Diamond Symmetry Research Articles

Optical and structural properties of SixSnyGe1−x−y alloys

Single-phase SixSnyGe1−x−y alloys (x⩽0.25,y⩽0.11) were grown on Si using chemical vapor deposition. First principles simulations predict that these materials are thermodynamically accessible and yield lattice constants as a function of Si/Sn concentrations in good agreement with experiment. An empirical model derived from experimental SixGe1−x and SnyGe1−y binary data also provides a quantitative description of the composition dependence of the lattice parameters. Spectroscopic ellipsometry of selected samples yields dielectric functions indicating a band structure consistent with highly crystalline semiconductor materials of diamond symmetry. Incorporation of Si into SnyGe1−y leads to an additional reduction of the E2 critical point, as expected based on the E2 values of Si and Ge.

Layer-by-layer diamond-like woodpile structure with a large photonic band gap

A layer-by-layer periodic dielectric structure with a large photonic band gap is presented. It consists of a layer-by-layer approximation to the triply periodic bicontinuous level set D surface structure having diamond (Fd3m) symmetry. The structure retains the ease of fabrication of the standard woodpile while increasing the maximum quality factor of the gap by 28%. Photonic band gap properties of this structure were calculated using the plane-wave method and its band gap optimized at a fixed index contrast of 3.6:1.

Holographic photonic crystals with diamond symmetry

We explore the analytical design of high-symmetry photonic crystals made by holographic lithography. We show how holographic lithography may be used to produce diamond-like photonic crystals that have a full, three-dimensional photonic band gap at a refractive index contrast equal to the lowest yet published.

Technique for design of two-channel approximately linear phase QMF filter bank and its application to image compression

The two-channel QMF filter bank based on allpass sections is one of the best known circuits for building up a multi-channel filter bank for signal compression. An analysis-synthesis combination can satisfy two of the three perfect reconstruction (PR) conditions. The third, the phase condition, can be met to any desired accuracy. However, when applied to images, PR is possible because non-causality can be allowed in the synthesis bank. The development of explicit formulae for the coefficients of such filters is considered. The resulting QMF designs can be used in a wavelet structure for image compression problems using rectangular or diamond symmetry. Several design examples are given, including a comparison of performance with FIR filter banks for such problems.

Effect of disorder on photonic band gaps

We study the transmission of electromagnetic waves propagating in three-dimensional disordered photonic crystals that are periodic on the average with a diamond symmetry. The transmission has been calculated using the transfer matrix method. We study two different geometries for the scatterers: spheres and rods connecting nearest neighbors. We find that the gaps of the periodic structure survive to a higher amount of disorder in the rods' case than in the spheres' case. We argue that this is due to the connectivity of the rod structure that exists for any amount of disorder.

Micro-Raman fingerprint of grain boundary in [100] oriented diamond films: Stress distribution and diamond phases

Local distribution of stress state and carbon bonding in diamond films are studied by micro-Raman spectroscopy. Large changes in intensity, line shape, and peak position of the diamond Raman line occur close to the grain boundary. The characteristic feature of such region is a 1326 cm−1 Raman peak, whose detection suggests that defect incorporation at the grain boundary may promote a diamond symmetry modification from a cubic to hexagonal one. Close to intergrain locations, large anisotropic stresses also induce frequency splitting of the Raman line. Suitable stress configurations consistent with the detection of an almost unshifted component and of a largely frequency-changing mode are analyzed.

X-ray topography of natural tetrahedral diamonds

AbstractThe symmetry of diamond is still sometimes questioned. Most people agree that diamond belongs to the space group Fdm and therefore to point group . Some however, on account of the existence of a few natural tetrahedral diamonds, have assigned diamond to the point group 3m. We report here on an X-ray topographic investigation, using both conventional and synchrotron sources, of eleven natural tetrahedral diamonds. Two large specimens (from the Alpheus Williams' collection) were studied and found to consist of two portions, unequal in size, that were twinned on a (111) plane. Another diamond (from Professor R. A. Howie's collection) was found to contain two non-parallel (111) twin planes with the diamond filling the space between them, giving the crystal a tetrahedral morphology. Four tetrahedral diamonds (selected by Tolansky) were shown to be either twinned on a (111) plane, or cleavage fragments consisting of one component of a made or single crystals that had been plastically deformed. Similar results were found for some diamonds from the Argyle Mine. Our findings are consistent with diamond belonging to the holosymmetric class () rather than to the hemihedral class (3m).

Correlated random walks on two-sublattice systems. I. Theory.

The theory of Tahir-Kheli and Elliott (TKE), for analyzing correlated random walks on uniform lattices with an arbitrary concentration of background particles, is extended to treat two-sublattice systems with a potential difference between the sublattices resulting in site-dependent hopping rates. We consider first systems with overall simple-cubic and body-centered-cubic structures, along with their two-dimensional analogs. Next, two face-centered-cubic sublattices with diamond symmetry and two triangular networks forming a honeycomb lattice are studied. The tracer diffusion correlation factor and the correlation effects at general k and \ensuremath{\omega}, leading to the incoherent scattering cross section, are calculated for these systems. The limiting cases where the potential difference between the sublattices is vanishingly small lead to the earlier TKE results for a uniform lattice.

