Showing papers in "Philosophical Magazine in 1958"
TL;DR: In this paper, the authors considered the elastic equations for the case in which the state of the solid is independent of one of the three Cartesian coordinates, and the stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field were obtained.
Abstract: The solution of the elastic equations is considered for the case in which the state of the solid is independent of one of the three Cartesian coordinates. The stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field are obtained. The results hold for the most general anisotropy in which no symmetry elements of the crystal are assumed.
1,479 citations
413 citations
TL;DR: In this paper, the authors described the properties of prismatio and concentric helical prismatic dislocations generated by the stress field which appears around a spherical glass inclusion in a silver chloride crystal when the crystal is cooled from a temperature of 370°c to room temperature.
Abstract: Prismatio and concentric helical prismatic dislocations are generated by the stress field which appears around a spherical glass inclusion in a silver chloride crystal when the crystal is cooled from a temperature of 370°c to room temperature. The properties of these dislocations are described and their origin is discussed.
358 citations
TL;DR: In this article, a method is developed which allows the evaluation of the closed formal expressions for electrical conductivity which have recently been developed by several authors, and a brief mention of the application of this method to liquids and alloys is made.
Abstract: A method is developed which allows the evaluation of the closed formal expressions for electrical conductivity which have recently been developed by several authors. The case of a random set of scatterers is treated in detail and the formal solution made to yield directly the solution to the Boltzmann equation. A brief mention of the application of this method to liquids and alloys is made.
341 citations
TL;DR: In this article, the work-hardening parameters obtained are discussed in terms of dislocation theory that has been developed mainly on the basis of data on Al and Cu, and the advantages of the temperature change method for an investigation of the flow stress are pointed out following a theoretical analysis of the relation between this method and that of the work hardening parameters.
Abstract: Single crystals of nickel (purities 99.98% and 99.4%) have been deformed in tension at various temperatures between 4.2°K and 300°K. Shear stress-shear strain relations have been determined as well as the reversible change of flow stress with temperature. The work-hardening parameters obtained are discussed in terms of dislocation theory that has been developed mainly on the basis of data on Al and Cu. From the temperature dependence of the stress at the beginning of dynamical recovery the activation energy of cross-slip is estimated to be slightly lower than that of copper, implying a somewhat higher stacking fault energy. The advantages of the temperature change method for an investigation of the flow stress are pointed out following a theoretical analysis of the relation between this method and that of the work-hardening parameters. The present results on nickel confirm this relation. Metallographic and x-ray evidence has been obtained in favour of deformation twinning in nickel at 4.2°K and 2...
302 citations
TL;DR: In this paper, electron transmission micrographs of polycrystalline aluminium quenched from ∼ 600°c into iced brine are shown to contain many dislocation loops with diameters of the order of several hundred A. The loops are thought to be producod by the collapse of discs of vacancies, and the corresponding vacancy concentration is 10−4.
Abstract: Electron transmission micrographs of polycrystalline aluminium quenched from ∼ 600°c into iced brine show that the specimens contain many dislocation loops with diameters of the order of several hundred A. Some of the loops are hoxagonal in shape, and occur on (111) planes, and have a Burgers vector ½ [110] not in the plane of the loop. The loops are thought to be producod by the collapse of discs of vacancies, and the corresponding vacancy concentration is 10−4 Some of the loops disappear, while under observation in the microscope, by a mechanism of prismatic slip. In the neighbourhood of grain boundaries there is a zone depleted of loops; similar zones are observed near dislocations, whose complex configurations suggest that climb may have taken place. The observations are discussed in relation to the problems of ‘annealing out’ of vacancies, of quench-hardening, and of the origin of the dislocation network.
298 citations
TL;DR: In this article, a criterion for the transition from ductile to cleavage is calculated for fracture at a notch, and it is concluded that the temperature-dependence of this transition probably arises from the ductile-to-cleavage transition.
Abstract: A criterion for the transition in fracture mode from ductile to cleavage is calculated for fracture at a notch. It is concluded that the temperature-dependence of this transition probably arises mo...
