Atomic plane

Single-crystal surfaces are characterized by a set of Miller indices that indicate tlie particular crystallographic orientation of the surface plane relative to the bulk lattice [5]. Thus, surfaces are labelled in the same way that atomic planes are labelled in bulk x-ray crystallography. For example, a Ni (111) surface has a surface plane... 

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). 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

The dislocation cannot glide upwards by the shearing of atom planes - the atomic geometry is wrong - but the dislocation can move upwards if atoms at the bottom of the half-plane are able to diffuse away (Fig. 19.2). We have come across Fick s Law in which diffusion is driven by differences in concentration. A mechanical force can do exactly the same thing, and this is what leads to the diffusion of atoms away from the... 

Hgura 5 (a) Schematic of a thin sample with atomic planes that are close to a Bragg... 

Figure 2 Several atomic planes and their d-spacings in a simple cubic (sc) crystal (al ...

When there is constructive interference from X rays scattered by the atomic planes in a crystal, a diffraction peak is observed. The condition for constructive interference from planes with spacing dhkl is given by Bragg s law. 

In the concepts developed above, we have used the kinematic approximation, which is valid for weak diffraction intensities arising from imperfect crystals. For perfect crystals (available thanks to the semiconductor industry), the diffraction intensities are large, and this approximation becomes inadequate. Thus, the dynamical theory must be used. In perfect crystals the incident X rays undergo multiple reflections from atomic planes and the dynamical theory accounts for the interference between these reflections. The attenuation in the crystal is no longer given by absorption (e.g., p) but is determined by the way in which the multiple reflections interfere. When the diffraction conditions are satisfied, the diffracted intensity ft-om perfect crystals is essentially the same as the incident intensity. The diffraction peak widths depend on 26 m and Fjjj and are extremely small (less than... 

Other excellent methods of phase identification include TEM and electron diffraction. These may be more useful for low-Z materials, ultrathin films, and for characterizing small areas, including individual grains. For multiphase films with incomplete texture, these methods and XRD are complementary, since in commonly used geometries, they probe atomic planes perpendicular and parallel to the thin film surface, respectively. 

What gives rise to streaks in a RHEED pattern from a real surface For integral-order beams, die explanation is atomic steps. Atomic steps will be present on nearly all crystalline surfaces. At the very least a step density sufficient to account for any misorientation of the sample from perfeedy flat must be included. Diffraction is sensitive to atomic steps. They will show up in the RHEED pattern as streaking or as splitdng of the diffracted beam at certain diffraction conditions that depend on the path difference of a wave scattered from atomic planes displaced by an atomic step height. If the path difference is an odd muldple of A./2, the waves scattered... 

For the particular calculations shown in Figures 1 - 4, it was assumed that the scattering rates are relatively high and that they are the same for all layers and for both spin channels. Both the field and the current are assumed to be parallel to the layers which consist of 111 atomic planes. 

Pyrophillite, talc, muscovite, and biotite have the following sequence of atom-planes along the pseudo-hexagonal axes ... 

Close approaches of arene. solvents to metalloporphyrins have been observed by crystallography. For example. Mn(TPP) crystallizes as a toluene. solvate with a toluene solvent molecule lying on either side of the porphyrin plane. The dihedral angle between the porphyrin plane and toluene plane is 10.7 (reduced to 6.7 for one of the pyrrole rings). The average perpendicular distance between the toluene ring and the mean 24-atom plane of the porphyrin is 3.30 A. One aromatic C—C bond of toluene approximately eclipses one N—Mn—N axis, with IVln- C distances of 3.05 and 3.25 There has been considerable effort invested in the... 

Fig. 4.4 Atomistic representation of successive steps in the ECALE synthesis of CdTe on an Au substrate. Observe the deposition and stripping of Te for assembling the correct atomic planes of the zinc blende structure. (Adapted from [27])...

Figure 1. High resolution Electron Micrograph of a cubic MgO crystal viewed in [100] direction showing square net of 22 fringes and apparent bending of atom planes at edges. Courtesy of Dr. T. Tanji.

For the smaller particles which Include only a few tens or hundreds of atoms, any twinning or faulting reduces the range of ordering to the extent that the pattern can not be Interpreted In the same way as a pattern from an extended crystal. The Individual single-crystal regions may contain only two or three atomic planes. Interpretation can be made only by calculation of patterns from postulated models for the configurations of atoms (22). 

Fig. 11 Formation of crystalline 3D super-lattices of tin nanoparticles a TEM view of a facetted super-crystal b SEM image showing particles included into a super-crystal as well as the organic surrounding c High resolution micrograph showing the alignment of the tin atomic planes inside the super-structure...

A second product is the ICE Solid-State Model Kit, developed by L. A. Mayer and G. C. Lisensky, which makes it possible to build extended three-dimensional structures Using a base with holes, templates for some 60 different structures, rods, and four sizes of spheres in radius ratios, common crystal structures can be assembled in a matter of minutes (3). Furthermore, many structures can be assembled from different perspectives by teams of students For example, the cubic NaCl unit cell can be assembled with its orientation on the face of the cube or on the body diagonal. Natural cleavage planes can be found with the kit Lifting one sphere will separate atomic planes from one another. (Contact ICE for ordering information.)... 

In Figure 1.12(b) the individual atomic planes within the film are shown, together with the changes in chemistry across the four interfaces included in the section. It can be seen, for example, that the CoFe/Cu interfaces are sharper than those between NiFe and CoFe layers. However, the interface with CoFe growing on NiFe shows a more diffuse interface than that where NiFe is deposited on CoFe. 

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