High resolution images of a reconstructed surface structure on (111) gold platelets: Interpretation and comparison with theoretical models

Reconstruction of the (111) gold surface has been previously observed, and it has been shown that the surface net is compressed in the <110> direction, as compared with the bulk lattice. We present here some high resolution studies made on this surface reconstruction: the problem was to obtain a structure image corresponding mainly to the uppermost plane which forms the surface. For this, we have formed high resolution images by interferences between the so-called forbidden diffracted beams $\text{1}\text{3}$ (4?22): bulk gold, when observed along the <111> direction, is better described as a stacking of hexagonal two-dimensional layers, and the $\text{1}\text{3}$ (4?22) beams occur as diffracted beams from 1 (or2) hexagonal layers; they nearly disappear every 3 slices. If the top layer is reconstructed, the diffracted beams from the first slice will be different and will not cancel with the diffracted beams from the bulk layers. Hence the image formed with these beams will give some information on the reconstructed top layer. Computed images have been obtained for different models of the reconstructed surface. They show that, indeed, images obtained under these conditions are linked with the topography of the surface. They also show the importance of different experimental parameters, in particular the beam divergence.     

High-resolution electron microscopy of disordered lithium ferrites

The disordered phase of lithium ferrite (α-LiFeO₂) shows characteristic circular short-range order (SRO) diffuse scattering around the 110 and the equivalent reciprocal lattice points in the diffraction pattern with the [001] incidence. The origin of the diffuse scattering has been explained by the SRO arrangement of lithium and iron ions inside an octahedron as the unit of the sodium chloride derivative structure (cluster model). In the present study, the local structure of the specimen is directly observed by high-resolution electron microscopy and microdiffraction to clarify the origin of the SRO diffuse scattering. The results obtained from the micrographs show that the SRO state of the specimen consists of regular arrangements of iron-rich regions with total size of 1.5 to 2.0 nm in the [001] and [0$\text{1}$1] projections. It is confirmed from the optical diffraction patterns of the micrographs and the microdiffraction patterns that the arrangements, as the results by the projections, explain the loci in the 001 and 0$\text{1}$1 sections of the characteristic SRO diffuse scattering. These results show that a part of the origin of the SRO diffuse scattering arises from ordering in the regions larger than the octahedral unit.     

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.     

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).     

The effect of amorphous surface layers on images of crystals in high resolution transmission electron microscopy

The effect of a surface layer of amorphous silicon dioxide on images of crystalline silicon has been investigated for a range of crystal thicknesses varying from zero to 2$\text{1}\text{2}$ times that of the surface layer. It is shown that an amorphous surface produces fluctuations in image contrast which introduces difficulties in the interpretation of defects in very thin specimens. These difficulties are less pronounced but still present in thicker crystals. It is also shown that an edge smoothly approaching zero thickness produces an image that changes gradually from crystalline to amorphous character.     

Correction of the spherical aberration of the CTEM objective lens using a foil lens

A foil lens has been applied to the objective lens of a conventional transmission electron microscope and its characteristics in correcting the spherical aberration have been investigated experimentally. Special polepieces of the objective lens were designed so that the foil lens can easily be inserted into them. The spherical aberration of a compound lens consisting of the objective lens and the foil lens was measured from the displacement of the {200} dark field image of a magnesium oxide crystal from its bright field image for various voltages of the foil lens. The experiment has shown that the spherical aberration of the objective lens, being excited at $\text{NI}\text{√V}\text{= 19.6 A V}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ at 100 kV, is reduced and becomes negative as the foil lens voltage is increased. The experimental result is in good agreement with calculations involving the third- and fifth-order spherical aberrations.     

Calcul de la matrice Jacobienne nécessaire à la commande coordonnée d'un manipulateur

This article deals with the coordination of the movements of a manipulator when the end effector has to follow a series of imposed positions and orientations. At any instant the position is defined by the three Cartesian components x₁, x₂, x₃ of the center of mass of the end effector, and the orientation by the Euler parameters x₄, x₅, x₆; this choice keeps the intrinsic symmetry of the problem. The vectorial relation $\text{f}$ - called the geometrical model of the manipulator - is established between the vector $\text{x}$ whose components are x₁, x₂, …, x₆ and the vector of generalized coordinates $\text{q}$ whose components are q₁, q₂,…, q_n. The calculation of the error δq generated on the generalized coordinates by an error δ$\text{x}$ between the vector $\text{x}$ and an input vector $\text{x}$

(t) requires the matrix expression - called the Jacobian matrix - of the partial derivatives of the function $\text{f}$ relative to the components of the vector $\text{q}$. In particular, the solution given in this article for obtaining the Jacobian matrix simplifies calculations which normally are very complicated. It consists of expressing certain elements of this matrix as a function of those of the generalized transformation matrix between a frame linked to the end effector and one linked to the structure. An example of the calculation of the Jacobian matrix of a manipulator having six degrees of freedom is given.     

