Cubic crystals

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

In fignre A1.3.9 the Brillouin zone for a FCC and a BCC crystal are illustrated. It is a connnon practice to label high-synnnetry point and directions by letters or symbols. For example, the k = 0 point is called the F point. For cubic crystals, there exist 48 symmetry operations and this synnnetry is maintained in the energy bands e.g., E k, k, k is mvariant under sign pennutations of (x,y, z). As such, one need only have knowledge of (k) in Tof the zone to detennine the energy band tlnoughout the zone. The part of the zone which caimot be reduced by synnnetry is called the irreducible Brillouin zone. 

Berrett J F, Molino F, Porte G, Diat O and Lindner P 1996 The shear-induced transition between oriented textures and layer-sliding-mediated flows in a micellar cubic crystal J. Phys. Condens Matters 9513-17... 

To verify effectiveness of NDCPA we carried out the calculations of absorption spectra for a system of excitons locally and linearly coupled to Einstein phonons at zero temperature in cubic crystal with one molecule per unit cell (probably the simplest model of exciton-phonon system of organic crystals). Absorption spectrum is defined as an imaginary part of one-exciton Green s function taken at zero value of exciton momentum vector... 

EXAFS spectra of platinum metal, having a face-centred cubic crystal stmcture, have been obtained at 300 K and 673 K. Explain what qualitative differences you might expect. How many nearest-neighbour atoms are there in this stmcture Illustrate your answer with a diagram. 

Alkali AletalIodides. Potassium iodide [7681-11-0] KI, mol wt 166.02, mp 686°C, 76.45% I, forms colorless cubic crystals, which are soluble in water, ethanol, methanol, and acetone. KI is used in animal feeds, catalysts, photographic chemicals, for sanitation, and for radiation treatment of radiation poisoning resulting from nuclear accidents. Potassium iodide is prepared by reaction of potassium hydroxide and iodine, from HI and KHCO, or by electrolytic processes (107,108). The product is purified by crystallization from water (see also Feeds and feed additives Photography). 

Sodium iodide [7681-82-5] Nal, mol wt 149.92, mp 662°C, 84.66% I, forms colorless cubic crystals, which are soluble in water, ethanol, methanol, and acetone. It is used in photography, for the production of organic chemicals, and as an expectorant in cough medicines. Nal is separated by addition of sodium hydroxide or sodium carbonate to an acidic iodide solution (see also Expectorants, antitussives, and related agents). 

Lead Telluride. Lead teUuride [1314-91 -6] PbTe, forms white cubic crystals, mol wt 334.79, sp gr 8.16, and has a hardness of 3 on the Mohs scale. It is very slightly soluble in water, melts at 917°C, and is prepared by melting lead and tellurium together. Lead teUuride has semiconductive and photoconductive properties. It is used in pyrometry, in heat-sensing instmments such as bolometers and infrared spectroscopes (see Infrared technology AND RAMAN SPECTROSCOPY), and in thermoelectric elements to convert heat directly to electricity (33,34,83). Lead teUuride is also used in catalysts for oxygen reduction in fuel ceUs (qv) (84), as cathodes in primary batteries with lithium anodes (85), in electrical contacts for vacuum switches (86), in lead-ion selective electrodes (87), in tunable lasers (qv) (88), and in thermistors (89). 

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). 

Methyllithium. MethyUithium [917-54 ] CH Li, crystallizes from benzene or hexane solution giving cubic crystals that have a salt-hke constitution (128). Crystalline methyllithium molecules exist as tetrahedral tetramers (129). Solutions of methyllithium are less reactive than those of its higher homologues. Methyllithium is stable for at least six months in diethyl ether at room temperature. A one-molar solution of methyllithium in tetrahydrofuran (14 wt %) and cumene (83 wt %) containing 0.08 M dimethyknagnesium as stabilizer loses only 0.008% of its activity per day at 15°C and is nonpyrophoric (117). 

For cubic crystals, which iaclude sUicon, properties described by other than a zero- or a second-rank tensor are anisotropic (17). Thus, ia principle, whether or not a particular property is anisotropic can be predicted. There are some properties, however, for which the tensor rank is not known. In addition, ia very thin crystal sections, the crystal may have two-dimensional characteristics and exhibit a different symmetry from the bulk, three-dimensional crystal (18). Table 4 is a listing of various isotropic and anisotropic sUicon properties. Table 5 gives values for the more common physical properties and for some of the thermodynamic properties. Figure 5 shows some thermal properties. 

