Showing papers in "Philosophical Magazine in 1988"

Simulation of gold in the glue model

Abstract: Many well known difficulties associated with the use of two-body forces for the description of metallic systems may be overcome by using an expression for the total energy of the form V = ½Σ ij φ(r ij ) + Σ i U(ni), where n i = Σiρ(r ij ) is a generalized atomic coordination. The three functions φ(r), U(n) and ρ(r) are constructed empirically, by fitting several physical quantities including thermal and surface properties. This simple many-body force scheme can be used in molecular-dynamics simulations with few overheads compared with pair-wise systems. We present our realization for gold and summarize the results of recent structural and dynamical studies of Au surfaces.

Weak-beam observation of a dissociation transition in TiAl

Abstract: TiAl is a L10 ordered alloy which exhibits a flow-stress anomaly peaking at approximately 600°C. In order to correlate the increase in flow stress with changes in deformation microstructure, the nature and dissociation of superdislocations are compared after deformation at 20 and 600°C. It is observed that superdislocations split into a triplet involving an antiphase boundary (APB) and a superlattice intrinsic stacking fault (SISF). In the screw orientation this configuration undergoes a glissile–sessile transition as the temperature of the deformation test is raised, since the APB plane changes from the octahedral plane of the SISF after deformation at room temperature to a cubic plane at 600°C. The abundant evidence for cross-slip onto octahedral planes at room temperature only supports the idea that the high-temperature configuration of the screw superdislocations controls the flow-stress peak in TiAl. The reported change in dissociation configuration is the equivalent, for the L10 struc...

Short and long fatigue crack growth: A unified model

Abstract: In this model the growth of a crack is analysed in terms of the successive blocking of the plastic zone by slip barriers (e.g. grain boundaries) and the subsequent initiation of the slip in the next grain. The discontinuous character of the slip process (slip jumps) plays a fundamental role in the model. The factor governing the transfer of slip across a grain boundary is considered to be the stress concentration ahead of the plastic zone which, for a constant applied stress τ, is found to be dependent only on a parameter n = a/c defining the position of the crack tip relative to the grain boundary. The discrete behaviour of the slip has a strong influence in the short-crack period and hence cannot be neglected in the analysis of the crack growth rate. This period is characterized by large variations in the parameter n. In the long-crack period the slip jumps do not influence the overall description of the growth and the parameter n is almost constant. By making the crack extension per cycle prop...

The low-temperature plastic deformation of α-titanium and the core structure of a-type screw dislocations

Abstract: α-titanium single crystals, containing three different amounts of interstitial impurities, have been tested in compression at temperatures between 77 and 700 K. The mechanical behaviour is characterized by a strong temperature dependence of the yield stress for slip on the primary prismatic slip plane (1010)[1210], a strong dependence of the critical resolved shear stress on the orientation of crystal axis and the failure of the Schmid law, an anomaly at temperatures between 300 and 500 K which is associated with cross-slip into a first-order pyramidal plane, and the occurrence of two hardening stages on the deformation curves at low temperatures. Both conventional and in situ transmission electron microscopy examinations revealed that a large lattice friction opposes the motion of a-type screw dislocations at temperatures below 550 K. Since edge dislocations are found to be highly mobile, it appears that, at low temperatures, the yield stress of pure α-titanium is governed by a Peierls force act...

Melting temperature of In particles embedded in an Al matrix

Abstract: The melting and freezing temperatures of small In particles with a radius r of less than 20 nm embedded in an Al matrix have been measured as a function of particle size using in situ heating in an electron microscope The melting temperature of In particles whose radii are smaller than 15 nm is higher than that of bulk material and increases with decreasing r The freezing temperature is lower than the melting temperature of bulk material for all radii studied and has a minimum at around r = 13 nm The behaviour of the melting of embedded particles contrasts sharply with that of free particles, for which the melting temperature decreases with decreasing r The difference is discussed in terms of the interfacial energies between the Al matrix and liquid or solid In

Defects in plastically deformed 6H SiC single crystals studied by transmission electron microscopy

Abstract: Transmission electron microscopic studies have been performed on lattice defects in 6H silicon carbide single crystals; the crystals were subjected to microhardness indentation tests between room temperature and 1200°C and then to uniaxial compression at temperatures from 1100 to 1650°C. It was observed that their basal dislocations, the main defects introduced by deformation, were dissociated into Shockley partials separated by very wide stacking faults, the energy of which was evaluated to be 2.5 ± 0·9 mJ m−2. The lineshapes of the partials varied considerably, depending on the sign and angle (with the dislocation line) of the Burgers vector; this suggests that the mobility of the partials is affected by the geometry of dislocations. The fact that basal dislocations were aligned more or less in crystallographic 〈1120〉 directions indicates the presence of a high Peierls potential. Macroplastic deformation was observed above 1000°C. This critical temperature seems to be determined by the motion o...

