Fcc Unit Cell Research Articles

A realistic molecular dynamics simulation of the plastic crystalline phase of neopentane. I. The model and its static properties

A molecular dynamics simulation of a realistic model of neopentane [C(CH3)4] in its plastic phase has been performed on a sample of 6×6×6 fcc unit cells (i.e., 864 molecules) at 135, 175, and 230 K. The molecules of the simulated sample interact through phenomenological exp-6, atom–atom potentials between all the atoms of nearest neighbor molecules. The orientational probability density function (opdf), the displacement probability density function (dpdf), and its second moment the Debye–Waller factor have been computed. We confirm the very large value and the important thermal variation of the Debye–Waller factor and the strong anisotropy of the opdf deduced from neutron diffraction experiments. The computed opdf is very well reproduced by a mean-field calculation making use only of the microscopic intermolecular potential and of the equilibrium position of the molecular centers of mass, a result in line with the isotropic character of the dpdf, but not valid for other plastic crystals made of molecules with different geometries.

Magnetovolume instabilities and ferromagnetism versus antiferromagnetism in bulk fcc iron and manganese.

Total-energy band calculations, including an antiferromagnetic extension of the fixed-spin-moment procedure, are used to study magnetovolume effects in bulk fcc iron and maganese. By constraining these systems to have a fixed total magnetic moment in a single-atom fcc unit cell, we find magnetovolume instabilities in the form of first-order transitions from nonmagnetic to ferromagnetic behavior. Constraining the moments to have fixed values in a CuAu unit cell of two atoms to allow for antiferromagnetic (and field-induced ferrimagnetic) order alters these instabilities and yields second-order transitions from nonmagnetic to antiferromagnetic behavior at volumes coincident with the equilibrium volumes for both metals.

A density functional approach to freezing transitions in molecular fluids: Dipolar hard spheres

We extend a density functional theory of atomic systems to simple molecules using first-order perturbation theory. We model the hydrogen halides as dipolar hard spheres and consider freezing into two orientationally different fcc lattices. In one of these, the dipoles may align parallel to a single, space-fixed axis while in the other, the dipoles in adjacent faces of the fcc unit cell are constrained to lie perpendicular to one another. The second structure approximates the experimentally observed molecular crystals of HF and HCl, and the phase diagram calculated from this model agrees qualitatively with experiment. At high temperatures, or for weak enough dipole moments, a plastic (orientationally disordered) solid precedes the molecular crystal. The plastic phase is unaffected by the dipolar perturbation but eventually becomes a molecular crystal upon lowering the temperature or increasing the density. We also discuss second-order perturbation theory, the effects of higher multipoles, and some general consequences of the density functional theory of molecular systems.

On voidites: a high-resolution transmission electron microscopic study of faceted void-like defects in natural diamonds

