Nonparallel Planes Research Articles

ChemInform Abstract: Decabenzylgermanocene: Synthesis and Structure of a Monomeric, Air‐Stable Germanocene.

AbstractDie Titelverbindung (II) entsteht durch Zugabe von Gelz zu einer frisch bereiteten Lösung von Pentabenzylcyclopentadienyllithium in THF und wird durch eine Röntgenstrukturanalyse (RG P21/n; Z=4) charakterisiert.

Decabenzylgermanocene: Synthesis and Structure of a Monomeric, Air‐Stable Germanocene

of a Monomeric, Air-Stable Germanocene** By Herbert Schumann, * Christoph Janiak, Ekkehnrdt Hahn. Jorg Loebel, and Jerold J . Zuckerman* symmetry with two parallel, staggered cyclopentadienyl rings and a stereochemically inert electron pair at Sn. It has not yet been determined whether the corresponding compounds of Ge['] or Pb] have similar structures. In the germanocenes studied up to now, (q5-CsH5)zGe,i'1 ( I ~ ~ C H & ~ H & G ~ , [ ~ I and ($C5Me5)2Ge,i51 on the other hand, the planes of the two cyclopentadienyl rings intersect at an angle of 34 to 50; the compounds are very reactive. We have now obtained decabenzylgermanocene, I , the first germanocene that, despite nonparallel cyclopentadienyl ring planes, is stable toward air. 1 is formed as large, pale yellow crystals by addition of germanium diiodide to a freshly prepared solution of pentabenzylcyclopentadienyllithium in tetrahydrofuran (THF).Ih1 Decaphenylstannocene' has S

$3$-manifolds which contain nonparallel projective planes

We show that if a closed, connected 3-manifold with a Heegaard splitting of genus three contains mutually disjoint and nonparallel 2-sided projective planes, then the manifold is homeomorphic to the connected sum of p2 x S' and the twisted 2-sphere bundle over the circle.

A comment on ‘Electron microscopy of “giant” platelets on cube planes in diamond’

Abstract The claim by Woods (1976a) to have good electron-microscopic evidence that the platelet defects on {100} planes found in natural Type Ia diamonds are composed of interstitial carbon atoms is disputed by examining his geometrical arguments. In particular, it is held that the evidence weighs against there having occurred a reaction he proposes in which perfect dislocation loops result from the interaction and annihilation of two platelet defects lying on non-parallel cube planes.

Determination of omega phase volume fraction in single crystals of beta titanium alloys

Single crystals of metastable BCC Ti-6.5 at.% Mo alloy have been aged at 350°C for varying times to precipitate the omega phase. The variation in volume fraction of precipitate was determined by a quantitative X-ray diffraction technique and correlated with transmission electron microscopy from thin foils. For Ti-Mo alloys the lattice misfit between omega and beta phases is small; reflections from parallel planes of both phases overlap necessitating the use of reflections from nonparallel planes. The 310 beta reflection and 31 4 1 and 30 3 2 omega reflections were selected. These two omega reflections occurred at 96° and 105° 2θ angles with CuKα radiation and required a 14° reorientation of the crystal.

Flow of viscoelastic polymeric melts through converging ducts

An experimental study has been carried out to better understand the flow behavior of viscoelastic polymeric melts in a converging channel which consists of two nonparallel planes. For the study, measurements were taken of both stresses and velocities, the former by means of the flow birefringence technique and the latter by means of streak photography. The material used was polystyrene. A comparison was made of the stress-birefringent patterns obtained in the present study with those obtained in an earlier study byHan andDrexler, who used a slit die having a tapered entrance. It has been found that both stresses and velocities in the converging flow field of polymeric melts do not exhibit any noticeable evidence of secondary motion, contrary to the theoretical prediction made by earlier investigators. The apparently unnoticeable secondary motion in the present study may be attributable to the extremely slow motion of the polymeric melts investigated. Also carried out was a theoretical analysis of converging flow. This was essentially the same as that carried out earlier byHan andDrexler, using a modified second-order fluid model which assumes that all three material functions depend on the second invariant of the rate of deformation. A comparison was made of the experimentally determined stress distributions with the theoretically predicted ones.

Elastic interaction between two parallel dislocations in non-parallel slip planes

The elastic interaction between two parallel dislocations which can glide in non-parallel slip planes is studied under the simplifying assumption that the dislocation glide velocity is proportional to stress. The motion of the two dislocations is represented by a motion of one reference point in a configuration plane. It is concluded that the contribution of the long-range elastic interaction between individual dislocations from different slip systems to work hardening is negligible, compared to the contribution from the formed attractive junctions. Especially, two parallel edge dislocations with mutually perpendicular Burgers vectors can co-exist in minimum energy positions, however, they can be separated by an arbitrarily small external stress.

