Showing papers in "Philosophical Magazine in 1964"

A new method for the electronic structure of metals

Abstract: A new method is described for setting up the effective potential for electrons in non-transition metals, including liquid metals and alloys. It is based on a model potential fitted to the spectroscopically measured energy levels of the free ions. The potential between the atomic cores is obtained from the dielectric screening calculation of Cohen and Phillips (1961) with some refinements. The method is tested on the band structures of the (solid) alkali metals. The Fermi surfaces of K, Rb and Cs are found to be considerably less distorted than calculated by Ham (1962), and thus in better agreement with experiment.

The growth and structure of gold and silver deposits formed by evaporation inside an electron microscope

Abstract: Single crystal films of gold and silver have been prepared by evaporation onto molybdenum disulphide inside an electron microscope, in order to allow direct observation of the mode of growth. These experiments provide detailed information on the remarkable liquid-like behaviour of the coalescence of the initial metal nuclei, and the mode of formation of a continuous film. In addition, re-orientation and re-crystallization phenomena are observed, and these effects are shown to be predominant during the growth of a polycrystal-line deposit on an amorphous substrate. The various possible mechanisms for the liquid-like behaviour are considered, by making use of mathematical expressions initially derived to describe the sintering of spherical particles. A semi-quantitative explanation of the liquid-like behaviour is given in terms of the surface diffusion of the metal atoms over the metal islands, the driving force for the mass transfer being the associated reduction in surface energy.

The self-stress of dislocations and the shape of extended nodes

Abstract: A definition of the self-stress of a dislocation is proposed which is closely related to the more usual notion of a line tension. The definition enables a numerical calculation to be made of the shape of extended nodes in dislocation networks, and such a calculation leads to revised values of the stacking-fault energies of alloys. It is found that (to within the scatter usual in these measurements) the values of stacking-fault energy deduced by Howie and Swann (1961) must be multiplied by 2·3.

Partial dislocations associated with NbC precipitation in austenitic stainless steels

Abstract: A systematic electron microscope investigation has been made of the partial dislocations bounding stacking faults in niobium-containing austenitic stainless steels. Observations of contrast for various reflecting conditions are explained on the basis of calculations carried out using the two-beam dynamical theory of Howie and Whelan, and it is concluded that the outer partials are Franks, the inner partials are Shockleys, and the faults are extrinsic. The invisibility criteria given by Howie and Whelan for partials are extended and a mechanism of NbC precipitation causing growth of the faults is proposed.

The measurement of volume diffusion by the method of autoradiography

Abstract: The application of autoradiography to the measurement of volume diffusion is limited because of the difficulty in interpreting the effects of the energy of the radiations, the scattering and absorption properties of the specimen and other complicating factors. A general method of interpretation is described in which the effects of these factors are suitably combined into a single function that is determined by one experiment. The method is applied by matching the experimental density trace of the diffusion zone, with a density curve which is computed from a derived expression. As a trial of this treatment, the diffusion of 124Sb into single crystals of copper has been studied over the penetration range 10 μ < (Dt)½ < 150 μ and in the temperature range 560°c to 896°c with specimens mounted singly and in a double sandwich-type arrangement. The results that have been produced show good agreement with the results obtained from mechanical sectioning and the accuracies of the two methods are comparable...

Dislocation distributions in deformed copper single crystals

Abstract: Dislocation etch pit distributions and slip lines were studied on copper single crystals oriented for single glide and deformed in tension at 4·2°K. Slip lines on the cross slip plane were observed from the earliest stages of deformation and their character changed during the transition to stage II. The distribution of forest dislocations is much more isotropic and less homogeneous than that of dislocations crossing other planes. The ratio of the forest to other dislocation densities in stage I is about 1:15 but tends to 1 in stage II. The flow stress correlates better with the forest than with main glide dislocation density; twist experiments support this conclusion.

The sintering and adhesion of Ice

Abstract: The current theory of sintering is incomplete and consequently previous experiments on the sintering of ice have been misinterpreted. The evaporation–condensation theory is now extended to include the case where material is transferred by diffusion through an environmental gas. Measurements were made on the rates of growth of the neck formed between single and polycrystalline ice spheres, 50 μ to 700 μ in diameter, in the temperature range −3°c to −20°c, in air at atmospheric pressure. The results are in quantitative agreement with the new evaporation–condensation theory, and further confirmation was obtained from experiments with spheres of heavy ice, and by the observed effects of replacing the air by either hydrogen or silicone oil. It is argued that the sintering of ice by either volume or surface diffusion would be slower by almost four orders of magnitude. No evidence is found for the recent suggestion that the sintering and adhesion of pure ice is caused by the existence of a liquid-like s...

