The principles and practice of the weak-beam method of electron microscopy

The weak-beam method of electron microscopy enables the high resolution capabilities of the electron microscope to be used in the study of lattice defects. In this paper, the principles of the method are outlined and the experimental procedures for obtaining weak-beam images are discussed. The experimental diffraction conditions necessary for obtaining quantitative results and the limitations of the method are summarized, and applications of the method to various problems in defect studies are reviewed.     

Observations of lattice defects using the weak-beam technique

The advantages of the weak-beam technique of electron microscopy for the study of small defects and dislocations are illustrated by micrographs taken of small loops in aluminium and Al–Ag alloys, GP zones and θ″ precipitates in Al + 4% Cu, and dislocation networks in Cu + 20% Zn. An estimate of 19·5 mJ m^?2 (erg cm^～2) is made for the stacking-fault energy of Cu–20% Zn from the size of extended nodes and the width of the dissociated dislocations imaged under weak-beam conditions.     

Resolution of dense dislocation networks using the weak-beam technique

The weak-beam technique has been used to investigate dislocation networks, which were too dense to be resolved in bright field where only Moiré-type fringes were found.     

Four-fold dissociations of super-lattice dislocations

The weak-beam technique of electron microscopy (Cockayne, Ray & Whelan, 1969) has been used to image the four components of super-lattice dislocations in a range of iron-aluminium alloys, between 26 and 30 at % aluminium, with D0₃-type long-range order. Values of the first and second nearest neighbour interaction energies have been measured from the observed separations of the components.     

The determination of the geometry and nature of small Frank loops using the weak-beam method

Theoretical and experimental investigations have been carried out to determine under which conditions weak-beam images can give useful information on the geometry, size and nature of small Frank loops. Suitable experimental conditions for obtaining such information were deduced from computed weak-beam images of Frank loops under various selected loop and foil orientations and diffraction vectors. Experiments to check these deductions were performed in silicon damaged by irradiation with phosphorus ions. It was found that the geometry and size of loops of diameter 8 nm (80 Å) viewed normal to their habit plane was well defined by weak-beam images taken in {220} reflections lying in the loop plane for which g.b = 0 and g.b × u ≠ 0. By imaging in reflections with g vectors not in the loop plane the enclosed stacking faults were imaged (thus confirming the loops to be Frank loops) and the sense of the Burgers vector (i.e. the loop nature) was determined.     

Transmission electron microscope observations of extended and unextended dislocation nodes in Si and Ge/Si layers using the weak-beam technique

The transmission electron microscope (TEM) weak-beam method was employed in a study of dislocation nodes both in deformed single crystal Si and at the Ge/(lll)Si interface. All intrinsic nodes were observed to be extended, and measurements of their geometry in Si were used to determine the intrinsic stacking-fault energy. However, only approximately half of the extrinsic nodes were extended and this was interpreted in terms of an energy barrier to node extension.     

Evidence of dislocation dissociation in nearly stoichiometric tantalum carbide using the weak-beam technique

The dissociation of dislocations in nearly stoichiometric tantalum carbide has been revealed by the weak-beam technique; this is in agreement with the assumptions of a model of dislocation glide which had been derived for this compound. An order of magnitude of the partial spacing for the screw and the edge dislocation is 2·7 and 5.2 nm respectively, which leads to a stacking-fault energy of about 170 mJ m^?2 (erg cm^?2).     

Image Contrast And Localized Signal Selection Techniques

A survey is made of a number of the localized signal selection methods and related techniques which may be used to improve the electron microscope image contrast from small regions of material and thereby bring the specimen resolution actually achieved somewhat closer to the electron-optical resolution of present-day instruments. Geometrical and stereo methods are discussed, as well as weak-beam and other coherent elastic scattering methods. Localization effects in inelastic scattering and the image contrast in energy loss electrons are examined in greater detail.     

Dislocation networks in tungsten carbide studied by the weak-beam technique

Dislocation networks in tungsten carbide (WC) have been studied in the HVEM. The nodes of the network have been resolved by using the weak-beam technique in the high voltage electron microscope. They consist of parallel partial dislocations, which are concluded to have Burgers vectors of the type b = 1/6 <20<23>.     

Investigation of dislocation geometries in the diamond cubic structure

The weak-beam technique of electron microscopy (Cockayne, Ray & Whelan, 1969) has been applied to the examination of dislocations in germanium. These are shown to be dissociated into partial dislocations with a separation in the edge orientation of 5.5 ± 1·0 nm. A value for the stacking-fault energy of γ = 60 ± 8 mJ m^?2 (erg cm^?2) is deduced from the measured dissociation width as a function of orientation, using anisotropic elasticity theory.     

