Gosset helicoids: I. 8D crystallographic lattice <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> and crystallographic,quasi-crystallographic,and fractional helicoidal axes determined by this lattice

It is shown that mapping of substructures of a semiregular Gosset polytope, whose 240 vertices form the first coordination sphere of a 8D lattice E ₈, determines the orders of p/d axes of helicoids that are set only by invariants of (sub)algebras. Axes of such (Gosset) helicoids are derived. These axes perform rotation by an angle (360°/p(d; can be crystallographic, quasi-crystallographic (p = 2, 3, 4, 5, 6, …; d = 1), or fractional (1 < d < p/2); and may belong to regular polytopes (conventional, starlike, etc.). Formation of ordered structures is considered as a formation of Gosset helicoids (rods) with their subsequent assembly. Helicoids with axes 15/4 and 15/7 are considered as examples. They correspond to crystallographic approximants—helicoids with axes 4₁ and 2₁ composed of deformed icosahedra (dodecahedra)—in a β-Mn crystal (clathrate IX).     

X-ray crystal structure of the complex of enniatin B with KNCS

The crystal structure of the complex of enniatin B, cyclo[-(L-MeVal-D-Hyi)₃-](C₃₃H₅₇N₃O₉), with KNCS is determined by X-ray diffraction [CuKαradiation, R = 0.0594 for 7925 reflections with I > 2 σ(I)]. The crystals belong to the space group P3, a = 24.448(5) Å, c = 23.578(5) Å, V = 12277(9) ų, and Z = 6. The unit cell contains 12 symmetrically independent molecules of the antibiotic, which are located on crystallographic threefold axes. The K⁺ ions are located on the threefold axes and are coordinated by the carbonyl oxygen atoms of the hydroxy acid or amino acid residues of the enniatin molecules to form prisms, twisted prisms, and antiprisms. All the independent enniatin molecules retain the principal conformational features revealed earlier in the structures of enniatin B and its complexes.     

Microstructure of eutectic composites Ln 1?x Ln′ x MnO3 (Ln = Eu or Tb; Ln′ = Y or Ho) near the transition between the orthorhombic structure and hexagonal structures

Multiferroic crystals Ln _{1 ? x} MnO₃ (Ln = Eu or Tb; Ln?? = Y or Ho) have been grown by floating-zone melting; the compositions of these crystals are close to the point of concentration transition from the orthorhombic structure to the hexagonal phase. Scanning microscopy has revealed that the crystal boules have a regular lamellar structure in the form of alternating layers of the orthorhombic and hexagonal phases; this structure is typical of the materials obtained by the directional solidification of eutectic composites. The local chemical and phase compositions and the unit-cell parameters of the phases have been determined. The microstructure and morphology of the lamellar structures are described for different growth conditions. The mutual orientation of the crystallographic axes of the orthorhombic and hexagonal phases in the neighboring layers has been determined by electron backscatter diffraction. The orientational features are considered from the point of view of the crystal structure of both phases.     

The cracking of Czochralski-grown crystals

Crystals of brittle materials are easily cracked during manufacture and processing. This paper examines the thermal strains existing in crystals during and after pulling and the strains which can be built-in by the facet effect. It is shown that during the growth of a crystal with a radius R, there is a maximum acceptable axial gradient roughly proportional to R^?1.5 and that to prevent cracking after growth there is a maximum rate of cooling proportional to R^?2. Results obtained with bismuth silicon oxide for which all the relevant parameters (breaking strain, expansion coefficient, thermal diffusivity and cooling constant) have been measured are in accord with these relations at least for 4 <R<23 mm. The analysis seems valid for other materials (e.g. lithium niobate) with small breaking strains and negligible plastic ranges. For bismuth silicon oxide, (110) and (100) facets have lattice constants larger than the bulk of the crystal by about 4 and 6 parts in 10⁵ respectively. The edges of these facets are thus regions which are strained by amounts corresponding to 20 or 30% of the breaking strain. Under normal growth conditions, this strain is not particularly significant, but it does affect post-growth handling and during rapid growth, interface instabilities develop first at the facet edges.     

Characterization of GaInN/GaN layers for green emitting laser diodes

An enhancement of radiative recombination in GaInN/GaN heterostructures is being pursued by a reduction of defects associated with threading dislocations and a structural control of piezoelectric polarization in the active light-emitting regions. First, in conventional heteroepitaxy on sapphire substrate along the polar c-axis of GaN, green and deep green emitting light-emitting diode (LED) wafers are being developed. By means of photoluminescence at variable low temperature and excitation density, internal quantum efficiencies of 0.18 for LEDs emitting at 530 nm and 0.08 for those emitting at 555 nm are determined. Those values hold for the high current density of 50 A/cm² of high-power LED lamps. In bare epi dies, we obtain efficacies of 16 lm/W. At 780 A/cm² we obtain 22 lm when measured through the substrate only. The 555 nm LED epi material under pulsed photoexcitation shows stimulated emission up to a wavelength of 485 nm. This strong blue shift of the emission wavelength can be avoided in homoepitaxial multiple quantum well (MQW) and LED structures grown along the non-polar a- and m-axes of low-dislocation-density bulk GaN. Here, wavelength-stable emission is obtained at 500 and 488 nm, respectively, independent on excitation power density opening perspectives for visible laser diodes.     

