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By using a nanoprobe electron beam 4 A in diameter, the [001] nanodiffraction patterns of AlGaAs‐GaAs multiple‐quantum‐well structures have been formed and the epitaxial relationship between AlGaAs and GaAs is confirmed. The intensities of the (200) diffraction disk, monitored by a spot detector, are displayed in two ways: (1) the (200) dark‐field scanning transmission electron microscopy (STEM), which shows the layers of AlGaAs and GaAs in contrast, and (2) the (200) line‐scan profile, which reveals the (200) intensity distribution of a specimen region of uniform thickness. The thickness and the absolute Al concentration of AlGaAs layers are, respectively, determined from the contrast of, and the (200) thickness contour position in, the (200) dark‐field STEM images. The microanalysis on the (200) line‐scan profile is used to find the local Al concentrations in AlGaAs layers and to study the interface boundary between the layers of AlGaAs and GaAs. Diffusion of the Al atoms from the AlGaAs layer into the ...

The oxidation of thin single-crystal (100) and (111) films of copper at pressures of around 10−5 Torr and temperatures of 400 to 700°C has been observed by medium-energy electron diffraction, scanning electron microscopy, scanning and conventional microscopy using diffracted electron beams in the reflection mode, transmission electron microscopy, and transmission electron diffraction. Epitaxed nuclei of oxide are observed to grow into very thin single-crystal plates, using oxygen previously trapped in the copper film. There is considerable diffusion of the copper film. There is considerable diffusion of the copper away from the oxide. Between the oxide crystallites the copper surfaces appear to be unoxidized. A mottled contrast of the diffracted beam images of the copper surface is shown to result from many-beam dynamical diffraction effects.

The electron microscope image intensity of a thin crystal is described as a time average of the image of a crystal perturbed by time-dependent fluctuations corresponding to thermal motion of the atoms or low-energy electronic excitations. For very thin crystals the phase-object approximation indicates that images having atomic resolution may be obtained from the inelastically scattered electrons. It is shown that the use of suitable approximations allows estimates to be made of the contribution of the inelastically scattered electrons to the high-resolution images of thicker crystals. The resolution of images formed by inelastically scattered electrons is not affected by the non-localization of the inelastic scattering process.

Continuous streaks and the displacement of diffraction maxima from the perfect-crystal positions, observed in electron diffraction patterns of magnesium fluorogermanate suggest the existence of planar faults at which the c-axis dimension of the unit cell is contracted by 25%. High-resolution electron microscope images of thin crystals confirm this deduction. It is shown that even in the presence of strong dynamical-diffraction effects, electron diffraction patterns from thin crystals can be interpreted, within well defined limitations, by use of a kinematical theory such as is given in part I [Cowley (1976). Acta Cryst. A32, 83-87]. Using this kinematical theory calculations of diffraction intensity are made for reasonable assumptions of the form of the faults. The effect of the modification of the structure at the fault planes on the peak intensities is shown to be small so that structure analyses based on peak intensities only should give the structure of the unfaulted crystal.

Electron diffraction patterns have been obtained from regions of a thin crystal of partially ordered copper-gold alloy, Cu3Au, which have a diameter of about 15 A and contain an antiphase domain boundary. The superlattice diffraction spots show a characteristic splitting similar to the splitting which appears in all spots, both fundamental and superlattice, when the beam irradiates a region at the edge of a crystal. By observing which of the superlattice spots are split and which are not, it is possible to deduce immediately whether the antiphase domain boundary is of the 'good' type or is one of the 'bad' types or whether more than one boundary is illuminated by the beam. The observations of split spots are in good agreement with the results of calculations made on the basis of kinematic theory. It is shown that these results remain valid in the presence of strong dynamical scattering for small specimen thicknesses.

