Crystal lattice, orientation

The electrode surface is uniform with respect to a known crystal lattice orientation... 

Flydrogen atoms inserted in TbFe6Co5Ti crystal lattice orient quadrupolar moment of the electronic 4f-subshell in an electric field created by a neighbouring ions and electrons along c-axis, that caused to orient of magnetic moment of Tb ion along basal plane. It is well known [4,10], that for the rare-earth ions with Stevens coefficient aj > 0 (Sm, Er, Yb) the magnetic moment is parallel, while for... 

Table 4.14 Spatial Orientation of Common Hybrid Bonds Figure 4.1 Crystal Lattice Types Table 4.15 Crystal Structure...

Oriented In-Plane Texture. In this kind of film the properties (H and in the various in-plane directions (texture and nontexture directions) are different. The texture of the film can be supported by the texture of the substrate and the crystal lattice can be smaller in the texture direction than in the transverse direction. This can be the source for strain-induced magnetic anisotropy (magnetostriction). It is also found that the crystal is aligned in the texture direction (92). 

Fig. 2. Schematic representation of the orientational distribution function f 6) for three classes of condensed media that are composed of elongated molecules A, soHd phase, where /(0) is highly peaked about an angle (here, 0 = 0°) which is restricted by the lattice B, isotropic fluid, where aU. orientations are equally probable and C, Hquid crystal, where orientational order of the soHd has not melted completely.

As with chemical etches, developing optimum conversion coatings requires assessment of the microstructure of the steel. Correlations have been found between the microstructure of the substrate material and the nature of the phosphate films formed. Aloru et al. demonstrated that the type of phosphate crystal formed varies with the orientation of the underlying steel crystal lattice [154]. Fig. 32 illustrates the different phosphate crystal morphologies that formed on two heat-treated surfaces. The fine flake structure formed on the tempered martensite surface promotes adhesion more effectively than the knobby protrusions formed on the cold-rolled steel. 

As we stated previously, particles usually grow from a nucleus to which atoms are added in a regular manner to form a three-dimensional structure. Such crystals cease grovidng when the "nutrient" (the material which serves to form the peirticle) becomes depleted. Such particles are known as "ciystalUtes". Each will consist of several grains, having a differing orientation of the crystal lattice, within each individual particle, namely ... 

The region within which k is considered (—n/a first Brillouin zone. In the coordinate system of k space it is a polyhedron. The faces of the first Brillouin zone are oriented perpendicular to the directions from one atom to the equivalent atoms in the adjacent unit cells. The distance of a face from the origin of the k coordinate system is n/s, s being the distance between the atoms. The first Brillouin zone for a cubic-primitive crystal lattice is shown in Fig. 10.11 the symbols commonly given to certain points of the Brillouin zone are labeled. The Brillouin zone consists of a very large number of small cells, one for each electronic state. 

Fig. 10. Relation between amphiphilic nature and orientation of crystal lattice and guest. Hydrophilic and hydrophobic interactions are indicated by circles in dotted and non-interrupted style of line representation, respectively...

Processes such as film extrusion, fiber spinning, injection molding, and drawing tend to impart orientation to products made from semicrystalline polymers. Mechanical, dielectric, and optical properties, to mention only three, are often strongly influenced by orientation. X-ray diffraction offers a direct approach to studying crystallite orientation because the Intensity that is diffracted into a detector placed at an appropriate position is directly proportional to the number of crystal lattice planes that are in the correct orientation for diffraction. The principles of such measurements are well described in textbooks 0,2). 

There are two major problems associated with the x-ray method. The first problem is encountered during sample preparation. At this step, preferred orientation of the particles must be minimized [1], Reduction of particle size is one of the most effective ways of minimizing preferred orientation, and this is usually achieved by grinding the sample. Grinding, however, can also disorder the crystal lattice. Moreover, decreased particle size can cause a broadening of x-ray lines, which in mm affects the values of /c and /a. The relationship between the crystallite size, t, and its x-ray line breadth, /3, (assuming no lattice strain) is given by the Scherrer equation [2] ... 

Preferred orientation of the particles must be minimized. One of the most effective ways to achieve this is to reduce the particle size by grinding the sample [1], As already discussed in Section III.A, however, grinding can disorder the crystal lattice. Grinding can also induce other undesirable transitions, such as polymorphic transformations [59]. In order to obtain reproducible intensities, there is an optimum crystallite size. The crystallites have to be sufficiently small so that the diffracted intensities are reproducible. Careful studies have been carried out to determine the desired crystallite size of quartz, but no such studies have been reported for pharmaceutical solids [60]. Care should be taken to ensure that the crystallites are not very small, since decreased particle size can cause a broadening of x-ray lines. This effect, discussed earlier (Eq. 9), usually becomes apparent when the particle size is below 0.1 jum. 

Crystal structures and crystal lattices are different, although these terms are frequently (and incorrectly) used as synonyms. A crystal structure is built of atoms. A crystal lattice is an infinite pattern of points, each of which must have the same surroundings in the same orientation. A lattice is a mathematical concept. 

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

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