Nature and origin of V-defects present in metalorganic vapor phase epitaxy-grown (InxAl1−x)N layers as a function of InN content,layer thickness and growth parameters

Our study of samples grown in different metalorganic chemical vapor deposition reactors and with different growth conditions reveals that V-pits are always present in (In_xAl_1?x)N films whatever the layer thickness and the InN content. V-pits are empty inverted pyramids terminating threading dislocations. InN-rich triangular regions are present around the threading dislocations terminated by pits with a hexagonal 6-fold symmetry distribution in {11?20} planes. The nature of the facets of the V-pits depends on the growth conditions: pits with either {11?2l}, l being between 1 and 3, or {1?101} facets have been observed. Moreover, the nature of the threading dislocations terminated by pits also depends on the growth conditions. Our observations suggest that with a high V/III ratio only edge a+c-type dislocations are terminated by pits whereas with a low V/III ratio both edge a-type and mixed a+c-type dislocations are terminated by pits.     

New schemes for recording electron diffraction patterns of hexagonal and monoclinic crystals

Some new schemes for recording electron diffraction patterns of hexagonal crystals rotating around the axes lying in the (hk0) plane of the reciprocal lattice and monoclinic crystals rotating around the a and b axes of the direct lattice and the a* axis of the reciprocal lattice have been developed. Formulas for interpreting electron diffraction patterns are reported. The electron diffraction patterns obtained based on these schemes were used to solve the 2H and 3R polytypes of CdInGaS₄ crystals and the 3R polytype of Zn_1.5In₃Se₆ crystal with the parameters a = 4.046 and c = 59.292 Å, sp. gr. R3m.     

Gyrotropic absorbing crystals of lower symmetries

The specific features of polarization of natural waves propagating in crystals near their optical axes have been studied successively in transparent gyrotropic, absorbing, and gyrotropic absorbing crystals of classes 222, 2, 1, m, and mm2. The dependences of the ellipticities of natural waves and the azimuth of polarization of light transmitted through a crystalline plate (the case of normal incidence) on the orientation of the optical-axis plane of the plate axes with respect to the normal to surface are calculated for these crystals. These characteristics are compared for crystals of axial and planal classes with two different orientations of the optical-axis plane with respect to the symmetry elements of crystal.     

Crystal and molecular structures of 11-hydroxy-7-oxodrim-8(9)-ene

The crystal structure of 11-hydroxy-7-oxodrim-8(9)-ene is determined. The crystals are monoclinic. The unit cell parameters are a = 16.716(4) Å, b = 11.052(3) Å, c = 7.542(3) Å, γ = 76.11°, Z = 4, μ = 1.476 cm⁻¹, ρ_calcd = 1.147 g/cm³, and space group P2₁. The structure is solved by the direct method and refined by the least-squares procedure to R = 0.045. There are two molecules of 11-hydroxy-7-oxodrim-8(9)-ene in the asymmetric unit. Both molecules have the same conformation of the skeleton and can be described as rotomers differing in orientation of the OH groups with respect to the skeleton. In both molecules, the cyclohexane rings have a usual chair conformation. In the crystal, two independent molecules are linked by a hydrogen bond. The molecular pairs related by the twofold screw axes are linked by hydrogen bonds into helices running along the z-axis of the crystal. The helices are bound through van der Waals interactions. __________ Translated from Kristallografiya, Vol. 45, No. 2, 2000, pp. 275–278. Original Russian Text Copyright ? 2000 by Chumakov, Simonov, Mazus, Popa, Vlad. Deceased.     

X-ray and neutron diffraction study of the defect crystal structure of the as-grown nonstoichiometric phase Y0.715Ca0.285F2.715

This work begins a series of papers aimed at studying the defect structure of nonstoichiometric phases R _{1 ? y} Ca _y F_{3 ? y} with a tysonite-type (LaF₃) structure. In the single-crystal structure of Y_0.715Ca_0.285F_2.715 with a tysonite-type small unit cell (sp. gr. P6₃/mmc, a = 3.9095(2) Å, c = 6.9829(2) Å; Z = 2; R _w = 2.16%), the displacements of Y³⁺ cations and F^2? anions from 6₃ symmetry axes were observed for the first time. The X-ray diffraction pattern shows weak satellites insufficient for structural calculations. The LaF₃ structure type is stabilized up and down on the temperature scale due to anion vacancies and the symmetrizing effect of Ca²⁺ cations lying on 6₃ symmetry axes. At 120°C the fluoride-ion conductivity in the nonstoichiometric phase Y_0.715Ca_0.285F_2.715 is five orders of magnitude higher than that in the stoichiometric phase β-YF₃. The transition to a superionic state is caused by a deviation from stoichiometry and is not associated with reconstructive phase transformation.     

