Showing papers in "Philosophical Magazine in 1973"
TL;DR: In this paper, the optical absorption spectra of amorphous and crystalline thin Wo3 films have been measured in the temperature range 110° to 500°K and the temperature coefficient of the band edges was found to be − 5.0 × 10−4 eV/°K.
Abstract: Thin films of Wo3 deposited on quartz substrates at room temperature have been shown to be amorphous in structure. The optical absorption spectra of the amorphous and crystalline films have been measured in the temperature range 110° to 500°K. The fundamental absorption edge of an amorphous film occurs at 3800 A which on crystallization moves to 4500 A. On the high-energy side of the absorption edge several absorption peaks are resolvable in both types of film. The frequency dependence of the absorption coefficient below 104 cm−1 is described by an expression of the form K (v, T) = K 0 exp[− (β/kT) (E 0 − hv)] and above 104 cm−1 it follows a square law dependency. The temperature coefficient of the band edges was found to be − 5.0 × 10−4 eV/°K and the estimated band gaps at 0°K were found to be 3.65 and 3.27 eV for the amorphous and crystalline films, respectively. The electrical conductivity of a thin film has been measured in the temperature range 298–573°K and the activation energy was found t...
1,060 citations
TL;DR: In this paper, a theory of yielding of glassy polymers by thermally activated production of local molecular kinks is described, and the authors obtain the activation free enthalpy of this process by modeling the intermolecular energy barrier as resulting from the stress fields of two equal and opposite closely spaced wedge disclination loops extending over the molecular cross section at the points of rotation of the molecular kink.
Abstract: A theory of yielding of glassy polymers by thermally-activated production of local molecular kinks is described. It is possible to obtain the activation free enthalpy of this process by modeling the intermolecular energy barrier as resulting from the stress fields of two equal and opposite closely spaced wedge disclination loops extending over the molecular cross section at the points of rotation of the molecular kinks. The theory predicts the yield stress at absolute zero to be dependent only on the shear modulus and the Poisson's ratio, and is capable of describing the temperature, pressure, and strain rate dependences of the flow stress from absolute zero to near the glass transition temperature. Comparison of the theory with the available experimental, results on polystyrene, polyethylene-terephthalate, polycarbonate of bisphenol A, and poly-methyl-methacrylate shows excellent agreement in nearly all respects.
776 citations
TL;DR: In this article, the effect of dislocation self-interaction on the Orowan stress was determined for collinear, impenetrable circular obstacles, and an appropriate integro-differential equation governing static equilibrium was solved by an algorithm based on curvature adjustments.
Abstract: The effect of dislocation self-interaction on the Orowan stress was determined for collinear, impenetrable circular obstacles. The line tension approximation was dropped and an appropriate integro-differential equation governing static equilibrium was solved by an algorithm based on curvature adjustments. When the interactions are taken into account, the Orowan stress varies as In where is the harmonic mean of the obstacle size and spacing. In addition, the configuration of a bowing dislocation at the Orowan stress is strongly influenced by the interactions: as the interactions increase in strength, i.e. as the ratio of obstacle size to spacing decreases, the bow-out and area swept are suppressed. The essential features of the interaction can be incorporated into a line tension framework by treating the impenetrable obstacles as if they were penetrable. Based on this line tension analogue, an approximate form for the flow stress of a random distribution of impenetrable obstacles was developed.
470 citations
TL;DR: In this paper, the angular distribution of back-scattered electrons can be observed in a scanning electron microscope, and the patterns observed can be used to obtain crystallographic information about the specimen.
Abstract: It is shown that the angular distribution of back-scattered electrons can be observed in a scanning electron microscope, and that the patterns observed can be used to obtain crystallographic information about the specimen. The patterns are termed electron back-scattering patterns (E.B.S.P.). The use of these patterns as a crystallographic techniques is shown to have several significant advantages over two other techniques currently in use in scanning electron microscopes.