Ordered and disordered states of potassium ions in (111) tunnels in the structure of cubic KSbO3 have been studied by high-resolution electron microscopy. N-beam calculations for the images of both the ordered and disordered states reproduce well the observed images. The disordered state changes into the ordered state under electron irradiation during the observations. Electron diffraction from the specimens and optical diffraction from the images show diffuse spots due to small domains of the long-range-ordered state, but no other diffuse scattering due to short-range order has been observed.

The REMEDIE system for reflection electron microscopy and electron diffraction at intermediate energies (0.5–20 keV) has been rebuilt with an improved imaging resolution of better than 10 nm, a convenient and versatile system for observation diffraction patterns and provision for specimen preparation and treatment suitable for surface structural studies. The current capabilities of the instrument are illustrated by results obtained from cleaved and annealed silicon (111) surfaces with or without thin deposited silver and gold layers.

Calculations based on n-beam dynamical diffraction theory have shown that the intensities of rings and arcs in diffraction patterns from polycrystalline materials are strongly dependent on the experimental conditions. For arc patterns from BiOCl, calculations confirm a revised formula for the intensities from very thin crystals and indicate dependences on the distributions of orientation, thickness and bending of the crystals which are sufficient to account for the wide deviations of recent experimental results from the predictions of the primary extinction formula, based on the two-beam approximation. Inferences regarding the possible errors in electron diffraction analysis of crystal structures, especially for materials containing heavy atoms, are drawn from calculations relating to the intensities of arc patterns from AgTISe2. It is suggested that n-beam calculations should be made in order to avoid serious error in the refinement stages of a structure analysis.

Electron diffraction rings from MgO and CdO smokes have previously been shown under high resolution to be multiple. More detailed observations of this phenomenon have been made It has been observed that the arcs given by tilting of oriented specimens are divided into several components, which vary in intensity and separation with angle of tilt of the specimen. Spotty rings given by brown CdO (containing excess metal atoms) and some MgO specimens are composed of short streaks forming groups of up to six radiating from the expected position of a single-crystal reflection, and in some cases these streaks are divided into inner and outer components. The theory that the fine structure of the rings arises from refraction at the faces of the regularly shaped particles (cubes) was suggested by Sturkey and Frevel (1945). On the basis of this theory, general expressions have been derived for the deviation of the direction of the diffracted beam owing to refraction at the faces of cubes. Application of these expressions to particular cases has shown complete agreement between the calculated and observed form of the fine structure of the rings, arcs and groups of streaks. Quantitative agreement for the separation of the arc components is obtained by assuming values of inner potential of the order to be expected. The value of the inner potential varies with the reflecting plane from 12 to 16 volts. For the doubled streaks the elongation of the inner component represents a varation of inner potential about this value, arising from excess metal atoms in the lattice. The outer component represents an unexplained value of about 25 volts. Streaks observed on ZnO smoke rings are explained as due to refraction by the long thin spines characteristic of this material. It is shown that refraction will have the effect of broadening diffraction rings, even for irregular particles, and will give rise to line breadth and intensity anomalies in diffraction patterns from specimens with regular crystal habit.

Single-crystal electron diffraction patterns with doubled spots obtained from zinc oxide smoke particles originate from pairs of thin sheets which are commonly seen in electron micrographs of this material joining up the members of a group of four spines. The plane of each sheet is parallel to a (1010)-type lattice plane. The sheets are continuous with one of the spines and spaced at 120° intervals around this spine. The other three spines, and additional spines which grow from corners of the sheets, are related to this one spine and the sheets by twinning on (1122) planes. Intensity measurements of single-crystal patterns allow the shape-transform and thickness of the sheets to be deduced. Sharp lines and extra spots indicate the occasional presence of lattice imperfections in the form of parallel faults. Electron micrographs show wide deviations from the idealized group of spines and sheets.

The structure of the disordered (high-temperature) phase of titanium monoxide has been studied by electron diffraction. Composition-dependent complex distributions of diffuse scattering are observed and interpreted in terms of short-range-ordered configurations of lattice vacancies. The proposition that the form of the diffuse scattering may correspond to ordering under the influence of long-range electronic energy terms and so show a direct relationship to the topology of the Fermi surface is examined.