A TEM weak-beam study of dislocations in γ' in a deformed Ni-based superalloy

Abstract: The dislocation structure in γ' in deformed single crystals of nickel-based superalloy SRR99 has been observed by weak-beam electron microscopy. Super-dislocations in γ', dissociated into Shockley partials, are continuous across the γ/γ' interface becoming a pair of unit dissociated dislocations in γ'. In γ' most dislocations are screws and their configurations are those of Kear-Wilsdorf locks; the complex stacking faults between the Shockleys lie on {111} and the antiphase boundaries between the superpartials lie on the cube cross-slip plane (010). Despite this sessile configuration of screw dislocation dissociation, the screw dislocations move on the primary slip plane (111) by the propagation of kinks whose four partials lie entirely on (111). Models of the anomalous increase of yield stress at high temperatures that assume a planar dissociation of screws on (111) require reconsideration in the light of these observations.

The quantum simulation of hydrogen in metals

Abstract: Realistic quantitative calculations on atomistic models for hydrogen in metals are difficult because quantum effects must be included. We show that quantum simulation based on Feynman's path-integral formulation of quantum mechanics gives a powerful way of making such calculations. After summarizing some essential facts about metal-hydrogen systems, we explain the principles of pathintegral simulation. We present the results of classical molecular-dynamics and quantum path-integral simulations of hydrogen in Pd and Nb based on simple empirical interaction models. Results are given for the probability density ρ(r) of hydrogen as a function of position r in the unit cell, and for a quantity proportional to the diffusion coefficient. We point out that diffraction measurements of ρ(r) would allow an important test of the interaction models. The simulated diffusion coefficient for H in Nb shows the experimentally observed break in Arrhenius slope at ∼250 K, which we argue represents a cross-over from ...

Inelastic scattering probabilities in scanning transmission electron microscopy

Abstract: In this paper, we derive a general expression for the excitation probability corresponding to the collection of inelastically scattered electrons in a scanning transmission electronic microscopy configuration. We prove that, if all inelastically scattered electrons are collected, then the fraction of electrons that will be determined to have given rise to excitation in a localized target at impact parameter b may be calculated by simply convoluting over b (1) the probability P c(b) that a classical electron with the same velocity well create the excitation at given b, with (2) the probability of finding the electron in the microprobe at that impact parameter. We also show that, even in the opposite extreme, when a small solid angle of axial collection is employed, the energy-loss spectrum will still approximate to the classical expression provided that it is normalized to the same zero-loss intensity and if the Fourier-transformed profile function does not become too small for some ranges of its ...

Shape-memory effect and pseudoelasticity associated with the R-phase transition in Ti-50·5 at.% Ni single crystals

Abstract: The rhombohedral phase (R-phase) transition and associated deformation behaviour in Ti-50·5 at.% Ni single crystals have been investigated systematically by tensile testing age-treated specimens in various orientations over a wide temperature range. Shape-memory effects and pseudoelasticity were observed in the first stage as well as in the second stage of the stress-strain curves; here we attempt to clarify the characteristics of the transition and deformation behaviour in the first-stage yielding. The strain in the first stage shows strong temperature and orientation dependences as follows: (1) the strain increases with decreasing temperature below the TR point, which is the critical temperature for the R-phase transition; (2) the strain is largest in the [111]B2 orientation and smallest in the [001]B2 orientation. Both the temperature and orientation dependences show excellent quantitative agreement with the calculated results based on the lattice distortion associated with the R-phase transit...

The pressure for dislocation loop punching by a single bubble

Abstract: A detailed analysis is given on the energetics of bubble growth in a solid by prismatic loop punching. Interactions between the bubble and the dislocation loop are included as well as the effect of the loop proximity on the actual bubble volume. It is shown that there exists an attraction between bubble and loop and that the bubble volume increases gradually as the loop recedes from the bubble. As a result, there exists an energy barrier for loop punching which requires a significantly higher pressure than previously assumed. Furthermore, the critical pressure for loop punching reaches a nearly constant value with increasing bubble radius. The calculations are carried out for the case of nickel at room temperature, and it is predicted that helium within the bubbles is in the solid state.