449 citations
TL;DR: In this paper, the stability of cylindrically symmetrical line disclinations is examined by continum theory calculations and topological arguments, to show that these singularities can almost always be replaced by a continuous structure of lower energy.
Abstract: The stability of cylindrically symmetrical line disclinations is examined by continum theory calculations and topological arguments, to show that these singularities can almost always be replaced by a continuous structure of lower energy. The calculations are applied to the four basic types of index ± 2 structures. Experimental observations are presented to support the proposed continuous structures as seen in cylindrical samples, and in the classical structures a fils and a noyaux.
302 citations
TL;DR: The surface structures and interior dislocation structures of fatigued copper and copper-5 at. % aluminium crystals have been studied using replicas and scanning and transmission electron microscopy techniques as discussed by the authors.
Abstract: The surface structures and interior dislocation structures of fatigued copper and copper-5 at. % aluminium crystals have been studied using replicas and scanning and transmission electron microscopy techniques. A very regular structure of walls of dislocations has been found; these walls consist of primary edge dipoles held together by a mesh of secondary dislocations. It is suggested that the wall structure is the ‘ideal structure’ to which other structures tend as the fatigue process progresses, and that this regular structure is found in the persistent slip bands.
262 citations
TL;DR: In particular, the critical condition for obtaining the ferroelastic loop can be experimentally determined by assuming a critical stress, which is termed "ferro-elastic limit", which lies in the region 6 Kg/mm- in the Au-Cd alloy as mentioned in this paper.
Abstract: Thermoelastic martensitic transformation has been studied by the analysis of stress-strain curves in binary Au-Cd alloys, containing 46·5, 47·5, 48·5, 49, 49·5, and 50 at. % Cd, respectively. The pseudoelastic characteristics, i.e. superelastic and ferroelastic behaviour upon tension compression test and that the origin of the shape memory effect bears a close relation to the ferroelastic loop, have been explained on the basis of the lattice softening, that is. the shear elastic constant, C′ = (C11-C12)/2, decreases toward zero in the vicinity of the transition temperature. In particular the critical condition for obtaining the ferroelastic loop can be experimentally determined by assuming a critical stress, which is termed ‘ferroelastic limit’. The ferroelastic limit may depend upon the elastic anisotropy of alloys and lies in the region 6 Kg/mm- in the Au-Cd alloy.
148 citations
TL;DR: In this paper, a cell structure consisting of nearly dislocation free regions of varying sizes surrounded by walls of dislocation networks without preferred orientation is observed which is, in principle, the same in all stages of deformation.
Abstract: DISLOCATION STRUCTURE AND WORK-HARDENING OF COPPER SINGLE CRYSTALS WITH [100] AXIS ORIENTATION I. DISLOCATION ARRANGEMENT AND CELL STRUCTURE OF CRYSTALS DEFORMED IN TENSION Copper single crystals with [100] axis orientation are deformed in tension at room temperature and after load-removal are irradiated with neutrons to stabilize the dislocation arrangement before the preparation of thin foils. TEM investigations of {111}-, {110}- and {100}-foils and the analysis of Burgers vectors and lino vectors yield the essential information about the dislocation arrangement. A cell structure is observed which is, in principle, the same in all stages of deformation. This cell structure consists of nearly dislocation free regions of varying sizes surrounded by walls of dislocation networks without preferred orientation. The most important parameters of this dislocation structure are measured as a function of stress: Dislocations of all 6 Burgers vectors—including those which do not operate under the external...
134 citations
TL;DR: In this article, the critical tensile strain for the formation of a craze in polystyrene was investigated under conditions of biaxial stress with one principal stress compressive, and the results were consistent with the suggestion of Sternstein and Ongchin that for crazes to form the hydrostatic component of the stress tensor must be tensile.