285 citations
TL;DR: In this article, it was shown that if the energies required to form positive and negative ion vacancies in an ionic crystal are unequal, then in thermal equilibrium dislocations in the crystal will be electrically charged and surrounded by a Debye-Huckel cloud of vacancies, and the yield stress of the crystal may then exhibit maxima and minima when plotted as a function of temperature.
Abstract: If the energies required to form positive and negative ion vacancies in an ionic crystal are unequal, then in thermal equilibrium dislocations in the crystal will be electrically charged and surrounded by a Debye-Huckel cloud of vacancies. If the vacancy cloud is immobile a finite force is required to separate the dislocation from the cloud, and so the crystal will possess a yield stress below which plastic flow will not occur. The presence of divalent impurities modifies the magnitude of the charge on a dislocation, and may oven reverse it. If precipitation of the impurity or association of impurity atoms and vacancies can occur, the concentration of impurities may be a complicated function of temperature. The yield stress of the crystal may then exhibit maxima and minima when plotted as a function of temperature. Experimental results showing this behaviour are presented and tentatively compared with the theory.
240 citations
TL;DR: In this article, the ligand field theory is applied to the hydrated manganous salts and the splitting of the degenerate levels of 4A1g and 4Eg is first investigated, and then the intensities of the transitions from the ground sextet 6Alg to these levels are calculated.
Abstract: The ligand field theory is applied to the hydrated manganous salts. The splitting of the degenerate levels of 4A1g and 4Eg is first investigated, and then the intensities of the transitions from the ground sextet 6Alg to these levels are calculated. The properties of the odd vibrations responsible for these transitions are also discussed. It is found that the calculated oscillator strengths are in good agreement with experiment if an appropriate model is used for the vibrations.
217 citations
TL;DR: In this article, a theoretical study of the structure of strong hydromagnetic waves which are propagated, across a magnetic field, in a low density plasma where collisions can be neglected is made.
Abstract: A theoretical study has been made of the structure of strong hydromagnetic ′ waves which are propagated, across a magnetic field, in a low density plasma where collisions can be neglected. Under these conditions the ions are accelerated in the direction of propagation and then brought to rest again. The thickness of the wave is determined by the characteristic distance ✓ (mc 2/4nnc 2) and the wave velocity lies between the Alfven speed and twice the Alfven speed.
164 citations
TL;DR: In this article, the rolling texture of drawn polythene is interpreted in terms of slip and twinning processes characteristic of ordinary crystal plasticity in combination with the rubbery elasticity characteristic of macromolecular amorphous substances.
Abstract: The rolling texture of drawn polythene is interpreted in terms of slip and twinning processes characteristic of ordinary crystal plasticity in combination with the rubbery elasticity characteristic of macromolecular amorphous substances. The principal crystal plasticity elements operative are (100) [010] slip and (310) [130] and/or (110) [110] twinning. The observations appear to indicate that (110) [110] slip is a less easy mode of deformation than these, at least initially. Under more general deformation conditions, it appears that these modes predominate at small strain, tending to a texture with [010] aligned to the axis of extension, giving place to [001] slip processes, which align [001] and the molecular chains along the axis of extension when the strain is large. Under certain conditions a second crystalline phase also appears which in terms of general crystal plasticity would correspond to a martensitic type transformation and might arise through a regular sequence of stacking faults on ...
TL;DR: In this article, the authors derived the stacking fault energies of various metals and derived relative dislocation widths for various metals based on the theoretical analysis relating dislocations width to stacking fault energy, and suggested tentative values for the stacking faults of Au, Ag, Al, Ni, Pb, Zn, Cd, Co and Pt.
Abstract: Experimental results obtained by studying the low temperature creep behaviour before and after a small stress change are interpreted in terms of barriers due to intersecting dislocations. Using the data available on the temperature dependence of the flow stress in conjunction with these experimental results, estimates of jog energies are derived and compared with values obtained from flow stress data alone. Relative dislocation widths for various metals are also deduced. From the theoretical analysis relating dislocation width to stacking fault energy, tentative values are suggested for the stacking fault energies of Au, Ag, Al, Ni, Pb, Zn, Cd, Co and Pt, relative to that of Cu. These values are in reasonable agreement with previous estimates where available, thus confirming the hypothesis that low temperature creep is controlled by the proposed mechanism. The significance of these results is discussed in terms of the exhaustion and work hardening theories of low temperature creep. It is shown th...
