Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1966"

Contact of Nominally Flat Surfaces

Abstract: It is usually assumed that the real area of contact between two nominally flat metal surfaces is determined by the plastic deformation of their highest asperities. This leads at once to the result that the real area of contact is directlyproportional to the load and independent of the apparent area-a result with many applications in the theories of electric contacts and friction. Archard pointed out that plastic deformation could not be the universal rule, and introduced a model which showed that, contrary to earlier ideas, the area of contact could be proportional to the load even with purely elastic contact. This paper describes a new theory of elastic contact, which is more closely related to real surfaces than earlier theories. We show how the contact deformation depends on the topography of the surface, and establish the criterion for distinguishing surfaces which touch elastically from those which touch plastically. The theory also indicates the existence of an 'elastic contact hardness', a composite quantity depending on the elastic properties and the topography, which plays the same role in elastic contact as the conventional hardness does in plastic contact. A new instrument for measuring surface topography has been built; with it the various parameters shown by the theory to govern surface contact can be measured experimentally. The typical radii of surface asperities have been measured. They were found, surprisingly, to be orders of magnitude larger than the heights of the asperities. More generally we have been able to study the distributions of asperity heights and of other surface features for a variety of surfaces prepared by standard techniques. Using these data we find that contact between surfaces is frequently plastic, as usually assumed, but that surfaces which touch elastically are by no means uncommon in engineering practice.

Studies in Electrohydrodynamics. I. The Circulation Produced in a Drop by Electrical Field

Abstract: The elongation of a drop of one dielectric fluid in another owing to the imposition of an electric field has previously been studied assuming that the interface is uncharged and the fluids at rest. For a steady field this is unrealistic, because however small the conductivity of either fluid the charge associated with steady currents must accumulate at the interface till the steady state is established. It is shown that equilibrium can only be established in a drop when circulations are set up both in the drop and its surroundings. A relation is found between the ratios of the conductivity, viscosity and dielectric constant for the drop and surrounding fluid which permits the drop to remain spherical when subjected to a uniform field. The streamlines of the circulation for this case are shown and criteria are given for distinguishing between circulations which carry the surface of the drop towards or away from the poles and for predicting whether the drop will become prolate or oblate. Experiments by S. G. Mason and his co-workers are compared with the theoretical predictions and agreement is found in all cases for which the necessary data are given.

The Polarization of Laser Light Scattered by Gases

Abstract: Measurements of the polarization of light scattered from the beam of a helium-neon gas laser at low pressures are described. The intensity, polarization and parallelism of the beam permit high accuracy, and new values for the depolarization ratios of twenty-four simple species are reported. The general quantum theory of scattering is discussed and applied in detail to the evaluation of a formula for the depolarization ratio of the scattered light. It is found that quantum corrections to the classical formula arise from ( i ) the effects of frequency changes due to rotational Raman scattering, ( ii ) changes in the molecular polarizability with rotational state due to centrifugal distortion, ( iii ) approximations inherent in the polarizability scattering formula, and ( iv ) vibrational Raman scattering. Effect ( i ) reduces the depolarization of hydrogen to 91% of its classical value; ( iii ) is unimportant unless the frequency of the light is near an absorption frequency of the molecule. The depolarization measurements have been combined with refractivity data to yield the anisotropies in molecular polarizabilities of the molecules studied.

On the theory of the effect of precipitate particles on grain growth in metals

Abstract: A theoretical model of the energy changes accompanying grain boundary movement has been developed. It has been shown that small boundary movements will reduce the energy of a polycrystalline metal only when there is a heterogeneous grain size. The pinning force exerted by precipitate particles of a second phase on the grain boundary has also been considered. The release of grain boundary energy which accompanies grain growth has been considered as a source of energy for the unpinning process. The theory predicts a critical particle size which is dependent on the volume fraction of second phase, the matrix grain size, and the degree of heterogeneity of the matrix. Coalescence of the precipitate to a size in excess of the critical radius will permit grain growth to occur. Theoretical predictions of the critical particle size are in good agreement with values determined experimentally. The essential difference between grain growth and secondary recrystallization is indicated by the theory.

