Al Planes Research Articles

Surfaces with maximal curvature of the Grassmann image

i. We shall denote by G(s s + p) (s ~ 2, p e 2) the Grassmann manifold of s al planes passing through the origin in s + p-dimensional Euclidean space. LetF s c Es be an s regular surface. At each point of the surface F s we construct the tangent space and parallel translate it to the origin 0 e Es We call the set of s sional planes obtained considered as points of the Grassmann manifold G(s Z + p) the Grassmann image of the surface F s and we call the corresponding map F: F s ~ G(s s + p) the Grassmann map. We shall assume, in addition, that the surface F s has outer null-index zero at each point, i.e., there does not exist a nonzero tangent vector corresponding to the zero eigenvalue of the second quadratic form of the surface with respect to an arbitrary normal. This requirement guarantees the nondegeneracy of the Grassmann map, i.e., F(F s will be a smooth submanifold of dimension s in G(s s + p).

HREm Study of Al-Si Interfaces

ABSTRACTInterfaces between aluminum and silicon in samples prepared by solidification of an Al-Si eutectic liquid have been studied by high-resolution electron microscopy. The Al and Si grains have a common [110] axis with a misorientation between grains of 70.5°, thus aligning the (lll)si plane with the (111)ALplane. In general, theinterfaces have a complex structurewith numerous interfacial dislocations and considerable facetting. The core structurescan be characterized in terms of structural unit models. The nature of the facetting has also been investigated, in particular one facet which lies approximately along the (111)AL, and (l15)si planes and another which lies approximately along the (110)AL and (l14)si planes.

HALF WAVELENGTH AND STOPPING POWER FOR PLANAR CHANNELED 4He+ IONS IN Al AND Si CRYSTALS

Using a detection system with high resolution, backscattering spectra for 1-2 MeV 4He+ incident along Al (100) and Si(l00) and (110) planes are measured at a variety of entrance (θin) and exit (θout) angles. The energy intervals between the peaks in the energy spectra are plotted as a function of cosθin/cosθout Half wavelength and stopping power for 1-2 MeV 4He+ in these three channeling planes are obtained. The experimental half wavelength is in agreement with the calculated value within the limit of error and the planar channeled stopping power is slightly greater than the random stopping power.

Channeling study of structural effects at the Al(111)/Si(111) interface formed by ionized cluster beam deposition

Epitaxial Al(111)/Si(111) films grown by the ionized cluster beam technique have been studied using the high-energy He+ channeling technique. No observable strain has been detected between the Si substrate and the Al layer despite their large (∼25%) lattice mismatch. Displaced Al atoms have been observed in the Al film, which increases with the depth and reaches 30% near the Al/Si interface. A large step increase of dechanneling occurs at the Al/Si interface which might be accounted for by the existence of ‘‘semicoherent’’ interface in which four Al planes are matched to three Si planes.

Examination of the Al/Al 2O 3 interface by high-resolution electron microscopy

The structure of the interface between aluminum and its amorphous oxide has been examined by high-resolution electron microscopy (HREM). The interface was generated on (110) and (111) Al surfaces by growing relatively thick oxide layers (≳ 20 nm) by thermal oxidation in air or by anodization. The examination by HREM was performed on foils (20 to 30 nm in thickness) cut from cross-sections of bulk specimens using an ultramicrotome. The interface was found to be undulatory but the deviations from planarity could be characterized by a long-range roughness, descriptive of the coarseness of the unoxidized Al surface, and a short-range roughness. The short-range roughness, relating to undulations over distances along the interface of the order of several tens of nanometers, arose solely from the presence of ledges on the aluminum. The height of the ledges in the (110) and (111) Al planes generally did not exceed two interplanar spacings.

Terminal vs bridge bonding of methylene to metal systems: Al2CH2 as a model system

The metal dimer-methylene system M2CH2 is the simplest which can in principle display both terminal M–M–CH2 and bridging M CH2 M geometrical structures. Having previously studied the terminal Al–CH, Al–CH2, and Al–CH3 metal-organic fragment species, the Al2CH2 system was chosen to allow a competition between the terminal and bridged structures. Nonempirical molecular electronic structure theory was used, with double zeta (DZ) and DZ + polarization basis sets in conjunction with both self-consistent field (SCF) and configuration interaction (CI) methods. Among structures considered, the bridging arrangement, with the Al C Al and CH2 planes perpendicular to each other, lies lowest energetically. For this structure the Al–Al distance is 3.61 Å, the Al–C distance 2.00 Å, and the methylene bond angle 105.5°. The completely planar structure, found by twisting the methylene group by 90°, is predicted to lie 31 kcal higher, but has a much shorter Al–Al distance 3.03 Å. The terminal structure lies 46 kcal above the absolute minimum on the energy surface and has re(Al–Al)=2.87 Å, re(Al–C)=1.81 Å, and a methylene bond angle of 112.2°. All of the above structures are closed-shell singlets in their lowest electronic states, but the energies of several triplet species are also discussed. The Al–C bond energy for the terminal structure is 81 kcal, in good agreement with that predicted (77 kcal) earlier by comparable methods for AlCH2. However, for the bridging Al2CH2, the Al2 ⋅⋅⋅ CH2 dissociation energy is much larger, 127 kcal. Vibrational frequencies for the bridging and terminal Al2CH2 species are presented and discussed.

The structure of G.P. I zones in Al-1.7 at.% Cu

The diffuse X-ray scattering has been measured from a single crystal of Al-1.7 at.% Cu, aged to contain G.P. I zones. A new method has been employed to separate the contributions from clustering from those due to atomic displacements. Computer simulations with 108,000 atoms were employed to examine the local atomic arrangements. The zones are a mixture of single (001) planes ≈ 100% copper and multilayer regions and with the nearest-neighbor spacing near that of the matrix. There is no significant copper concentration in the matrix. The Al (100) planes near the zone collapse toward it, the displacement decreasing more rapidly (with increasing distance from the zone) than in Gerold's model. A model recently derived from EXAFS data is shown to be inconsistent with the X-ray data.