Showing papers in "Philosophical Magazine in 1975"

States in the gap and recombination in amorphous semiconductors

Abstract: The paper examines states in the gap in amorphous silicon and chalcogenides and their effect on photoconductivity, luminescence and drift mobility. It is supposed that carriers in an ‘ideal’ glassy semiconductor without defects would move by hopping at the band edge at low temperatures and by excitation to a mobility edge at high temperatures, and that the carriers do not form polarons; the results of Spear and co-workers (e.g. Spear 1974 a) for glow-discharge-deposited silicon and of Nagels, Callearts and Denayer (1974) for quenched As2Te3 containing silicon are considered. The effectively zero value of the Hall coefficient in the hopping regime is discussed. States in the gap are supposed to be due to dangling bonds which may form pairs at divacancies; if the concentration is high, these may have a predominating effect on the conductivity and in this case polaron-type hopping could occur, both for chalcogenides and for silicon. For the chalcogenides (in contrast to silicon), it is proposed, ada...

Strain localization in cyclic deformation of copper single crystals

Abstract: The localization of plastic strain into macroscopic groups of persistent slip bands has been determined on copper single crystals strain-cycled into saturation. The macroscopic bands traverse the whole cross section and undergo complete reversibility of plastic strain with load reversibility. Although overall, surface slip steps form in proportion to the applied plastic strain, individual steps are not always completely reversed, leading to the rapid formation of a notch-peak topography within the bands. The dislocation structure of the persistent slip bands was determined, permitting a critical assessment of the various mechanisms proposed for saturation in low-strain cyclic deformation. Using existing ideas, an adequate model of saturation is based upon the cooperative movement of primary links between the persistent slip-band walls, but impeded in their motion by point-defect clusters and small dislocation debris.

The brittle-to-ductile transition in pre-cleaved silicon single crystals

Abstract: A series of fracture experiments were carried out at various strain-rates on pre-cracked silicon single crystals between – 196° and 1000°C. The surface energy for cleavage was determined from many tests to be 2500 erg/cm2. A transition from pure cleavage to general yielding at the crack-tip was found to occur over several degrees centigrade. The brittle-to-ductile transition was rate dependent and obeyed an activation energy close to that for thermally-activated dislocation glide. A mechanism based on crack-tip blunting through dislocation nucleation and glide was developed to explain the abruptness of the brittle-to-ductile transition. The crack-tip dislocation arrangements were analysed by Lang X-ray topography.

The role of charge density waves in structural transformations of 1T TaS2

Abstract: Electron and X-ray diffraction studies have identified three metastable phases in 1T TaS2. Extra reflexions are interpreted as arising from charge density waves coupled to periodic distortions modulating a trigonal lattice. These waves are incommensurate with the matrix in 1T1 and 1T2, but form a commensurate super-lattice in 1T3. Within 1T2, the temperature dependence of the wave vector is correlated with a change in the cross-section of the Fermi surface, while the diffuse scattering which accompanies the discrete reflexions in 1T1 is discussed as an image of this surface in the phonon spectrum. Changes in the stacking of distortions and in their amplitude are also reported.

The structures of the β-cristobalite phases of SiO2 and AlPO4

Abstract: The crystal structures of the ‘cristobalite’ phases of SiO4 and AlPO4 have been determined from X-ray data collected at high temperatures. A model is suggested which gives a much better fit to the data than previously published structures. In this model, the 16 oxygen atoms of the unit cell are statistically distributed over the 96 positions (h) of the space group Fd3m. This averaged structure is interpreted as comprising domains of ‘ideal’ cristobalite (space group 142d) joined together in six different orientations as a kind of micro-twinning. In this way the structure retains a short-range order similar to low cristobalite, but loses part of the long-range order of the oxygen atoms. From the results of least-squares refinements at several temperatures, a static disordering is calculated, equal to (U x 2 )1/2=0·18 A for the silicon atoms. The β-cristobalite phase of AlPO4 is similarly disordered, with a short-range structure isomorphous with BPO4.

