Dynamical excitation of thermal diffuse scattering in crystals of rutile

Observations of thermal diffuse scattering (TDS) for the [001] projection of rutile are presented. New phenomena include: intense diffuse scattering directed inwards from {200} reflections, a sharply-defined square of continuous intensity having {200} positions as vertices, relatively sharp <110> streaking along radial and non-radial directions, and a distinct deficit scattering region surrounding the transmitted beam. Both the angular dependence of the TDS with respect to crystal tilts and the temperature variation of TDS in the range —180 <T < + 150°C are described. The observed features are interpreted using calculations of the site dependence, within the [001] projection of the rutile unit cell, of the electron current density and its strong dependence on crystal tilt. N-beam dynamical interactions generate a sophisticated probe of the atomic sources of inelastic scattering within the unit cell, a detailed understanding of which is necessary also for further improvement of energy dispersive X-ray and electron energy loss spectroscopic analysis.     

Position averaged convergent beam electron diffraction: Theory and applications

A finely focused angstrom-sized coherent electron probe produces a convergent beam electron diffraction pattern composed of overlapping orders of diffracted disks that sensitively depends on the probe position within the unit cell. By incoherently averaging these convergent beam electron diffraction patterns over many probe positions, a pattern develops that ceases to depend on lens aberrations and effective source size, but remains highly sensitive to specimen thickness, tilt, and polarity. Through a combination of experiment and simulation for a wide variety of materials, we demonstrate that these position averaged convergent beam electron diffraction patterns can be used to determine sample thicknesses (to better than 10%), specimen tilts (to better than 1 mrad) and sample polarity for the same electron optical conditions and sample thicknesses as used in atomic resolution scanning transmission electron microscopy imaging. These measurements can be carried out by visual comparison without the need to apply pattern-matching algorithms. The influence of thermal diffuse scattering on patterns is investigated by comparing the frozen phonon and absorptive model calculations. We demonstrate that the absorptive model is appropriate for measuring thickness and other specimen parameters even for relatively thick samples (>50 nm).     

Uniqueness and the inversion problem of incoherent multiple scattering

It is shown that a unique retrieval of the single scattering electron energy loss distribution from experimental multiple loss data is only possible if it can be assumed that energy gain of the fast electron does not occur. The method given holds for any value of the scattering parameter $\text{t}\text{λ}$ and to spectra to which many distinct processes contribute. An example of the retrieval method is given, applied to the experimental loss spectrum of a thin aluminum foil with $\text{t}\text{λ = 10}$.     

The phonon contribution to high-resolution electron microscope images

The amount of phonon scattering as a function of specimen thickness is determined for a clean silicon sample, free from amorphous surface layers, by measuring the diffuse scattering in energy-filtered convergent-beam diffraction patterns. It is found that for a 25 nm thick sample, only 7.5% of the intensity scattered to less than 18 nm(-1) is phonon scattered. This means that in a typical high-resolution sample most of the diffuse scattering is caused by surface amorphous layers rather than phonon scattering.     

Determination of an improved gear surface of helical gears for pumping actionZur synthese optimaler maschinenelemente — optimale zahnflächen für schraubenpumpen

An improved gear surface of helical gears for pumping action is obtained mainly by theoretical investigation, and partly by test results. This is a further study following the research on gears[1]. A new theory is presented here by selecting characteristic function sequences

$\text{s = Φ}{}_{\mathrm{n}}\text{(t) = 1 ? (1?t)}{}^{\mathrm{n}}\text{, n = 1, 2, 3, … n}{}_0$

which is monotone increasing. The larger n becomes, the larger rate of mass flow $\text{V}\text{and effective work ratio}\text{=}\text{E.W.R.}\text{=}\text{E}$ increases at the same time, thus the optimum tooth profile of gears (consequently the optimal gear surface) can be determined under the assumption that the minimum available cutting pressure angle (θ_ON_O be given in advance.     

Structural and electron diffraction data for sapphire (α-al2o3)

Crystallographic and electron diffraction data for sapphire (α-Al₂O₃) are presented which enable ready and unique identification of TEM diffraction patterns and facilitate image analysis. Crystallographic data is presented in the form of stereographic projections and in figures listing angles between planes and angles between zones. Electron diffraction data consist of computer-simulated diffraction patterns and tables of extinction distances calculated using atomic and ionic electron scattering factors.     

Displacement analysis of the generalised RSSR mechanism

The generalised 4-link RSSR mechanism is analysed which is kinematically equivalent to the more general 7-link spatial $\text{R}$

$\text{R}$ mechanism.

and

joint arrangements represent, respectively, two and three co-intersecting revolute pairs.     