TL;DR: In this paper, Bragg diffraction from regions distorted by elastic coherency strains between the precipitate and the matrix is interpreted in terms of Bragg diffusion from regions near precipitated particles.
Abstract: Transmission electron micrographs of aged aluminium 4%-copper foils have shown unusual contrast near precipitated particles. This is interpreted in terms of Bragg diffraction from regions distorted by elastic coherency strains between the precipitate and the matrix.
TL;DR: In this paper, the authors examined polycrystalline specimens of copper, aluminium and gold and found that they were fatigued in, reversed bend in various pressures of air and in water vapour and inert gases.
Abstract: Polycrystalline specimens of copper, aluminium and gold were fatigued in, reversed bend in various pressures of air and in water vapour and inert gases. The ratio of life in atmosphere of air 60 that. in vacuum (∼ 10−6 mm Hg) at lives of about 106 cycles was 1:20 for copper, 1:5 for aluminium and about 1:1 for gold. Some specimens were examined at intervals during the test. Small cracks a few microns deep formed in the first few hundredths of the life in air and after the same number of cycles in vacuum. The effect of air was to speed the propagation of cracks in copper and aluminium but not gold. Electron micrographs showed that extrusions and intrusions can occur close to each other in the same slip band.
TL;DR: In the face-centred cubic lattice, a stacking fault caused by the condensation of vacancies on a {111} plane, is converted into a dislocation source of Frank-Read type if it is swept by a half-dislocation of a kind that restores lattice order.
Abstract: In the face-centred cubic lattice a stacking fault, caused by the condensation of vacancies on a {111} plane, is converted into a dislocation source of Frank-Read type if it is swept by a half-dislocation of a kind that restores lattice order. Dislocation sources will also arise in other major lattice types through the condensation of vacancies on close-packed lattice planes. It is proposed that these are the dislocation sources which release a major proportion, if not all, of the dislocations formed during plastic deformation. Besides several minor advantages, the introduction of this kind of dislocation source can account for all the important glide systems found in crystals of the most common lattice types.
TL;DR: In this paper, the Gruneisen γ was calculated for the limiting cases of low and high temperatures for KCl, NaCl, and KCl and NaCl for cubic crystals.
Abstract: The thermal expansion of a solid is due to anharmonicity of the interatomic forces. It may therefore be calculated, on the basis of a continuum model, from the observed elastic anharmonicity, i.e. the third-order elastic constants. Using Lazarus' (1949) measurements on the pressure variation of the elastic moduli of several cubic crystals, the Gruneisen γ is calculated for the limiting cases of low and high temperatures. For KCl, NaCl the high temperature values agree with those obtained from thermal expansivities, and a decrease in γ at low temperatures is predicted. However, Lazarus' data on metals cannot be reconciled with the thermal expansions, which suggests that the continuum model is inapplicable to these cases.
TL;DR: In this article, electrical resistivity measurements at liquid nitrogen temperature have been carried out on the isochronal annealing out of quenchedin vacancies in 99.995% Al.
Abstract: A study based on electrical resistivity measurements at liquid nitrogen temperature has been carried out on the isochronal annealing out of quenchedin vacancies in 99.995% Al. The procase of annealing takes place in two stages; the first stage is centred at about room temperature and takes place at a lower temperature the higher the quenching temperature; also the observed migration energies (in the range 0.37 to 0.58ev) and the mean number of jumps for annihilation (in the range 104 to 109) are very sensitive to the initial concentration of defects, that is to the quenching temperature. The second stage takes place at about 160°c and its amount increases largely with quenching temperature; its activation energy results in 1.3±0.2 ev. The results have been interpreted as due principally to a clustering of vacancies (first stage) and subsequent dispersion of clusters by self-diffusion (second stage).