Experimental Observations of the Transition to Detonation in an Explosive Gas

Abstract: The experimental study of transition to detonation has been enhanced recently by two novel techniques. One exploits simply the fact that a self-sustained detonation front, unlike any other wave associated with the transition process, is capable of leaving imprints on the wall along which it travels. The other is based on the adaptation of an amplitude modulated, giant pulse, laser system as a light source for stroboscopic schlieren photography. The insight gained by the utilization of these techniques into the wave processes accompanying the onset of detonation is unparalleled in the long history of the study of these phenomena. The results demonstrate that the transition can take place in various modes depending on the wave interaction processes which occur ahead of the accelerating flame.

The Expulsion of Magnetic Flux by Eddies

Abstract: A convective eddy imposed on an initially uniform magnetic field in a highly conducting fluid distorts the lines of force and amplifies the field. Flux is concentrated outside the eddy; within it, the field grows and its scale of variation decreases until resistive effects become important. Closed lines of force are then formed by reconnexion. The central field decays and a steady state is reached. Within a period, small compared with the characteristic time for resistive decay, magnetic flux is almost entirely expelled from regions of rapid motion and concentrated at the edges of convection cells. This process is demonstrated from numerical experiments. The results are applied to the sun, where the concentrated fields are strong enough to inhibit convection locally.

The Occurrence of Singularities in Cosmology. II

Abstract: It is shown that singularities of space-time are inevitable if the Einstein equations hold, if matter has normal properties and if the universe satisfies certain reasonable global conditions. The singularities would be in the past and would, in principle, be observable. Observation to determine whether such singularities actually occurred would provide a powerful test of the Einstein equations in strong fields. The singularity would not necessarily constitute a beginning of the universe.

Unstable oscillation of tubular cantilevers conveying fluid I. Theory

Abstract: When the velocity of fluid flow in a tube, fixed at the upstream end and free at the other, is increased beyond a certain critical value, the system becomes unstable and small random perturbations grow into lateral oscillations of large amplitude. This paper is concerned with establishing the conditions of stability in the case of a system which is constrained to move in a horizontal plane. Neglecting internal friction in the material of the tube and the effect of the surrounding fluid, a universal stability curve is constructed corresponding to conditions of neutral stability and hence separating stable and unstable regimes. This is done by finding solutions to the equations of motion both by exact methods and also approximately by expressing the motion as the sum of the first few eigenfunctions of a cantilever beam. The complex frequency of the four lowest modes of the system is calculated in two representative cases for successively increasing values of the flow velocity to demonstrate how transition from stability to instability takes place.

Theoretical and Experimental Studies of the Oil Film in Lubricated Point Contact

Abstract: A technique using Newton’s rings for mapping the oil film of lubricated point contacts is described. A theoretical value for the film thickness of such contacts in elastohydrodynamic lubrication is derived. The experimental results give the exit constriction predicted by previous theory but never shown in detail. The comparison of theoretical and experimental oil film thicknesses, which is satisfactorily accurate, gives strong evidence for a viscous surface layer some 1000A thick. This film agrees with the known ‘lubricating power’ of the various oils tested.

Radiation from cosmic-ray air showers

Abstract: Cosmic ray showers passing through the atmosphere produce electromagnetic disturbances. It has been suggested that these can be detected by means of a radio telescope. We set up a simple model for a shower and find that the time-integrated energy flux in its radiation field, at say 45 Mc/s, is of the order of 60 000 flux units x microseconds, when the shower contains 10$^6$ electrons and 10$^6$ positrons. The radiation pattern depends on the decay rate of the shower. We have done this calculation in order to give some guidance to experimentalists who are planning to observe cosmic ray showers by radio means. $(1 flux unit = 10^{-26} Wm^{-2} (c/s)^{-1}.)$

