Showing papers in "Philosophical Magazine in 1990"

Deformation of polysynthetically twinned crystals of TiAl with a nearly stoichiometric composition

Abstract: Polysynthetically twinned crystals of TiAl with a nearly stoichiometric composition have been grown and deformed in compression at room temperature. The yield stress and deformation behaviour depend strongly on the angle between the twin boundaries and the compression axis rather than on the crystallographic orientation of the compression axis. The yield stress is high when compression is perpendicular or parallel to the twin boundaries, and is generally very low for specimens where the twin boundaries are at an intermediate angle to the compression axis. The ratio of the highest to the lowest values of yield stress is almost 8:1. This large difference in yield stress has been found to be related to the difference in the deformation mode; for compression perpendicular or parallel to the twin boundaries, shear deformation always occurs across them while, for compression at an intermediate angle, shear deformation is parallel to the boundaries. The former mode of deformation is much harder than the...

TEM in situ deformation study of the interaction of lattice dislocations with grain boundaries in metals

Abstract: The passage of dislocations across grain boundaries in metals has been studied by using the in situ TEM deformation technique. A detailed analysis of the interaction of glissile matrix dislocations with grain-boundary dislocations has been performed. The results show that the dislocations piled-up at the grain boundary can: (1) be transferred directly through the grain boundary into the adjoining grain; (2) be absorbed and transformed into extrinsic grain-boundary dislocations; (3) be accommodated in the grain boundary, followed by the emission from the grain boundary of a matrix dislocation; and (4) be ejected back into their original grain. To predict which slip system is favourable for slip transfer, three criteria have been considered, namely: (1) the angle between the lines of intersection of the incoming and outgoing slip planes with the grain boundary, this should be as small as possible; (2) the resolved shear stress acting on the possible slip systems in the adjoining grain, this should ...

The energy of an array of dislocations: Implications for strain relaxation in semiconductor heterostructures

Abstract: An exact closed-form formula is given for the energy of an array of dislocations, arranged periodically on the interface between an epitaxial layer and its substrate, when these are modelled as elastically isotropic with the same elastic constants. In the course of the formulation, the exact equivalence of equilibrium theories originating in the work of Frank and van der Merwe and of Matthews and Blakeslee is established. The new formula allows the exact assessment of arrays of dislocations in equilibrium, for layers thicker than critical. This demonstrates that previous approximations may be seriously in error.

A computer simulation study of the defect structure of calcia-stabilized zirconia

Abstract: The defect structure of calcia-stabilized zirconia, a topic of long-standing controversy, has been examined by atomistic computer simulation techniques. Defect association energies for an anion vacancy and a dopant calcium ion at both nearest-neighbour and next-nearest-neighbour (NNN) positions have been determined and suggest the preferential siting of oxygen vacancies in the NNN position with respect to the dopant cation, at low dopant concentrations. A structural explanation for this is proposed. Our calculations also suggest Schottky intrinsic disorder in cubic zirconia which may be atypical compared with other fluorite-structured oxides; we advance an explanation for this in terms of lattice relaxation. Excellent agreement between experimental and calculated values shows the reliability and potential of computer simulation techniques. Binding energies of various types of defect cluster were calculated to check their relative stabilities. Also the migration energy of the oxygen vacancy was ca...

Deformation mechanisms in the intermetallic compound TiAl

Abstract: Samples of a polycrystalline Ti-52at.°Al alloy have been deformed in compression at room temperature and 600°C to strains of ≈3°. The deformation microstructures have been characterized using transmission electron microscopy. It is found that, at room temperature, glide of dislocations with b = <101] has occurred, with some contribution from twinning. Dislocations with b=1/2<110] make up a negligible fraction of the dislocation density, and it is argued that these defects are in essence sessile at room temperature. However, in samples deformed at 600°C, the dislocation population is dominated by those with b=1/2<110], whereas those with b = <101] are most often involved in Kear-Wilsdorf configurations. These various results, including the line directions of the dislocations, are interpreted on the basis of the effect of covalent bonding on the anisotropy of the Peierls stresses (following the work of Greenberg, Anisimov, Gornostirev and Taluts) and therefore dislocation mobilities in this compoun...

Correlation between the energy and structure of grain boundaries in b.c.c. metals. II. Symmetrical tilt boundaries

Abstract: The correlation between the structure and zero-temperature energy of symmetrical tilt grain boundaries (STGBs) in b.c.c. metals is investigated using a many-body potential of the Finnis-Sinclair type for Mo and Johnson's pair potential spline-fitted for α-Fe. As in free surfaces, the misorientation phase space associated with these simple planar defects consists of only two macroscopic degrees of freedom, namely those defining the grain-boundary (GB) plane normal. In a novel approach, the two-dimensional phase space is investigated in terms of a stereographic triangle and not in terms of the usual three parameters associated with the boundary misorientation. A comparison with similar calculations for free surfaces demonstrates the importance of the translational (microscopic) degrees of freedom in grain boundaries, while the comparison with STGBs in f.c.c. metals elucidates the important role played by the GB plane.

