Cubic Systems

Crystals of the dihydrate belong to the monoclinic system and have lattice parameters a = 659 pm, b = 1020 pm, and c = 651 pm. The anhydrous crystal belongs to the cubic system, a = 596 pm. Other physical properties of the anhydrous salt are Hsted iu Table 1. The anhydrous salt is hygroscopic but not dehquescent. 

Sodium iodide crystallizes ia the cubic system. Physical properties are given ia Table 1 (1). Sodium iodide is soluble ia methanol, ethanol, acetone, glycerol, and several other organic solvents. SolubiUty ia water is given ia Table 2. 

Titanium pyrophosphate [13470-09-2] TiP20y, a possible uv reflecting pigment, is a white powder that crystallizes ia the cubic system and has a theoretical density of 3106 kg/m. It is iasoluble ia water and can be prepared by heating a stoichiometric mixture of hydrous titania and phosphoric acid at 900°C. 

The above technique has the practical inconvenience of requiring as many different sets of Tchebyschev coefficients as the unit cell non equivalent sublattices. Furthermore, for non cubic systems, these coefficients depend on the lattice distortion ratios. Namely, for tetragonal lattices different sets of coefficients are required for each value of c/a. This situation has made difficult the implementation of KKR and KKR-CPA calculations for complex lattice structures as, for example, curates. 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

In general, CijU is a 9 x 9 tensor with 81 terms, but symmetry reduces this considerably. Thus, for the cubic crystal system, it has only three terms (Cmi, Cm2, and C4444) and for an isotropic material only two terms remain B = bulk modulus and G = shear modulus. A further simplification is that the bulk modulus, B for the cubic system is given by (Cmi + 2Ci2i2)/3, and the two shear moduli are C44 and (Cmi - Ci2i2)/2. 

II + A, and 62+ -> II + A + d>, and second order spin-orbit calculations (4 7) show that such effects will be relatively large compared to the octahedral situation, yielding/) of the order of 2 cm-1 for V(Cp)2 and around 20 cm-1 for Ni(Cp)2. Furthermore, spin-spin terms cannot be neglected for non-cubic systems, and for systems with smaller values of j- may make appreciable contributions to the value of/). 

Note that the Zeeman interaction for a cubic system results in an isotropic g-value, but the combination with strain lowers the symmetry at least to axial (at least one of the 7 -, 0), and generally to rhombic. In other words, application of a general strain to a cubic system produces a symmetry identical to the one underlying a Zeeman interaction with three different g-values. In yet other words, a simple S = 1/2 system subject to a rhombic electronic Zeeman interaction only, can formally be described as a cubic system deformed by strain. 

In crystals of high symmetry, there are often several sets of (hkl) planes that are identical. For example, in a cubic crystal, the (100), (010), and (001) planes are identical in every way. Similarly, in a tetragonal crystal, (110) and (110) planes are identical. Curly brackets, hkl, designate these related planes. Thus, in the cubic system, the symbol 100 represents the three sets of planes (100), (010), and... 

Several types of unit cells are found in solids. The cubic system is the type most commonly appearing on the AP exam. Three types of unit cells are found in the cubic system ... 

Other representations may be obtained by subdividing the unit cell into a number of similar subcells. In the cubic system the subdivision is made along the three axes by the same factor which is used as a subscript in the new lattice complex... 

In metallic solids, the reticular positions are occupied by cations immersed in a cloud of delocalized valence electrons. In sohd Na, for instance (figure 1.2D), the electron cloud or electron gas is composed of electrons of the s sublevel of the third shell (cf table 1.2). Note that the type of bond does not limit the crystal structure of the solid within particular systems. For example, all solids shown in figure 1.2 belong to the cubic system, and two of them (NaCl, Ne) belong to the same structural class Fm3m). 

The plane is usually identified by three indices enclosed in parentheses (hkl) the vector that is normal to the plane (in cubic systems) is enclosed in square brackets [hkl. ... 

Cadmium cyanide, CdCCN), is analogous to Si02 with respect to the AB2 composition, the tetrahedral confiugration of A, the bridging behavior of B between a pair of A atoms, and the ability to build a three-dimensional framework in which cavities of molecular scale are formed. Cadmium caynide itself crystallizes in a cubic system of the anticuprite type, in which two identical fr-cristobalite-like frameworks interpenetrate each other without any cross-connection the cavity formed in one framework is filled by the other. When we replace one of the frameworks by appropriate guest molecules such as those of CCl, CCl CH, etc., we may obtain a novel clathrate structure with an adamantane-like cavity, as shown in Fig. 1 [1], Our results including those recently obtained are summarized in Table 1. 

As the cubic system was often found to be an important structural class for good superconductors, another myth was generated that suggested one should focus on compounds having a cubic-type crystalline structure, or a structure possessing high symmetry. This myth was also abandoned when lower symmetry systems were found... 

In extended defects, the displacement vector b (or R) associated with them can be defined from the Burgers Circuit shown in figure 2.4(a), for a simple cubic system (Frank 1951, Cottrell 1971, Amelinckx et al 1978). In the defective crystal (A), a sequence of lattice vectors forms a clockwise ring around the dislocation precisely the same set of lattice vectors is then used to make a second... 

Crystal Systems. The cubic crystal system is composed of three space lattices, or unit cells, one of which we have already studied simple cubic (SC), body-centered cubic (BCC), anA face-centered cubic (FCC). The conditions for a crystal to be considered part of the cubic system are that the lattice parameters be the same (so there is really only one lattice parameter, a) and that the interaxial angles all be 90°. 

Continuing with our survey of the seven crystal systems, we see that the tetragonal crystal system is similar to the cubic system in that all the interaxial angles are 90°. However, the cell height, characterized by the lattice parameter, c, is not equal to the base, which is square (a = b). There are two types of tetragonal space lattices simple tetragonal, with atoms only at the comers of the unit cell, and body-centered tetragonal, with an additional atom at the center of the unit cell. 

For a cubic system (a = b = c), this expression simplifies even further to... 

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