TL;DR: In this paper, it was concluded that grain boundaries are effective sources of vacancies, but twin boundaries are not, and there is no evidence that the dislocation network generates appreciable numbers of vacancies.
Abstract: Helium atoms have been injected into copper by alpha-particle bombardment in a cyclotron. On subsequent heating, the helium precipitates out as small gas bubbles in those parts of the metal where the helium atoms receive vacancies from nearby sources. From the distribution of the gas bubbles it is concluded that grain boundaries are effective sources of vacancies, but twin boundaries are not. Isolated sources of vacancies exist within the crystals, but there is no evidence that the dislocation network generates appreciable numbers of vacancies.
TL;DR: In this article, it was observed that minute cracks had been formed in the region of a kink band generated by nonhomogeneous plastic strain, and these cracks lay on conjugate {110} slip planes and not on the usual {100} cleavage planes.
Abstract: Experimental evidence is presented which lends direct support to the Stroh mechanism for crack formation. After a magnesium oxide crystal was compressed about 3%, it was observed that minute cracks had been formed in the region of a kink band generated by non-homogeneous plastic strain. These cracks lay on conjugate {110} slip planes and not on the usual {100} cleavage planes. They extended in the form of [001] direction slits running right through the crystal.
TL;DR: In this paper, it was shown that the Gruneisen constant derived from the elastic properties of a solid can be negative in certain cases, such as when the shear modulus of the lattice is sufficiently small and when the volume expansion coefficient of the cubic lattice would be negative at sufficiently low temperatures.
Abstract: It is shown that the Gruneisen constant derived from the elastic properties of a solid can be negative in certain cases The lattice models examined are (a) ionic lattices with the zinc blende structure, (b) ionic lattices with the rocksalt structure In the first case it is found that a negative value is obtained over the whole range of parameters examined In the second, negative values are obtained when the shear modulus of the lattice is sufficiently small In all these cases the volume expansion coefficient of the cubic lattice would be negative at sufficiently low temperatures
TL;DR: In this paper, a model of cleavage applicable to metals cleaving on the slip plane is developed in which a crack is initiated at the end of a low angle tilt boundary terminating inside the crystal.
Abstract: A model of cleavage applicable to metals cleaving on the slip plane is developed in which a crack is initiated at the end of a low angle tilt boundary terminating inside the crystal. The strength of the metal is determined by the difficulty of growth of the crack. Satisfactory agreement is obtained with the experimental results for zinc.
TL;DR: In this article, the average transverse momentum resulting from the measurements is pT = 0.5 Bev/e for pions and pT=l-2 Bev /c for heavy particles.
Abstract: Twenty nuclear interactions produced by protons and ten produced by α-particles of energies above 1000 Bev have been analysed. The proportion of pions amongst the secondaries is found to be 80% for the core and less than 70% for the wide angle tracks. The average transverse momentum resulting from our measurements is pT=0.5 Bev/e for pions and pT=l-2 Bev/c for heavy particles. It appears to be independent of angle of emission and primary energy. The multiplicity of the interaction, ns shows no variation with primary energy; it varies, however, with the anisotropy of the angular distribution, and shows wide fluctuations at a fixed primary energy. The inelasticity, K, of the collisions is close to unity for secondary interactions of mean energy ∼100 Bev and about 0.2 for jets produced by protons of energy ∼10 000 Bev. At a fixed energy, K does not appear to be strongly dependent on ns. None of the current theories appears capable of giving a satisfactory explanation of the experimental results, and...
TL;DR: In this article, Zener's theory of the volume expansion of self-strained elastic bodies is applied to screw and edge dislocations in isotropic media and the important physical parameters entering are the pressure depe...
Abstract: Zener's theory of the volume expansion of self-strained elastic bodies is applied to screw and edge dislocations in isotropic media. The important physical parameters entering are the pressure depe...
TL;DR: In this article, the contours of the slip bands produced by fatigue straining of metals are viewed by a process of taper-seotioning and optical microscopy which permits effective magnifications of some 20000 times.