Transport of Gases To and From Grass and Grass-Like Surfaces

Abstract: A radioactive vapour of thorium-B (lead-212) has been used to measure the vertical flux of a gas to grass and similar surfaces in a wind tunnel, as a function of the difference in vapour concentration between the air and the surface. Experiments were done over a range of values of the parameters friction velocity (u$\_*$) and roughness length (z$\_0$). The results have been analysed in terms of the reciprocal sublayer Stanton number B$^{-1}$ of Owen & Thomson (1963), which is a measure of the degree to which Reynolds's analogy between transport of momentum and matter (or heat) breaks down at the surface. B$^{-1}$ is equal to the difference between the dimensionless resistances of the boundary layer for momentum and for mass. Experiments with grass and other surfaces having roughness elements of a fibrous character gave values of B$^{-1}$ in the range 6 to 12. Some variation of B$^{-1}$ with u$\_*$ was found, but less than expected from Owen & Thomson's work. Little effect of variation in z$\_0$ was found. For values of u$\_*$ and z$\_0$ applicable in normal conditions to vapour transport to or from short grass in the field, B$^{-1}$ was found to equal 8 $\pm$ 1. Experiments with a surface of rough glass, having roughnesses of a pyramidal nature, confirmed Owen & Thomson's results, and gave values of B$^{-1}$ in the range 20 to 40. The dependence of B$^{-1}$ on the shape of the roughness elements, suggested by Owen & Thomson, was strongly exhibited in the present work, and B$^{-1}$ cannot be considered to be a single function of the roughness Reynolds number u$\_*$z$\_0$/v. Comparative experiments were done on the rate of evaporation of water from two of the surfaces (artificial grass and towelling) used in the experiments with thorium-B, in order to obtain an estimate of the dependence of B$^{-1}$ on the molecular properties of the vapour. The ratio of the molecular diffusivity of water vapour to that of thorium-B vapour is 4.4:1. The ratio of values of B$^{-1}$ was found to be 1:1.6, with some variation according to the surface and the wind speed. Under average conditions of evaporation in the field, a value about 5 is suggested for B$^{-1}$, but this may not apply for values of z$\_0$ outside the range of the experiments. The dimensionless resistance for momentum, between a height z$\_1$ and the surface, is u$\_1$/u$\_*$, and if z$\_1$ is of order 1 m, this term is several times larger than B$^{-1}$. Since it is the sum of u$\_1$/u$_*$ and B$^{-1}$ which enters into the formula for the rate of evaporation, it is sufficient to obtain B$^{-1}$ to a moderate accuracy. The wetted artificial grass, subjected to forced evaporation in the wind tunnel, could be considered as a wet-bulb thermometer, and the surface temperature was found to approximate very closely to the wet-bulb temperature of the air, especially at high wind speeds, when the transport of heat to the surface by radiation from above or conduction from below was relatively small. It follows from this that the eddy diffusivities of heat and vapour in the boundary layer are equal, at least to within 10%. Moreover the molecular diffusivity of water vapour is not very different from the thermometric conductivity of air at room temperature, and therefore nearly the same values of B$^{-1}$ should apply to the transport of heat and water vapour. Temperature profiles obtained by Pasquill and Rider over short grassland at Cambridge are shown to give values of B$^{-1}$ of 5.7 and 3.9, in good agreement with the results from the wind tunnel.

The Spectrum and Structure of Singlet CH$_2$

Abstract: The red absorption bands of CH$\_2$, previously shown to correspond to a transition between singlet states, have been analysed in detail. In the lower electronic state $\tilde a^1$A$\_1$ the molecule is a strongly asymmetric top with rotational constants A$\_{000}$ = 20$\cdot$14, B$\_{000}$ = 11$\cdot$16 and C$\_{000}$ = 7$\cdot$06 cm$^{-1}$. From these constants a CH distance of 1$\cdot$11 $\overset{\circ}{\mathrm A}$ and an HCH angle of 102$\cdot$4$^\circ$ is obtained. In the upper state b$^1$B$\_1$ the molecule is nearly linear, having an HCH angle of about 140$^\circ$ and a CH distance of 1$\cdot$05 $\overset{\circ}{mathrm A}$. Most of the observed absorption bands correspond to excitation of the bending vibration $ u'\_2$ in the upper state (v'$\_2$ = 6, 8, $\ldots$, 18). In some of them in addition the symmetric stretching vibration $ u\_1$ is singly excited. The levels 1, v$\_2$-4, 0 cause strong perturbations in the levels 0, v$\_2$, 0 for v$\_2$ = 8, 10, 12, 14. In the lower state only one excited vibrational level 0, 1, 0 has been established which yields $ u''\_2$ = 1352$\cdot$6 cm$^{-1}$. Fragments of some other singlet absorptions in the near ultraviolet and in the vacuum ultraviolet have been observed and are briefly described. The upper state of the near ultraviolet system is probably the predicted $^1$A$\_1$ state corresponding to $^1\Sigma^+$ in the linear conformation.