The Orowan mechanism in anisotropic crystals

Abstract: The static equilibrium configurations of a dislocation bypassing a periodic row of impenetrable circular obstacles were obtained for various crystals by means of a self-stress method wherein the elastic anisotropy of the crystal and the dislocation self-interaction could be taken into account. A correlation was developed from the results which related the Orowan stress values to the obstacle size and spacing. This correlation demands two parameters to account for the anisotropy, and these appear as a suitably defined anisotropic shear modulus and Poisson's ratio. The self-interactions are taken into account by a single logarithmic parameter which is the harmonic mean of the obstacle size and spacing, and is independent of anisotropy. The shapes of the bowing dislocation loops are strongly influenced by the anisotropy and interactions. The combined effects on shape can bo simply described in the line-tension framework, using the de Wit—Koehler solutions. In particular, the swept areas and overall ...

Inelastic scattering of 80 keV electrons in amorphous carbon

Abstract: The cross-section for inelastic scattering of 80 keV electrons in thin films of evaporated carbon has been measured as a function of energy loss (from 10 to 600 eV) and scattering angle (up to 0·1 rad). The onergy-loss spectrum shows a broad peak around 24 eV, believed to arise mainly from plasmon oscillation of valence electrons. Losses between 50 and 280 eV are principally due to single interband transitions of the valence electrons, their intensity being proportional to (energy loss)−r , with r in the range 4 to 4·5. Their angular distribution shows a broad peak within the range 20—50 mrad (dependent on the energy loss) which can be explained using oither a wave-mechanical or a ballistic model. The cross-section for K-shell excitation (energy loss > 285 eV) was measured as a function of scattering angle; the results appear to be in good agreement with Bethe theory. Implications of inelastic scattering in transmission electron microscopy of carbon and organic materials are discussed with refore...

Surface segregation and its relation to grain boundary segregation

Abstract: Equilibrium surface segregation concentrations have been measured for iron-tin alloys over the temperature range 500° to 850°C using Auger electron spectroscopy. The results are compared with the grain boundary segregation measurements reported earlier for these alloys, over the same temperature range, and also with the surface and grain boundary segregation data deduced from surface and interfacial energy measurements at 1420°C (Seah and Hondros 1973). The observations are all fully compatible with the theoretical predictions which incorporate the appropriate entropy terms. At low temperatures, in dilute solutions, it is found that the surface enrichment is approximately 130 times that at the grain boundary, whereas at 1420°C the ratio is only six. This difference, which will depend on the particular system considered, indicates that careful correlation experiments are required if surface segregation is to be used as a direct guide to grain boundary segregation. A second practical difference is ...

The stress-induced point defect-dislocation interaction and its relevance to irradiation creep

Abstract: The general interaction energy between an applied stress and a misfitting inhomogeneity is presented and used to deduce the accurate elastic interaction between edge dislocations and point defects in a body subjected to uniaxial tension. It is shown that the external stress does, as conjectured by Heald and Speight (1974), cause a preferential drift of interstitials and vacancies to dislocations with particular orientations to the external stress axis. Moreover, for a physically plausible range of the inhomogeneity representation of the point defects the particular preferences found are consistent with those necessary to validate the mechanism of irradiation creep proposed by Heald and Speight.

High-confidence measurement of solid/liquid surface energy in a pure material

Abstract: A new method for measuring solid/liquid surface energies, with a total systematic and random error of well under 10%, is described. The surface energies are derived from measurements of grain-boundary grooves in solid/liquid interfaces which are maintained in shallow temperature gradients. The gradients are established by an axial heater wire in a cylindrical specimen chamber. Applying the method to highly-purified succinonitrile, a solid/liquid surface energy of 8·94±0·5 erg/cm2 was determined. This corresponds to 37% of the heat of fusion per surface molecule.

Creep behaviour in the superplastic Pb–62% Sn eutectic

Abstract: The creep behaviour of the superplastic Pb-62% Sn eutectic was investigated for grain sizes from 5·8 to 14·5 μm and at temperatures in the range from 336 to 422 K. The results showed a sigmoidal relationship between strain rate and stress. At intermediate strain rates (∼ 10−5–10−2 sec−1), the stress exponent was ∼1·65, the exponent of the inverse grain size was ∼2·3, and the activation energy was similar to the value anticipated for grain boundary diffusion. At very low strain rates (≲10−5 sec−1), the stress exponent was ∼3·0, the exponent of the inverse grain size was ∼2·3, and the activation energy was similar to the value anticipated for lattice self-diffusion. The results are not entirely consistent with either of the two major theories of superplasticity, but suggest instead the sequential operation of two different deformation processes.