Dislocation identification and in situ straining in the spinodal Fe30Ni20Mn25Al25 alloy

Dislocations in the spinodal alloy Fe(30)Ni(20)Mn(25)Al(25), which is composed of alternating BCC and B2 (ordered BCC) phases, have been investigated using weak-beam transmission electron microscopy (TEM). The alloy was compressed at room temperature in an as-hot-extruded state to strains of approximately 3% for post-mortem dislocation analysis. Dislocations with a/2<111> Burgers vectors were found to glide in pairs on both {110} and {112} slip planes. TEM in situ straining experiments were also performed on both the as-extruded alloy and an arc-melted alloy. The in situ straining observations confirmed that dislocations were able to pass between both spinodal phases. Partial dislocation separations were relatively wide in the BCC phase and narrow in the B2 phase. Dislocation glide, as opposed to twinning (both of which have been observed in other BCC-based spinodals), was also found to be the only room temperature deformation mechanism.     

The determination of the 1/2<lll> {110} antiphase boundary energy of NiAl

A value for the 1/2 <111> {110} antiphase boundary (APB) energy in stoichiometric NiAl has been obtained by employing the weak-beam technique to resolve the separation of the two 1/2 <111> partial dislocations composing the <111 superdislocation. A separation of 4·5 nm is obtained corresponding to an APB energy of 200 ± 40 mJ m^?2 (erg cm²).     

The application of weak-beam imaging to studies of small dislocational loops

Coupled differential equations for calculating diffracted ands tranmitted intensities from thin crystals have been solved numerically for many beam diffracting conditions. This approach has been used to enable us to study weak-beam dark-field images from small circular edge dislocation loops. The exact displacement field around such loops has been calculated using isotropic elasticity theory. Crystal orientations have been chosen to obtain single systematic rows of low order reflections and loop images have been calculated for different combinations of strong and weak beams. Although emphasis has been placed on investigating the application of weak beam imaging to determine the nature of small loops (diam. < 10 nm) a preliminary study has also been made of g.b = 0 residual images. The calculated images have been compared with experimental weak beam images of small loops in neutron irradiated molybdenum.     

Calculations and observations of the weak-beam contrast of small lattice defects

Dynamical many-beam calculations were performed for the investigation of the diffraction contrast of small lattice defects observed in the electron microscope under weak-beam conditions. A new computational method was developed with which the depth position z_o of the defect and the thickness t of the foil were eliminated from the integration procedure of the differential equations. The contrast figures for dislocation loops which were inclined to the foil plane and for spherical inclusions were calculated for various excitation errors of the weakly excited beam and for various combinations of t and z₀. The dependence of the contrast figures on z₀ (‘depth oscillations’) were studied in detail. The results of the calculations are compared with experimental observations.     

Burgers vector determination in deformed perovskite and post-perovskite of CaIrO3 using thickness fringes in weak-beam dark-field images

The thickness-fringe method [Ishida et al., Philosophical Magazine 42 (1980) 453] for complete determination of the character of a dislocation Burgers vector has been performed in CaIrO₃ perovskite and post-perovskite deformed at high pressures and high temperatures. By selecting several main zone axes and determining the number of terminating thickness fringes at the extremity of a dislocation from a wedge-shaped thin-foil specimen in weak-beam dark-field transmission electron microscope (TEM) images, the Burgers vectors were unambiguously determined. The results demonstrate that [1 0 0] screw and edge dislocations on the (0 1 0) slip plane are dominant in the post-perovskite phase. Curved [1 0 0] and [0 1 0] dislocations and straight 〈1 1 0〉 screw dislocations on a potential (0 0 1) slip plane were identified in the perovskite phase as well as a high density of {1 1 0} twins. Low-angle tilt boundaries consisting of different groups of parallel edge dislocations on the {1 1 0} and (0 0 1) planes indicate diffusion-assisted climb in perovskite at high temperatures. The differences in dislocation microstructures could be due to activations of limited numbers of slip systems for post-perovskite and of a large number of multiple slip systems for perovskite, which may result in the strong crystallographic preferred orientation (CPO) in post-perovskite and the lack of CPO in deformed perovskite.     