Weak-beam study of superlattice dislocations moving on cube planes in Ni3(Al, Ti) deformed at room temperature

Abstract: The dislocation structure resulting from the compression of single crystals of Ni3(Al,Ti) at room temperature has been studied using transmission electron microscopy imaging methods. Deformed samples of e = 1% and e = 9% true strain were sliced parallel to (111) and (010) planes. Weak-beam imaging methods reveal the (010) planes to be the dissociation planes of the screw superlattice dislocations. Transition of superlattice dislocations from (111) onto (010) planes by the Kear-Wilsdorf mechanism was identified. Remarkable dislocation movement on (010) planes was found. The flow stress is interpreted as a dislocation interaction on octahedral and cube planes. Measurements of the antiphase-boundary energies on (111) and (010) planes yielded values of γ111 = γ010 =250±30mJm−2

On precipitate shearing by superlattice stacking faults in superalloys

Abstract: Superlattice intrinsic stacking faults (SISFs) constitute one of the major features of the deformation microstructure of superalloys. It is pointed out that they may result from the dissociation, in the precipitates, of a single perfect matrix dislocation by a process essentially similar to the formation of SISFs in single-phase Ll2 ordered alloys. By using transmission electron microscopy under weak-beam conditions, it is demonstrated that SISFs originate mostly at the precipitate corners and that they may then interact attractively with secondary matrix dislocations, in order to form stable junctions. Energy calculations of the growth conditions of a SISF are performed as a function of precipitate size, SISF energy and applied stress, in the case of several alternative crystallographic configurations. It is shown that, although the dislocation dissociation is unfavourable on a per-unit-length basis, the nucleation and growth of SISFs is easy in superalloys since specific geometrical conditions ...

Triple-line disclinations representations, continuity and reactions

Abstract: In a polycrystalline material it is usual for three grains, and therefore three grain boundaries, to meet on a line, the ‘triple line’. Since grain boundaries can be interpreted as dislocation networks, a question arises about the dislocation balance at the triple line. It is shown that, if the dislocation balance is not satisfied, the triple line acquires the character of a disclination, an oriented line with a tensor of rank 2 attributed to it. The paper deals with the mathematical representation of these ‘triple-line disclinations’, their balance in a triple-line node and their reactions.

Adhesion of spheres by thin liquid films

Abstract: Thin liquid films may produce significant adhesion between solid bodies, such as powder agglomerates and ultra-flat surfaces. The adhesive force can be split into two components; the meniscus force and a viscous component which, at sufficiently high deformation rates, will become dominant. This paper presents an analysis for the viscous component of adhesion acting between spheres coated by thin liquid layers, which is expressed as the impulse required to separate the spheres. This impulse depends on the radii and surface roughness of the spheres, and the fluid viscosity and thickness. The dependence on the roughness and quantity of fluid is unexpectedly weak (i.e. logarithmic). The predictions of the analysis are confirmed by direct experiment using a simple force pendulum.

Study on the substructure evolution and flow behaviour in type 316L stainless steel over the temperature range 21-900°C

Abstract: Tensile specimens of type 316L stainless steel with a grain size of 5.0 μm have been deformed at a constant strain rate of 10−3 s−1 over the temperature range 21–900°C and by differential strain-rate test technique over strain rates from about 10−5 to 10−3 s−1 at temperatures in the range 750–900°C. The normalized yield and flow stresses against temperature plots exhibit three regions. While in regions I and III the stresses decrease with increasing temperature, they increase with increasing temperature in region II. Transmission electron microscopy studies on deformed specimens show that at small strains the dislocations generated at grain boundaries have characteristic distributions: in region I the dislocations are confined to the vicinity of the grain boundary, in region II the dislocations are spread into the grain interior, and in region III the dislocations rearrange to form walls. The evolution of substructure and the work-hardening behaviour are explained by considering both intragranula...

Parameter-free calculations of total energies, interatomic forces and vibrational entropies of defects in semiconductors

Abstract: We discuss calculations from first-principles (using the local-density approximation for exchange and correlation) of defect total energies, vibrational modes, internal energies and entropies. Results are presented for the defect-induced distortion field of an arsenic impurity in silicon and for the vibrational entropy of a silicon vacancy. We also discuss the important role of electron and atom chemical potentials, presenting results for the Ga vacancy in the GaAs bulk and at the (111) surface.

An alternative model of the blocking of dislocations at grain boundaries

Abstract: The blocking of dislocations at a slip barrier, such as a grain boundary, is modelled by considering, in the domain of distribution of dislocations ahead of the slip band, a small zone representing a locked source or the width of the boundary itself. The ‘friction stress’ in this small zone is calculated so that no infinite stresses appear in the analysis. Hall–Petch type relationships are derived for the yield stress and the fatigue limit. When the length of the additional zone is sufficiently small in comparison to the total length of the array, the solution is very close to the one obtained by the common modelling of the block by an infinite delta-type function.