The influence of temperature and alloying additions on the mechanisms of plastic deformation of Ti3Al

Abstract: Samples of polycrystalline Ti3Al and Ti3Al containing 4 at.°Nb in solution (substituted for Ti) have been deformed at room temperature and at 650°C and examined subsequently by transmission electron microscopy in order to determine the influence of temperature and alloy content on the relative activity of the various slip systems. It has been shown that at room temperature in Ti3Al the deformation mechanisms involve glide of coupled pairs of dislocations with b=1/6 on {1010} and, to a rather limited degree, glide of pairs of dislocations with b=1/6 on {112 1}, with the extent of the particular slip system which operates varying between grains of different orientations. At 650°C, glide of these two types of slip system occurs, but the morphology of slip of the dislocations with b =1/6 changes at the elevated temperature. Furthermore, evidence for the climb of dislocations has been obtained, which may produce strain at elevated temperatures. Only limited activity of the <11...

Computer simulation of Zener pinning

Abstract: In this paper we describe analytical and computer models of the inhibition of grain growth in two and three dimensions. In two dimensions (thin films), all the models agree that the ratio of the stagnant grain size R to the particle size r is proportional to f −½, where f is the volume fraction of particles. In three dimensions the analytical models are only valid when f 1% gives the result R/r oc f −1/3. Experimental data from the literature support these conclusions and there is some evidence that there is a discontinuity in R/r at f≈1%.

Heterogeneous nucleation of In particles embedded in an AI matrix

Abstract: A hypomonotectic alloy of Al-7 wt% In has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. The rapidly solidified hypomonotectic Al-...

Theoretical and experimental descriptions of grain boundaries in rhombohedral α-Al2O3

Abstract: Tables are given of all coincidence orientations with multiplicity Σ ≤ 36 for rhombohedral lattices with axial ratios in the range of corundum type structures (2.696 < c/a < 2-765). Measurements of the relative orientation of 133 pairs of neighbouring grains in sintered a-alumina showed that near-coincidence boundaries (14 cases) and one-dimensional coincidence boundaries (17 cases) occurred more frequently than would be the case for randomly distributed orientations and that many of these special boundaries contained periodic arrays of grain boundary dislocations. Their Burgers vectors have been determined for a rhombohedral twin boundary in order to decide which one among three possible coincidence descriptions best represents the boundary structure.

Heavy-ion irradiation tracks in zircon

Abstract: Heavy-ion irradiation (14 MeVu−1 Pb ions) of zircon crystals gives rise to linear latent tracks of 80 A diameter and length 140 μm. Direct observation of the track core, by high-voltage high-resolution electron microscopy at atomic resolution, reveals a core having roughly circular cross-section, with some facetting of the core/matrix interface on {101} planes of zircon. The core diameter appears quite uniform. Conventional transmission electron microscopy (bright- and dark-field imaging) reveals an elastic strain field extending for a short distance into the zircon matrix. This appears to drop off more rapidly with distance, say 1/R2, than do dislocation strain fields (∼ 1/R). Analysis of the various contrast mechanisms yields the result that the core is essentially amorphous. Our observations confirm directly the conclusions of Fleischer, Price and Walker, based on track etching and electrical conductivity measurements, that the irradiation damage is confined to a 50–100 A core region of atomic...

High-resolution electron microscopy of neutron-irradiation-induced dislocations in SiC

Abstract: Neutron-irradiation-induced dislocations in β- and α-silicon carbide (SiC) were observed using a high-resolution electron microscope. In β-SiC, small planar defects about 20 nm in diameter lying on {111} planes were determined as interstitial Frank loops, having a Burgers vector b=⅓〈111〉. On the basis of image simulation by the multislice method, it was determined that the loops consist of an insertion of a single Si-C layer into {111} stacking to create two rotated layers. These loops were induced by heavy neutron irradiation doses of above approximately 5 × 1026 neutrons m−2 (E>0.1 MeV) in a fast reactor. Defect nuclei a few nanometres in diameter in hexagonal α-SiC were induced by lower doses in a thermal reactor (2 × 1025 neutrons m−2) (E > 0.1 MeV). They are on the (0001) basal plane and have a Burgers vector b=⅙[0001].