On the Formation of Fatigue Cracks at Twin Boundaries

Abstract: Fatigue crack formation at twin boundaries in OFHC copper has been studied as a function of twin boundary orientation with respect to applied stress. The operation of slip planes immediately adjacent to and parallel to the twin boundaries was found to be essential for crack formation at the boundaries. The role of twin boundary steps as dislocation sources is discussed with respect to increased plastic deformation at twin boundaries. Finally the cracking of alternate twin boundaries was observed and correlated with the operation of secondary slip planes.

The freezing of some continuous binary eutectic mixtures

Abstract: Directional freezing experiments have been carried out with the binary eutectic mixtures, Al–Ag2Al, Al–CuAl2, Al–Zn, Al–Al3Ni, Ag–Cu, LiF–NaF and NaF–NaCl. Various aspects of eutectic solidification are discussed with particular reference to the importance of solid interfacial energy. The work is divided into three parts. I. A description of the observed microstructures, with discussion of the type of dispersion occurring in unmodified eutectics and the modification of lamellar arrangements by impurity cell formation. II. An account of the development of preferred orientations during the directional freezing of some eutectics. III. Measurements of the interphase separations as functions of the freezing rates and a discussion of the influence of solid interfacial energy upon these.

Effects of surface stress relaxation on the electron microscope images of dislocations normal to thin metal foils

Abstract: The two-beam dynamical theory of Howie and Whelan is used to calculate the electron microscope image contrast from dislocations normal to a thin crystal and parallel to the direction of the incident electron beam. Bending of the lattice planes due to surface relaxation and change in lattice parameter are taken into account. Strong contrast in the form of black-white spots is predicted for dislocations with a screw component, while contrast from pure edge dislocations is expected to be very weak. Observations on platinum and copper are in good agreement with the predictions for dislocations with a screw component. It is possible from these contrast effects to determine the sense of the screw component of the dislocation.

Deformation structures in zone-melted molybdenum

Abstract: Glide dislocation configurations in zone-melted single crystals of molybdenum, deformed in tension at temperatures in the range 4·2–300·K, have been examined by thin film electron transmission microscopy. A majority of the crystals were oriented for single slip on the (011) [111] system, and were sliced and thinned parallel to (011). The slip band structure is characterized by long primary screw dislocations having a Burgers vector α/2[111], and by secondary glide dislocations parallel to [111] or [111]. Consistent with the presence of secondary slip, the bulk stress–strain curves do not exhibit a region of easy glide. The primary screws have a high jog density (∼5 × 104 cm−1) which can be accounted for by the cutting of secondary dislocations intersecting the (011) glide plane. The jogs lower the velocity of the screw components relative to that of the edges, and from dislocation mobility data the calculated velocity ratio of edge: screw is ≈ 40: 1; this appears to be a realistic ratio in terms ...

Relationship between flow stress and atomic order in the FeCo alloy

Abstract: Stress–strain curves in compression were obtained as a function of temperature for both the disordered and fully ordered FeCo–B2 type superlattice only. Supplementary observations were made of the surface slip markings after various strains, as well as of the dislocation configurations existing after these strains, using transmission electron microscopy techniques. It has been found that the deformation process occurring in the disordered alloys is similar at all strains. Furthermore, the flow stress is strongly dependent on temperature and nearly independent of strain. The profuse stepped slip lines observed on the surface of these specimens suggests that thermally activated cross-slip is the controlling mode of deformation in the disordered alloys. The ordered alloys, on the other hand, show three distinct deformation stages similar to those observed in face-centred cubic metals and alloys. The flow stress in Stage I is independent of strain. On the other hand, the flow stress in Stage II incre...

Grain boundary mobility and its effects in materials containing inert gases

Abstract: The conditions under which grain boundaries can be pinned by solid precipitates are established but precipitates in the form of inert gas bubbles are known to move by surface diffusion of the matrix atoms which surround them and so they may remain attached to the boundary and merely retard its movement. The magnitude of this retarding force is calculated and the condition under which the boundary can become detached from the bubbles is evaluated. Detachment occurs most readily from bubbles of a critical size and under conditions where there is a large driving force for grain boundary movement. The smallest bubbles move sufficiently rapidly that they tend to remain attached to the boundary, whereas the largest bubbles, for a given spacing, have greatest effect in impeding grain boundary mobility. Their effect is compared and contrasted with that of boundary pinning by solid precipitates. The analysis is used to interpret observations of the behaviour of fission gases after grain boundary movement.

The stress-fields around groups of dislocations in face-centred cubic metals

Abstract: The various components of the stress-fields of piled-up groups of screw and edge dislocations are calculated by replacing the array of discrete dislocations by a continuous distribution. The stress-fields are resolved onto each of the eleven secondary systems of the face-centred cubic lattice; by mapping out the stress-fields, it is shown that secondary slip can occur in the localized region at the head of the pile-up. This secondary slip modifies the stress-field of the pile-up and gives rise to dislocation tangles containing a high density of forest dislocations. The amount of secondary slip depends on the sum of the resolved applied stress on each secondary system and the resolved stress from the pile-up, so that the amount of secondary slip is orientation dependent. In addition, latent hardening of the secondary systems, such as occurs in alloy crystals, can be taken into account and it is shown that secondary slip near a pile-up is inhibited by latent hardening. The calculations are discusse...

