Cubic crystal states

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Sharma, R.R., Das, T.P., and Orbach, R. 1968. Zero-field splitting of S-state ions. III. Corrections to part I and II and application to distorted cubic crystals. Physical Review 171 378-388. 

The equation of state of a cubic crystal under hydrostatic pressure is given by... 

Hard blue-white metal body-centered cubic crystal density 7.19 g/cm melts at 1,875°C vaporizes at 2,199°C electrical resistivity at 20°C, 12.9 microhm-cm magnetic susceptibility at 20°C, 3.6x10 emu standard electrode potential 0.71 V (oxidation state 0 to -i-3). 

Zinc sulfide is white to gray-white or pale yellow powder. It exists in two crystalline forms, an alpha (wurtzite) and a beta (sphalerite). The wurtzite form has hexagonal crystal structure refractive index 2.356 density 3.98 g/cm3 melts at 1,700°C practically insoluble in water, about 6.9 mg/L insoluble in alkalis soluble in mineral acids. The sphalerite form arranges in cubic crystalline state refractive index 2.368 density 4.102 g/cm changes to alpha form at 1,020°C practically insoluble in water, 6.5 mg/L soluble in mineral... 

Because of the orientational freedom, plastic crystals usually crystallize in cubic structures (Table 4.2). It is significant that cubic structures are adopted even when the molecular symmetry is incompatible with the cubic crystal symmetry. For example, t-butyl chloride in the plastic crystalline state has a fee structure even though the isolated molecule has a three-fold rotation axis which is incompatible with the cubic structure. Such apparent discrepancies between the lattice symmetry and molecular symmetry provide clear indications of the rotational disorder in the plastic crystalline state. It should, however, be remarked that molecular rotation in plastic crystals is rarely free rather it appears that there is more than one minimum potential energy configuration which allows the molecules to tumble rapidly from one orientation to another, the different orientations being random in the plastic crystal. 

The first attempt to calculate realistic wave functions for electrons in metals is that of Wigner and Seitz (1933). These authors pointed out that space in a body-or face-centred cubic crystal could be divided into polyhedra surrounding each atom, that these polyhedra could be replaced without large error by spheres of radius r0, so that for the lowest state one has to find spherically symmetrical solutions of the Schrodinger equation (6) subject to the boundary condition that... 

PETN usually forms needle or column-shaped crystals, in which state it pours with difficulty. It is however possible to produce cubic crystals, which pour easily, by recrystallization from ethyl acetate. PETN has been subjected to many crystallographic studies. On the basis of X-ray measurements carried out by Booth and Llewellyn [9] the interatomic distances have been shown to be ... 

Millions of years ago, the Great Plains of the United States were ocean. As sea levels fell and at the same time the North American continent rose, many isolated pockets of seawater, called saline lakes, formed. Over time, these lakes evaporated, leaving behind the solids that had been dissolved in the seawater. Most abundant was sodium chloride, which collected in cubic crystals referred to by mineralogists as the mineral halite. When conditions were right, halite crystals like the ones in this chapter s opening photograph would grow to be several centimeters across. 

The alkali metal hydrides contain alkali metal cations and H- anions in a face-centered cubic crystal structure like that of sodium chloride (Section 10.9). Alkali metal hydrides are also ionic in the liquid state, as shown by the fact that the molten compounds conduct electricity. 

The coupling of plasmons with LO phonons leads to coupled plasmon-pho-non states. For a cubic crystal with 2 atoms in the elementary cell and one infrared-active eigen frequency cop, the frequency-dependent dielectric constant is according to Eq. (11.17)... 

Lead Although lead occurs in nature as the carbonate, cerrusite, PbC03 and the sulphate anglesite, PbS04, the principal ore of lead is galena, PbS, which occurs as greyish-black cubical crystals. The chief producing countries are the United States, Spain and Mexico. 

The subscript i refers to the two polarization states parallel (i = ) and perpendicular [i = L) to the c-axis, which have to be distinguished for optically uniaxial samples, for instance wurtzite-structure ZnO or sapphire. Cubic crystals, for instance rocksalt-structure Mg Zni- O, are optically isotropic and have only one DF, because the dielectric tensor is reduced to a scalar. 

Abstract. Geometrical parameters, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) are determined by using of semi-empirical quantum chemistry PM3-method for isolated molecules Cn, dimers (Cn)2 and cuban-like clusters (Cn)8 for n = 20, 24, 28, 32. The results of calculations allow assuming the existence of polymerized cubic crystal structure on base of all considered small fullerenes. 

For WZ compounds, we must consider hexagonal symmetry in the effective Hamiltonian. The Luttinger-Kohn Hamiltonian is constructed under the condition of cubic symmetry and the form reflects cubic crystal symmetry. Thus, in the analysis of WZ nitrides, we must use a k-dependent parabolic band for the conduction band state and Bir-Pikus Hamiltonians for the valence band states. The Hamiltonians for the upper six valence bands and the lowest two conduction bands are given by [28]... 

The double nitrates Mg3M2(N03)12, 24 H20 can be recrystallized in strong nitric acid and serve to separate the lighter lanthanides M = La, Pr, Nd and Sm (where Ce has been removed after oxidation to the quadrivalent state). Judd noted 109) that the fine-structure of the absorption band belonging to each /-level of M(III) was so peculiar that it looked as if the chromophore was icosahedral with N = 12 (which is almost unheard about, outside boron chemistry). The crystal structure 110) of the cubic crystals confirmed entirely Judd s proposal, it is indeed [Mg(OH2)6]3 ... 

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