The effect of variable permeability on the performance characteristics of porous bearing

An analytical solution for the performance characteristics of a short bearing having an axial and radial permeability of $\text{k}{}_{\mathrm{z}}\text{[1 + cos(}\text{πz}\text{L}\text{)]}$ and $\text{k}{}_{\mathrm{z}}\text{[1 + (}\text{2}\text{π}\text{)]}$, respectively, is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for various design variables. These results are compared to the results obtained for an isotropic bearing having a permeability of $\text{k}{}_{\mathrm{z}}\text{[1 + (}\text{2}\text{π}\text{)]}$.     

The Third International Conference on Scanning Tunnelling Electron Microscopy

The transition quasi-crystalline→crystalline is found to be very sluggish in the ternary alloy Al₆₀Mn₁₁Ni₄. This makes it possible to study in detail the relationship between the decagonal phase, obtained after furnace cooling, and two different crystalline phases, which result after long annealing at 400°C. Use is made of electron diffraction, high resolution electron microscopy and optical diffraction. The crystalline phases still exhibit features which are closely related to those of the decagonal phase. This can be concluded from a comparison of the electron diffraction patterns of the quasi-crystalline phase along a number of zones, with those of the crystalline phases along corresponding zones. The crystalline phases contain different types of defects which are analysed in detail using high resolution images and diffuse scattering in the electron diffraction patterns. The close relationship between the electron diffraction patterns of the crystalline and quasi-crystalline phases is explained in terms of general optical principles. Some characteristic features of a model of the quasi-crystalline phase are tentatively proposed.     

Interactive adjustment of surfaces

The dilation or contraction of either a sub-region or the whole of an arbitrary, smooth, single v?alued surface-patch defined in an $\text{X,Y}$ plane by Monge's equation, $\text{Z = F(X,Y)}$, is achieved by superposition of influence surfaces without loss of smoothness.The arbitrary surface is first transformed into a surface defined above the projection of its boundaries into a unit square in the $\text{x,y}$ plane. The unit-square is next partitioned by an orthogonal rectangular grid and then, by a series of further transformations, approximately into a circle of unit radius.Within the circle of unit radius a second, influence surface is next postulated and its $\text{z}$ values superimposed on the transformed arbitrary surface at corresponding nodes of the partitioning grid. This influence surface is defined as the shape assumed by a thin flexible elastic plate bounded by the circle and subjected to an eccentric, normal point-displacement at any desired grid-node. Displacements at other nodes are calculable by Michell's two-term closed solution for encastré boundaries or approximately by Föppl's or Clebsch's series solutions for semi-restrained boundaries.If an arbitrary surface is displayed as a net of profile-curves on a computer graphics terminal, the locations and amounts of desired displacements to effect shape-changes can be estimated. Influence surfaces “centred” at such nodes can then be specified and superimposed in the unit circle. Inverse transformation from unit circle to the original arbitrary surface then yields a modified surface for redisplay and reassessment.If a surface having a set of arbitrary $\text{Z}$ values at particular grid-nodes is required, a set of influence surfaces, each appropriate to unit-displacement at each node of the set may be scaled and superimposed to yield a smooth corrective surface or to generate a surface, ab initio.In all cases the influence of corrective surfaces may be limited to sub-regions within the global boundaries of arbitrary surfaces.     

Computer simulation of the contact of rough surfaces

Rough contact was simulated by adding height measurements of a number of pairs of real surfaces, both isotropic and anisotropic, by computer and analyzing the resulting contour maps. The number of contours per unit area was computed for various separations, where a contour may enclose either a contact or a void. Measurements of the contour density agreed well with theory. Voids begin to appear at a separation of about $\text{1}\text{1}\text{2}$ times the roughness, and it is suggested that they may act as lubricant traps. The size distribution of contacts was also investigated and was found to be log-normal.     

Structural study of new hydrocarbon nano-crystals by energy-filtered electron diffraction

A new brittle hydrocarbon has been successfully synthesized in polycrystalline form, and its crystal structure solved by quantitative electron diffraction. By 3D tilting of the nano-crystals, the lattice type and unit cell parameters were determined. (Triclinic, [Formula: see text] A, [Formula: see text] A, [Formula: see text] A, [Formula: see text] degrees, [Formula: see text] degrees, and [Formula: see text] degrees.) Spot diffraction patterns were obtained at -165 degrees C using the Koehler selected-area mode on a LEO 912 TEM fitted with an omega in-column elastic energy filter. The direct methods algorithm was then applied to merged intensities and a trial structure obtained assuming single scattering. This was further refined to obtain good agreement with a small residual of about 10% using multiple scattering calculations. A diagram of the proposed structure is given.     