Abstract: The contours of the slip bands produced by fatigue straining of metals are viewed by a process of taper-seotioning and optical microscopy which permits effective magnifications of some 20000 times. The observations indicate ways in which the slip bands may turn into cracks and start disintegration of the metal surface. They also show that the mechanism of deformation and failure changes as the amplitude of the cyclic straining increases, the general form of the fatigue SIN curve arising from auperposition of two distinct mechanisms. The observations support the view that fatigue craoking is primerily a simple geometrical consequence of to-and-fro fine slip movements in the fatigue slip-bands.
TL;DR: In this article, a simplification of the theory of the optical constants of metals is given which fits the experimental data for Na, K, Rb and Cs satisfactorily.
Abstract: Thermal and optical effective masses are defined and expressions for them obtained for metals with arbitrary Fermi surfaces. The ratio of these two effective masses is shown to depend on the shape of the Fermi surface. It follows from experimental values of the optical constants and the electronic heat capacity that the Fermi surface is not spherical in Cu, Ag and Au and that it contacts the surface of the first Brillouin zone to an appreciable degree in Cu and Ag. Similar evidence indicates a non-spherical Fermi surface in Li, Na and K. A simplification of the theory of the optical constants of metals is given which fits the experimental data for Na, K, Rb and Cs satisfactorily. Values of the plasma frequencies and widths of the plasma resonances of the alkali metals are calculated.
TL;DR: In this article, the well-known processes of magnetization of rocks are discussed and compared and contrasted with the magnetization formed when a ferromagnetic mineral undergoes a chemical change within the influence of an external magnetic field.
Abstract: In this paper the well-known processes of magnetization of rocks are discussed and compared and contrasted with the magnetization formed when a ferromagnetic mineral undergoes a chemical change within the influence of an external magnetic field. The thermal stability of the ‘chemical-magnetization’ so produced is examined and compared with the magnetizations produced isothermally and thermo-remanently in iron oxides under similar field conditions. The theoretical aspects of such a process of magnetization are considered and the nature of the resulting magnetization is accounted for theoretically. Possible applications in rock magnetic studies are also discussed.
TL;DR: In this article, the conditions under which thin metal specimens can be produced by electro-polishing for examination by transmission electron microscopy are described, and some practical hints are given relating to the use of the transmission electron-microscope technique for the study of dislocations in metals.
Abstract: The conditions are described under which thin metal specimens can be produced by electro-polishing for examination by transmission electron microscopy. The method has been applied to Mg, Co, Cu, Ni, Al, α-brass and Fe, and representative micrographs showing the arrangement and movement of the dislocations are presented. Some practical hints are given relating to the use of the transmission electron-microscope technique for the study of dislocations in metals.
TL;DR: In this paper, the electrical resistivity of pure polycrystalline specimens of bismuth and antimony over the range 2 to 300°K and of the thermal conductivity up to 150°K were measured.
Abstract: Measurements are reported of the electrical resistivity of pure polycrystalline specimens of bismuth and antimony over the range 2 to 300°K and of the thermal conductivity up to 150°K. Som...
TL;DR: In this paper, it was concluded that most trigons are etch pits; there is evidence that these particular trigons were centred on dislocations, and possible explanations were considered for the fact that the usual laboratory etchants develop pits oppositely oriented to trigons.
Abstract: On the faces of a type I diamond octahedron of particularly good quality there have been observed clusters of trigons which appear to be associated with a centre of strain in the interior of the stone. The trigon patterns show features which can only have been the result of surface dissolution. These observations are discussed, and it is concluded that most trigons are etch pits; there is evidence that these particular trigons are centred on dislocations. Possible explanations are considered for the fact that the usual laboratory etchants develop pits oppositely oriented to trigons.
TL;DR: In this article, the theory of the properties of an electron in a polar crystal is investigated by means of a model which takes account of the atomicity of the lattice, and the method used is essentially that of a tigh...
Abstract: The theory of the properties of an electron in a polar crystal is investigated by means of a model which takes account of the atomicity of the lattice. The method used is essentially that of a tigh...