitrary thicknesses can be prepared (see Thin films, film deposition techniques). Most semiconductors used for lasers are cubic crystals where the lattice constant, the dimension of the cube, is equal to two atomic plane distances. When the thickness of this layer is reduced to dimensions on the order of 0.01 )J.m, between 20 and 30 atomic plane distances, quantum mechanics is needed for an accurate description of the confined carrier energies (11). Such layers are called quantum wells and the lasers containing such layers in their active regions are known as quantum well lasers (12). 

For a two-dimensional array of equally spaced holes the difftaction pattern is a two-dimensional array of spots. The intensity between the spots is very small. The crystal is a three-dimensional lattice of unit cells. The third dimension of the x-ray diffraction pattern is obtained by rotating the crystal about some direction different from the incident beam. For each small angle of rotation, a two-dimensional difftaction pattern is obtained. 

Lattice parameters to four significant figures using convergent beam diffraction... 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

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