Net Planes Research Articles

Effect of Higher-Order Spherical Aberration Term on Transfer Function in Electron Microscopy

The effect of the higher-order spherical aberration coefficient on the transfer function in transmission electron microscopy was calculated. In order to simplify the system, the optical illumination system was assumed to be perfectly coherent and axially symmetric. The result shows that the effect of the fifth-order spherical aberration coefficient, C5, on the usual transfer function with the third-order spherical aberration coefficient C5≡C3=0.5 mm for 100 keV electrons cannot be neglected, if high-order Bragg reflections from net planes with smaller lattice spacings than 0.1 nm are utilized for lattice imaging. The effect of the higher-order term due to the defocussing on the transfer function is also discussed.

Spectral analysis of adsorbate induced field-emission flicker noise.

Spectral analysis of field-emission flicker noise is developed for a probe current originating from a portion of a single (hkl) plane of the emitter. The current noise is related to equilibrium absorbate density fluctuations in the probed region with the total number of net plane adatoms constant. The noise spectrum factors as S(\ensuremath{\omega})=${S}_{\ensuremath{\infty}}$(\ensuremath{\omega})+${S}_{B}$(\ensuremath{\omega}) when the finite size of the net plane is accounted for. The spectrum due to unbounded diffusion ${S}_{\ensuremath{\infty}}$(\ensuremath{\omega}) is proportional to one derived in Burgess's model of semiconductor contact noise. The boundary-effect contribution ${S}_{B}$(\ensuremath{\omega}) increases dS(\ensuremath{\omega})/d\ensuremath{\omega} at low frequency, whereas anisotropic diffusion decreases it.

On crystal growth of orthorhombic alkali acid phthalates. An application of fourier transform of crystal morphology to tracht and habitus

AbstractThe orthorhombic alkali acid phthalates crystallize in three different structure types. The structure of potassium acid phthalate (P21ab) can be regarded as a basic structure. The elementary cells of ammonium (Pcab) and sodium crystals (B2ab) contain two potassium structure units which are connected to each other along [001] by a symmetry centre in the first case and by a twofold rotation axis in the second case. It will be shown that close morphological relations between the crystals also can be observed. The morphological lattices of the substances agree fairly well with the centres of gravity of the phthalate ions (HP). The reciprocal crystals have mmm (KHP, NH4HP) and mm2 symmetry (NaHP), respectively. The growth rates of the faces are proportional to the areas of the net plane meshes, divided by the number of the morphological units per growth layer. The thickness of the growth layer is determined by the morphological extinction rules. The specific surface energies are proportional to the surfaces of the reciprocal crystals parallel to the crystal faces, divided by the areas of the net plane meshes. The theoretical growth and equilibrium forms of the hydrogen phthalates are in good agreement with the experimental observations.

The structure of sheared ordered latices

Shear-induced changes in the structure of ordered latices of moderate volume fractions have been observed by grating diffraction and right angle Bragg diffraction. The former method provides information about the two-dimensional lattice structure of the particle layers (net planes) parallel to the wall, while the latter gives information about the spacing between the layers. Both methods showed that the order was maintained when ordered latices were subjected to shear. Grating diffraction revealed that at moderate shear rates the two-dimensional lattice was compressed in the flow direction and expanded in the direction normal to the flow, and that at high shear rates the lattice was compressed in all directions. Bragg diffraction revealed that at high shear rates the spacing between the layers increased by 1.5 to 10%. These observations are qualitatively explained by a sliding layer model.

Effect of twisting of the diffraction net planes on the integral intensities at Laue diffraction of X-rays in elastically bent silicon crystals

Effect of twisting of the diffraction net planes on the integral intensities at Laue diffraction of X-rays in elastically bent silicon crystals

Unwinding of the Eshelby twist in sodium chloride whiskers

Sodium chloride whiskers, at first sight useful for precise X-ray lattice constant measurements, were found to have not only the well-known Eshelby twist, but also slight deformations of their cross sections. When the twist was mechanically reversed, net planes parallel to the whiskers axis proved to be nearly perfect: measurements carried out in a three-crystal arrangement showed a narrowing of the reflection range and a subsequent increase in peak intensity by a factor of about 100. The half width of the diffraction pattern, however, still had twice the value expected from perfect crystal theory: obviously not all deformations had been removed.

Analysis of the Net Tension Failure Mode in Composite Bolted Joints

A failure analysis has been developed to predict the net tension strength of composite bolted joints. The analysis involved: 1) the development of a representative stress profile along the net tension failure plane and 2) the in corporation of this stress distribution into the appropriate failure criterion. A two-dimensional, plane stress finite element analysis employing quadrilateral elements with orthotropic material properties was used to determine the state of stress along the failure plane. The stress distribution along this plane was described by a polynomial expression and was generalized to apply to a wide range of geometries. The "point stress" failure criterion was applied to the generalized stress distribution equation resulting in the desired net tension strength prediction. Development of the failure criterion for a particular material system and laminate configuration involved empirically determining two notch sensitivity parameters, m and C. In this study, notch sensitivity parameters were determined for a [45/0/-45/02/-45/0/45/02/90] s graphite/epoxy laminate. The strength predictions were verified using ex perimental net tension strength data.