Abstract: The critical stress for craze formation in four different grades of polystyrene has been investigated under conditions of biaxial stress with one principal stress compressive. The results are consistent with the suggestion of Sternstein and Ongchin (1969) that for crazes to form the hydrostatic component of the stress tensor must be tensile. It has further been shown that a convenient way to express the criterion for the formation of crazes is in terms of a critical tensile strain, ∊c, which is a function of the hydrostatic component of the stress tensor. This critical-strain criterion can readily be applied to predict the onset of crazing under a general triaxial state of stress, and it may be possible to interpret the variation of the two parameters in the criterion in terms of two distinct critical processes in the formation of a craze, one process pressure-dependent the other not.
131 citations
TL;DR: The authors showed that metastable crack growth dictates the environment free strength of sapphire at low temperatures, and that plastic deformation by dislocation motion or twin formation and growth plays no role in the fracture process at temperatures below 400°C.
Abstract: At low temperatures, metastable crack growth dictates the environment free strength of sapphire. Plastic deformation by dislocation motion or twin formation and growth plays no role in the fracture process at temperatures below 400° C. These conclusions are supported both by crack growth studies and critical stress intensity factor measurements on sapphire crystals, and by transmission electron microscopy studies of arrested cracks in sapphire and alumina.
116 citations
TL;DR: In this article, a rate theory of the growth of irradiation-produced interstitial loops in uniaxially stressed materials which also contain voids, coherent and/or incoherent precipitates and network dislocations is derived and the resulting creep behaviour is determined.
Abstract: A rate theory of the growth of irradiation-produced interstitial loops in uniaxially stressed materials which also contain voids, coherent and/or incoherent precipitates and network dislocations is derived and the resulting creep behaviour is determined. Allowance is made for the preferential nucleation of loops oriented perpendicular to the stress axis and for the subsequent enhanced growth of these same loops. It is shown that the first of these mechanisms dominates and gives a creep rate which can be correlated with the volume swelling rate. The magnitude of the effect is shown to be consistent with the limited amount of available experimental data appropriate to the void-swelling temperature regime.
TL;DR: In this article, it has been demonstrated that the void or bubble arrays act as diffraction gratings and produce extra reflections centred around the molybdenum matrix reflections.
Abstract: Electron diffraction patterns from irradiated molybdenum specimens containing periodic arrays of voids or helium gas bubbles have been studied. It has been demonstrated that the void or bubble arrays act as diffraction gratings and produce extra reflections centred around the molybdenum matrix reflections. This technique enables a rapid evaluation to be made of the average void lattice parameter, and it is shown to be particularly useful for the study of arrays where spacing measurements are not feasible from micrographs of the direct images. It is pointed out that an important potential application of the technique, is for the study of ordered arrays of sub-microscopic defects.
TL;DR: In this paper, single crystal samples have been irradiated in a high voltage (1 MeV) transmission electron microscope and the defects formed are described as a function of specimen temperature and compared with similar defects formed by proton irradiation in an accelerator-electron microscope link.
Abstract: Silicon single crystal samples have been irradiated in a high voltage (1 MeV) transmission electron microscope. The defects formed are described as a function of specimen temperature and compared with similar defects formed by proton irradiation in an accelerator-electron microscope link. The defects are contrasted with those obtained with heavy ions with particular regard to possible mechanisms for the crystalline to amorphous transition which was not seen for electron and proton bombardments. For irradiations at 450°C needle-shaped precipitates were formed on {113} planes.
TL;DR: In this article, a general method for analysing dislocation loops formed in zirconium after neutron irradiation and subsequent annealing between 450° and 500°C is discussed and a technique for determining the loop plane normal to within ± 5° is described.
Abstract: Dislocation loops formed in zirconium after neutron irradiation and subsequent annealing between 450° and 500°C are not pure edge loops. A general method for analysing such loops by transmission electron microscopy is discussed briefly and a technique for determining the loop plane normal to within ± 5° is described. The Burgers vectors of the loops in annealed irradiated zirconium are found to be of the type a/3 〈1120〉 while the loop plane normal is tilted by up to 35° towards the adjacent {2021} pole. Two thirds of the loops present after annealing at 490°C are vacancy loops, while the remainder are interstitial. Zirconium irradiated at 300°C and not annealed also shows only loops with a/3 〈1120〉 Burgers vectors. The significance of these results in interpreting previously reported irradiation growth data is briefly discussed.