Interatomic potentials for oxides

Abstract: We review the current status of potential models for oxide materials, with emphasis on the applications of potentials in simulation studies. We pay special attention to transition-metal oxides, silicates and ternary metal oxides. Extensions of potentials beyond the two-body formulation are discussed.

Dislocation motion in ice: A study by synchrotron X-ray topography

Abstract: The synchrotron radiation source at the Daresbury Laboratory, Science and Engineering Research Council, has been used to obtain white X-radiation topographs of high-quality single crystals of ice with exposure times of about 20 s. Sequences of topographs show the motion of individual dislocations under stress in the very early stages of plastic deformation at temperatures from −10 to −35°C. Glide on the basal plane appears to be limited by a Peierls barrier in the screw and 60° orientations. Edge, but not screw, dislocations on non-basal planes glide faster than dislocations on the basal plane and act as sources of dislocation multiplication. The velocities of both basal and non-basal dislocations are found to be linear functions of stress. Much recovery occurs on the time scale of previous experiments to measure dislocation velocities. The implications of the observations for theories of dislocation mobility are discussed.

Interactions of deformation-induced dislocations with Σ = 9(122) grain boundaries in Si studied by HREM

Abstract: The mechanisms of interaction between a twin boundary and dislocations created during the deformation of a bicrystal are analysed by means of HREM. It is shown, on an atomic scale, that intrinsic dislocations enter the grain boundary where they decompose into discrete grain-boundary dislocations with Burgers vectors belonging to the DSC lattice. These residues can migrate along the interface and interact, giving rise to new residues. It is shown that, when the strain remains low enough, the grain-boundary deformation history can be deduced from the HREM observations.

The interphase boundary structure of precipitates in a Ni-Cr alloy

Abstract: The interfacial structure of lath-shaped b.c.c. Cr-rich precipitates in an Ni-45 wt% Cr alloy has been studied by transmission electron microscopy. Two sets of ledges were observed at the (121)F habit plane interface. The first set lay parallel to the invariant line of the transformation and were associated with the thickening mechanism of the precipitates. The effective strain field displacement vector of this set was [121]F, normal to the habit plane. The ledges were observed to terminate at the points of intersection of (a/2)[101] matrix dislocations with the interface. The second set of ledges, seen only at the end of the habit plane, are believed to be related to the lengthening mechanism of the laths. A single set of dislocations, parallel to the invariant line, was found to form on prolonged ageing at the side facet plane of the laths. The spacing and effective Burgers vector of this set of dislocations were explained by a plane-matching model, the dislocations relieving the misfit between...

Transient creep of olivine: Point-defect relaxation times

Abstract: The time taken for San Carlos olivine specimens to reach a new steady-state creep rate after a change in either po2 or oxide activity has been used to calculate a diffusivity for the defect species which rate-limits the re-equilibration process. For temperatures between 1200 and 1400°C, the calculated diffusivities are approximately equal to reported values for the chemical diffusion coefficient for metal vacancies (Nakamura and Schmalzried 1984). These experimental results are consistent with a model in which dislocation glide or cross-slip rate-limits the high-temperature deformation of olivine, since changes in creep rate need only involve the motion of majority defects (metal vacancies and electron holes). However, if dislocation climb rate-limits the high-temperature deformation of olivine, and if local equilibtium is attained on the experimental timescale, these experimental results demonstrate that the minority defects that control diffusion on the silicon and oxygen sublattices re-equilib...

On the correlation between self-diffusion and the low-frequency LA ⅔⟨111⟩ phonon mode in b.c.c. metals

Abstract: A new approach is proposed for understanding the strongly diverging self-diffusion behaviour in b.c.c. metals by relating the atomic mobility to the characteristic low-frequency LA 2/3⟨111⟩ phonon mode. The frequency v 2/3 of this mode is controlled by restoring forces, which oppose in particular the atomic displacements for a diffusion jump in the ⟨111⟩ direction, influencing in this way the migration enthalpy H M. A simple semi-empirical expression is derived which relates H M to the square of v 2/3. On the basis of experimental results an excellent correlation between the activation energy for self-diffusion and the LA 2/3⟨111⟩ phonon frequency is found. It is concluded that the extremely different mobilities in b.c.c. metals result from corresponding alterations in H M. Changes in H M originate from systematic variation in the d electron charge density distribution, which is responsible for the strength of the ⟨111⟩ directional bond-bending forces in b.c.c. transition metals. This model of ph...