Field evaporation of silicon (111) surfaces in the presence of hydrogen

The field evaporation rate of Si(111) face in H 2 imaging gas is measured by counting the removal rates on individual net planes in a field ion microscope. The rate is found to decrease with increasing temperature and to be proportional to H 2 gas pressure. The evaporation voltage increases with temperature ( T<300). A model explaining this temperature dependence is based on the rate-determining formation of surface hydrides due to field-induced chemisorption of hydrogen.

A Study of Gamma-Ray Diffraction Caused by Thermal Diffuse Scattering in KCl Single Crystal Using the Mössbauer Effect

Dips of the inelastic intensity profiles in 200, 400 and 600 Bragg reflections from a KCl crystal were observed by means of Mossbauer diffraction using 14.4 keV γ-rays and a position sensitive detector. It is concluded that the dips are caused by the thermal diffuse scattering of γ-rays which is reflected secondarily by the net planes in the same crystal.

Morphological Lattice and Reciprocal Crystal. Remarks on Morphology of Barite and Cerussite

AbstractThe relationship between partitions of the three‐dimensional space into Dirichlet domains of morphological points and the face forms observed on crystals will here be examined. Dirichlet domains, the central points of which are to be found on the exterior net plane, can be connected two or one‐dimensionally through face‐sharing or they occur as isolated groups. If the crystal faces are arranged according to the proportion of these surface polyeder on the total surface of the net plane, the order of rank of barite and cerussite agree excellently with the experimental observations. The packings of space filling polyeder allow conclusions on growth mechanisms.

5256. Progress with a theory of noble-gas field adsorption: Richard G. ForbesVacuum,31 (10–12), 1981, 567–570

Abstract Field adsorption may provide information about the nature of highly-charged surfaces, and is thought to be essential to the formation of field-ion images. This paper briefly reviews the state of the theory. Recent calculations, for He on W(111) at a field of 45 V nm−1, suggest a short-range binding energy of order 15–30 MeV. But such binding energies would not allow the existence at 80 K of the firmly field-adsorbed layer that is currently thought to be essential to image formation; hence a discrepancy exists. The following possibilities are considered: (1) Partial coverage in the surface-adsorbed layer; (2) Use of a more sophisticated surface model in the calculations; (3) Introducing terms related to the higher polarizabilities of the noble-gas atoms; (4) The existence of bonding-points shifts. The last of these is difficult to calculate because there seems the possibility that a ‘repulsive depolarization’ effect may be operating. It is concluded that the discrepancy has not yet been resolved, and that experimental evidence as to the adsorbate-atom coverage in the interior of resolved net planes would be useful, particular for W(111) when this is resolved.

Progress with the theory of noble-gas field adsorption

Field adsorption may provide information about the nature of highly-charged surfaces, and is thought to be essential to the formation of field-ion images. This paper briefly reviews the state of the theory.Recent calculations, for He on W(111) at a field of 45 V nm−1, suggest a short-range binding energy of order 15–30 MeV. But such binding energies would not allow the existence at 80 K of the firmly field-adsorbed layer that is currently thought to be essential to image formation; hence a discrepancy exists.The following possibilities are considered: (1) Partial coverage in the surface-adsorbed layer; (2) Use of a more sophisticated surface model in the calculations; (3) Introducing terms related to the higher polarizabilities of the noble-gas atoms; (4) The existence of bonding-points shifts. The last of these is difficult to calculate because there seems the possibility that a ‘repulsive depolarization’ effect may be operating.It is concluded that the discrepancy has not yet been resolved, and that experimental evidence as to the adsorbate-atom coverage in the interior of resolved net planes would be useful, particular for W(111) when this is resolved.

X-ray diffraction measurements on PE 2000 between 10 K and 300

It was possible to obtain film exposures of the WAXS-diagram (2ϑ ≲ 50°) of a PE-fraction $$(\bar M = 2000)$$ in the temperature range from 10 K to 300 K by using a special low temperature Guinier-chamber. The crystallographica-,b-andc-axis has been calculated from the positions of all reflexions. The different behaviour of their expansion coefficients can be explained by activation of rotational- and torsional-vibrations. If we take the number of net planes as constant and consider a temperature-independent part resulting from paracrystalline disorder (built up during crystallization), we can describe the linear increasing of the integral widths of the reflexions with decreasing temperature (10 ... 100%) with building up of inherent stresses inside the crystals.