TL;DR: In this paper, the authors examined aluminum bicrystals containing a symmetrical tilt grain boundary with thin-foil electron microscopy after high-temperature shear deformation.
Abstract: Aluminium bicrystals containing a symmetrical [011] tilt grain boundary have been examined by thin-foil electron microscopy after high-temperature shear deformation. In all tests abundant crystal shear deformation had accompanied grain boundary shear. Grain boundary dislocations were observed and their Burgers vector was always [011]. They originated from lattice dislocations which entered the boundary and dissociated. It is deduced that the reactions: occurred. The component (R) was not visible in the electron microscope and is presumed to consist of several Bollmann dislocations with small Burgers vectors. Movement of the a/4[011] grain boundary dislocations along the boundary plane was observed. It is suggested that this took place by a process of glide and climb, and represented the mechanism of grain boundary shear. Multiplication of the grain boundary dislocations on the boundary plane and slide hardening processes are also discussed. Fine grain boundary lines were sometimes observed in bot...
TL;DR: In this paper, a Hall-Petch relation was found not to describe work hardening in the cases of copper and aluminium, and an approach to poly-crystal workhardening, based in part on Ashby's concepts, was also unsuccessful in describing the behaviour of the same materials.
Abstract: Stress-strain data were obtained over a wide range of grain sizes for brass, copper and aluminium. A Hall-Petch relation was found not to describe work hardening in the cases of copper and aluminium. An approach to poly-crystal work hardening, based in part on Ashby's concepts, was also unsuccessful in describing the behaviour of the same materials. These results indicate the need for a new viewpoint on the influence of grain size on poly-crystal work hardening.
TL;DR: In this paper, the image contrast from amorphous materials studied by dark field or by interference electron microscopy using tilted illumination is quantitatively discussed in terms of the microcrystallite model and of the random network model using a network model for SiO2.
Abstract: The image contrast from amorphous materials studied by dark field or by interference electron microscopy using tilted illumination is quantitatively discussed in terms of the microcrystallite model and of the random network model using a network model for SiO2. The experimental observations of bright spots of diameter > 10 A. in dark field and of lattice fringes in interference micrographs are well explained by the microcrystallite model but cannot be accounted for by the random network model. The random network gives rise to a number of interesting diffraction effects, however, in particular to very small rather intense bright spots of diameter <3 A. in dark field images. On the basis of the microcrystallite model some further improvements are described for the analysis of the diffraction pattern interference function to allow for intercrystalline effects and grain boundary material.
TL;DR: In this paper, an electric field dependence of the d.c. conductivity and of the trap-limited carrier drift mobility is shown to occur in a range of non-crystalline semiconductors.
Abstract: An electric field dependence of the d.c. conductivity and of the trap-limited carrier drift mobility is shown to occur in a range of non-crystalline semiconductors. Furthermore, the functional form of the dependence is found to be closely similar in each case. This behaviour is examined in terms of the models commonly proposed to explain field-dependent transport, but the data do not appear to be consistent with such models. It is suggested that the dependence may be due to a field modification of parameters controlling carrier motion in the region of the ‘mobility edge', but a quantitative analysis in such terms does not appear possible at present.
TL;DR: In this article, a cooperative diffusion mechanism involving Wilis 2:2:2 defect clusters in UO2+x has been shown to have a correlation factor greater than unity.
Abstract: Diffusion in lattice arrays reducible to cubic symmetry can be simulated by Monte Carlo procedures. Tracer correlation factors can be derived for diffusion mechanisms in such arrays which include simple solids with point defects and non-stoichiometric materials with complex defect structures subject to defect-defect interactions. It is shown that such interactions can substantially reduce the correlation factor. A cooperative diffusion mechanism involving Wilis 2:2:2 defect clusters in UO2+x is shown to have a correlation factor greater than unity.