Non-parallel dissociation of dislocations in thin foils

Abstract: The equilibrium shape of dissociated dislocations in thin foils of Cu-10 at.% Al is investigated by weak-beam electron microscopy. It is found that dislocations assume a truncated triangular shape caused principally by the reduction in line energy when Shockley partials rotate towards screw character. The effects of interaction image stresses and surface slip steps are generally small, but the former may be important in the case of spontaneous cross-slip of a dislocation at a surface.

Interfacial dislocation networks around γ′ precipitates in nickel-base alloys

Abstract: The three-dimensional dislocation network covering the γ–γ′ interface in a nickel-base superalloy was observed and identified by transmission electron microscopy Estimates of the lattice misfit yielded about – 0·3% in the alloy considered Assuming all dislocations to be of pure edge character the complete network could be analysed as formed by a/2〈110〉 dislocation loops extending over a tetrakaiUdecahedron: the eight {111} faces are covered with hexagonal dislocation networks, while the six {001} faces exhibit square and octagonal dislocation arrangements resulting from the interaction of dislocations with orthogonal Burgers vectors The importance of interfacial dislocation networks and the role of the lattice misfit in oriented γ′ coalescence during creep are pointed out

The influence of the interatomic force law and of kinks on the propagation of brittle cracks

Abstract: Cracks in brittle crystals can be lattice-trapped, as dislocations are by the Peierls barrier. Previous estimates of the range of loads within which a crack will not propagate more than one atomic spacing have varied greatly. The author's earlier computer model is extended to examine the effects of varying the shape of the interatomic force law and of the introduction of kinks in the crack edge. The system studied is a (111) cleavage crack in silicon, with edge either parallel to [OT1], or at a small angle to this direction, so that a series of kinks forms. The boundary conditions, being derived from a general continuum theory solution containing variable terms dependent on the core conditions, are ‘flexible’, allowing free motion of the crack inside the crystallite. The numerical relaxation method allows energy minima or saddle points to be located, thus making possible the calculation of migration activation energies. Several non-central interatomic force laws are employed, all matched to the e...

Dissociation of near-screw dislocations in germanium and silicon

Abstract: The separation of Shookley partial dislocations in Si and Ge has been measured for dislocations at and near screw orientation using the weak-beam method of electron microscopy. The separations appear to fall into two categories. The first category has dissociations which agree with those expected from previous measurements for dislocation orientations above 30°, and the stacking fault between the partials is intrinsic in character. The second category has dissociations which are wider than those in the first category, and the stacking fault is extrinsic in character. A model to explain these observations is proposed.

The preferential trapping of interstitials at dislocations

Abstract: The swelling of metals during irradiation is due to the preferential drift of interstitials to dislocations thus allowing vacancies to condense in excess of interstitials at voids. Previously the dislocation preference for interstitials has been calculated from an isolated dislocation model, here the effect of the competition between neighbouring dislocations as interstitial sinks is assessed. It is found that the effect is appreciable only for high dislocation densities.

A refinement of the structure of vitreous silica

Abstract: The experimental data of Mozzi and Warren have boon re-evaluated. One of the numerical constants in the analytical technique has been altered and a continuous analytical distribution function has boen substituted for the discrete or non-analytical distributions of interatomic distances used by Mozzi and Warren. Thoir overall conclusions are not altered, but new values are obtained for some of the structural parameters. The most probable Si-O-Si bond angle is found to be 152° instead of 144°. This value is in good agreement with the findings of Bell and Dean who were unable to construct a successful model with 144°, but found satisfactory agreement with 153°.

