ENERGIES OF TWO INTERSTITIAL CONFIGURATIONS IN A FACE-CENTERED CUBIC CRYSTAL
Energies of formation in face-centered cubic crystal
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Energies of formation in face-centered cubic crystal
Formation energy for interstitials in a face- centered cubic crystal
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Classical hard spheres have long served as a paradigm for our understanding of the structure of liquids, crystals, and glasses and the transitions between these phases. Ground-based experiments have demonstrated that suspensions of uniform polymer colloids are near-ideal physical realizations of hard spheres. However, gravity appears to play a significant and unexpected role in the formation and structure of these colloidal crystals. In the microgravity environment of the Space Shuttle, crystals grow purely via random stacking of hexagonal close-packed planes, lacking any of the face-centered cubic (FCC) component evident in crystals grown in 1 g beyond melting and allowed some time to settle. Gravity also masks 33-539 the natural growth instabilities of the hard sphere crystals which exhibit striking dendritic arms when grown in microgravity. Finally, high volume fraction "glass" samples which fail to crystallize after more than a year in 1 g begin nucleation after several days and fully crystallize in less than 2 weeks on the Space Shuttle.
The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.
The configuration of the atoms surrounding a vacancy in four face-centered cubic and three body-centered cubic metals has been computed, using a pairwise, central-force model in which the energy of interaction between two atoms was taken to have the form of a Morse function. Only radial relaxations were considered. The first and second nearest-neighbor relaxations for the face-centered systems were found to be: Pb (1.42,−0.43), Ni (2.14,−0.39), Cu(2.24,−0.40) and Ca (2.73,−0.41, expressed in percentages of normal distances. For the body-centered systems the relaxations out to the fourth nearest neighbors to the vacancy were: Fe (6.07,−2.12, −0.25, −), Ba (7.85, −2.70, 0.70, −0.33) and Na (10.80, −3.14, 3.43, −0.20). The positive signs indicate relaxation toward the vacancy and the negative signs indicate relaxation away from the vacancy. The energies of relaxation (eV) are: Pb (0.162), Ni (0.626), Cu (0.560), Ca (0.400), Fe (1.410), Ba (0.950) and Na (0.172).
High resolution selected zone dark field, Bragg reflection imaging and weak beam dark field techniques of transmission electron microscopy were used to determine the structure of small gold particles vapor deposited on NaCl substrates. Attention was focused on the analysis of those particles in the 50-150 A range that have pentagonal or hexagonal bright field profiles. These particles have been previously described as multiply twinned crystallites composed of face-centered cubic tetrahedra. The experimental evidence of the present studies can be interpreted on the assumption that the particle structure is a regular icosahedron or decahedron for the hexagonal or the pentagonal particles respectively. The icosahedron is a multiply twinned rhombohedral crystal and the decahedron is a multiply twinned body-centered orthorhombic crystal, each of which constitutes a slight distortion from the face-centered cubic structure.
The calculations in a majority of previous works for the fulleride (AqC-60) crystals were performed within the framework of the rigid-lattice model, neglecting the distortion relaxation of the host fullerene (C-60) crystal caused by the interstitial alkali-metal (A) cations. However, an each cation is a source of a static distortion field, and the resulting field is a superposition of such fields generated by all cations. This is a reason why the host-crystal distortions depend on the A-cations configurations, i.e. on a type of a spatial bulk distribution of interstitial cations. The given paper seeks to find a functional relation between the amplitudes of the doping-induced structure-distortion waves and of static concentration ones. A semiphenomenological model is constructed here within the scope of statistical-thermodynamic treatment and using the lattice-statistics simulation method(*). In this model the effects due to the presence of q solute A cations over available interstices (per unit cell) on the static inherent reorientation and/or displacements of the solvent molecules from the 'average-lattice' sites' as well as on the lattice parameter a of a elastically-anysotropic 'cubic' C-60 crystal are taken into account.
Millimeter-sized single crystals of C60 were grown by sublimation of C60 powder in a vacuum for 6-24 h. The crystals had excellent facets, were free of C70 or solvent, and showed face-centered cubic symmetry with a very small mosaic spread down to 0.01 deg.
A method has been developed for the determination of trapped hydrogen in metal alloys, involving the determination of mobile hydrogen using the electrochemical method and the determination of total hydrogen with the fusion method, the difference in hydrogen concentrations being due to trapped hydrogen. It has been found that hydrogen enters body-centered cubic structures through the grain bodies rather than through the grain boundaries. Hydrogen also diffuses much more rapidly in body-centered cubic structures on charging than in face-centered cubic structures, the hydrogen distribution being more uniform in nature. The energy necessary to cause hydrogen embrittlement is postulated to arise from the changes in crystal lattice energies brought about through interaction of hydrogen with atoms in the metal lattice. The total energy change is more negative for body-centered cubic structures, believed to be the cause of a greater tendency toward hydrogen embrittlement. Finally, the agreement of hydrogen concentrations obtained at 25 C by the electrochemical method with those obtained by the fusion method are taken as a strong indication of the power and validity of the electrochemical method.
Our solar system formed from nuclei produced in earlier generations of stars. Mixing in the proto-solar nebula isotopically homogenized most of this material, but some grains, called presolar grains, retain their original isotopic composition. The isotopic properties of presolar SiC grains indicate that most of the grains formed in the outflows of carbon-rich Asymptotic Giant Branch (AGB) stars. The microstructure of these presolar grains reflects the conditions of the dust formation and subsequent alteration. Early microstructural studies of SiC grains obtained by acid dissolution from meteorites show that most isotopically anomalous SiC grains have the face-centered cubic b- SiC structure. However, Daulton et al. have shown that a small fraction of sub-micron presolar SiC grains are of the hexagonal 2H polytype (a-SiC). Although the harsh chemical treatments of these grains does not alter their crystal structure, significant alteration of the surface morphology of the grains due to the acid treatments has been observed. In addition, the acid treatments may preferentially remove cracked or fissured grains, and possible sub-grains, such as graphite. By studying SiC grains isolated by physical separation and found in situ, we attempt to obtain a more complete analysis of presolar SiC microstructures, including the surface morphology, in order to address the formation and processing history of the grains. In our prior work, we reported on one in situ SiC grain (hereafter CBIS1). Here we present results from two additional grains, one in situ, and one prepared as a physical separate.
A curve of applied pressure versus lattice constant is calculated for single-crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The latter is taken from Fermi-surface analysis, and it is verified that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the curve should have reasonable a priori accuracy and can admit possible improvement if experimental data in the intermediate-pressure region can be provided to refine the (in principle) energy-dependent pseudopotential. At three megabars, the lattice constant is reduced by only 22 per cent; the ion cores at this pressure are still very well separated.
A curve of applied pressure P versus lattice constant a is calculated for single crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The method is taken from Fermi surface analysis . This essentially experimental information is used to verify that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the P versus a curve should have reasonable a priori accuracy, which may be improved if experimental data in the intermediate pressure region can be provided to refine the energy dependent pseudo-potential. At 3 megabars the lattice constant is reduced by only 22%; the ion cores at this pressure are still very well separated.