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.     

On the dual spherical motions—ISur les mouvements spheriques duaux (lére partie)

In this paper it is shown that if the axes of curvature of the ruled surfaces $\text{U}{}_1\text{(t)}$ in the moving and fixed spaces intersect each other perpendicularly then the dralls (or distribution parameter) of the ruled surfaces, which are generated by the geodesic trihedron U₁, U₂, U₃s of a dual curve $\text{U}{}_1\text{(t)}$, satify the A. Mannheim and R. Hamilton's formulae. Furthermore, the “explicit characterization” of the spherical curve of striction is given in terms of U₃-surface and the skewness of distribution of the generator of U₁-surface.     

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.     

A tension-torsion machine for testing yield criteria and stress-strain relationships at T = 78°K

A tension-torsion machine in which aluminium and copper specimens are pulled and twisted while being immersed in liquid nitrogen is described. The incorporated load cell and extensometer offer very accurate readings at $\text{T = 78°}\text{K}$.The test materials are especially treated to approach conditions of isotropy and homogeneity. Stress-strain curves in simple tension and pure shear are obtained at $\text{T = 292°}\text{K}$ and $\text{T = 78°}\text{K}$. It can be seen that at 78°K the initial yield surface obeys the von Mises yield criterion.     

Subsurface hardening in erosion-damaged copper as inferred from the dislocation cell structure,and its dependence on particle velocity and angle of impact

Previously published measurements of the cell diameters d of dislocation cells underneath copper surfaces exposed to particle erosion were evaluated in terms of the subsurface stresses τ to which they correspond. These were compared with the elastic stresses expected underneath spherical indenters impacting on the surface with different speeds. The inferred stresses differ markedly from theoretical predictions, not only in regard to the dependence on speed and angle of impact but even in regard to their decay along the z axis, the direction normal to the surface. Instead of τ decreasing as z^?n with n continuously rising from 0 at a shallow depth to 2 at large depths, as predicted from elastic theory, the stresses follow a z^?1 dependence throughout the measured range. All data are satisfactorily explained by the relationship $\text{1/d = (7/z)v}{}^{\mathrm{<mtext>2</mtext><mtext>5</mtext>}}\text{sin α ≈ τ/100}$ (using MKS units), where v stands for the velocity of the impacting particles, namely rather irregularly shaped alumina particles 50 μm in diameter, and α is the angle of impact. No theoretical explanation has so far been found to account for this result. It is noted, however, that previously a z^?1 decay of stress had already given excellent results in a theoretical interpretation of the subsurface shear strain underneath a surface subject to sliding wear. Further, sin α is the direction cosine for the normal force component, whereas a velocity dependence of $\text{v}{}^{\mathrm{<mtext>2</mtext><mtext>5</mtext>}}$ is found from elastic theory for the depth scaling of the elastic stress due to a spherical indenter. Suggestions are made for further experiments.     

A vectorial method using combination theory in the term 2Wi × Vrel to calculate the acceleration of a point in the space kinematics of rigid bodies

This study to calculate the acceleration of a point using combination theory for compound accelerations constitutes a new interpretation of the general relative acceleration equation. The advantages of this new approach are the easy tabulation and the simple order of the solution and the preservation of the physical concepts. Also, the student has the opportunity to distinguish between $\text{2w}{}_{\mathrm{i}}\text{× V}{}_{\mathrm{<mtext>rel</mtext>}}\text{and}\text{2W × V}{}_{\mathrm{P/M}}$, the Coriolis acceleration. This distinction is useful in avoiding an erroneous physical interpretation.     

Classification of real measurement representations by scale type

The scale type ($\text{M, N}$) of an ordered relational structure is defined in terms of two properties, called $\text{M-}\text{point}$ homogeneity and $\text{N-}\text{point}$ uniqueness, of the automorphism group of the structure. For real structures on an open interval, scale types (1, 1) and (2, 2) correspond to ratio and interval representations, respectively. Accepting certain key properties, such as transitivity of the ordering relation and, in the case of a binary operation, monotonicity, and assuming that a real representation exists, then for each scale type whose real transformation group is known, the possible forms for the representation can be derived. For structures with a monotonic, binary operation, this is done completely for the ratio and interval cases, and incompletely in what is shown to be the only other interesting case exhibiting substantial symmetry, (1, 2). These results are then used to gain a better understanding of the psychological theory of utility of gambles and the possible generalisations of multiplicative conjoint structures, which are of importance in dimensional analysis.     

