Other crystal lattices

The number of independent elastic parameters can also be determined for the other crystal lattices and is listed in table 2.2. Generally, couplings between shear stresses and normal strains and normal stresses and shear strains can occur when the number of independent parameters is larger than three. In this case, a uniaxial stress can cause not only normal strains, but also shear strains as we already saw for the example of the orthorhombic crystal. 

---

The other crystal lattices can be generated by adding to some of the above-defined cells extra high-symmetry points by the so-called centering method. TableB.2 shows the new systems added to the simple crystal lattices (noted s, or P, for primitive) and the numbers of lattice points in each conventional unit cell. The body-centred lattices are noted be or I (for German Innenzentrierte), the face-centred, fc or F, and the side-centred or base-centred lattices are noted C (an extra atom at the Centre of the base). These 14 lattice systems are known as the Bravais lattices (noted here BLs). A representation of their unit cells can be found in the textbook by Kittel [7]. 

Many industrial crystallization processes, by necessity, push crystal growth rates into a regime where defect formation becomes unavoidable and the routes for impurity incorporation are numerous. Since dislocations, inclusions, and other crystal lattice imperfections enhance the uptake of impurities during crystallization, achieving high purity crystals requires elimination of impurity incorporation and carry-over by both thermodynamic and non-thermodynamic mechanisms. Very generally, the impurity content in crystals can be considered as the sum of all of these contributions... 

Since the number of slip systems is not usually a function of temperature, the ductility of face-centered cubic metals is relatively insensitive to a decrease in temperature. Metals of other crystal lattice types tend to become brittle at low temperatures. Crystal structure and ductility are related because the face-centered cubic lattice has more slip systems than the other crystal structures. In addition, the slip planes of body-centered cubic and hexagonal close-packed crystals tend to change at low temperature, which is not the case for face-centered cubic metals. Therefore, copper, nickel, all of the copper-nickel alloys, aluminum and its alloys, and the austenitic stainless steels that contain more than approximately 7% nickel, all face-centered cubic, remain ductile down to the low temperatures, if they are ductile at room temperature. Iron, carbon and low-alloy steels, molybdenum, and niobium, all body-centered cubic, become brittle at low temperatures. The hexagonal close-packed metals occupy an intermediate place between fee and bcc behavior. Zinc undergoes a transition to brittle behavior in tension, zirconium and pure titanium remain ductile. 

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. 

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. 

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. 

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. 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

Conformational analysis has been used to find and predict conformations which maximize antibiotic activity, using x-ray crystal stmctures coupled with nmr and cd spectra. An early approach utilized the Dale diamond lattice conformational model (480), which was extended to other diamond lattice models (472,481—483). Other studies have reHed on nmr data (225,484—491). However, extensive correlations between conformation and biological activity have not been successful (486,492). 

The fluorite stmcture, which has a large crystal lattice energy, is adopted by Ce02 preferentially stahi1i2ing this oxide of the tetravalent cation rather than Ce202. Compounds of cerium(IV) other than the oxide, ceric fluoride [10060-10-3] CeF, and related materials, although less stable can be prepared. For example ceric sulfate [13590-82-4] Ce(S0 2> certain double salts are known. 

The role of cerium in these lighting phosphors is not as the emitting atom but rather as the sensitizer. The initial step in the lighting process is the efficient absorption of the 254 nm emission Ce ", with broad absorption bands in the uv, is very suitable. This absorbed energy is then transferred to the sublattice within the crystalline phosphor eventually the activator ion is fed and emission results. Cerium, as a sensitizer ion, is compatible in crystal lattices with other lanthanide ions, such as Eu and Tb, the usual activator atoms. 

J) The extreme fineness of iadividual clay particles, which may be of colloidal size ia at least one dimension. Clay minerals are usually platy ia shape, and less often lathlike and tubular or scroU shaped (13). Because of this fineness clays exhibit the surface chemical properties of coUoids (qv) (14). Some clays possess relatively open crystal lattices and show internal surface colloidal effects. Other minerals and rock particles, which are not hydrous aluminosihcates but which also show colloidal dimensions and characteristics, may occur intimately intermixed with the clay minerals and play an essential role. 

Effect of Thermal History. Many of the impurities present in commercial copper are in concentrations above the soHd solubihty at low (eg, 300°C) temperatures. Other impurities oxidize in oxygen-bearing copper to form stable oxides at lower temperatures. Hence, because the recrystallization kinetics are influenced primarily by solute atoms in the crystal lattice, the recrystallization temperature is extremely dependent on the thermal treatment prior to cold deformation. 

---