Atomic structure of dislocations in silicon, germanium and diamond

Abstract: Atomic structures of perfect (90° and 60°) and partial (90°) dislocations including total and core energies have been calculated using four different interatomic potentials in silicon, germanium and diamond. The core energies of dislocations do not scale with the magnitudes of Burgers vectors associated with them. However, the energies of dislocations in the elastic region are found to be directly proportional to the square of the Burgers vector, as predicted by the theory of elasticity. The Stillinger-Weber (SW) and TersofT(T) potentials are more suitable for calculating the core structures with large distortions including the dangling bonds such as found in 60° dislocations. In the absence of dangling bonds, the core energies are highest for Keating (K) potentials, followed by T, SW and Baraff-Kane-Schluter (B) potentials (Si). The core energies calculated using B potentials are considerably lower as a result of much lower values for the bond-bending parameter. As an example, the core energies ...

Considerations of grain orientation and work hardening on short-fatigue-crack modelling

Abstract: Methods which consider the effect of grain orientation and work hardening on short-fatigue-crack growth are examined. Fatigue cracks are assumed to form in the most favourably oriented grains on the surface of the specimen and propagate through less well oriented grains. A method of deriving the sequence of orientation factors as the crack front traverses an increasing number of grains is presented. Grain boundaries act as barriers to plastic flow in the zone ahead of the crack tip. This has the effect of hindering dislocation movement in the plastic zone, which can be expressed in terms of an increase in the frictional stress. A method of calculating this work-hardening rate is proposed. The condition for transition from short to long fatigue cracks is established.

On the origin of the intrinsic thermoelasticity associated with a single-interface transformation in Cu-Zn-Al shape-memory alloys

Abstract: Thermoelasticity is one of the important characteristics of the martensitic transformation in shape-memory alloys, that is the need for continuous undercooling (overheating) in order to force the transformation (reversion) to proceed. In this work the thermoelastic behaviour of a single-interface L21-to-18R transformation has been studied. It was found that the slope of curves of interface position against temperature varied from 0.05 to 0.004 K μm−1 depending on the thermal treatment to which the sample had been subjected. The smallest hysteresis width in a carefully polished material was found to be about 0.06 K. A simple model suggests that the thermoelasticity is ultimately related to the interaction of the martensite with pre-existent dislocations in the matrix.

Plastic deformation of GaAs single crystals as a function of electronic doping I: Medium temperatures (150–650°C)

Abstract: Plastic deformation of GaAs single crystals has been studied in the temperature range 20-650°C as a function of electronic doping, using different deformation techniques. In this paper, experiments conducted between 150°C and 650°C, using suitable pre-deformation conditions, are reported. The effects of electronic doping on macroscopic plasticity have been found to be consistent with dislocation velocity measurements for temperatures larger than 200°C. Activation Gibbs free energies were derived from activation volume measurements and found to be in reasonable agreement with activation energies of dislocation velocities. Observations of deformation substructures by transmission electron microscopy show that screw dislocations control the deformation at the lower temperatures.

Quasi-static indentation cracking of thermally tempered soda-lime glass with spherical and Vickers indenters

Abstract: An experimental study of the indentation cracking behaviour of thermally tempered soda-lime glass flats is described The indenters were steel and tungsten carbide spheres of radii in the range 0·5 to 2·5 mm and a Vickers diamond pyramid They were loaded normally on to the flats and particular attention was paid to the evolution (ie initiation and growth) of the Hertzian cone cracks formed under the spherical indenters and to the median cracks which were generated under the Vickers indenter With the spherical indenters, the Hertzian ring‐cone cracks have been shown to initiate most frequently at the circle of contact between the indenter and the specimen surface Moreover, with increasing indenter load, the skirt of the cone crack has been found to extend almost parallel to the indented surface; this is shown to be consistent with the principal stress trajectories within the tempered glass The implication of such cone cracks for the strength degradation of the tempered glass is discussed Wi

Self-diffusion in body-centred cubic metals: Analysis of experimental data

Abstract: The self-diffusion coefficients of b.c.c. metals are analysed assuming a two-defect model and different one-defect models. The two-exponential fits reveal large error limits for the diffusion parameters. Only for V, Nb and Na are highly accurate monovacancy diffusion energies evaluated. The analysis shows that for the refractory metals and for the alkaline metals the competition of two mechanisms is more probable than a strong temperature dependence of the monovacancy diffusion parameters.