TL;DR: Burgers vectors of grain boundary dislocations in important coincidence boundaries are calculated from a set of general equations derived for the three principal cubic structures in this article, and the Burgers vectors in high-order coincidence systems are mostly small in magnitude, but a large vector can occur for a coincidence system involving a low-index rotation axis.
Abstract: Burgers vectors of grain boundary dislocations in important coincidence boundaries are calculated from a set of general equations derived for the three principal cubic structures. The Burgers vectors in high-order coincidence systems are mostly small in magnitude, but a large vector can occur for a coincidence system involving a low-index rotation axis. It is suggested that the boundary dislocations observed by transmission electron microscopy in usual polycrystalline specimens are of this type.
TL;DR: In this paper, a model of the β to ω phase transformation in Ti, Zr and Hf alloys is proposed whereby the three-dimensional displacive transition is decomposed into one-dimensional and two-dimensional components.
Abstract: A model of the β to ω phase transformation in Ti, Zr and Hf alloys is proposed whereby the three-dimensional displacive transition is decomposed into one-dimensional and two-dimensional components. The one-dimensional component is postulated to be a linear displacive defect along 〈111〉 closepacked rows of the b.c.c. structure, the two-dimensional component then consists of the cooperative ordering of neighbouring parallel linear defects in the (111) planes normal to the linear component. That the two-dimensional cooperative ordering of displaced row segments can lead to a sharp phase transition has been demonstrated by a two-dimensional Monte Carlo simulation involving three types of symbols with nearest-neighbour interactions. Computer simulation exhibits characteristic two-domain ω structures which, along with the linear defect structure, appear to explain, at least qualitatively, observed electron and neutron diffraction patterns. It is tentatively suggested that the postulated linear defects ...
TL;DR: In this paper, a detailed study of the deformation modes which operate in polyethylene single crystals when drawn on a Mylar substrate was made, and the orientation relationships associated with the stress-induced twinning and monoclinic phase transformations were determined by electron diffraction and compared with predictions based on recently developed theories of the crystallography of martensitic transformations.
Abstract: A detailed study has been made of the deformation modes which operate in polyethylene single crystals when drawn on a Mylar substrate. The orientation relationships associated with the stress-induced twinning and monoclinic phase transformations have been determined by electron diffraction and compared with predictions based on recently developed theories of the crystallography of martensitic transformations. The agreement between theory and experiment is good and the identification of the deformation modes has enabled the criteria which govern the operation of these modes to be established. These criteria and the crystallography of the transformation processes are discussed in detail.
TL;DR: In this article, the metal-to-non-metal transition in shallow donor states of Ge and Si is studied by means of Hubbard's tight-binding model, where the donors are assumed to form a regular lattice, and the hopping integral and the intra-donor repulsion integrals are calculated from the wavefunctions of single isolated impurities.
Abstract: The metal-to-non-metal (MNM) transitions in shallow donor states of Ge and Si are studied by means of Hubbard's tight-binding model. The donors are assumed to form a regular lattice, and the hopping integral and the intra-donor repulsion integrals are calculated from the wavefunctions of single isolated impurities. The calculated critical densities for the onset of the MNM-transitions compare well with empirical values and with Mott's criterion. The only input parameters to the calculations are the experimentally determined ionization energies, the effective masses in the conduction band, and the background dielectric constants. Estimates are also made for the concentration at which the impurity band merges into the conduction band.
TL;DR: Weal-beam high-resolution micrographs were taken of dislocations in germanium which had been generated by plastic deformation at 520°C and τ = 2 kp/mm2 as discussed by the authors.
Abstract: Weal-beam high-resolution micrographs were taken of dislocations in germanium which had been generated by plastic deformation at 520°C and τ=2 kp/mm2. All dislocations examined were found to be at least partially dissociated with a partial dislocation separation of (54 ± 11) A for edge type observed double contrast of the dislocations cannot be due to dipoles.