A perturbation method for nonlinear dispersive wave problems

Abstract: The nonlinear partial differential equations for dispersive waves have special solutions representing uniform wavetrains. An expansion procedure is developed for slowly varying wavetrains, in which full nonlinearity is retained but the scale of the nonuniformity introduces a small parameter. The first-order results agree with those obtained previously by averaging techniques (Whitham 1965 a, b). The perturbation method provides a detailed description and deeper understanding, as well as a consistent development to higher approximations. This method for treating partial differential equations is analogous to the ‘multiple time scale9 methods for ordinary differential equations in nonlinear vibration theory. It may also be regarded as a generalization of the geometrical optics approximation to nonlinear problems.

Dislocation Arrangement in Copper Single Crystals as a Function of Strain

Abstract: Deformed copper single crystals were sectioned both parallel and perpendicular to the primary slip plane by spark erosion and then electropolished to obtain thin foils Transmission electron microscopy was used to determine both the large scale (01 mm) features of the dislocation array and also details of characteristic configurations Comparison of the observations from the mutually orthogonal sections made it possible to construct a three-dimensional model of the internal structure An extensive Burgers vector survey was conducted by a bright field technique making use of dislocation disappearance criteria Observations were almost entirely restricted to specimens with two seeded orientations, one for single and the other for double slip Crystals were examined in each of the three stages of the work hardening curve Dislocation loss during thinning is not considered to be of major importance and reasons for this opinion are given In stage I primary screw dislocations were absent from the foils and it is concluded that when screws of opposite sign pass on sufficiently close slip planes ($\lesssim$200 $\overset{\circ}{\mathrm A}$) they can cross-slip and annihilate Under similar conditions edge dislocations form stable arrays and these accumulate more edges through glide polygonization and thus form extensive walls perpendicular to the primary plane A very high density of secondary dislocations was observed throughout stage II and this can be reconciled with the macroscopic secondary strain because the secondary slip distance was found to be very short It is proposed in this paper that secondary slip occurs in the regions of high internal stress at the heads of pile-ups and tests of this proposal are applied No classical pile-ups were observed; instead the secondary slip converts the pile-up into a complex tangle which is stable on unloading Some of the predictions of a work hardening theory arising out of these observations (Hirsch 1964) are compared with experiment Lomer-Cottrell dislocations were found to be unstable at room temperature Faint lines of contrast along close packed directions in the primary plane were shown to be elongated faulted loops Their observed maximum width gives, in principle, an estimate for the stacking fault energy of copper

Experiments on the Capillary Instability of a Liquid Jet

Abstract: The stability of a vertical jet of water has been examined by imposing audio frequency disturbances. Flash photographs allow a direct measurement of the growth rate of the disturbances and the complete dispersion curve has been investigated. The effects of viscosity on the stability have been examined with glycerine-water solutions and have been found to be in good agreement with Chandrasekhar’s calculations.

Corrosion-resistant alloys in chloride solutions: materials for surgical implants

Abstract: The behaviour of a number of corrosion-resistant alloys in chloride solutions. in Hanks's physiological solution (simulating the extracellular body fluids) and as surgical implants has been investigated by electrochemical means, namely potential-time curves for isolated specimens, potential-current density curves for anodes, and current density-time curves for anodes maintained electronically at constant potential. Microscopical observation of pitting attack has also been made. Alloys based on iron (e.g. stainless steels), nickel (e.g. Inconel, Nimonic 75, etc.), cobalt (Vitallium), titanium and tantalum exposed to chloride solutions all show a range of potential in which they are passive, and, at sufficiently high chloride concentration and sufficiently positive potential, breakdown giving rise to pits that are electrobrightened. This general phenomenon occurs. in 0$\cdot$17 M sodium chloride solution, at 0$\cdot$2 to 0$\cdot$5 V (normal hydrogen scale) for stainless steels, ca. 0$\cdot$9 V for the cobalt-based alloys, and ca. 20 to 30 V for certain titanium alloys and tantalum. In the passive range, all the alloys show anode current densities in the range 10$^{-6}$ to below 10$^{-9}$ A/cm$^2$, the smaller current densities given by the most passive alloys (e.g. titanium-5% niobium) often tending to decrease yet further with passage of time. We conclude that stainless steels (even of the higher chromium-nickel quality) and nickel alloys are unlikely to resist all breakdown by pitting when exposed to the body fluids (or other media containing chloride) indefinitely; that the cobalt-based alloys may well withstand such exposure for very long times; and that titanium and (especially) some of its alloys should withstand such exposure for an indefinite period. The (extremely slow) passage of cobalt and titanium into the environment is caused by passage of cations through their passivating oxide films, without breakdown.