Plastic flow of B2-type CoTi single crystals

Abstract: B2-type CoTi single crystals show a positive temperature dependence of the yield stress at intermediate temperatures, and a negative temperature dependence at low and high temperatures. High yield stress is commonly accompanied by a high work-hardening rate. At temperatures below the peak temperature, single crystals with an orientation close to [001] show marked serrations in the stress-strain curves and corresponding kink bands accompanied with slip. Also, the yield stress of CoTi single crystals is almost independent of strain rate at low temperatures and positively dependent on the strain rate at intermediate and high temperatures. The operative slip system is determined to be {110}〈001〉 in all orientations tested at temperatures below the peak temperature. The CRSS on (T10)[001] is independent of the orientation at low temperatures but is very dependent on the orientation at intermediate temperatures. A possible explanation for the positive temperature dependence of the yield stress based on...

60° dislocations in (001) GaAs/Si interfaces

Abstract: The geometry of 60° dislocations at the (001) GaAs/Si. heterojunction is discussed considering transmission electron microscopy images of plan-view samples. The GaAs examined was grown by molecular beam epitaxy on to a Si substrate, which had been polished to be 4° off the exact (001) plane, towards the [110] direction. Both 60° and pure edge dislocations may be present at the interface to accommodate the lattice misfit. The Burgers vectors of all the dislocations involved are (a/2)(110). The 60° dislocations interact with the network of orthogonal edge dislocations which is present at the interface and cause displacements of the edge dislocations. Because of the tilt of the heterojunction away from the exact 〈001〉 plane, the density of these 60° dislocations along [110] direction is different from that along ]110] direction. The changes in geometry when like 60° dislocations are dissociated is described.

Dislocation mobility for non-basal glide in ice measured by in situ X-ray topography

Abstract: Glide motion of edge dislocations in non-basal planes in ice has been observed under a compressive stress in the 〈1100〉 direction by X-ray topography using a high-power X-ray generator. From the observations, the dislocation velocities were determined quantitatively as a function of temperature in the range 223 to 263 K and stress in the range 0·1 to 1·4 MPa. The velocities obtained are proportional to an effective shear stress and are approximately five times larger than those for basal glide but with approximately the same activation energy of 0·6 eV.

On the transition between the C and B kinetic regimes for grain-boundary diffusion

Abstract: It is shown that, in the transitional region between the B and C kinetic regimes for grain-boundary diffusion, the product of the grain-boundary width δ, the segregation factor K and the grain-boundary diffusion coefficient D b= KδD b), as well as the grain-boundary diffusion coefficient itself, can be estimated. From penetration plots measured at different annealing times in the transitional region (0.01 < α < 10, where α = Kδ/2(Dt)1/2 is the relative grain-boundary width and D is the volume diffusion coefficient) by fitting with solutions in the B and C kinetic regimes, one can obtain the apparent values for P and D b. From the solution of the general problem of grain-boundary diffusion, correcting functions are given for the calculation of the true values of P and D b (and consequently of Kδ). This procedure is illustrated by several experimental examples published in the literature as measurements in the C kinetic regime.

Instability origin of dislocation substructure

Abstract: The formation of a dislocation substructure in high-temperature deformation is treated as a stability problem. A crystal in which dislocations can glide and climb is modelled as an anisotropic viscous medium. The subgrain structure development is interpreted as a deformation-induced instability of internal bending (folding) type first described by Biot. The suggested continuum mechanics model seems to provide a rational explanation of the main observed features of the subgrain structure: misorientation, tendency to regularity and relatively uniform subgrain size.

Direct evidence of dislocation transmission through ∊= 9 grain boundaries in germanium and silicon by in situ high-voltage electron microscopy observations

Abstract: Le microscope electronique a haute tension, utilise dans l'etude in situ de la deformation de bicristaux de silicium et de germanium, a revele que des dislocations traversaient des joints de grains e=9, meme lorsque leurs vecteurs de Burgers n'etaient pas vecteurs de reseau du deuxieme grain. Ces dislocations sont parfaites (b=1/2 ) ou, le plus souvent, partielles de Shockley, entrai←nant des defauts d'empilement lies au joint. Les dislocations peuvent se dissocier dans le joint en dislocations glissiles DSC; les dislocations residuelles peuvent etre deplacees. Les caracteristiques observees de ce phenomene peuvent s'expliquer par un modele base sur des calculs des energies des configurations possibles des dislocations formees lors des etapes successives du processus de transmission

Atomic step and defect structure on surfaces of Si{100} and Si{111} observed by low-energy electron microscopy

Abstract: The Si{100} and Si{111} surfaces are studied by low-energy electron microscopy. Atomic step and terrace structure formed by misorientation of Si wafers is investigated as well as various migration patterns of atomic steps formed during sublimation. Slip traces ending typically at screw dislocations form along ‘110’ directions in the surface and create additional atomic steps. Analysis of migration patterns near slip traces implies that both partial and perfect dislocations (or their equivalent, namely two partials) form on Si {100}. Perfect dislocations are seen on Si{111}. Regions with the (7×7) structure on Si{111}, which contain stacking faults, are imaged. Surface domain structure and domain boundaries are seen on Si{111}. On Si{100} the partial dislocations create two new types of surface domain displaced relative to the two pre-existing (2 × 1) and (1 × 2) domains. The potential for in situ studies of process-induced defects on Si wafers is demonstrated.