In natural diamonds of optical classification type la , nitrogen is the major identified impurity and is distributed mainly in point defects known as A defects (probably a pair of nitrogen atoms substituting for a pair of adjacent carbon atoms) and B defects (probably four substituted nitrogen atoms tetrahedrally surrounding a carbon vacancy), and also in the electron-microscopically visible platelet precipitates on {100}. This paper is concerned with other electron-microscopically detectable defects, discovered by R. F. Stephenson (Ph.D. thesis, University of Reading (1977)), that lie in {100} planes in circumstances strongly suggesting that they result from the decomposition of platelets. High-resolution electron microscopy shows these defects to be {111}-faceted cavities. They behave as pure phase-contrast objects whose interior density does not exceed about one-third that of the diamond matrix: we call them ‘voidites’. The experimental background to voidite observation is reviewed, including electron-microscopic measurements on normal {100} platelets and models of their structure, and the optical, X-ray diffraction and cathodoluminescence evidence for unusually large platelets whose presence, together with a relative richness in B defects, indicates an environment in which voidites are likely to be discovered. Almost all observed voidites are confined to sheets strictly parallel to {100}. Some voidite sheets occur in ‘ partial platelets’, where they replace part of the original area of normal platelet. Other voidite sheets occur within dislocation loops whose size and shape are similar to those of the peripheries of normal platelets in the specimen. Voidites occur in a wide range of sizes. The largest equiaxed voidites observed measure about 10 nm between opposite {111} facets, and the smallest resolved about 0.5 nm. Many voidites are elongated in one of the <110> directions in the plane of the voidite sheet: the most highly elongated voidites seen approach 100 nm in length, with diameters of a few nanometres. Variations in size, shape and number density of voidites, together with many other characteristics relevant to the microscopic processes of voidite formation, are discussed in detailed descriptions of about 40 voidite sheets occurring in partial platelets and dislocation loops in two diamond specimens. One specimen was free from both grown-in dislocations and dislocations associated with plastic deformation. It contained zones of highly elongated platelets and it appeared that transformation of a platelet into a voidite sheet surrounded by a dislocation loop was triggered by the mutual very close approach of platelets. The second voidite-containing specimen had suffered plastic deformation at some stage in its history, but did not exhibit direct evidence that glide dislocations had triggered the transformation. The Burgers vectors of 24 dislocation loops enclosing voidite sheets in the second specimen were determined. Twelve were of normal ½<110> type having a component ½a 0 normal to the voidite sheet, and twelve were non-primitive, the Burgers vector being a 0 normal to the voidite sheet (a 0 is the diamond face-centred cubic (fcc) unit cell edge). The volumes of over 2000 individual voidites, representing all or major parts of 12 voidite sheets, have been measured. Values found for the ratio ∑ V /Aa 0 (where ∑ V is the aggregate voidite volume in a sheet area A ) averaged about unity for 9 sheets of generally similar, voidite-rich appearance. Other sheets are poorer in voidites of measurable dimensions: the ratios for two such sheets averaged 0.25. In the concluding analysis, a reaction involving A and B point defects is proposed for the production of platelets. Other reactions including voidites (but no dislocations) are suggested in which both platelet production and elimination might occur. For the dominating reaction, when a platelet is replaced by a voidite sheet surrounded by an interstitial dislocation loop, models are developed for the cases when the Burgers vector component perpendicular to the loop is either a 0 or ½ a 0 , with the assumption that the platelet nitrogen is dispersed partly into B defects and partly into the voidites. The predicted values of ∑ V /Aa 0 come out as about unity and as 0.25 (or lower) for the larger and smaller Burgers vectors, respectively.

Spin density waves in Cu-Mn

The incommensurate magnetic peaks occurring in Cu1−x Mnx at (1,0.5±δ,0) and equivalent positions in reciprocal space have been studied in an extensive series of neutron scattering experiments. It is found that δ varies linearly with composition, and that the width of these peaks corresponds to a correlation range of about 10 fcc unit cells. The symmetry of the magnetic scattering indicates that there are 12 spin density wave domains. Experiments performed under high-resolution conditions (61 μ eV) show that the elastic component of the magnetic scattering cross section at (1,0.5±δ,0) approaches zero in the vicinity of the ‘‘freezing’’ temperature Tf, closely resembling the behavior of an order parameter going to zero at a Néel point.

Mechanism of decomposition of dolomite, Ca 0.5Mg 0.5CO 3, in the electron microscope

Decomposition of dolomite, Ca 0.5Mg 0.5CO 3, induced by the electron beam in the transmission electron microscope, was studied by means of electron diffraction patterns and high-resolution images. Radiolysis of the carbonate ion gives a metastable, fcc solid solution, Ca 0.5Mg 0.5O, which is formed by a topotactic process so that a body diagonal of the fcc unit cell is coincident with the original dolomite c-axis. The fcc lattice constant of 0.461 ± 0.006 nm is 2% larger than the mean value for CaO and MgO. Subsequently, the fcc domains lose orientation, the specimen passes through an amorphous state, and randomly oriented crystallites of CaO and MgO are formed. The diameters of the crystallites of both the solid solution and the final CaO and MgO are in the range 1 to 10 nm. Thermal decomposition in vacuum differs from electron-beam decomposition in that the range of solid-solution compositions is much more limited in the former case. Electron-beam decomposition of minerals may be a useful method of preparation of highly reactive solid solutions that are not otherwise obtainable.