Comparison of the radii of latent tracks induced by high-energy heavy ions in Y3Fe5O12 by HREM, channelling Rutherford backscattering and Mössbauer spectrometry

Abstract: Y3Fe5O12 garnets have been irradiated by Mo and Xe ion beams at 2.3 and 3.3 GeV respectively. High-resolution electron microscopy (HREM), channelling Rutherford backscattering (RBS) and Mossbauer s...

Structural fluctuations in small particles

Abstract: We present a theoretical analysis of a phenomenon recently observed by high-resolution electron microscopy that involves rapid structural fluctuations in small f.c.c. particles below 10 nm in size. The different energy contributions to the total energy of the particle and the magnitude of the potential energy barrier between different shapes is evaluated and compared with the available energy during particle-beam interactions. The results indicate that the activation energy barrier existing between different shapes is only a few electron volts, whilst a rough estimate indicates that during electron-beam irradiation the available energy may be as much as 100–1000eV.

Cyclic deformation of single crystals of iron–silicon alloys oriented for single slip

Abstract: Single crystals of iron and its alloys with 0·5, 0·9, 1·8 and 3 wt% Si oriented for single slip have been cyclically deformed in tension–compression at plastic strains between 10−4 and 10−2. The effects of cyclic hardening, changes of specimen cross-section, slip traces and dislocation arrangements have been studied at 295 and 524 K and a strain rate of 1·6 x 10−3 s−1. The cyclic deformation of b.c.c. Fe–Si alloy crystals at both temperatures and of f.c.c. metal crystals shows similarly shaped cyclic hardening and cyclic stress–strain curves, and similar strain localization in the persistent slip bands (PSBs) and development of the dislocation arrangement. Unlike in f.c.c. metals, in Fe–Si crystals there is appreciable secondary slip at the beginning of the saturation stage, leading to a cell structure in PSBs. The dislocation cell structure is typical of PSBs throughout their whole existence. The surface relief of emerging PSBs also differs from that in f.c.c. metals. Changes in specimen cross-s...

Deformation and improvement of ductility of the intermetallic compounds Al3 V and Al3(V, Ti)

Abstract: Polycrystalline specimens of the intermetallic compounds Al3V and Al3(V, Ti) containing 1 - 25 at.% Ti with the D022 structure have been deformed under compression temperatures between 20 and 900°C. Al3V shows only a small fracture strain at low temperatures. The deformation is mainly controlled by the motion of 〈110〉-type dislocations without twinning. The activation of 〈110〉 and 〈010〉 slip in addition to 〈110〉 slip contributes to the ductility improvement at high temperatures. Ductility of Al3V has been found to be induced by the replacement of vanadium by titanium. For example, Al3(V0.95Ti0.05) shows 7% compressive fracture strain at room temperature. In Al3(V0.95Ti0.05) deformed at room temperature, not only dislocations but also numerous deformation twins and stacking faults are observed. Therefore, the improvement of ductility of Al3V by the partial replacement of vanadium by titanium arises from a substantial increase in the activity of the ordered twinning which is not operative in the bi...

Lattice distortions induced by carbon in silicon

Abstract: X-ray double-crystal diffractometry has been used to investigate the lattice distortions in silicon crystals containing carbon impurities. Precise lattice-spacing measurements have been carried out with a double-source double-crystal transmission technique. A linear correlation between the absolute value of lattice spacing and the carbon concentration was observed. X-ray double-crystal reflection topography was used to measure residual minute lattice strains also as a function of the carbon atom number density. A similar relationship was found. A comparison of the results of the lattice-spacing measurements and of the topographic investigations indicates that the lattice consists of consecutive layers which are alternately more and less carbon enriched. The observed lattice deformations arise from the substitutional exchange of silicon and carbon atoms.

Glass formation in binary alloy systems: A prediction of the composition range

Abstract: A semi-empirical theory is used to calculate the composition range of binary amorphous alloys. The theory is based on the comparison of the free energies of the amorphous alloy and competing crystalline phases: terminal solid solutions and intermetallic compounds with simple structures. The enthalpy of formation of the solid solution is expressed as a sum of two contributions: a chemical contribution arising from electronic redistribution in forming the alloy, and an elastic contribution arising from the difference in size between solute and solvent atoms. The enthalpy of formation of the amorphous phase has only the chemical contribution. The theory clearly shows the key role that atomic size mismatch plays in determining the glass-forming concentration range, which is successfully computed for an illustrative sample of binary alloy systems. A connection of our treatment with the work of other authors is also provided. © 1988 Taylor & Francis Group, LLC.