Experiments with the Graph Traverser Program

Abstract: An automatic method is described for the solution of a certain family of problems. To belong to this family a problem must be expressible in the language of graph theory as that of finding a path between two specified nodes of a specified graph. The method depends upon the evaluation of intermediate states of the problem according to the extent to which they have features in common with the goal state. We define evaluation functions each of which assigns to any state of the problem a value which is in some way related to its ‘distance’ from the goal state. Equivalently we assign to nodes of the corresponding graph values which are related to the distance over the graph from the goal node. Distance is reckoned as the smallest number of arcs needed to connect two nodes. An Algol program, the Graph Traverser, has been written to operate in this context. It is designed in a completely general way, and has two ‘empty’ procedures one of which must be written to specify the structure of the graph, that is the constraints of the problem, and the other to define an evaluation function. Results obtained by supplying the program with definitions of various sliding block puzzles and also a simple problem of algebraic manipulation are reported for a range of evaluation functions.

Viscous Behaviour of Supercooled Liquids

Abstract: The viscosities and densities of a number of aromatic hydrocarbons and esters have been measured from room temperature down to temperatures in the highly supercooled region. The densities of these liquids show a linear variation with temperature. The viscosities cannot be described by an Arrhenius-type equation but they can be represented precisely by a modified form of the Doolittle free volume equation. ln $$\eta = A'+B'/(T-T\_0),$$ in which T$\_0$ is the fundamental reference temperature for all molecular transport and relaxation processes. This temperature is below the normal glass-transition temperature, the latter being solely determined by kinetic effects. The constants $A'$, $B'$ and T$\_0$ are determined for each liquid by a digital computer procedure, which minimizes the sum of the squares of the difference between the experimental and the predicted viscosity values. In di-n-butyl phthalate and di-(2-ethyl hexyl) phthalate, the molecules of which have relatively long side group attachments to the benzene ring, the above equation fits the observed viscosity values over the complete temperature range of measurement (approximately 210 to 370 $^\circ$K) with one set of values for $A'$, $B'$ and T$\_0$. However, for some molecules with shorter side group attachments a discontinuity is found in the viscosity behaviour in the region of an 'intersection temperature', T$\_K$. Below T$\_K$ the above equation fits the observed viscosity values with one set of values for $A'$, $B'$ and T$\_0$. A similar fit is found at temperatures above T$\_K$ but with a different set of values for $A'$, $B'$ and T$\_0$. This discontinuity in viscosity behaviour is attributed to the onset of aggregation of small numbers of molecules as the liquid is cooled through the temperature T$\_K$, which is at or below the melting point. At temperatures below T$\_K$ the molecular aggregate constitutes the unit of flow, while above T$\_K$ the molecules flow as single units. This effect is strikingly apparent as the length of the side group attached to the benzene ring is reduced. Thus di-n-butyl phthalate exhibits no discontinuity whilst di-iso-butyl phthalate shows a marked discontinuity. Likewise a discontinuity is found in n-butyl benzene but not in n-hexyl benzene. At higher temperatures approaching the boiling point, the free volume description of viscous flow is superseded by an Arrhenius type of behaviour where the free volume is greater than 10 to 16% of the specific volume, depending on the liquid in question.

Finiteness Conditions for CW Complexes. II

Abstract: A CW complex is a topological space which is built up in an inductive way by a process of attaching cells. Spaces homotopy equivalent to CW complexes play a fundamental role in topology. In the previous paper with the same title we gave criteria (in terms of more-or-less standard invariants of the space) for a CW complex to be homotopy equivalent to one of finite dimension, or to one with a finite number of cells in each dimension, or to a finite complex. This paper contains some simplification of these results. In addition, algebraic machinery is developed which provides a rough classification of CW complexes homotopy equivalent to a given one (the existence clause of the classification is the interesting one). The results would take a particularly simple form if a certain (rather implausible) conjecture could be established.