Theory of non-Newtonian flow through porous media in narrow three-dimensional channels

A theory for the flow of non-Newtonian fluids through porous media in narrow three-dimensional channels of varying gap is presented. The treatment is not restricted to Stokesian fluids, but is equally valid for fluids that exhibit normal force and elastic effects. The only rheological data required are experimental pressureflow results in one-dimensional flow for the porous medium of interest. The flow geometry is restricted to a channel in which the gap spacing varies slowly with position, leading to the assumption of local two-dimensional flow everywhere in the flow field. The equations presented are solved for a particular narrow channel formed from two non-parallel planes for the cases of (i) Newtonian fluid and (ii) pseudoplastic power-law fluids. The results for flow through porous media are compared with those for lubrication flow in an identical channel. A perturbation scheme is presented so that the validity of the original approximation of local two-dimensional flow may be checked for any numerical solution. It is shown that in general the theory will break down if the local channel angle exceeds approximately 10°.

X-RAY MONOCHROMATORS AND RESONATORS FROM SINGLE CRYSTALS

Single-crystal specimens shaped so as to permit successive x-ray diffraction by two nonparallel atomic planes are fixed wavelength monochromators. It is shown that certain plane pairs in Si and Ge pass wavelengths sufficiently close to strong characteristic lines to allow production of intense highly monochromatic beams. For tautozonal planes belonging to the same crystal form, resonators and retroreflectors are possible.

Dislocations in evaporated single crystal tin films

Dislocations in evaporated single crystal tin films have been investigated by means of the electron microscope. The operation of the following slip systems was directly observed: (121) [1̄01], (101̄) [101], (100) [011], (1̄10) [111] and (001) [ hkl]. (001) slip has not been reported previously and may occur only in thin films. (110) [001] and (100) [001] slip were not observed, possibly because of unfavorable diffraction conditions in the [001] oriented films. Most of the dislocations had screw character. The following cases of screw dislocation cross-slip between different slip systems were observed: (100) [011] ↔ (01̄1) [011], (100) [011] ↔ (21̄1) [011] and (01̄1) [011] ↔ (21̄1) [011]. Cross-slip between non-parallel planes of the same slip system was observed in only one case: (12̄1) [1̄01] ↔ (121) [1̄01]. A consideration of the available qualitative evidence suggests that the stacking fault energy in tin is relatively high.

Cross-slip and Fatigue in Metals at Low Temperatures

The mutual annihilation of jogged screw dislocations approaching one another on non-parallel slip planes is shown to give rise to a type of recovery which accounts satisfactorily for the pronounced decline in the rate of work-hardening observed in f.c.c. metal crystals above a certain shear stress, frequently denoted by τIII(T). The relation τIII =(τIII)o[1-(mkT/Q)], deduced from the model, where (τIII)0 = τIII(0), m =30 and Q the energy of vacancy formation, agrees well with the experimental data for aluminium, copper, gold and nickel up to about 0·15 Tm, where Tm (°K) is the temperature of melting. It is suggested that the heat evolved during such dislocation annihilations facilitates the clustering of slip into bands observed at stresses above τIII by catalyzing further destructive interactions, and that condensation of vacancies formed in the process of cross-slip provides the crack nuclei in slip clusters from which fatigue fractures spread. The temperature dependence of the fatigue limit appears to be the same as that of τIII.

Cross-slip and fatigue in metals at low temperatures

The mutual annihilation of jogged screw dislocations approaching one another on non-parallel slip planes is shown to give rise to a type of recovery which accounts satisfactorily for the pronounced decline in the rate of work-hardening observed in f.c.c. metal crystals above a certain shear stress, frequently denoted by τIII(T). The relation τIII =(τIII)o[1-(mkT/Q)], deduced from the model, where (τIII)0 = τIII(0), m =30 and Q the energy of vacancy formation, agrees well with the experimental data for aluminium, copper, gold and nickel up to about 0·15 Tm, where Tm (°K) is the temperature of melting. It is suggested that the heat evolved during such dislocation annihilations facilitates the clustering of slip into bands observed at stresses above τIII by catalyzing further destructive interactions, and that condensation of vacancies formed in the process of cross-slip provides the crack nuclei in slip clusters from which fatigue fractures spread. The temperature dependence of the fatigue limit appears to be the same as that of τIII.

Observation of the Grain Boundary in Soap Bubble Raft Part I. Static Feature of the Grain Boundary

The grain boundary is constructed in the soap bubble raft by the procedure of progressively increasing the angle of disorientation between two grains. The grain boundaries observed are classified into three types in respect to the statical transition structure. At an angle of disorientation θ∼0°, the grain boundary (type A) is constituted of the dislocations all on parallel slip planes. At an angle of disorientation θ∼60°, the grain boundary (type C) is constituted of two sorts of dislocations each on nonparallel slip planes. At an intermediate angle of disorientation, the, grain boundary (type B) is composed of disordered groups of atoms or the diffused holes. The mechanism of the varying nature of the grain boundary with the angle of disorientation is discussed in the light of the current theory of dislocations, where the stress is laid on the predominance of reactions between the dislocations and the relative shortage of thermal agitation.