Electron diffraction patterns from films of long-chain paraffins show the effects of secondary elastic scattering of electrons in the form of extra spots, groups of spots, arcs of circles, diffuse bands with sharp edges, and forbidden reflections in single-crystal patterns. Examples of such effects are given and analysed to demonstrate their origin in the successive diffraction of electrons from two different single-crystal regions. It is pointed out that many effects recorded in the literature on electron diffraction may be explained in the same way. The modification of the intensities in single-crystal patterns and the appearance of forbidden reflections are treated quantitatively on the basis of secondary diffraction by parallel but non-coherent regions of crystal. Expressions are derived whereby observed intensities may be corrected for secondary scattering when once the scattering efficiency of the crystal has been deduced from the observed intensities of forbidden reflections. The importance of such corrections for purposes of structure analysis is demonstrated in the comparison of two Fourier projections made from a cross-grating pattern of dicetyl (C32H66), one using observed intensities and the other using corrected intensities. Both show clearly the general arrangement of the molecules, but that based on corrected intensities contains much less spurious detail than the other, and gives greater accuracy and a much clearer indication of the positions of the hydrogen atoms

Wide-angle convergent-beam electron diffraction patterns from thin single crystals show sets of parallel lines somewhat similar to Kikuchi or Kossel lines. In some cases, each line separates into a black and white line pair when the electron beam is defocused. It is shown that this separation depends on the curvature of the crystal. A method for analysis of the line geometry is proposed which takes into account the aberrations of the electron lens. Using a high-voltage transmission scanning electron microscope, through-focus series of patterns from graphite crystals have been obtained and analyzed to give values for the radius of curvature of the crystal. In defocussed patterns the distortions of the lattice by defects are clearly visible.

In order to obtain accurate data on structure factors from electron diffraction data, it is necessary to take into account the inevitable n-beam dynamical diffraction effects. The comparison of intensity values from detailed computer calculations with observed intensities from perfect crystals is reviewed for the cases of convergent beam diffraction patterns from MgO crystals of uniform thickness and of dark-field images of wedge-shaped crystals of silicon. An analysis of the sources of error in each case suggests that it may be possible to derive structure factor values with an accuracy of better than one per cent. The method, recently proposed by Watanabe et al. [Acta Cryst. (1968). A24, 249] for deriving structure factors from the values of accelerating voltages for which some Kikuchi lines disappear, is reviewed and possible sources of error are examined.

The conditions governing high resolving power in electron diffraction cameras are discussed, and, in particular, those determining the quality of resolution of the fine-structure in single-crystal reflexions. Limitation of resolution may arise from large source size, instability of electrical supplies, misalinement of the electron-optical system, interference from mechanical vibration and stray magnetic fields, grain in the photographic emulsion or too high an operating gas pressure in the camera. A camera designed to minimize these limitations is described, and its performance illustrated. Detailed fine structure, such as the subsidiary maxima of the shape transforms for small crystals, has been resolved.

Some aspects of the diffraction of electrons by single crystals are discussed using low-order approximations to the general theory developed in the first paper of this series (Cowley & Moodie, 1957) and some qualitative arguments concerning general results are presented. The first-order approximation involves the treatment of a crystal as a phase object for electrons. This leads to a complex form for the atomic scattering factor and the structure factor which introduces complications to, but opens up new possibilities for, the process of structure analysis from single-crystal electron diffraction patterns. It is shown that forbidden reflections cannot be generated by dynamic scattering effects in the symmetrical spot patterns obtained when the electron beam is parallel to a principal crystal axis, but lattice defects can give rise to forbidden rcflections in such pattcrns from thick crystals. (auth)