Nonlinear Interactions of Random Waves in a Dispersive Medium

Abstract: A study is made of the way that the spectrum function of random, spatially homogeneous, dispersive waves varies slowly with time owing to weak nonlinear interactions between the waves. A continuous representation is used throughout and the slow variation is obtained with the aid of the multiple time scale method of nonlinear mechanics. It is shown that provided the dispersion equation satisfies a fairly general requirement (the non-existence of 'double resonance'), a closed integro-differential equation for the energy spectrum function can be obtained which describes asymptotically the transfer of energy between wave numbers on a time scale є^(-2) times a characteristic period of the waves, where the parameter є measures the relative order of the nonlinear terms. The equation is derived without imposing restrictions on the probability distribution of the waves, and in particular it is not found necessary to assume that the distribution is Gaussian. Nevertheless, the result is the same as if the distribution were Gaussian to zero order in e and this is true for arbitrary initial probability distributions. For a conservative system where total energy is conserved, the equation simplifies to a form previously derived by Litvak (1960), according to which transfer of energy takes place between resonant triads of wave numbers if they exist.

The Shearing and Dilatation of Dry Sand and the 'Singing' Mechanism

Abstract: The state of internal stress existing within a uniformly dilated array of solids undergoing uniform shear, and the relation of the stresses to the dilatation and shear rate, were examined experimentally in a previous paper (Bagnold 1954). Since the dilatation could only be controlled under gravity-free conditions wherein the solids were suspended in a liquid of the same density, the generality of the results remained uncertain. As a test of the generality these results are now applied to the very different conditions in which a mass of dry natural sand is bull-dozed over a single shear surface. When the push is applied by a force which is virtually independent of the motion it causes, e. g. via a long spring, the displacement of the sand mass occurs by a succession of intermittent jumps, each at a velocity which is predictable from the earlier work. It also appears possible from the earlier work to explain the cause of the hitherto mysterious sounds emitted by certain natural sands and to predict the frequencies of the sounds.

Interactions of H$_2$O Molecules in Ice. I. The Dipole Moment of an H$_2$O Molecule in Ice

Abstract: The dipole moment of an H$\_2$O molecule in ice is greater than the moment of an isolated H$\_2$O molecule, 1.84 D, owing to the electric fields of neighbouring molecules. The magnitude and direction of the field arising from the nearest 85 neighbours is computed here by representing each molecule as a series of electric multipoles. It is found that the field has the direction of the dipole moment of the central molecule and is sufficiently strong to increase its total dipole moment to about 2.60 D.

Unstable oscillation of tubular cantilevers conveying fluid II. Experiments

Abstract: The experiments described here were designed to check various aspects of the theory presented in part I. Experiments were conducted mainly with rubber tubes conveying water or air and with metal tubes conveying oil; some experiments were also conducted with a tube fitted with various nozzles at the free end. The theory of part I is extended to take account of internal damping in the tube material and to obtain an indication of the effect of viscous damping forces associated with the surrounding fluid. It is shown that damping may de-stabilize the system. Agreement between experimental observation and theoretical predictions is shown to be satisfactory.

Hydrogen permeation in metals as a function of stress, temperature and dissolved hydrogen concentration

Abstract: An investigation of the diffusion of electrolytic hydrogen through membranes of: (1) polycrystalline Armco iron; (2) single crystal Armcoiron; (3) zone refined iron; and (4) A.I.S.I. 4340 has been made. The temperature and stress dependence of the permeation rate through (1) and (4) was investigated, while (1) to (3) have been investigated under varying concentrations of hydrogen in the metal. From the results concerning Armco iron polycrystals and single crystals, and zone-refined iron it has been concluded that trace impurities and grain boundaries have negligible effects on the hydrogen permeation rate. Stress has been shown not to affect D , but it increases the solubility of hydrogen in the lattice. The D 0 and Δ H p value for α-iron and the stress dependence of the hydrogen solubility indicate that the rate-determining step in diffusion is the formation of a cavity (a dilated octahedral hole) to accommodate the diffusion hydrogen. Maxima observed in the relation of the rate of permeation to time were explained in terms of ‘blister´ formation; the temperature dependence of the critical hydrogen concentration necessary to form these blisters is in concordance with this hypothesis. The nucleation sites for such blisters are aggregates of dislocations. The mechanism proposed to explain the maxima in the permeation transients was used to rationalize the existing discrepancies in diffusion data found in the literature. It is suggested that the crack initiation site for stress corrosion cracking may be a highly localized density of dislocations, on a metal surface, generated by blister formation due to hydrogen.