The low-energy absorption edge in 2H-MoS2 and 2H-MoSe2

Abstract: The optical transmission of thick samples of 2H-MoS2 and 2H-MoSe2 has been measured below the A exciton energy for each material. The absorption coefficients have been calculated, and the low absorption starting at 1·1–1·2 eV has been attributed to an indirect d-d transition for both materials. There appears to be considerable d-p valence band overlap giving rise to further higher absorption before the strong A, B excitons, which have been associated with direct transitions from a p-like valence band. An energy band scheme has been sketched on the basis of these interpretations.

The influence of strain rate on ductility in the superplastic Zn–22% Al eutectoid

Abstract: There is an optimum range of strain rate for maximum ductility in the superplastic Zn–22% Al eutectoid, and the elongation at fracture decreases at both low and high strain rates. For a testing temperature of 473 K and a grain size of 2·5 μm, tensile specimens deform to strains in excess of 2000% over almost two orders of magnitude of strain rate.

Luminescence in deformed MgO, CaO and SrO

Abstract: Plastic deformation in the alkaline-earth oxides results in optical absorption bands, the most pronounced of which occur at 5–7 eV in MgO, 4–6 and ∼5–8 eV in CaO, and 4–1 and ∼5–0 eV in SrO. Excitation in these energy regions generates luminescence bands, with peaks at 2–9 (violet), 2–6 (blue), and 2–3 (green) eV in MgO, CaO and SrO, respectively. The temperature- and anisotropy-dependence of the emission spectra gives clear indications that multi-bands are involved. The visible emission provides a convenient means of observing slip systems without artificial decoration techniques. Correlation between emission intensity pattern and dislocation etch-pit density has been demonstrated in MgO. The luminescence effect permits an instantaneous and clear observation of gross imperfections as they are being formed in a solid, either on the surface or in the bulk. Dynamic studies of dislocation interaction can be made. By monitoring the emission intensity as a function of stress and strain, it was found t...

Defect structure of degraded GaAlAs-GaAs double heterojunction lasers

Abstract: Detailed transmission electron microscopy contrast analysis is presented revealing the interstitial nature of the defect networks associated with the active region of a degraded double heterojunction GaAs laser. Three different dislocation networks with Burgers vectors of (a) a/2[011] inclined at 45° to the (001) junction plane, (b) a/2[110] lying in the junction plane and (c) a[001] normal to the junction plane have been observed and investigated. A model is proposed showing how restricted climb of dislocations threading the active region could explain the growth of dislocation networks of the types (a) and (b) and would account for the observed preferred ⟨100⟩ and ⟨110⟩ orientations of darkline defects.

The structures of 3d-transition metals in the liquid state

Abstract: The structures of 3d-transition metals (Ti, V, Cr, Mn, Fe, Co, Ni and Cu) in the liquid state have been systematically examined by X-ray diffraction at temperatures above their melting points. In terms of the usual Fourier analysis, the atomic radial distribution functions were obtained from which interatomic distance and coordination number were estimated.

A computer simulation study of the structures of twin boundaries in body-centred cubic crystals

Abstract: The structures of {112} twin boundaries in body-centred cubic crystals have been studied using computer simulation methods and interatomic potentials representing iron, molybdenum and tungsten. Two distinct structures were found to be stable or metastable in the models used. These were the conventional twin boundary defined by a reflection orientation relation and a twin in which the boundary consisted of a layer of cells which project on the {110} plane as interlocking isosceles triangles. In the case of iron the two boundaries, when fully relaxed, are found to have almost identical energies but for molybdenum and tungsten the reflection boundary is preferred. The twin boundary energies for these two metals are three or four times as large as those for iron. Volume increases are predicted for the reflection twins in all throe metals but for molybdenum a surprising volume decrease arises for the isosceles twin. The results suggest that in some b.c.c. metals both types of boundary may arise in whi...