The general method of computing the intensities of diffuse scattering in electron diffraction patterns, outlined by Cowley & Pogany in Part I, has been applied to the case of diffuse scattering given by the short-range ordering in binary solid solutions. If the diffuse scattering from individual crystal slices, of thickness greater than the effective range of ordering, can be assumed to be kinematical, the total diffuse scattering can be expressed in terms of the usual short-range order parameters, αi, and `dynamical factors'. When the diffuse scattering from a slice cannot be assumed to be kinematical, as in the case of copper–gold alloys, a new type of order parameter, involving some higher-order correlations, must be introduced. Expressions are derived for the absorption coefficients which must be applied to the Bragg reflections. The intensity of diffuse scattering from a single slice of crystal is calculated for a simple domain model of short-range order to evaluate the order of magnitude of departures from kinematical scattering and the possible sensitivity of the diffuse intensity to higher-order correlations. The methods are outlined by which diffuse intensity could be calculated for the whole crystal by a modification of the n-beam dynamical multi-slice procedure and a procedure for the approximate calculation of multiple-diffuse scattering is suggested.

The various methods of deducing the structure of crystals from electron diffraction data are reviewed. A rational and uniform nomenclature is proposed in an effort to resolve the present confusion. A critical review of the theory of electron scattering, including discussion of the nature of the approximations, is given. The application of Fourier methods to the analysis of crystal structure from both diffraction intensities and fine structure of dynamic origin is outlined and illustrated for polycrystalline and single-crystal specimens. Some remarks are made on the possibilities of direct observation of crystal structure by electron-optical methods.

The solution of the n-beam dynamical theory of the diffraction of electrons by crystals is generalized to cover the case of diffraction by crystals containing defects and disorders, including thermal motion. The conditions and assumptions under which practical computer calculations of diffuse intensities can be made are explored on the basis of the slice approach of Goodman and Moodie, although matrix methods are equally applicable. It is shown that, if the range of correlation of the deviations from the perfect crystal lattice is small, the total diffuse scattering can be expressed in terms of dynamical factors which multiply the intensities calculated using the kinematical approximation. Simple expressions are derived for the absorption coefficients which must be applied to the sharp Bragg reflexions to take account of the energy lost from them into the diffuse scattering. The possibility that the intensity of diffuse scattering may show dependence on the range of correlation of the defects is discussed.

By use of a “ Gegenfeld ” filter the ratios of intensities of electron diffraction rings from evaporated aluminium films (100∼550 A in thicknesses) have been measured from various energy losses of the incident electrons. For elastic scattering and for 7 eV loss (surface plasmon loss) the intensity ratios show some effects of dynamical scattering. For 15 eV loss (volume plasmon loss) they are more nearly kinematical. For a narrow loss region at 3 eV and again at 10 eV the ratios show strong anomalies. These results are explained through intensity calculations band on n -beam dynamical diffraction theory. In particular, the anomalous intensity ratios are attributed to the effects of single-electron excitations in the crystals.

A novel method for determining the local concentration of Al in the AlxGa1−xAs layer of AlxGa1−xAs‐GaAs multiple quantum well structures is reported. By scanning a 10 A electron beam across the interface, the (200) dark‐field scanning transmission electron microscopy (STEM) image shows the contrast of the AlxGa1−xAs‐GaAs multilayer since the intensity of the (200) diffraction is sensitive to the Al concentration. The line scan intensity profile of the (200) diffraction, along a uniform specimen region of known thickness, shows the intensity variation of the (200) diffraction and reflects the local content of Al in each region. The simulation of the nanodiffraction patterns produces a chart of the (200) diffraction intensity versus the Al concentration for the determination of the local change of the Al concentration. A molecular beam epitaxy grown AlxGa1−xAs‐GaAs specimen (x=0.57 as determined from Raman spectroscopy) is tested and the dark‐field STEM studies show two thin layers of x=0.46 at the 1/3 and ...

High-resolution electron-microscope images in conjunction with selected-area electron diffraction were used to investigate the short-range order in PbMg1/3Nb2/3O3. Intensity fluctuations of the [110] image indicated ordered domains extending over about 20 to 50 A. Decomposition phases were observed.