Modelling of Coulomb damping and wear of vibrating systems

Coulomb damping is often relied upon to control the response of nuclear boiler tube banks acted upon by fluctuating eddy forces from turbulent coolant flow. The required energy dissipation is affected by relative sliding movements between the clamped joints of the tube and support structure. These movements Z are in general related to the centre span deflection y which is coupled to the exciting forces by the relation

$\text{Z=}\text{∑}\text{n=1}\text{∞}\text{α}{}_{\mathrm{n}}\text{y}{}^{\mathrm{n}}$

where the α_n are termed coupling coefficients. Specific models of the damping are developed for direct Coulomb damping (n = 1) and second-order damping (n = 2) under conditions where a constant friction force, i.e. static loading, is assumed to act. The effects of partial slip across the joint are examined, and this gives rise to a damping contribution at amplitudes that lie below the threshold y_p for gross slip at the joint. In general direct Coulomb damping gives rise to a non-linear type of damping and also changes natural frequency with amplitude. Second-order damping tends asymptotically to a constant loss factor $\text{1}\text{Q}{}_{\mathrm{r}}$ at large amplitudes but in general would be comparable with the hysteretic damping.The penalty from frictional damping is the occurrence of an associated wear rate which can be expressed by

$\text{dW}\text{dt}\text{=}\text{k}\text{μ}\text{dξ}{}_{\mathrm{D}}\text{dt}$

where K is the specific wear rate, ξ_D is the energy dissipated as wear and μ the friction coefficient. Since K and μ are defined by environmental and material properties compatible with nuclear environments, the design should be optimized to minimize the energy dissipation.     

Solid particle erosion of mullite

The solid particle erosion of mullite (3Al₂O₃·2SiO₂ plus approximately 12% glass phase) was investigated using angular A1₂O₃ particles whose mean diameters D were varied between 23 and 270 μm. A range of impact angles α between 15° and 90° was used and the impact velocity V was varied from 60 to 100 m s^?1. The results of these experiments are in agreement with the general predictions of the two models developed to describe erosion in brittle materials on the basis of the formation of lateral cracks. The velocity exponent of the steady state erosion rate ΔW is between 2.2 and 2.8, being larger for smaller particles. For normal incidence, $\text{ΔW ∝ D}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ in accord with both theories. For α > 15° only the normal component of velocity need be considered, but for smaller α there is evidence of plasticity both in the α dependence of ΔW and as observed using scanning electron microscopy.     

The high speed size effect in grinding: The role of heat generation

Experimental data on the depth dependence of the specific energy of grinding and of single-point scratching does not agree with the predictions of the ploughing model. In this paper the model is extended to take into account the heat generated beneath the scratching point, the subsequent softening of the material and the influence on the specific energy e and the scratch hardness H_s. For pyramidal points $\text{e = H}{}_{\mathrm{s}}\text{∝ d}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{v}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$; for spheres $\text{e ∝ d}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>4</mtext>}}\text{v}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, whereas H_s shows a different behaviour which depends on the choice of parameters. The dependence on depth d and speed v_s agrees with experimental data on the grinding and scratching of steel.     

The use of finite element creep solutions to obtain J integrals for plane strain cracked members

Numerical values are obtained for the path independent $\text{J}$ integral and for crack opening displacement δ, for internally and externally cracked tension members under conditions of plane strain. These parameters have been obtained, for an $\text{n-}\text{power}$ creeping material, from stationary state solutions using the finite element method. Values of $\text{J}$ and δ are compared with available results and are shown to be in good agreement.     

Elastohydrodynamic analysis of a cylindrical journal bearing with a flexible bearing shell

The effect of the elastic deformation of a bearing shell was considered in the determination of the performance characteristics of a hydrodynamic journal bearing. The finite element method with an iteration scheme was employed to solve the Reynolds equation governing flow in the clearance space and the three-dimensional linear elasticity equations representing the displacement vector field in the bearing shell. For design convenience a nondimensional deformation coefficient ψ relating μ, E_m, U₀ , C, R_j and tis defined. The performance characteristics were obtained in terms of load-carrying capacity, fluid flow, power loss and attitude angle for an aspect ratio $\text{L}\text{D = 1}$, eccentricity ? = 0.6 and for a wide range of deformation coefficients. The results are compared for bearing materials having Poisson's ratio v equal to 0.3 and 0.4.