Domain structure in strontium tetraborate single crystal

Partially ordered domain structure is discovered for the first time in strontium tetraborate single crystal that is not known to be a ferroelectric. Domains are visualized by etching and are shown to have the form of sheets with domain walls perpendicular to a-axis. The structure is rather well-ordered along b and c crystallographic axes of the crystal but highly randomized along a-axis.     

Nature of large-scale oscillations in oxygen concentration along the growth axis in Czochralski-grown silicon crystals

Oxygen distribution in a Si crystal (100 mm in diameter) has been studied by the absorption method in the range of the absorption band of interstitial oxygen, λ = 5.81 μm. Large-scale fluctuations (～1 cm) of the oxygen concentration (N ₀) along the growth axis were determined. Depending on the melt height, the regions of the chaotic and quasiperiodic changes were established, as well as the region of the constant N ₀ value, and their relation to turbulent, quasiperiodic, and stationary modes of melt convection in crystallization. The values of the critical Rayleigh number for the melt transition from stationary to quasiperiodic (3 × 10³) and from quasiperiodic to turbulent (1.7 × 10⁴) convection modes are determined for growth of silicon crystals by the Czochralski method. The dominating modes of N ₀ concentration oscillations at two incommensurable frequencies, f ₁ = 1.3 × 10^?3 and f ₂ = 6 × 10^?4 Hz, are assumed to be related to the oscillatory transfer of oxygen from the walls of the quartz crucible to the crystallization front and restructurization of the convective flow pattern of the melt in the course of crystal growth.     

Electrical and structural characteristics of metamorphic In0.38Al0.62As/In0.37Ga0.63As/In0.38Al0.62As HEMT nanoheterostructures

The influence of the metamorphic buffer design and epitaxial growth conditions on the electrical and structural characteristics of metamorphic In_0.38Al_0.62As/In_0.37Ga_0.63As/In_0.38Al_0.62As high electron mobility transistor (MHEMT) nanoheterostructures has been investigated. The samples were grown on GaAs(100) substrates by molecular beam epitaxy. The active regions of the nanoheterostructures are identical, while the metamorphic buffer In _x Al_{1 ? x} As is formed with a linear or stepwise (by Δ _x = 0.05) increase in the indium content over depth. It is found that MHEMT nanoheterostructures with a step metamorphic buffer have fewer defects and possess higher values of two-dimensional electron gas mobility at T = 77 K. The structures of the active region and metamorphic buffer have been thoroughly studied by transmission electron microscopy. It is shown that the relaxation of metamorphic buffer in the heterostructures under consideration is accompanied by the formation of structural defects of the following types: dislocations, microtwins, stacking faults, and wurtzite phase inclusions several nanometers in size.     

Specific features of the crystal packing that enable styryl dyes of the pyridine series to undergo the solid-phase [2 + 2] photocycloaddition including the process with single crystal retention

The crystal packing of a number of styryl dyes of the pyridine series is analyzed. The structures of three dyes and three [2 + 2] photocycloaddition (PCA) products, 1,2,3,4-tetrasubstituted cyclobutanes, obtained in single crystals are determined by X-ray diffraction. Stacks of planar organic cations are characteristic of styryl dye packings. The proceeding of the PCA reaction as a single crystal-to-single crystal transformation in the syn head-to-head stacks is in principle impossible. The syn head-to-tail stacking packings are favorable for the PCA reactions resulting in the centrosymmetric rctt isomers of cyclobutane. The stacking packings, in which molecules are related by the twofold axes (the anti arrangement of molecules), are also favorable for PCA in single crystals. In this case, the products are the rtct isomers of cyclobutane. The presence of the I^? counterions in a packing is a factor impeding the PCA reaction, because the secondary I…H-C bonds increase the rigidity of the crystal lattice. The conditions necessary for proceeding the PCA reactions in styryl dyes as single crystal-to-single crystal processes are as follows: (1) the stacks split into pairs of organic cations (dimers) with the d distances within 4.2 Å in a dimer and d exceeding 4.2 Å between the dimers; and (2) the dimers are surrounded by flexible shells consisting of anions, solvate molecules, or flexible moieties of the organic cations themselves.     