In recent years low energy electron diffraction (LEED—electron energy range 10–500 eV), and to a lesser extent reflection high energy electron diffraction (RHEED—energy range 40–100 keV), have played an important role in the investigation of surfaces of solids. Both techniques are however beset with many experimental and theoretical difficulties. Diffraction techniques in the medium energy range (MEED—energy range 1–10 keV) should have theoretical and experimental advantages over both LEED and RHEED. These advantages are discussed and a review is made of the available theoretical methods suitable for this energy range.

Application of the novel techniques developed in this laboratory and especially those resulting from our modifications of the scanning transmission electron microscope, have allowed considerable progress with studies on the oxidation of chromium and chromium-iron alloys and on the surface structure of magnesium oxide and related materials. Microdiffraction from regions 10 to 20A in diameter has allowed clarification of the nature and epitaxial relationships of the very thin oxide layers formed when chromium films are heated. The new observations include the existence of a uniform thin layer of a previously undetected spinel-structure phase. Deductions have been made on the factors influencing growth of the oxide layers. Also it has been shown by use of STEM imaging, microdiffraction and ELS that the oxide film formed on thin chromium films in air at room temperature is amorphous and about 5A thick. The development of techniques for the study of surfaces by reflection diffraction imaging have allowed the visualization of growth steps only 2 to 5A high on the surfaces of MgO smoke particles and a combination of ELS, imaging and diffraction methods has permitted the detection of excited surface states of the first few atomic layers on crystal surfaces. The observation of a new type of interference fringe in defocussed images of small crystals promises to provide extremely sensitive methods for study of the variations of potential at crystal surface. Remodelling of the medium-energy electron diffraction and microscopy system should allow greatly improved performance for surface studies.

Electron diffraction patterns with incidence of f.c.c. plate-like crystals prepared by gas evaporation technique show forbidden spots such as the $$1/3.4\bar 2\bar 2$$ spot. The origin of the spots has been explained in terms of planar defects such as (i) fractional unit cells on (111) surfaces, (ii) repeated thin twins and (iii) stacking faults or hexagonal layers. In the present study, the defect structures are examined by CBED and HRTEM techniques. The CBED pattern of the platelet shows three-fold symmetry for the whole pattern. The dark field patterns of $$ \pm \;1/3.4\bar 2\bar 2$$ discs show symmetry of $$\hat 1$$ . These features prove that the platelet ha-s no center of symmetry for the three dimensional crystal (3m) and irregular arrangements of twins parallel to (111) planes. The electron micrographs taken along the and directions can give “cross-section” images of the platelet. The images show a few repeated twins with a thickness of several nm. The dark field images taken with the forbidden spots with incidence show weak step contrast. The contrast may be due to fractional unit cells. Consequently, the forbidden spots of the platelet are mostly due to the fractional unit cells.

The possibility of obtaining electron diffraction patterns from very small specimen regions combined with high resolution imaging by use of scanning transmission electron microscopy (STEM) allows the detailed study of small nuclei of reaction products or of crystal defects. The capabilities of this method have been extended by the design and construction of a TV system for the viewing and recording of microdiffraction patterns from our STEM instrument so that clear patterns can be obtained from regions as small as 10A in diameter. This system has been applied to the study of initial stages of oxidation of chromium films, revealing the presence of very small oxide nuclei and identifying these crystals as having a previously unsuspected spinel structure. The further stages of growth of oxides on chromium are being investigated. Initial results have also been obtained on the surface structure of oxides such as MgO. The extension of previous work on the diffraction from, and imaging of crystal surfaces by the use of medium-to-low energy electrons (15 to 1 keV) has allowed a much more complete understanding of the contrast-producing mechanisms. Application to the study of pyrolytic graphite surfaces has given a clear picture of the mosaic structure and defectmore » distribution and provided a basis for the more reliable and quantitative general use of these techniques in surface structure analysis.« less