Zur geometrie der Joukowsky-transformation und über die kinematische erzeugung von tragflügelprofilenOn the geometry of Joukowski transformation and the kinematical generation of wing profiles

In its first part the paper considers, from an advanced point of view, the essential properties of Joukowski's conformal mapping $\text{J: z}{}^1\text{= z+z?}{}^1$. In general, the point $\text{Z}{}^1\text{(z}{}^1\text{=x}{}^1\text{+iy}{}^1\text{)}$ corresponding to a real point Z (z=x+iy) is uniquely determined, with the exception of the fundamental points situated at the origin O and the circular points $\text{I,}\text{I}$ (Fig. 1). Conversely, a real point $\text{Z}{}^1$ arises from two real points Z, Z′ and two conjugate imaginary points Z″, Z3? are related by the involutary Moebius transformation V: z.z′ = 1.The circle k (1.8), determined by its complex center coordinate M≠0 and radius r≠|m|, is carried by the cubic transformation J into a rational bicircular quartic $\text{K}{}^1$ (1.10), but the same curve is also the mapping of a second circle k′ (1.11), connected with k by V (Fig. 4). The singular foci $\text{M}{}^1$ and $\text{N}{}^1$ correspond to the centers M and N of k and k′. The proper point-pair D, D′ common to k and k′ is mapped onto the proper double point $\text{D}{}^1$ of $\text{k}{}^1$.The second part deals with the kinematic generation, at first by means of an antiparallelogram, of such a quartic $\text{k}{}^1$, determined by $\text{M}{}^1\text{, N}{}^1\text{, D}{}^1$ and an arbitrary simple point $\text{Z}{}^1$. The foci $\text{M}{}^1\text{, N}{}^1$ are the fixed pivots of the four-bar linkage $\text{M}{}^1\text{A}{}_1\text{A}{}_2\text{N}{}^1$, and the position $\text{A}{}_1\text{A}{}_2\text{Z}{}^1$ of the coupler triangle is to be found as the mirror image of the triangle $\text{N}{}^1\text{M}{}^1\text{D}{}^1$ with respect to the perpendicular bisector of $\text{D}{}^1\text{Z}{}^1$ (Figs. 5 and 6). According to the theorem of Roberts, there exist two additional kite linkages generating the same quartic $\text{k}{}^1$. The third fixed pivot $\text{L}{}^1$ corresponds to $\text{D}{}^1$ in the reflection $\text{M}{}^1\text{? N}{}^1$ (Fig. 6).The essential dimensions of all generating linkages are given by formulae (2.2–2.7).     

Below the “Scherzer resolution” limit: Fact and artefact

Although modern HREMs have stabilities such that spacings considerably smaller than the “point resolution” of the instrument - the “Scherzer limit”, 0.7 C_s^{$\text{1}\text{4}$}λ^{$\text{3}\text{4}$} - may readily be recorded, the interpretation of such images in terms of the atomic structure of the object is not straightforward. A familiar example of such images, the “dumbbell images” of 〈110〉 oriented silicon and related materials, is discussed in some detail, and it is shown that accurate imaging of individual atomic columns, in the axial mode, requires rather better resolution than is currently available. Secondly, an HREM study of certain defects in natural diamonds is presented, in which a probable structure for the controversial “{100} platelets” is derived from critical image-matching experiments, thus demonstrating that, if parameters such as defocus and specimen thickness can be measured (or estimated) accurately, it is possible to extract meaningful information from images which utilise the full instrumental resolution capabilities available, and which are not limited by the “point resolution” of the microscope.     

Dispersive equations for high resolution imaging and lattice fringe artifacts

The imaging equations for high resolution electron microscopy are analysed using an approach based upon expanding the electron wave as positionally modulated diffraction beams. A high-order semi-linear approximation is derived which includes the leading non-linear effects of a reciprocal space integration and can be conveniently expressed in real space. This allows a direct visualisation of imaging effects in real space using a conventional wave dispersion approach. Based on this, the primary sources of lattice fringe artifacts and errors in the 2$\text{1}\text{2}$D technique are briefly discussed, and an experimental technique for guarding against them employing dark field imaging is described.     