Dissociation of basal dislocations in hexagonal barium titanate

Dislocation substructure in hot-pressed hexagonal BaTiO₃ ceramics was analysed by transmission electron microscopy. Two dislocation networks each consisting of dissociated half-partials were determined for the Burgers vectors ( b ) using the g · b  = 0 effective invisibility criteria, and the true directions ( u ) by trace analysis. Each of the networks contains three partial nodes that are in the form: 1/3[010]+1/3[100]+1/3[100]+1/3[100] = 0, where four partials meet at a point and the Burgers vectors are conserved, as analysed by the weak-beam dark field technique. Basal dislocation with b _b = 1/3<110> is dissociated into two prism plane half-partials with b _hp = 1/3<100> by: 1/3<110> → 1/3<010> + 1/3<100>. Dissociation of basal dislocation by a glide mechanism creates a stacking fault when shear occurs along <100> in the c-layer of (000l), where l = 1, 3, 4 and 6, of the (chc)₁(chc)₂ (or (CBC)(ABA)) stacking sequence. The slip system of 1/3<110>(0001) in hexagonal BaTiO₃ has been activated at 1300 °C by hot-pressing under ∼25.8 MPa. Plastic flow contributing to the densification of hexagonal BaTiO₃ ceramics occurs through glide of half-partials in the basal plane by a glide-controlled dislocation glide mechanism. Dislocation motion governed by the Peierls mechanism, where velocity is determined by both correlated and uncorrelated double-kink nucleation on two half-partials, is discussed.     

FLUID MECHANICS APPROACH TO MACHINING AT HIGH SPEEDS: PART II: A POTENTIAL FLOW MODEL

Finite element models of machining at high speeds usually assume that there is a stagnation point at the tool tip as is the norm in the machining community. However, at ultra-high speeds the yield strength of the workpiece is easily exceeded in the material around the tool tip, allowing that material to “flow” and possibly allowing the stagnation point to migrate away from the tool tip. A potential flow solution is used to model the behavior of the material around a sharp tool tip during machining at high speeds. Interestingly, the flow solution predicts that there is a stagnation point on the rake face, not at the tool tip as is usually assumed. Because the stagnation point is not at the tool tip, the flow solution predicts a significant amount of deformation in the workpiece resulting in large residual strains and a possible related temperature rise on the finished surface.     

Fretting corrosion of lubricated tin plated copper alloy contacts: Effect of temperature

The fretting corrosion behaviour of lubricated tin plated copper alloy contacts at ambient and elevated temperatures is addressed in this paper. At 27 °C, lubrication is very effective and the contact resistance remains stable for several thousand fretting cycles whereas at elevated temperatures (155 °C) the performance of lubricated contact is not appreciable. Surface profile and surface roughness confirm that the lubricated contacts have a smoother profile and experience a lesser damage at the contact zone at ambient as well as at elevated temperatures. The mechanism of fretting corrosion of tin plated contacts appears to be similar with and without lubrication at all the temperatures studied. The difference in performance of the lubricated contacts at ambient and elevated temperatures is due to the faster wear rate of tin coating at elevated temperatures. Oxidation of the contact zone of the lubricated contacts is prevented at all temperatures studied. The study concludes that lubrication is effective in improving the life of the tin plated copper alloy contacts under fretting conditions at ambient temperatures whereas at elevated temperatures lubrication provides only a marginal improvement in performance. The decrease in performance of lubricated tin plated contacts at elevated temperatures is due to the higher wear rate of tin coating and not due to evaporation of the lubricant.     

Effect of γ irradiation on the scintillation and optical properties of lead tungstate crystals

The radiation hardness of a test batch of lead tungstate crystals grown by a new technology at the Bogoroditsk Technochemical Plant for the PANDA experiment has been measured. The optical properties of the crystals have been investigated at temperatures ranging from +20 to ?20°C under irradiation with a ¹³⁷Cs radionuclide source. The light yield in the crystal is seen to considerably increase with a decrease in its temperature. In addition, the loss of the crystal transparency under irradiation at low temperatures is higher than under irradiation at room temperature. As a result, at a fixed dose rate, the signal from the crystal at a negative temperature may be considerably greater than the signal at room temperature even if the accumulated dose is high.     

An oscillator with low phase noise based on active resonator using metamaterial in K-band

An oscillator(OSC)with a metamaterial resonator based on high-Q is designed to improve the phase noise in Kband.The proposed metamaterial resonator is a lattice structure resonator(LSR)that is designed to be high-Q by a strong coupling of E-field at the resonance frequency.Thus the output of OSC is about 12.5dBm at the f0.The phase noise is 109.477dBc/Hz at 100kHz offset frequency.