The Crystal Lattice

The crystal lattice consists of points given by positions of the vectors r 

One says that vectors ai generate the primitive crystal lattice. Magnitudes of vectors aj and angles between them determine a symmetry class of the crystal. It is convenient to consider the crystal structure in Cartesian coordinates. Vectors a are chosen perpendicular to each other, if possible. 

In most cases a crystal structure consists of identical copies of the same physical unit called the basis, not the primitive cell. For example, the body-centered cubic stmcture consists of two primitive cubic cells displaced along the body diagonal of the cubic cell by one half of the length of the diagonal. 

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Burger s vector A measure of the crystal lattice displacement resulting from the passage of a dislocation. 

The sensitive layer of the systems under investigation eonsists of a mixture of BaFBr with Eu dotation. Other systems are available in the mean time too. X-ray- or y-quants initiate transitions of electrons in the crystal lattice. Electrons are excited from the valence band to the conduction band [2]. Electrons from the conduction band are trapped in empty Br -lattice places. They can return to the valence band via the conduction band after an excitation by... 

The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

The salt-like carbides. Among these are aluminium tricarbide imethanide) AI4C3 (containing essentially C ions) in the crystal lattice and the rather more common dicarbides containing the C ion, for example calcium dicarbide CaCjt these carbides are hydrolysed by water yielding methane and ethyne respectively ... 

The variation of Cp for crystalline thiazole between 145 and 175°K reveals a marked inflection that has been attributed to a gain in molecular freedom within the crystal lattice. The heat capacity of the liquid phase varies nearly linearly with temperature to 310°K, at which temperature it rises more rapidly. This thermal behavior, which is not uncommon for nitrogen compounds, has been attributed to weak intermolecular association. The remarkable agreement of the third-law ideal-gas entropy at... 

FIGURE 1 4 An ionic bond IS the force of attrac tion between oppositely charged ions Each Na ion (yellow) in the crystal lattice of solid NaCI IS involved in ionic bonding to each of six surrounding Cl ions (green) and vice versa... 

Precipitate particles grow in size because of the electrostatic attraction between charged ions on the surface of the precipitate and oppositely charged ions in solution. Ions common to the precipitate are chemically adsorbed, extending the crystal lattice. Other ions may be physically adsorbed and, unless displaced, are incorporated into the crystal lattice as a coprecipitated impurity. Physically adsorbed ions are less strongly attracted to the surface and can be displaced by chemically adsorbed ions. 

Inclusions are difficult to remove since the included material is chemically part of the crystal lattice. The only way to remove included material is through reprecipitation. After isolating the precipitate from the supernatant solution, it is dissolved... 

Alexandrite, like ruby, contains Cr ions but they are substituted in the lattice of chrysoberyl, BeAl204. The chromium ions occupy two symmetrically non-equivalent positions which would otherwise be occupied by aluminium ions. In this environment the 2 ground state of Cr is broadened, compared with that in ruby, by coupling to vibrations of the crystal lattice. 

Processes have been developed whereby the oxygen is suppHed from the crystal lattice of a metal-oxide catalyst (5) (see Acrylonitrile Methacrylic acid AND derivatives). 

The many commercially attractive properties of acetal resins are due in large part to the inherent high crystallinity of the base polymers. Values reported for percentage crystallinity (x ray, density) range from 60 to 77%. The lower values are typical of copolymer. Poly oxymethylene most commonly crystallizes in a hexagonal unit cell (9) with the polymer chains in a 9/5 helix (10,11). An orthorhombic unit cell has also been reported (9). The oxyethylene units in copolymers of trioxane and ethylene oxide can be incorporated in the crystal lattice (12). The nominal value of the melting point of homopolymer is 175°C, that of the copolymer is 165°C. Other thermal properties, which depend substantially on the crystallization or melting of the polymer, are Hsted in Table 1. See also reference 13. 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). 

Packing of the cyclodexthn molecules (a, P, P) within the crystal lattice of iaclusion compounds (58,59) occurs in one of two modes, described as cage and channel stmctures (Fig. 7). In channel-type inclusions, cyclodextrin molecules are stacked on top of one another like coins in a roU producing endless channels in which guest molecules are embedded (Fig. 7a). In crystal stmctures of the cage type, the cavity of one cyclodextrin molecule is blocked off on both sides by neighboring cyclodextrin molecules packed crosswise in herringbone fashion (Fig. 7b), or in a motif reminiscent of bricks in a wall (Fig. 7c). 

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). 

Magnetic Anisotropy Energy. There are several kinds of magnetic anisotropy energy and perhaps the most weU known is the magnetocrystaUine anisotropy. Only a crystalline soHd has this property because the energy is dictated by the symmetry of the crystal lattice. For example, in bcc Fe, the easy axis is in a (100) direction and in fee Ni, it is in a (111) direction. 

Hydrogenis prevented from forming a passivating layer on the surface by an oxidant additive which also oxidizes ferrous iron to ferric iron. Ferric phosphate then precipitates as sludge away from the metal surface. Depending on bath parameters, tertiary iron phosphate may also deposit and ferrous iron can be incorporated into the crystal lattice. When other metals are included in the bath, these are also incorporated at distinct levels to generate species that can be written as Zn2Me(P0 2> where Me can represent Ni, Mn, Ca, Mg, or Fe. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

Minerals normally considered nonmagnetic may be rendered magnetic by elemental substitution of a small amount of a magnetic element in the crystal lattice. Magnetic properties may also be affected by partial alteration in weathering effects. 

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