Stability limits of elliptical journal bearings supporting flexible rotors

The stability of a system consisting of a flexible shaft with a single central rotor supported by two finite elliptical journal bearings was considered. The Reynolds equation was solved numerically for several values of the eccentricity ratio, the $\text{L}\text{D}$ ratio and the dimensionless velocity of the journal centre. The resulting pressure profiles are used to determine the load capacity and the spring and damping coefficients. Limiting speeds of stable operation are obtained from the roots of characteristic equations for the corresponding bearing-rotor system. The operating load, ellipticity, $\text{L}\text{D}$ ratio and shaft flexibility significantly affect the limit of stable operation. Elliptical bearings are suitable for stiff and moderately flexible rotors.     

Trochoidenhüllbahnen in Grenzfällen

Let B be the planetary motion with the rolling polecircle P and the fixed polecircle P′ and let k be a trochoid, generated by the planetary motion b with p rolling on p′. We assume a common centre of k and P. In [1–4] a lot of results can be found about the envelope h of k moved by B. In this paper the four cases are discussed, where pole curves of B or b degenerate into a line.In the case α with a line p the involute k performs a planetary motion B. Satz 1 shows, that the same envelope can be derived, if the cycloid k? performs the involute motion B? in (5). Assuming a cusped k the envelope h consists of the trace of the cusp and of cusped involutes of the circle $\text{P}\text{?}\text{′}$ (Abb. 1). This last result is well known from the involute profile of gear teeth.In case βp′ and P are taken as parallel lines. Choosing equal diameters of p and P the envelope h can be drawn easy as the envelope of a set of circles (Abb. 3). Without changing h the cycloid k can be substituted by a second cycloid $\text{k}$. If k is cusped, h consists of two cusped involutes (Satz 2).The envelope h of case γ with a line P′ is also the envelope of the cycloid k performing the translatory motion B in (15).Finally in case δp and P′ are lines. h can be drawn as the envelope of a set of lines (Abb. 4). We can interpret h as the contour of a helicoid ruled surface in a special oblique projection. Under the assumption P = p′h consists of discrete supporting points and of one cusped cycloid. This result of Meyer[4] is extended on Satz 4 and shown, that there is a continuum of different involutes k with the same cusped cycloid as the remaining envelope.     

An electron microscopy study of the phase Al3Fe

The phase Al₃Fe (monoclinic C2/m, a = 1·549 nm, b = 0·808 nm, c = 1·248 nm, β = 107·8°) has been studied by transmission electron microscopy (TEM) and high resolution electron microscopy (HREM). Crystals were obtained from a direct chill-cast ingot of an Al-0·25 wt% Fe-0·13 wt% Si alloy. Extracted crystals were prepared by dissolving the aluminium phase in butanol and filtering off the particles. The extracted Al₃Fe crystals were mainly (100) platelets. The monclinic lattice was confirmed by tilt experiments and the mirror plane was confirmed by convergent beam electron diffraction. Experimental HREM images from the [100] and [110] projection agreed with images calculated by the multislice method. The interpretation of images in terms of a projected crystal structure is discussed. Common defects in Al₃Fe crystals were: twins on (100) and faults on (001). The (001) faults could be described by a displacement 1/2·[100] on a fault plane at z = 0·5 in the unit cell. A model for (001) faults, based on multiple twinning, is proposed.     

Deformation by scratches and frictional properties of MgO crystals

The subsurface structure of MgO crystals frictionally damaged on their (001) faces by scratching with a diamond stylus in the 〈100〉 direction was investigated using a scanning electron microscope in both the cathodoluminescence and the secondary electron modes. The friction is independent of the load below a critical value, and above this value it depends on the load W according to μ ∝ Wⁿ where μ is the coefficient of friction.The subsurface beneath the sliding contact consists of four characteristic material zones: zone I is severely deformed with a high defect density which causes quenching of the luminescence; zone II is a plastically deformed intermediate zone showing enhanced luminescence; zone III is a slipped zone which on etching shows a dislocation pit pattern; zone IV consists of non-deformed crystalline material. The normalized depth $\text{d}\text{a}$, where d is the depth of each deformed zone and a is the track half-width, is independent of the load.The frictional behaviour was examined by using empirical relations for the damage to estimate the plastic work done during the scratching process.     

The effect of different contact materials on the fretting fatigue strength of an aluminium alloy

The fretting fatigue strength of Al-4Mg-0.7Mn in contact with pads of aluminium, copper, $\text{70}\text{30}$ brass, and 0.7 C steel has been determined. Copper and brass produced little reduction in fatigue strength because of the severe wear of the pads, The steel and aluminium pads produced reductions of 34% and 28% respectively. The effect of fretting on fatigue strength is explained in terms of the added shear stress arising from the frictional force between the pad and the specimen. Although the coefficient of friction is initially low it rises after 500–1000 cycles to approximately 1.0 and remains constant at this figure.