The Crystal Dynamics of Lead Telluride

Abstract: The frequencies of the normal modes of vibration of lead telluride propagating in certain symmetric directions have been determined by inelastic neutron scattering techniques. The results have been used to deduce the parameters of rigid ion models and of shell models for the interatomic forces. The latter models take account of the polarizability of the ions. Neither type of model is very successful, but the best shell model does provide a good fit to the results and has been used to calculate the frequency distribution and specific heat. Calculations of the thermal expansion, and of the lifetime of the transverse optic modes, show that anharmonic interactions in lead telluride are considerably more complex than in the simple alkali halides. A detailed account of the effect of doping on the lattice vibrations is given, in which it is shown that large effects are limited to the long wavelength regions of the dispersion curves. Detailed calculations are presented for the dispersion of the optical branches as a function of the dopant concentration. The importance of these effects for different kinds of experimental studies is briefly discussed.

A General Theory of Rods

Abstract: Three main methods have been used to develop one dimensional theories of rods, mostly in the context of isothermal linear elasticity. The first consists of ad hoc assumptions which are apparently independent of any general theory. In the second approach one can start with the three-dimensional equations of elasticity and use an expansion or perturbation procedure, see for example Hay [1]. However, most of the authors who adopt the three-dimensional approach employ additional assumptions or variational methods. The third approach may be called the direct approach. This is the method employed by Green and Laws [2] whose work we discuss here. A further contribution has been given by Cohen [3) who uses a variational method to produce a theory of elastic rods, but his idea of a rod differs from that of Green and Laws.

The Time-Dependent Coupled Hartree-Fock Approximation

Abstract: A coupled Hartree-Fock approximation for describing the effects of time-dependent perturbations on many-electron systems is presented. It is applied to the calculation of the frequency-dependent refractive index of helium gas with results that differ by between 4 and 8% from the accurate values obtained by a refined variational calculation.

The pyrolysis of monosilane

Abstract: A detailed analytical and kinetic study of the thermal decomposition of monosilane in the temperature range 375 to 430 °C and the initial pressure range 35 to 230 mmHg has been conducted. The gaseous products in the very early stages of the reaction are hydrogen, disilane and trisilane. In addition, later in the reaction a solid silicon hydride is formed, its composition varying as the reaction progresses. The kinetic features of product formation during the first 3 % of decomposition have been studied in detail, while those relating to higher extents of decomposition have been investigated less fully. The reaction is accelerated by the addition of certain foreign gases, but is unaffected by packing of the reaction vessel. A tentative mechanism involving the species silene, SiH 2 , is proposed.

Measurements on turbulent vortices in a cylinder wake

Abstract: The wakes of circular cylinders were explored by means of hot wire anemometers in the range of Reynolds numbers based on diameter of from 10 3 to 4 x 10 4 . The vortex strength was determined and its variation with distance downstream and with Reynolds number was investigated. The vortex strengths agree with those obtained by application of Roshko’s (1954) method to our mean flow measurements. The vortex velocity distribution assumed was that of Hoffman & Joubert (1963) which was found to agree with our measurements when slight adjustments were made in the inner core region. Vortex paths, the formation region and three dimensional effects are also discussed.

Anisotropic acoustic attenuation with new measurements for quartz at room temperatures

Abstract: New measurements of the attenuation of acoustic waves in quartz have been obtained from surface excitation in a novel type of resonant cavity configuration. These are believed to be more accurate than previously published values. The attenuation is found to be proportional to the square of the frequency over the range 300 to 3000 Mc/s at a temperature of 30°C. A general theory, involving a viscosity tensor, is developed for the calculation of the attenuation of acoustic waves in crystalline solids. Symmetry of the viscosity matrix is determined by the crystal class and is the same as that of the elastic constant matrix. Numerical values for the viscosity coefficients are specific to the material and from a knowledge of these the attenuation of a given mode in a selected direction of propagation can be calculated. The validity of this analysis is confirmed by the results of the attenuation measurements in quartz and is further supported by data for silicon.