Progress is reported in the evaluation and comparison of various electron optical techniques for the study of surface reactions on single-crystal materials. The principal reaction studied has been the oxidation of copper at temperatures of 400 to 800/sup 0/C in oxygen partial pressures of 10/sup -5/ torr and less using thin single crystal films of copper on solid substrates. This reaction has been followed from the initial formation of oxide nuclei (100A diameter) to the growth of oxide crystals several micrometers in diameter. New information has been provided on the mechanism of the growth of the oxide and on the diffusional processes in the surrounding copper. The techniques used have included scanning electron microscopy (including electron channelling observations), scanning reflection microscopy using diffracted beams at medium energies (a technique unique to our laboratory), medium energy (1 to 15 keV) electron diffraction, transmission electron microscopy, transmission electron diffraction, high energy reflection electron diffraction and high energy reflection electron microscopy. New methods have been developed for the preparation of thin single crystal films and bulk crystals suitable for use as specimens. Exploratory studies have been made on graphite single crystals and thin chromium films. Theoretical studies have revealed possible errors in themore » interpretation of diffraction patterns from small crystals on mono-crystalline supports and have shown the importance of multi-beam dynamical diffraction effects in reflection-diffraction imaging of mosaic single crystals.« less

Ordering theories for binary alloys valid above the critical temperature provide a relationship between the intensities of the diffuse scattering in X-ray, neutron or electron diffraction patterns and the Fourier transform of the pair-wise interaction energy function. Available diffraction data has been used to derive information on the form of the long-range oscillatory potentials attributable to conduction-electron energy terms. On this basis, the relationship of the diffuse scattering to the form of the Fermi surface is discussed. Consideration is given to the possibility of detecting and analyzing the effects of nonpair-wise interaction energies from diffraction data.

In many high resolution electron micrographs of oxides, minerals and other materials, planar faults, often nearly parallel to the electron beam, are visible. When the crystal structure is clearly resolved the nature of the faults may be evident from the images, as in the case of the faults in the periodicities of the block structures of niobium and niobium-titanium oxides (Iijima, 1973; Iijima, Kimura and Goto, 1973), the shear planes (Wadsley defects) occuring in reduced tungsten trioxide (Iijima, in preparation) and the micro-twins occuring in the mineral enstatite (Iijima and Buseck, in preparation).

Reflection electron microscopy (REM) relies on the surface resonance (channeling) conditions for enhancement of the intensity of the specular reflection from a flat surface of a single crystal. The two most frequently cited geometries for attaining surface resonance conditions are: i) tilting the incident beam such that the specular beam in the RHEED pattern falls on an intersection of a K-line parallel to the surface with some oblique K-line; ii) positioning the specular beam on an intersection of a K-Iine parallel to the surface with some of the surface resonance regions bound by parabolas. Parabolas are also observed in the transmission diffraction patterns and have been explained as Kikuchi envelopes. Recent studies indicated a similarity between the CBED transmission and reflection patterns. We will describe a simple geometry which can be used to interpret the above observations.A parabola is by definition a curve of equal distance from a point (called focus) and a line (called directrix; see Fig.1 ).Simple previously unnoticed facs are that the zone axis is a focal point of all the parabolas belonging to a given zone, and that the directrix of each parabola corresponds to a K-line.

Apart from its well-known applications for phase identification and determinations of geometry and orientations in conjunction with bright- and darkfield electron microscopy, electron diffraction has undergone considerable development in the last few years, principally in the direction of a more quantitative use of the technique. Computing methods are available for the calculation of intensities with arbitrary accuracy for well-characterized specimens. Instruments for the accurate measurement of diffracted intensities and for energy analysis have been developed. The major lack, in many cases, is a systematic method for combining data from diffraction and microscopy to determine the crystal morphology, perfection and orientation with sufficient precision. Each of these factors can affect the diffraction intensities strongly. Any one of them may be determined if the others and the crystal structure are known.In cases for which the specimen characteristics may be defined with sufficient precision, the comparison of intensities calculated by use of n-beam dynamical theory and experimental observation has shown excellent agreement and led to the determination of Fourier coefficients of potential distribution with an accuracy of the order of 0.5 per cent, which is more than comparable with the most precise X-ray measurements.