TL;DR: In this paper, the change in shape of cylinders of liquid lead entrained in a matrix of solid aluminium has been followed using micro-radiography and a study of the kinetics of the process has yielded an estimate of the diffusion coefficient of A1 in liquid Pb between 450° and 620°C and an activation energy of 17.3 Kcal/mol.
Abstract: The change in shape of cylinders of liquid lead entrained in a matrix of solid aluminium has been followed using micro-radiography. A study of the kinetics of the process has yielded an estimate of the diffusion coefficient of A1 in liquid Pb between 450° and 620°C and an activation energy of 17.3 Kcal/mol has been derived. The spheroidization process has been charaterized by comparing the rate of spheroidization of cylindrical inclusions with the rate of growth of grain boundary grooves at the solid/liquid interface.
TL;DR: The authors observed the nucleation of surface disclination lines in nematics and showed their correspondence to emergences of walls at the boundary of the sample; these lines have no core discontinuity and t...
Abstract: Observation of the nucleation of surface disclination lines in nematics shows their correspondence to emergences of walls at the boundary of the sample; these lines have no core discontinuity and t...
TL;DR: The plastic deformation of sapphire by mechanisms other than slip on the basal plane has been studied by bending crystals of orientations such that extension and contraction normal to the basal planes (0° specimens) or parallel to the baselines (90° specimens), are required as discussed by the authors.
Abstract: The plastic deformation of sapphire by mechanisms other than slip on the basal plane has been studied by bending crystals of orientations such that extension and contraction normal to the basal plane (0° specimens) or parallel to the basal plane (90° specimens) are required. 0° specimens could not be plastically bent below 1600° C. Above 1600° C there was extensive plasticity but no single slip system could be identified. 90° specimens could be plastically bent by the operation of the slip system at temperatures as low as 1150°C. The temperature dependences and strain rate sensitivities of the flow stresses for 0° and 90° have been determined. There are striking differences between the characteristics of the two types of deformation, which are attributed to the fact that different dislocations are involved.
TL;DR: In this paper, an etching technique was used to study the dislocation microstructure in single crystals of copper fatigued to saturation in push-pull at constant plastic strain amplitude.
Abstract: An etching technique was used to study the dislocation microstructure in single crystals of copper fatigued to saturation in push-pull at constant plastic strain amplitude. In agreement with earlier electron microscope studies a structure of plane, regularly spaced walls of dislocations perpendicular to the primary slip direction was found to be associated with the persistent slip bands. The wall spacing (1·38 ± 0·05 yum) was measured and found to be virtually independent of fatiguing frequency (between 0·01 and 25 Hz) at room temperature. The internal consistency of the results was used to justify the etching technique.
TL;DR: In this article, the relaxation time of the conduction electron due to G.P. zone scattering, changes of the Hall coefficient and the electrical resistivity during ageing at 20°C have been measured at 4-2 and 77°K, and in addition, X-ray small-angle scattering measurements were carried out at low temperature.
Abstract: In order to determine experimentally the relaxation time of the conduction electron due to G.P. zone scattering, changes of the Hall coefficient and the electrical resistivity during ageing at 20°C have been measured at 4–2 and 77°K, and in addition, X-ray small-angle scattering measurements were carried out at low temperature. By employing a rigid two-band model, the partial resistivity due to G.P. zone scattering was found to have a maximum during ageing. However, taking account of the log normal size distribution, the scattering power of an individual particle of G.P. zones was shown to increase monotonically with increasing zone size.
TL;DR: In this paper, it was shown that the correct space group for MgAl2O4 spinel is F43m and not double diffraction, non-zero Laue zones, or a second phase.
Abstract: [001] electron diffraction patterns of MgAl2O4 spinel show (hk0) reflections with h + k = 4n + 2 ((200), (420), etc.) that violate the accepted Fd3m space group of this material. Since these ‘forbidden’ reflections cannot be attributed to double diffraction, non-zero Laue zones, or a second phase, this result is consistent with Grimes' recent suggestion that the correct space group for MgAl2O4 spinel is F43m.