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We considered the analysis of bioassay data resulting from the treatment of fruit that has been naturally infested, when the treatment sample size is unknown. Natural infestation may cause considerable variability between fruit. We described a procedure to quantify this variability and account for it in the bioassay analysis. We also discussed the optimal numbers of control and treatment fruit.

We developed a probability model to quantify the quarantine risk from importing fruit fly hosts. Bayesian theory is used to show how sample size at point of entry is related to the number of test insects used to determine efficacy of the postharvest disinfestation treatment. The model assumes that other variables such as lot size, average number of insects in an infested fruit, and maximum pest limit (or tolerance) are fixed and known. Examples are given using data for the fruit fly species Bactrocera melanotus (Coquillet) and Bactrocera xanthodes (Broun).

The problems of satisfactorily describing fruit fly host status for quarantine purposes are explored. A definition is provided based on the ability of a commodity to sustain fruit flies from the egg laying stage through to the next generation of reproducing adults. Experimental procedures required to determine host status for multivoltine fruit flies are described. These methods include both laboratory and field cage trials, field collection of fruit, and methods demonstrating fruit fly presence in a study area.

A methyl bromide quarantine fumigation schedule of 32 g /m3 for 4 h at 21-26°C and under normal atmospheric pressure is reported for watermelons grown in Tonga and shipped to New Zealand. This fumigation schedule is effective against Bactrocera xanthodes (Broun), which was recorded from watermelons for the first time in 1985. A work plan permitting resumption of watermelon trade from Tonga to New Zealand specifies production, culling, inspection, treatment, holding, and transport conditions which must be fulfilled to ensure that defined maximum pest limits are not exceeded.

New Zealand is the only major fruit-producing nation that has remained free of economically important fruit fly species. Maintenance of this status is essential not only to guarantee horticultural exports but also to minimize production costs associated with field control and disinfestation treatments against fruit flies after harvest. To guarantee continued freedom from fruit flies, the concept of a maximum pest limit is developed as an alternative to a very restrictive import policy. The maximum pest limit is defined as the maximum number of immature fruit flies that may be present in consignments imported during a specified time to a specified location. To preclude the establishment of fruit flies, we propose a maximum pest limit of three live larvae per day. Applying a treatment of known efficacy ensures that this limit is not exceeded only if the infestation level is below a predetermined value. We describe a sampling model for accurate assessment of the infestation level and examine the practical implications of setting the maximum pest limit.

In recent years the surfaces of Cu3Au, a typical ordering alloy, have attracted interest from many aulhors[l-6], because the surface is a good example for testing general theories of the 2-D order-disorder phase transition, and also because it is a good material for studying the behavior of bimetallic alloy surfaces and their reactions with surface impurities. Previous work on Cu3Au surface mostly used macroscopic techniques and provided only information averaged over a largearea. In this work the microscopic imaging and diffraction methods are used to study the (111) surface on a more localized scale. Reflection Electron Microscopy (REM) was used to directly image the surface, and the selected-area RHEED was used to determine the local surface crystal structure and orientation.The samples used for observation are single crystal spheres prepared by melting a small piece of Cu3Au suspended on a thin Mo wire. The actual compositions of the samples are about Cu0.7Au0.3. The (111) facets on these spheres were then cleaned by the conventional ion-milling-heating method in a UHV environment.

The long-period structure (LPS) has long been known to exist in bulk ordering alloys such as CuAu and Cu3Au. in the structure the ordered lattice shifts back and forth by a vector every M unit cells and forms a super cell 2M unit cells long. The planes where the lattice shifts are usually called antiphase boundaries (APBs) and the LPS can be regarded as periodically arranged antiphase domains. This superstructure can be detected by the splitting (∝1/M) of some superlattice spots in the diffraction panern. One may ask whether the LPS also occurs on the surface; if so, what is its effect onthe diffraction pattern. The answer to them is important to explain some unknown features observed in the RHEED experiment. They also have significance for the surface transition theories.Ideal termination of a LPS Cu3Au crystal gives a surface first-layer atomic arrangement shown in fig.1a. In this arrangement the basic vectors a and b of the surface hexagonal ordered structure are two bulk {110} vectors. Every M unit cells in a direction the lattice shifts by(1/2)b. This forms the 2-D super unit cell with a size of 2Ma×b. The relatively shifted areas are actually 2-D antiphase domains. The boundaries between them are the periodically arranged linear APBs. All these features indicate that the ideal Cu3Au(111) surface is indeed a 2-D LPS. Fig.1b and 1c show the 2-D reciprocal lattice calculated from the above surface arrangement.

Transmission electron microscopy (TEM) has been used to study the microstructures, especially the ferroelectric domains and boundaries, of ferroelectric crystals and free-standing thin films because they are closely related to the ferroelectric properties of thin films. But, for a long time observations have been made on the assumption that the properties of ferroelectric domains and domain boundaries are the same as those of the bulk crystal, even though sometimes some evidence may have been shown that ferroelectric domains in thin films could be different from those in the bulk material. In fact, weak ferroelectricity of thin films has been noticed. It was found that the ferroelectric characteristics of thin BaTiO3 ferroelectric films deposited on substrates are different from those of bulk materials. Although in their analysis interfaces and grain boundaries are involved, the mechanism of weak ferroelectricity of thin films and the microstructures which are related to the ferroelectricity of the film remains unclear.