On the Determination of the Nature of Dislocation Loops

Abstract: A simplication of the electron microscope method for determination of the nature of dislocation loops is described. Full determination of the relevant diffraction conditions and of the Burgers vectors of the loops are avoided and knowledge of the sense of inclination of the loops and of the rotations of image and diffraction pattern is not required. An example is given of the application of the method.

The behaviour of type ii superconductors

Abstract: By treating the flux lines in a type II superconductor as a compressible fluid Friedel et al. (1963) have shown that, for a non-uniform distribution of lines, the force per unit length acting on one line is (φ04π). dH(B)/dx. Here B is the induction at x and H(B) the external field which would be in equilibrium with B if the material were reversible. The flux lines in an irreversible type II superconductor in the critical state of Kim et al. (1963) are in virtual equilibrium under the forces due to the flux concentration gradient and a pinning force F. F arises from the interaction between the flux lines and structural defects in the material. It follows that F = (φ0/4π)(dH/dB) a(dB/dx) s, where (dH/dB) a is the gradient of the reversible B/H curve and (dB/dx) s the field gradient in the specimen.

A determination of the stacking-fault energy of some pure F.C.C. metals

Abstract: A method for determining the stacking-fault energy of f.c.c. materials has been developed using an already-established dependence of preferred orientation on stacking-fault energy. An empirically determined parameter, characteristic of the type of rolling texture exhibited by the metal, is related to the stacking-fault energy value obtained by measurements of dislocation node radius, and from the γ value for the three metals, Ag, Cu and ni the stacking-fault energy of Th, Au, Pd, Rh, Pt and Yb has been obtained by interpolation using measured values of the texture parameter.

Strain hardening in polycrystalline copper

Abstract: Strain hardening in polycrystalline copper is shown to be the net result of two competing processes: (i) a basic process of strain hardening which occurs during deformation under a wide range of experimental conditions, and (ii) ‘dynamic recovery’ which removes a proportion of the obstacles produced during deformation. Arguments are presented which suggest that the basic process would give a linear rate of hardening but for an effect which occurs at high obstacle densities; this effect is also responsible for variation of the Cottrell–Stokes ratio at high degrees of hardening.

On the mean free path of low energy phonons in single crystal quartz

Abstract: The attenuation of mechanical waves in single crystal quartz at low temperatures and at frequencies in the range 600 Mc/s to 1110 Mc/s has been measured. The results are interpreted in terms of collisions between the low energy phonons, constituting the sound wave, and thermal phonons.

The effect of neutron irradiation on the elastic moduli of graphite single crystals

Abstract: The resonant frequency in transverse vibration of natural single crystals of purified Ticonderoga graphite has been measured as a function of neutron dose The resonant frequency increases on irradiation by a factor of two and saturates at a dose of ∼4 × 1017 nvt Annealing reduces the resonant frequency again The indentation hardness of the crystals has been measured and an electron microscopic investigation of the dislocation distribution in irradiated crystals carried out The increase in resonant frequency on irradiation is shown to be due to a reduction of the strain produced by dislocation motion Experimental values for 1/S44 and 1/S11 for graphite are derived

The effect of hydrostatic pressure on brittleness in chromium

Abstract: Recrystallized chromium, which is normally brittle, shows high ductility at atmospheric pressure after subjection to a hydrostatic pressure of 104 atmospheres. The pressurization does not produce microscopically detectable deformation, but there is a marked drop in yield stress similar to that found in iron (Bullen et al. 1964); it is suggested that in each case the effect is due to the appearance of free dislocations during pressurization. It is argued that the stress at yield in pressurized material is insufficient to initiate cracks and that the stress required to initiate cracks is substantially increased by deformation. This accounts for the high ductility of pressurized specimens, the brittle appearance of their fracture even after ∼60% strain and the observation that specimens pre-strained during or subsequent to pressurization remain ductile after ageing or in further straining at high strain rates.

The elastic energy of a rhombus-shaped dislocation loop

Abstract: The elastic strain energy of a rhombus-shaped dislocation loop is calculated for an arbitrary rotation about the minor or major diagonal axis. For loops less than about one micron in size and constrained to move on the glide prism a shallow minimum in the energy exists displaced from the pure edge loop orientation. The depth of the minimum and its displacement from the pure edge orientation increase as the loop size decreases. The results provide an explanation for the observation by Makin and Hudson (1963) of such loops lying in {012} planes rather than in the {011} plane normal to the Burgers vector. The importance of the work done by the dislocation core tractions is emphasized and in particular its dependence on the method adopted for formally generating the dislocation loop. The misorientation effect is enhanced if the loop becomes extended into a pair of partials with a ribbon of stacking fault. An estimate of the core energy on the basis of an extended Peierls model does not preclude the e...