The symmetry of diamond

The symmetry of diamond

The origin of a tetrahedral diamond

SummaryThe symmetry of diamond is still disputed, and is usually regarded as 4/m3̄2/m or 4̄3m. The (rare) development of tetrahedral morphology has been cited in favour of the lower symmetry. A tetrahedral crystal of c. 4 mm edge-length was studied for evidence relevant to this controversy. Three similar quadrants have nearly plane tetrahedron faces, each surrounded by six curved surfaces belonging to forms {hkl}. The fourth (unique) quadrant, containing (IĪĪ), differs topographically. In the three similar quadrants the tetrahedron faces exhibit coplanar banding of trigons parallel to (IĪĪ), and the curved surfaces have striations parallel to it. The banding and striations are interpreted as stratigraphic etching of nitrogen-rich layers parallel to (IĪĪ) in a type I diamond. Slip, and apparently polygonization, occur in the unique quadrant. The three similar {III} faces were formed by cleavage, and the curved surfaces, banding, and striations by subsequent dissolution. It is probable that (IĪĪ) was part of an original octahedral surface, since tetrahedra of diamond are so rare. The tetrahedral morphology does not necessarily indicate that this crystal belongs to class 4̄3m. The doubt cast upon tetrahedral morphology (and the inferred twinning on {100} or about (100>) as evidence in favour of lower symmetry strengthens the case for assigning diamond to class 4/m3̄2/m.

The infra-red absorption spectrum of diamond

The absorption spectra of four typical diamonds, three of them luminescent and the fourth non-luminescent, have been investigated in the infra-red in the wavelength range 4·5 μ to 13 μ with a rock-salt prism spectrometer and radiomicrometer. Allowing for reflection, the non-luminescent diamond is found to be completely non-absorbing in the frequency range 770 cm.−1 to 1400 cm.−1. The luminescent diamonds show a band in this region with a number of absorption maxima whose frequencies may be identitied with those of the lattice and superlattice vibrations. The intensity of this band is greatest in the weakly blue-fluorescent diamond, somewhat weaker in the intensely blue-fluorescent diamond and still weaker in the diamond showing both blue and yellow fluorescence. These results are accounted for on the basis of the crystal structure and symmetry of diamond in its various allotropic modifications. The absorption peaks appearing in the region between 1400 to 2700 cm.−1 are accounted for as octaves and combinations of the lattice and superlattice frequencies which are allowed by virtue of the anharmonicity of the vibrations. The appearance of the superlattice frequencies in the 8 μ band is closely associated with the infra-red activity of the fundamental lattice vibration and is in the nature of a resonance effect.

On the crystal symmetry of diamond and its X-ray reflections

The problem of the symmetry of the diamond structure in relation to its X-ray behaviour is considered in a formal manner. It is shown that the presence or absence of the 200 or the 222 reflection cannot uniquely decide whether the symmetry is tetrahedral or octahedral. The 200 reflection is shown to be absent if the structure is either completely symmetric or antisymmetric with respect to the centre of inversion at 1/8, 1/8, 1/8 or if the two distributions are superposed in any arbitrary ratio. The 222 reflection is, however, absent only in the fully antisymmetric case. Making use of these results, the nature of the structures that are possible for the tetrahedral and the octahedral modifications of diamond are discussed.

Infra-Red Absorption Spectrum of Diamond

The absorption spectra of four typical diamonds, three of them luminescent and the fourth non-luminescent, have been investigated in the infra-red in the wavelength range 4·5 μ to 13 μ with a rock-salt prism spectrometer and radiomicrometer. Allowing for reflection, the non-luminescent diamond is found to be completely non-absorbing in the frequency range 770 cm.−1 to 1400 cm.−1. The luminescent diamonds show a band in this region with a number of absorption maxima whose frequencies may be identitied with those of the lattice and superlattice vibrations. The intensity of this band is greatest in the weakly blue-fluorescent diamond, somewhat weaker in the intensely blue-fluorescent diamond and still weaker in the diamond showing both blue and yellow fluorescence. These results are accounted for on the basis of the crystal structure and symmetry of diamond in its various allotropic modifications. The absorption peaks appearing in the region between 1400 to 2700 cm.−1 are accounted for as octaves and combinations of the lattice and superlattice frequencies which are allowed by virtue of the anharmonicity of the vibrations. The appearance of the superlattice frequencies in the 8 μ band is closely associated with the infra-red activity of the fundamental lattice vibration and is in the nature of a resonance effect.

The crystal symmetry and structure of diamond

Scanned from Vol.4 of Scientific Papers of C.V. Raman. Ed. by S. Ramaseshan. Published in 1988 by the Indian Academy of Sciences, Bangalore.

An investigation into the piezo-electric effect of diamond

Introduction—Opinion is divided as to the true crystal symmetry of diamond. Some authors, notably Fersman and Goldschmidt, who have investigated its morphological and etch characters, consider it is always hemihedral, whilst others, by the same methods, have obtained results which indicate holohedrism. Early work by A. Artom showed that it was seldom piezo-electric, but more frequently pyro-electric. Van der Veen also carried out avery thorough investigation and found no piezo- or pyro-electricity in his five diamonds. These were octahedral in shape, and not very suitable for this experiment.