The theoretical and experimental advantages of using medium energy electrons (1-10 keV) instead of LEED and RHEED methods for quantitative surface studies were discussed by Moon and Cowley. A highly versatile ultra high vacuum system that exploits some of these advantages was constructed in our laboratory. The purpose of this paper is to describe design details of the instrument and to present initial data obtained.An overall view of the jinstrument is shown in Fig. 1. A commercially available field emission gun was attached to a Varian 240 LEED chamber. The pumping system is oil free and consists of cryosorbtion and Vaclon pumps.

In the BJR theory of electron diffraction an absorption effect due to weak beams is introduced into the two-beam approximation for the dynamical diffraction of electrons by thick crystals. This is shown to be unjustified for diffraction from perfect crystals. The use of the theory to derive the temperature dependence of diffraction intensities must therefore be modified.

IN recent years the techniques of X-ray diffraction structure analysis have been refined to such an extent that, with careful work, the positions of hydrogen atoms in a structure may be determined when each hydrogen atom is bound to a single atom. The detection of a hydrogen ion in a hydrogen bond, however, is a much more difficult task, since only a fraction of an electron can be considered as localized near the proton. This amount of ionization reduces the atomic scattering factor for X-rays. However, the atomic scattering factor for electrons is correspondingly increased since this is given by ɛ = (Z − ƒ)λ2/sin2θ, where Z is the atomic number, ƒ is the X-ray scattering factor, λ is the effective wave-length of the electron beam and θ is the Bragg angle. Hence, hydrogen ions in hydrogen bonds should be detected more readily in structure analyses based on electron diffraction data. Techniques for structure analysis using single-crystal electron diffraction patterns have been evolved and will be described elsewhere. They have been applied to the study of the structure of boric acid layers.

The diffraction of electrons is, in principle, a very sensitive probe of the relative atomic positions in ordered or disordered crystals. The full potential of electron diffraction and electron microscopy methods for the study of local atomic arrangements has not been realised because of the difficulties of conducting experiments under sufficiently well defined conditions and because of the complications introduced by the dynamical diffraction processes involved.

A system employing medium energy electrons (1–15 keV) for scanning microscopy and diffraction intensity measurements has been constructed. The specimen is situated in an UHV environment and can be cleaned by argon ion sputtering and heated up to 1000 °C. The resolution is currently about 300 A for scanning images formed when secondary electrons are detected. The use of diffracted beams to form images is shown to provide new types of information regarding the structure and defects of crystal surfaces. Intensities and intensity profiles of diffracted beams can be measured for comparison with theoretical data and structure analysis.

The oxide layer, giving the so‐called electron diffraction pattern and formed by heating copper in air at 600°C, has been examined by high‐resolution electron diffraction and electron microscopy. It is shown that the intensity anomalies which differentiate the pattern from the normal pattern are not due to impurities as has been suggested. The oxide grows in the form of long needle‐like spines approximately perpendicular to the copper surface, with one or more screw dislocations along the axis of each spine. Each spine is a single crystal of , about 1000 A in diameter, elongated along the (110) zone axis. Intensity anomalies of the pattern result from this particular morphology.

A formulation for scalar problems in physical optics is presented. Approximations involve the neglecting of the obliquity factor and the dependence of amplitude on distance and the replacement of spherical by paraboloidal wavefronts. Expressions are obtained for wave function in a multi-component system in terms of convolution integrals, the components of the system being described by functions of either direct or Fourier space. The formulation is equally applicable to light optics, electron microscopy or electron diffraction and permits interchange in the techniques of these disciplines. Some elementary examples of the application to thin lenses, and to periodic objects are given.