Theory of impurity diffusion in metals

Abstract: In a previous paper (Le Claire 1962) a simple electrostatic model was proposed for calculating the difference ΔQ between the activation energy for diffusion of an impurity in a metal and that for self-diffusion in the pure metal. The model is extended in the present paper to deal with the diffusion of impurities having the same valency as the solvent (homovalent impurities). For such cases the impurity is represented by a square potential well of depth equal to the difference between the electron-ground state energies of solute and solvent. Values of the perturbation potential due to such an ‘impurity’, calculated in both a Thomas-Fermi approximation and from a first-order solution of the March and Murray equations, are used to calculate ΔQ. For all presently known cases of homovalent diffusion the calculations give values for ΔQ close to those observed and always of the correct sign.

The annealing of vacancies and vacancy aggregates in quenched gold, silver and copper

Abstract: It is shown, using electrical resistance measurements and transmission electron microscopy, that the annealing behaviour of copper quenched from high temperature is similar to that of silver, provided that care is taken in both cases to avoid contamination by oxygen. To achieve this, copper was quenched from an atmosphere of carbon monoxide. The results obtained under these conditions suggest that the divacancy is the principal defect retained in copper after quenching from high temperatures. The temperatures at which stacking-fault tetrahedra anneal out in silver and gold were studied by transmission microscopy. In silver, tetrahedra are stable up to at least 930°c. The stability of tetrahedra in gold depends on their size, being greater the larger the tetrahedra. Finally it has been shown that dislocation loops, not tetrahedra, predominate as the clustered vacancy defect in gold if, after quenching from high temperature to 0°c, the gold is rapidly upquenched to 100°c.

On moiré patterns in the electron microscopy of polymer crystals

Abstract: Bi-layer crystals of polyoxymethylene and of poly(4-methylpentene-1) have been grown from dilute solution which exhibit extensive and regular moire patterns when examined in the electron microscope. The origin of the patterns is related to double diffraction and certain characteristic features in them are discussed. The spacing of a family of planes is shown to differ depending on whether or not they contain chain-folds. In polyoxymethylene crystals, the change is ∼0.012 A for the {10.0}s planes; it is ∼0.008 A for the {200}s planes in poly(4-methylpentene-1) crystals. These changes occur sharply at sector boundaries and are usually exactly compensated by a rotation of the crystal lattice. Occasionally in polyoxymethylene, compensation in inexact and edge dislocations, with Burgers vectors of a/3〈112 l〉s along the boundary, are introduced. The same Burgers vector is found for all dislocations observed in this polymer. Most dislocations detected in poly(4-methylpentene-1) have a/2〈11l〉s Burgers ve...

Stacking fault energies of Ni-Co-Cr alloys

Abstract: The stacking-fault energies of a number of Ni–Co–Cr alloys are determined using the node method. The results are based on the calculations by Brown (1964). Contours of constant stacking-fault energy are shown, which evidently have a certain tendency to follow the boundary of the f.c.c. region.

The effect of hydrostatic pressure on yielding in iron

Abstract: Armco iron normally shows a sharp yield point in tension at atmospheric temperature and pressure. This yield is either absent or substantially reduced in specimens subjected to hydrostatic pressures of 103–104 atmospheres prior to test. Removal of the yield point indicates that free dislocations are created during pressurization, apparently at elastic inhomogeneities such as inclusions. Evidence is presented to support this view, e.g. the fact that high-purity iron is not greatly affected by pressure. The observations are discussed in terms of recent theories of the influence of free dislocations on yielding.

Influence of oxidizing and reducing treatments on vacancy clustering in gold

Abstract: The stacking-fault tetrahedra observed in specimens of gold, quenched from a reducing atmosphere, are found to be smaller by a factor of four than in specimens quenched from an oxidizing atmosphere. This result is discussed in terms of the different distribution of impurities after oxidation and reduction. The effect of the impurities on the measured stacking-fault resistivity is also examined. It has been observed that tetrahedra grow during isothermal annealing at 40°c. The results of experiments where quenched specimens are aged at different temperatures, between 40°c and 200°c, support the hypothesis that the initial tetrahedron nucleus is a small three-dimensional vacancy cluster. These experiments show that the proportion of clustered vacancy defects which are not tetrahedra, but dislocation loops, increases with increasing ageing temperature. In the specimens pre-treated in an oxidizing atmosphere, it was found that the stacking-fault tetrahedra commonly occur in rows along the 〈110〉 direc...