On crystal chemistry and morphology of extended organic molecules

AbstractThe present paper is concerned with the morphology and crystal structure of extended organic compounds in the space group P 21/c. In the structures with molecules in general position (Z = 4) the longitudinal axis of all molecules run parallel to a (h0l)‐plane. The molecule arrangements are based on four different structure types. The planes through the molecule axis contain a) 21‐axis and symmetry centres (l = 2n), b) 21‐axis or symmetry centres (l = 2n + 1) and c) respectively d) no symmetry element (l = 2n resp. 2n + 1). In the last two cases the net plane distances are to be halved. As in P 21/c the a‐und c‐axis are not set, one can confine oneself to the examination of the net planes (102), (202), (204), and (404). In the cases of a) and b), only certain morphological lattices appear, which distinguish themselves through additional translations in three‐dimensional space resp. in the projections. In the cases of c) and d) there are also found morphological lattices which generate additional “morphological extinctions” (consequently possessing a higher symmetry than the generating space group), but which contain no translationally higher symmetry. (h0l)‐faces, to which the molecule axis run parallel, appear with preference on crystals. As a rule the first two and the last two cases can be differentiated on account of the position of the (h0l)‐faces in the Donnay‐Harker series. Some examples will show that the morphological lattice can be preserved through Fourier transformation of crystal morphology.

Structure of molluscan thick filaments: A common origin for diverse appearances

Thick filaments from the smooth adductor muscles of the oysters Ostrea edulis and Crassostrea angulata have been examined in the electron microscope after negative staining. The two well-known patterns of stain (whose origin and relation have been uncertain), one a series of transverse narrow lines at intervals of 144 Å along the filament axis and the other a regular two-dimensional arrangement of stained spots (Bear & Selby, 1956), are found to be mutually interconvertible by rotating the grid around the filament axis. This is interpreted to mean that the spots are the projections of stained regions running through the filament in a common direction. Only when looking along this direction will the net pattern be seen with maximum clarity and sharpness. On rotation of the filament round its axis, the spots broaden transversely to the axis, overlapping and ultimately only the axial periodicity will remain. The structure is therefore not helical, but resembles a crystal lattice, although no period can be discerned normal to the net plane. The addition of 10 m m-EDTA to all solutions used in the filament preparation (except the stain), especially when ammonium molybdate is the stain employed, removes many puzzling appearances (probably caused by positive staining) which render the interpretation difficult. The appearance of the negatively stained filament can be related to the stain patterns in negatively stained paramyosin paracrystals (Cohen et al., 1971).

Triangular Spin Ordering in Mn3Sn and Mn3Ge

The Fourier-transformed exchange matrix for the crystalline structure of Mn 3 Sn and Mn 3 Ge is analyzed in the case of a propagation vector parallel to the hexagonal principal axis and two modes of spin ordering are predicted, a helix of ferromagnetic basal net planes and a helix of triangular basal net planes. The effect of anisotropy energies is studied for the triangular spin ordering with zero propagation vector to uniquely determine the spin configuration and to account for the observation. Triangular helix, observed in Mn 3 Sn at low temperatures, is also discussed.

Intensity of Laue diffracted beams in the general case of diffraction in an elastically bent crystal

Good agreement between theoretical and experimental data concerning the dynamical scattering of X-rays (FeKα, CuKα, MoKα radiations) is obtained in the general (asymmetrical) case of the Laue diffraction in an elastically bent crystal. The deformation of dislocation-free silicium crystals is achieved by means of single-side oxidation. Variation of the strain gradient parameter B up to the limiting value 0.15 at fixed thickness of all samples is provided by changing of the deflection angle Ψ between the surface normal and a diffraction net plane in the interval ranging from Ψ = 24° 48′ to Ψ = 35° 12′. [Russian text Ignored]

A neutron three-beam calculation

A first calculation for a particular neutron three-beam case, (111, 1 11), is presented using the dynamical theory of diffraction. By simultaneous reflection on the net planes (111) and ( 1 11) one gets a forward (0) beam and two diffracted ( G and H) beams with different properties. This paper reports on dispersion surfaces, ψ-functions, pendellösung and intensity calculations for the waves leaving a perfect crystal slab, reflection curves for all three beams and the integrated reflection.

Importance of lateral grain boundaries in synthetic polymers

Abstract Combined wide-and small-angle x-ray scattering studies (WAXS and SAXS) of line profiles of polymers prove the existence of small mosaic blocks (50-1500 A in size). They all have liquid like distortions quantitatively defined by a g value and are identified therefore as microparacrystallites (mPC's). Unlike crystals, they can crystallize only in coherent units of not more than N net planes with N = (α*/g)2. Electron micrographs of strain-crystallized transpolyisoprene show directly the grain boundaries between adjacent mPC's within one lamella which appear in temperature range III. The free lateral surfaces of mPC's at the lamella ends are mostly responsible for the long-period growth during annealing in temperature range II. Annealing experiments with poly-1-butene prove that no premelting occurs but solely a solid-state diffusion. This apparently occurs mostly starting from the lateral grain boundaries on account of their larger excess free energy. In stretched isotactic polypropylene films, the...

角度分解光電子分光法による固体表面の研究

Present status of researches on clean and adsorbed surfaces of solids by means of photoemission spectroscopy is briefly reviewed. Theoretical background developed in last decade is summarized very simply, in which the classical three-step-process is derived naturally from a view-point of recent one-step process as a special case. Some experimental results are shown as the examples for practical analyses of the data in order to get inf ormations about the electronic structures and also the atomic geometries on the surfaces. A shorthand bibliography for the experiments performed within last few years on this concern is given in the Appendix, where the papers are classified into the sample, surface net plane and adatoms.