The anisotropic thermal expansion of boron nitride

Abstract: Interferometric measurements of the linear thermal expansion coefficients αc and αa in the c and a axial directions of well-orientated hexagonal pyrolytic boron nitride are reported for temperatures between approximately 80 and 780 K. The primary data for the direction parallel to the c-crystallographic axis yield smoothed results which are believed to be accurate in an absolute sense to within 3% at 780 K, falling to 5% at 80 K. The corresponding figures for the direction perpendicular to the c-crystallographic axis are 9% at 780 K, passing smoothly through 3% at 230 K to 6% at 80 K. In association with earlier specific heat capacity results and provisional values for the elastic constants c 13 and c 33, a Gruneisen parameter corresponding to the direction parallel to the c-crystallographic axis has been calculated as a function of temperature. This parameter has been applied to the determination of the temperature dependence of averaged reduced vibrational frequencies associated with this axial...

Study of intercrystalline boundaries in terms of the coincidence lattice concept

Abstract: By using the 0-lattice formalism of Bollmann, Burgers vectors of intercrystalline boundary dislocations are defined from the knowledge of two near-coincident cells M1 and M2 of lattices 1 and 2. Internal points belonging to M1 and M2 are taken into account to construct the DSC lattices related to the given boundary. A fully analytic method permits the prediction of the special orientations of good coincidence between the two crystal lattices. They depend on the principal strains of the pure deformation transforming M1 into M2.

The structures of orthorhombic and vitreous arsenic

Abstract: The structure of the orthorhombic crystal modification of arsenic has been determined from an analysis of X-ray powder diffraction data The structure is confirmed as being similar to that of black phosphorus, with space group Bmab and eight atoms per unit cell Each atom is covalently bonded to three neighbours, with two bonds in an ab plane, of length 2·49 A, making an angle of 94·1° and the third bond, of length 2·48 A, at an angle of 98·5° with each of the other two The structure differs significantly from that deduced from the black phosphorus structure by a simple scaling with bond lengths The relationship of the glass structure with the structures of both orthorhombic and rhombohedral (metallic) arsenic has been considered The structure of the vitreous phase is much closer to that of the orthorhombic crystal A good description of the glass structure may be obtained using a quasi-crystalline model based on this structure with some expansion of the interlayer spacing and some additional

Theory of the resistivity and Hall effect in alloys during Guinier-Preston zone formation

Abstract: The theory of the resistivity maximum, based on Bragg scattering of electrons from Guinier-Preston zones, is described and is used to construct semi-phenomenological formulae for the resistivity appropriate to various types of alloy configuration. When the parameters are determined from transport calculations the formulae will be useful in analysing the state of an alloy during ageing. It is shown, for example, that the size of cluster associated with peak resistivity varies with solute concentration and ageing temperature, but this is much less so for spherical zones than for flat zones. The theory is also able to reproduce the behaviour of the Hall coefficient in Al-Zn, which also peaks during ageing. It is argued that other zone-forming alloys may exhibit a maximum, a minimum or neither.

On the structure of non-equilibrium high-angle grain boundaries

Abstract: The incorporation of lattice dislocations into high-angle grain boundaries either with small radii of curvature or absorbing lattice defects is observed by the in situ heating of thin foils in a transmission electron microscope. At a given temperature, the rate of incorporation is higher than for equilibrium boundaries. The observations indicate that the forces acting on the types of boundaries studied have displaced some of the atoms in them from their equilibrium sites.

Kinetics of phase formation in Au—A1 thin films

Abstract: Phase formation was studied in Au-A1 thin films by means of MeV He+ back-scattering and glancing angle X-ray diffraction techniques In the initial stages of compound formetion where both unreacted Au and unreacted A1 layers are present, the phases Au5Al2 and Au2Al are found The end phases of the low-temperature treatments (150–300°C) are AuAl2 or Au4Al in the presence of only unreacted Al or Au, respectively The kinetics of the growth of the Al-rich compounds follow a (time)1/2 dependence The activation energies for the growth of Au2Al and AuAl2 are 10 and 12 eV, respectively

Dislocation structures in deformed single-crystal Ni3(Al, Ti)

Abstract: A transmission electron microscopy investigation of deformed Ni3(Al, Ti) single crystals has shown that, over the temperature range − 107°C to 917°C, there exist five distinct regions, each having a characteristic dislocation structure. No primary cube slip was observed at temperatures below approximately 450°C, the temperature of the peak proof stress. This observation makes untenable any theory which attributes the anomalous, positive dependence of the proof stress to an interaction between primary cube and octahedral slip.