The intersections of ferroelectric domain boundaries with crystal surfaces have been studied by optical microscopy. The method is widely used but usually of low resolution. Transmission electron microscopy (TEM) can provide high-resolution images but may not be appropriate for studying crystal surfaces. Scanning electron microscopy (SEM) has also been used to study the intersections of ferroelectric domain boundaries with the surfaces of ferroelectric crystals. However, the resolution is still low and is destructive if an etched crystal surface is used. Other alternatives have also been attempted to study ferroelectric domain boundaries on surfaces, such as scanning tunneling microscopy (STM), atomic force microscopy (AFM). But, no reports have been known so far.On the other hand, reflection electron microscopy (REM), as a branch of dark-field imaging technique dedicated for surface studies in TEM, has been developed to study crystal surfaces, surface reconstruction and surface defects with a resolution of about 10Å. It has been considered as a powerful technique to study surface defects and may be used to study the ferroelectric domain boundaries emerging on surfaces.

The behavior of impurities on the surfaces is an important topic in surface science. Cu3Au is a typical ordering bimetalic alloy whose bulk and clean surface have been extensively studied.This make it a good material for studying the effect of impurities such as sulfur on the properties of the alloy surfaces. Some work has been done by the present authors on the structure and compositionchange of the Cu3Au (110) surface with the sulfur adsorption . It was found that when S isadsorbed on the surface the ratio of the surface Au concentration over Cu concentration decreases drastically. The reason of this change was explained as movement of Au atoms into the bulk and Cu atoms from the bulk to the surface due to the difference in the affinity of Au and Cu for S.The previous observations were based on macroscopic RHEED and AES techniques, the information was averaged over a large area. In order to obtain more localized information such as surface morphology andthe element distribution, secondary electron microscopy (SEM) and scanning Auger microscopy (SAM) were used to study the clean and S-adsorbed Cu3Au (110) surfaces. The experiment was carried out in a modified UHV VG HB501.

In reflection electron microscopy (REM), the surface reflection electrons undergo both elastic and inelastic scattering within a crystal. The dominant inelastic processes are phonon scattering, valence electron excitation, bulk and surface plasmon excitation and combinations of these processes. Multiple inelastic scattering processes are also probable as the mean traveling distance of surface reflection electrons is about 10 to 100 nm. In reflection high energy electron diffraction pattern (RHEED), 50% to 90% of the electrons contributing to surface reflection spots used for imaging have suffered energy loss of more than 10 eV, thus the main limitation on REM image resolution is due to the chromatic aberration effects given by the energy spread from inelastic scattering. An energy filter fitted inside a TEM microscope can remove most of the inelastic scattering contribution and so improve the contrast and resolution. Oxygen-annealed rutile (001), (100) and (110) surfaces were previously studied by REM and RHEED techniques without energy filtering.

Reflection electron microscopy (REM) has been used to study surface defects such as surface steps, dislocations emerging on crystal surfaces, and surface reconstructions. However, only a few REM studies have been reported about the planar defects emerging on surfaces. The interaction of planar defects with surfaces may be of considerable practical importance but so far there seems to be only one relatively simple theoretical treatment of the REM contrast and very little experimental evidence to support its predications. Recently, intersections of both 90° and 180° ferroelectric domain boundaries with BaTiO3 crystal surfaces have been investigated by Tsai and Cowley with REM.The REM observations of several planar defects, such as stacking faults and domain boundaries have been continued by the present authors. All REM observations are performed on a JEM-2000FX transmission electron microscope. The sample preparations may be seen somewhere else. In REM, the incident electron beam strikes the surface of a crystal with a small glancing angle.

Calcia stabilized zirconia(CSZ) and ceria(CeO2) doped with rare-earth oxides have been used as electrolytes in solid oxide fuel cells(SOFC). Such ceramics are usually good ionic conductors for oxygen ions at elevated temperatures. A few studies have attempted to correlate the microstructures with ionic conductivity. It was suggested that the grain boundaries play a role in depressing the ionic conductivity. In their study, it was found that continuous “thick” boundary layers of secondary phases existed on the grain boundaries and blocked ion transport.In the present studies, high resolution transmission electron microscopy has been used to investigate the microstructures of grain boundaries in zirconia doped with calcia (ZrO2 + 13%CaO) and ceria ceramics doped with calcia (CeO2 + 10% CaO). The ceramics was made in our Solid State Ionics Laboratory. Transport number measurements on zirconia samples showed that the transport number tO2- =1 from PO2 = 10-17 atm to PO2 =1 atm.