I = ∞ Hubbard model on finite systems

Ferromagnetism of the single band Hubbard model at I = ∞ is analyzed numerically. The lowest energies at given electron number and total spin are calculated for various finite lattices, such as bcc and fcc unit cells and a 2×2×3 simple cubic lattice. It is found that the three-site exchange is important for strong ferromagnetism.

Polymorphism of crystalline poly(hydroxymethyl) compounds. VI. The crystal structure of 2-hydroxymethyl-2-nitro-1,3-propanediol

O2NC(CH2OH)3 is triclinic from room temperature to 347.4 K, where it forms an orientationally disordered fcc phase I. The room temperature form (phase II) has two molecules per unit cell (asymmetric unit) in space group P1, with a=6.203(2), b=9.823(3), c=6.095(2) Å, α=91.68(1), β=109.59(1), γ=89.74(1)°, Dx=1.440 g/cm3, and Dm=1.458 g/cm3. Although phase II is triclinic, it approximates a body-centered monoclinic cell, which is easily related to the high-temperature phase I fcc unit cell. In phase II, a total of 728 independent reflections were refined to a final agreement factor of 0.0304. The nitro groups on both crystallographically independent molecules are disordered and do not participate in the three-dimensional hydrogen-bonded network (which does involve all the hydroxymethyl groups).

NMR, Calorimetric, and Diffraction Study of Molecular Motion in Crystalline Carboranes

Molecular motion of two nearly icosahedral molecules, ortho- and meta-carborane, in the solid state has been studied by x-ray diffraction, calorimetric, and NMR techniques. At 25°C the powder diffraction patterns for both crystals are consistent with a fcc unit cell of dimension 9.86 Å containing four molecules. For both isomers the corresponding molecular site symmetry is higher than the molecular symmetry, implying molecular orientational disorder at this temperature. That the orientational disorder is of a kinetic nature is confirmed by NMR measurements. The proton resonance line second moment at 25°C is 0.711 ± 0.051 G2 for o-carborane and 0.82 ± 0.10 G2 for m-carborane. This can be compared with a line second moment of 0.630 G2 calculated assuming rapid isotropic molecular reorientation and a line second moment of 34 G2 calculated for the rigid lattice. For both isomers the observed second moment is much smaller than calculated assuming rotation about the molecular twofold axis, implying rapid reorientation between thermodynamically indistinguishable orientations. Measurements above and below room temperature were made only for the ortho isomer. A phase transition was observed at 4.0 ± 3.0°C both by calorimetry and x-ray diffraction. The associated transition enthalpy and entropy were respectively 0.84±0.05 kcal/mol and 3.0 e.u. The proton resonance line second moment observed at − 0.6°C is 1.13 ± 0.1 G2, implying a rather general molecular reorientation between indistinguishable molecular orientations at this temperature in the low temperature phase. With decreasing temperature the line second moment rapidly increases in the vicinity of − 80°C. At − 98°C, the lowest temperature measurement, molecular reorientation is still rapid enough to significantly narrow the resonance line. No high entropy phase transition was found by calorimetric measurements from below the 4°C transition to − 130°C, indicating either that an order–disorder transition lies below − 130°C or that for kinetic reasons the ordered phase is not attained, necessitating a nonzero entropy at 0°K. On increasing temperature above 25°C, no change was observed in line second moment until about 200°C. Above this temperature the linewidth and second moment decrease due to rapid molecular translational diffusion. Apparent activation parameters for molecular rotation and for translational diffusion have been obtained from linewidth measurements.