Atomic structure of (111) twist grain boundaries in f.c.c. metals

Abstract: In this paper we have studied the atomic structures of (111) twist boundaries and investigated the applicability of the structural unit model which has previously been established for tilt boundaries and (001) twist boundaries by Sutton and Vitek. The calculations were carried out using two different descriptions of interatomic forces. A pair potential for aluminium, for which the calculations were made at constant volume, and a many-body potential for gold, for which the calculations were performed at constant pressure. The atomic structures of all the boundaries studied were found to be very similar for both the descriptions of atomic interactions. This suggests that the principal features of the structure of (111) twist boundaries found in this study are common to all f.c.c. metals. At the same time it supports the conclusion that calculations employing pair potentials are fully capable of revealing the generic features of the structure of grain boundaries in metals. The results obtained here,...

Transmission electron microscopy of dislocations in YBa2Cu3O7−x deformed plastically at high temperatures

Abstract: Dislocation structures in single crystals of YBa2Cu3O7−x with a tetragonal structure, deformed by indentation at 650 and 850°C, have been studied in detail using transmission electron microscopy. The Burgers vectors of the dislocations were determined by standard contrast experiments. At 850°C, perfect dislocations with Burgers vectors (100) were dominant; occasionally 〈110〉 dislocations were observed when two types of 〈100〉 dislocation, that is [100] and [010] dislocations, reacted with each other. At 650°C 〈100〉 dislocations were dissociated into two partial dislocations. Contrast experiments revealed that a 〈100〉 perfect dislocation is dissociated into two 1/2(100) partial dislocations, leaving a stacking fault in between. The stacking-fault energy decreases with decreasing temperature. This is explained by a model in which the stress-induced ordering of oxygen vacancies takes place.

Mechanisms of swelling suppression in cold-worked phosphorous-modified Fe-Ni-Cr alloys

Abstract: Three cold-worked phosphorous-modified Fe-15Ni-13Cr-base alloys were irradiated with simultaneous Fe- and He-ion beams to doses of about lOOdpa at a helium implantation rate of 20at.p.p.m./dpa. The three alloys correspond to compositions that led to increasing densities of a very fine phosphide precipitate. In the case of the alloy with the highest precipitate density, the swelling was suppressed to the greatest extent. The results are interpreted in terms of the theory of cavity swelling, which provides the central concept of a critical radius and critical number of gas atoms required for cavity swelling. The large interfacial area of the needle-shaped phosphide precipitates led to profuse bubble nucleation at the interface. The high density of bubbles slowed the accumulation of gas atoms in individual bubbles and thus delayed the onset of point-defect-driven cavity swelling. After interpreting the present data in terms of these concepts, more general features of cavity swelling reduction by an ...

Chi-phase precipitation in ion-irradiated molybdenum‐rhenium alloys

Abstract: Chi-phase precipitation was observed by transmission-electron microscopy (TEM) in Mo-30at.%Re and Me-27at.%Re specimens that had been irradiated with 1·8 MeV He ions at temperatures from 750°C to 1075°C. The precipitates formed at the rhenium-rich external surface and adopted both parallel and (111) twin orientations with respect to the matrix. Details of precipitate morphology and crystallogaphic orientation are reported.

Strain contrast of coherent precipitates in bright-field images under zone axis incidence

Abstract: It has been proposed that bright-field imaging of coherent spherical precipitates under zone axis incidence would give improved resolution in the strain contrast compared with the weak-beam dark-field imaging. We observed the strain contrast from coherent Co-precipitates in Cu-Co alloys, and simulated the images on the basis of many-beam dynamical electron diffraction, taking into account the elastic anisotropy. Zone axis incidence such as [001] or [001] considerably reduces the effective extinction distance of the transmitted beam, and suppresses the intensity oscillation with foil thickness, in comparison with a conventional two-beam condition. The contrast in the bright-field images is straightforwardly related to the precipitate geometry. Individual precipitates are well resolved in the image when the number density of precipitates is fairly high. It has been demonstrated that the imaging under zone axis incidence is quite useful to understanding of microstructures in phase transformation in ...