P. B. Hirsch

ELECTRON DIFFRACTION BASED TECHNIQUES IN SCANNING ELECTRON MICROSCOPY OF BULK MATERIALS

Abstract The three scanning electron microscope diffraction based techniques of electron channelling patterns (ECPs), electron channelling constrast imaging (ECCI), and electron backscatter diffraction (EBSD) are reviewed. The dynamical diffraction theory is used to describe the physics of electron channelling, and hence the constrast observed in ECPs (and EBSD) and ECCI images of dislocations. Models for calculating channelling contrast are described and their limitations discussed. The practicalities of the experimental methods, including detector-specimen configurations, spatial resolution and sensitivities are given. Examples are given of the use of ECCI for imaging and characterising lattice defects, both individually and in groups, in semiconductor heterostructures and fatigued metals. Applications of the EBSD technique to orientation determination, phase identification and strain measurement are given and compared with use of ECPs. It is concluded that these techniques make the SEM a powerful instrument for characterising the local crystallography of bulk materials at the mesoscopic scale.

The brittle-ductile transition in silicon

Experimental and theoretical studies of the brittle-ductile transition (BDT) of precracked single crystals of silicon are discussed. For a given strain-rate the temperature T c at which the BDT occ...

A new theory of the anomalous yield stress in l12 alloys

Abstract A new theory for the yield stress anomaly in L12 alloys for slip on (111) is developed and applied to Ni3Al. Following Paidar, Pope and Vitek (PPV theory), it is assumed that the superpartial screws cross-slip from (111) to (010) in steps of b/2 (where b is the magnitude of the Burgers vector), but that the jogs created are highly mobile. Contrary to PPV, this leads to the formation of long cross-slipped screw segments. A second cross-slip step by the leading superpartial leads to the formation of strong edge dipole barriers at the ends of the cross-slipped superdislocations. These barriers can be unlocked by the movement of edge character superkinks joining adjacent cross-slipped screw segments, by a thermally activated mechanism which has a large athermal component. Before unlocking occurs the screws continue to cross-slip forming Kear-Wilsdorf (KW) type locks. These latter can also be unlocked by a similar mechanism, controlled by a similar athermal stress, but with a larger activation energy....

Some comments on the interpretation of the ‘kikuchi-like reflection patterns’ observed by scanning electron microscopy

Abstract Interesting observations of bands of contrast on scanning electron micrographs of bulk single-crystal specimens reported by Coates (1967) are interpreted in terms of anomalous absorption effects similar to those discussed earlier for x-ray emission from thin foils by Hirsch et at. (1962). It is shown that the bands may be considered as ‘inverse’ channeling patterns. Some possible consequences of the effect are discussed.

The brittle-ductile transition in silicon. II. Interpretation

A dynamic crack tip shielding model has been developed to describe the brittle-ductile transition (BDT) of precracked crystals in constant strain-rate tests. Dislocations are emitted from a discrete number of sources at or near the crack tip. At the BDT the dislocations are emitted and move sufficiently rapidly to shield the most vulnerable parts of the crack, furthest away from the sources, such that the local stress intensity factor remains below KIc for values of the applied stress intensity factor K above KIc. Computer simulations of the dynamics of dislocation generation from the crack tip sources, assuming mode III loading, suggest that a sharp transition as observed in silicon is predicted only if generation starts at K ≡ K0 ≈ KIc, but then continues at K ≡ KN ≪ KIc. Dislocation etch pit studies reported by Samuels & Roberts (Proc. R. Soc. Lond. A 421, 1─23 (1989)) (hereafter called I) confirm that generation begins at K0 ≈ KIc. It is suggested that K0 corresponds to the value of K at which a crack tip source is nucleated by movement of an existing dislocation in the crystal to the crack tip. The model accounts quantitatively for the strain-rate dependence of the transition temperature Tc reported in I, and predicts a dependence of Tc on dislocation density, in qualitative agreement with (unpublished) experiments. Calcluations of the strees field around the crack tip of a semicircular precrack, suggest that the ends of the half loops emitted by crack tip sources undergo multiple cross slip to follow the crack profile. The predicted dislocation configurations agree with etch pit observations reported in I.

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.

A dynamical theory for the contrast of perfect and imperfect crystals in the scanning electron microscope using backscattered electrons

Abstract A many-beam dynamical theory, which apporoximately takes into account multiple inelastic scvattering, has been formulated and used to calculate the intensity of electrons backscattered from perfect and imperfect crystals. The contrast of channelling pattern lines is discussed, and the occurrence of ‘missing’ lines is explained. the backscattered intensity due to an inclined stacking fault is calculated. The image consists of damped fringes of periodicity ζ g ; the nature of the first fringe depends on the sign of g . R and no contrast occurs for integral values of g . R. Similar calculations have been made for dislocation. Reversing the sign of g . b reverses the image contrast for dislocations near the surface, and the usual TEM invisibility criteria hold, namely invisibility for g . b = g . b ∧ u = 0. The experimental conditions necessary for the imaging of defects are discussed. Imaging defects in solid specimens should be possible using cold field emission electron sources.

The Bauschinger effect, work-hardening and recovery in dispersion-hardened copper crystals

Abstract Single crystals of copper containing dispersions of small Al2O3 particles have been deformed in tension and subsequently in compression at 77°K and the nature of the stress-strain curves and the dislocation structure have been investigated. As predicted, a large Bauschinger effect is observed, but this is substantially reduced by annealing at 295°K prior to reverse straining, and effectively disappears after an anneal at 423°K. The number of Orowan loops produced during the tensile deformation is calculated from the magnitude of the Bauschinger effect, and from the amount of recovery in tension. These analyses suggest that at 77°K the number of Orowan loops around particles increases with increasing strain, reaching a limit of ∼3–5 loops after a few percent strain, further dislocation-particle interactions producing primary prismatic loops by cross-slip. The effect of these processes on the flow stress is calculated and Orowan loops are found to contribute substantially to the work-hardening, par...

The strain rate sensitivity of the flow stress and the mechanism of deformation of single crystals of Ni3(Al Hf)B

Abstract The strain rate sensitivity (SRS) β = δτ/δ (In σ) of the flow stress τ, has been measured for crystals of Ni3(Al, Hf)B over a range of temperatures T in the yield stress anomaly up to 500 K, and as a function of strain E and of crystal orientation. β obeys a Cottrell-Stokes low when plotted against τ - τy, where τy, is the yield stress at 0·01% strain. The slopes are about 1%, decrease with increasing T and are approximately independent of orientation. The results show that the yield stress and work-hardening rates (WHRs) are controlled by different mechanisms. The flow stress τ=τy + τh, where τh is due to work hardening. τy is a reversible function of T, but independent of pre-strain ∊ and σ τh is a function of ∊, T and σ; it controls the SRS of τ. At yield, both edge and screw dislocations propagate on (111), the latter via lateral glide of edge character superkinks which bypass screws locked by cross-slip on to (010), allowing source operation and slip lines to be formed rapidly. Work hardenin...

Indentation plasticity and polarity of hardness on {111} faces of GaAs

Abstract Hardness measurements have been carried out as a function of temperature on {111} faces of n- and p-type GaAs. The plastic zone has been studied by observations of slip-line patterns on the surface and dislocation etch pit patterns in sections at different depths from the indentation surface. The nature of the plastic zone, the types of cracks observed, the recovery slip after removal of the load and the polarity in hardness have been explained in detail in terms of slip geometry, sense and type of slip expected, dislocation interactions and the known differences in velocities of As(g) and Ga(g) dislocations.