Crystal structure of <Emphasis Type="Italic">L</Emphasis>-serine phosphate

The crystal structure of L-serine phosphate (C₃O₃NH₇ · H₃PO₄) is determined by single-crystal X-ray diffraction. The unit cell parameters are as follows: a = 9.134(5) Å, b = 9.489(5) Å, c = 4.615(5) Å, γ = 99.54(5)°, space group P2₁, and Z = 2. The amino group of serine is protonated by a hydrogen atom of the phosphoric acid. The H₂PO ₄ ^1? ions are linked by hydrogen bonds into infinite ribbons aligned along the twofold screw axes. The ribbons form layers alternating with layers of serine molecules, which are directly linked by hydrogen bonds.     

Kinetics of (R,S)- and (R)-mandelic acid in an unseeded cooling batch crystallizer

The objective of this work is to determine the nucleation and growth kinetics of (R,S)-mandelic acid ((R,S)-MA) and (R)-mandelic acid ((R)-MA) in aqueous solutions using an unseeded cooling crystallization process. To obtain the nucleation and growth kinetics, the solubility, metastable zone limits, and supersaturation were measured by in-situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and focused beam reflectance measurement (FBRM). The nucleation rate and growth rate parameters were determined by a nonlinear optimization algorithm. The effects of initial concentration and cooling rate on supersaturation and the nucleation rate are also discussed.     

Crystal structure of a new representative of the cancrinite group with a 12-layer stacking sequence of tetrahedral rings

The crystal structure of a 12-layer tounkite-like mineral of the cancrinite group was determined for the first time by single-crystal X-ray diffraction analysis (the unit-cell parameters are a = 12.757 Å, c = 32.211 Å). The structure was refined in the space group P3 to R = 0.035 using 3834 reflections with | F| > 2σ(F). Si and Al atoms occupy tetrahedral framework positions in an ordered fashion. The average distances in the tetrahedra are 〈Si-O〉 = 1.611 Å and 〈Al-O〉 = 1.723 Å. The stacking sequence of the layers is described as CACACBCBCACB, where A, B, and C are six-membered rings arranged around the [2/3 1/3 z], [1/3 2/3 z], and [0 0 z] axes, respectively. In the structure of the mineral, the columns along the [0 0 z] axis are composed of cancrinite cages. The columns along the [2/3 1/3 z] and [1/3 2/3 z] axes contain alternating cancrinite, bystrite, and liottite cages.     

Packing motifs as predictors of the propensity of antibody fragments to crystallize

A recurring theme in the crystallization of antibody fragments in our laboratory has been a packing pattern involving formation of intermolecular, antiparallel β-pleated sheets across two-fold axes. The most common motif is the antiparallel stacking of constant (C) domains of light (L) chain dimers or Fab molecules. Here, cross-molecule six-stranded sheets are produced by hydrogen-bonding interactions of three-residue polypeptide segments (triads), in the i, i+2 and i+4 positions of the final strands (designated 3–3) of the three-chain layers from two adjacent molecules. In the variable (V) domains the triads are supplied by the first strands (4–1) of the four-chain layers and the resulting cross-molecule sheets contain eight strands. The latter type of packing is more likely to be seen in crystals of Fv fragments (V domains only) than in those of L chain dimers or Fabs. Amongst the triads from either the V or C domains, there are on average four sets of backbone carbonyl and amide groups within hydrogen bonding distance (<3.2 Å) of each other. In at least one example, the adjacent antiparallel strands are sterically aligned, but only two of the appropriate sets of atoms are sufficiently close to meet the distance criteria for intermolecular hydrogen bonding. These observations have been used to construct a list of rules for predicting which types of L chain dimers, Fab and Fvs are likely to crystallize in these packing patterns.     

Effects of initial stages on the crystal quality of nonpolar a-plane AlN on r-plane sapphire by low-pressure HVPE

A 4–6 μm thick a-plane (1 1 2¯ 0) AlN was grown on r-plane sapphire substrate by low-pressure hydride vapor phase epitaxy (LP-HVPE), using a direct growth without any nitridation and buffer layer, a single-step nitridation growth, a two-step nitridation growth and a two-step buffer growth method. For the two-step buffer growth procedure, smoother surface is observed with the lower full widths at half maximum (FWHM) of X-ray rocking curves (XRC) compared with the other two kinds of nitridation procedures. A smaller FWHM of in-plane XRC peak anisotropy features are reversed, which is consistent with the smaller in-plane stress anisotropic distribution in a-plane AlN, when the two-step nitridation or buffer growth method is used. In four kinds of initial growth procedures, the two-step buffer method is the suitable method for the growth of a-plane AlN by HVPE with the high crystal quality and more isotropic distribution.