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... 

Strontium chloride [10476-85-4] SrCl2, is similar to calcium chloride but is less soluble in water (100.8 g in 100 mL water at 100°C). The anhydrous salt forms colorless cubic crystals with a specific gravity of 3.052 and a melting point of 873°C. Strontium chloride is used in toothpaste formulations (see... 

Strontium fluoride [7783-48-4] SrF2, forms colorless cubic crystals or a white powder with a specific gravity of 4.24 and a melting point of 1190°C. 

Anhydrous BaCl2 exists as monoclinic or cubic crystals. The transition to cubic occurs at 925 °C. Barium chloride melts at 962°C the dihydrate, which has monoclinic crystals, loses water at 113 °C. Barium chloride, which is very hygroscopic, is sold in moisture-proof bags and steel or fiber dmms. 

Impute barium sulfide witb 20—35% contaminants is produced in large volume by tbe black asb kibi. Pure barium sulfide [21109-95-5] BaS, occurs as colodess cubic crystals, sp gr 4.25 and as hexagonal plates of barium sulfide hexabydrate [66104-39-0] BaS BaS melts at 2227°C. Solubibty in water... 

Calcium has a face-centered cubic crystal stmcture (a = 0.5582 nm) at room temperature but transforms into a body-centered cubic (a = 0.4477 nm) form at 428 2° C (3). Some of the more important physical properties of calcium are given in Table 1. For additional physical properties, see references 7—12. Measurements of the physical properties of calcium are usually somewhat uncertain owing to the effects that small levels of impurities can exert. 

In bulk form cerium is a reactive metal that has a high affinity for oxygen and sulfur. It has a face centered cubic crystal stmcture, mp 798°C, bp 3443°C, density 6.77 g/mL, and a metallic radius of 182 pm. Detailed chemical and physical property information can be found in the Hterature (1,2). 

Calcium chloride (anhydrous) [10043-52-4] M 111.0, m 772 , b >1600 , d 2.15. Available as fused granules or cubic crystals. It is very hygroscopic. Very soluble in H2O (exothermic), and EtOH. Store in a tightly closed container. 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

EtOH). No methoxyl is present. It forms a series of crystalline double chlorides with cadmium, zinc or copper, does not give the thalleioquin reaction, and solutions of its sulphate are not fluorescent. It is diacidie and forms two series of salts of which the nitrate, B. HNOj, crystallises in minute prisms, m.p. 196°, insoluble in water. Cinchonamine hydrochloride, B. HCl, laminae or B. HCl. HjO, cubical crystals, has been suggested for use in the estimation of nitrates. When warmed with strong nitric acid the alkaloid furnishes dinitrocinchonamine. It gives an amorphous, monoacetyl derivative, and forms a methiodide, m.p. 208 , which with silver oxide yields an amorphous methylcinchonamine. Raymond-Hamet found that cinchonamine ves typical indole colour reactions and is probably an indole alkaloid. This seems to have been... 

The properties of water near ionic salt surfaces are of interest not only for the understanding of the mechanism of dissolution processes but also for the understanding of the chemistry in the atmosphere next to oceans [205]. Experiments in UHV [205-208] indicate that the water-covered NaCl surface is quite stable at low temperatures. An early simulation study by Anastasiou et al. [209] focused on the arrangements and orientations of water molecules in contact with a rigid NaCl crystal. Ohtaki and coworkers investigated the dissolution of very small cubic crystals of NaF, KF, CsF, LiCl, NaCl, and KCl [210] and the nucleation [211] of NaCl and CsF in a... 

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

Solids tend to crystallize in definite geometric forms that often can be seen by the naked eye. In ordinary table salt, cubic crystals of NaCl are clearly visible. Large, beautifully formed crystals of such minerals as fluorite, CaF2, are found in nature. It is possible to observe distinct crystal forms of many metals under a microscope. 

Analcite (NajOAljOj SiO I O), a cubic crystal structure, is formed at high temperatures. It is similar to acmite and also invariably is found beneath sludges of hydroxyapatite or serpentine or under porous deposits of iron oxides. 

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