Shadow images are obtained on the detector plane when the specimen in a STEM instrument is illuminated by a stationary beam formed with a very large or no objective aperture. It has been recognized for some time that the shadow image formed after a thin crystal specimen in the diffraction plane of a STEM instrument with a field emission gun can be treated as an in-line hologram. Since the transmitted and diffracted beams are added to give interference effects, all the information on the relative phase of the scattered beams is recorded in the shadow image. In fact, this is basically equivalent to the original scheme envisioned by Gabor, where he proposed that a reconstruction could be made from a hologram so that the imperfection due to spherical aberration of the objective lens could be corrected and improved resolution could be achieved.

Single crystal TiO2 (rutile) (110) surface has been characterized by several experimental techniques. In this paper, we report the investigations of “optically polished” as well as high temperature oxygen annealed rutile (110) surfaces by using reflection electron microscopy (REM) and reflection high energy electron diffraction (RHEED) techniques.The crystal was purchased, “optically polished” as-received, from Commercial Crystal Laboratories, Inc.. The details in specimen cutting and surface cleaning procedures have been reported previously. The samples were annealed in pure oxygen at 1425°C for 36 h. The experimental observations were carried out in a Philips 400T microscope operated at 120 kV. The REM images were obtained by selecting the specular reflection spots satisfying surface resonance conditions.Figure 1 is a REM image of as-received rutile (110) surface. The corresponding RHEED pattern is shown in the inset. The azimuthal angle of the incident beam was at 3.9° away from [001] zone axis and the image was formed by choosing (440) specular reflection spot under surface resonance condition.

Lead zirconium titanates(PZT) are ferroelectric materials of considerable current interest because their potential for applications in memory devices and electrooptics has drawn the attention of industry. The performance of the devices made of PZT largely depends on the behaviors of ferroelectric domains and domain boundaries. TEM has been proved to be a very powerful tool in the study of ferroelectric domains and domain boundaries in ferroelectric materials. It is suggested that around the domain boundaries in BaTiO3 there is a distribution of lattice distortion and strain field. However, few references have been found on the study of ferroelectric domains and domain boundaries in PZT materials by TEM.

Reflection high energy electron diffraction (RHEED) has been used extensively to observe changes in surface reconstructions by analyzing the geometry of the RHEED pattern and to monitor growth of layers in MBE systems by measuring the changes of the intensity of the specular spot with time. RHEED is also capable of yielding the structure of the surface by using dynamical diffraction theory to analyze experimental reflection rocking curves. These rocking curves trace the change in the intensity of the RHEED spots as a function of the angle of incident illumination. They are equivalent to the intensity vs. voltage curves (I-V) obtained in low energy electron diffraction (LEED) which have been used to determine most of the known surface structures. The LEED I-V curves are energy filtered and the theoretical calculations consider only the elastically-scattered electrons. The RHEED theory is also developed only for elastic scattering, but the experimental measurements so far have not been energy filtered.

Reflection high energy electron diffraction (RHEED) has been widely used to study surface reconstructions, surface morphology and crystal growth. In a transmission electron microscope RHEED can be combined with reflection electron microscopy (REM) to study the structures of surfaces with high spatial resolution. In this paper we report some preliminary results of RHEED investigation of the reconstruction of the oxygen annealed sapphire surfaces.The optically polished sapphire samples were obtained from Saphikon Inc. The specimens were cut, cleaned and chemically etched in boiling phosphoric acid before annealing in pure oxygen. Details of the sample preparation procedure was reported elsewhere. Oxygen annealing prevented change of surface stoichiometry and surface reactions with elements other than oxygen. The RHEED experiments were conducted in a Philips 400T transmission electron microscope operated at 120 kV with a vacuum pressure about 10-7 Torr and equipped with cold and hot stages.

Rutile (single crystal TiO2) is widely used in electrochemistry, photochemical energy conversion and photocatalytic reactions of gases as a catalytic material. It is important to characterize the surface properties of rutile in order to understand its catalytic behavior. The rutile (001) surface is extremely unstable, forming facets on annealing as revealed by the LEED results. In this paper we report some preliminary results on the investigation of oxygen annealed rutile (001) surface, obtained by reflection high energy electron diffraction (RHEED) and reflection electron microscopy (REM) techniques.The crystal was cut into strips, finely polished, cleaned and chemically etched in NaOH and H2SO4 before annealing. The samples were annealed in pure oxygen at 1473 K for 36 h. The purposes of annealing the samples in pure oxygen are to preserve surface stoichiometry and to prevent surface reactions with elements other than oxygen during the annealing process. The RHEED and REM observations were performed in a Philips 400T microscope operated at 120 kV.

Scanning transmission electron microscopy (STEM) with a high angle annular detector has become a useful technique in material science. The atomic number sensitive contrast (Z-contrast) of the Annular Dark-Field (ADF) image is good for looking at the distribution of heavy elements in a relatively light substrate. In many cases the impurity distributions are substantially affected by the defects in the materials and their interaction with the impurities. Therefore it is also desirable to observe defects with ADF images. This is possible and has some advantages over normal STEM. We have studied the ADF imaging of dislocations, its contrast mechanism and visibility in the ADF image.

The (100) surface of magnesium oxide is of considerable interest because of its frequent use as substrate for epitaxial growth of metal films, high Tc superconductors and model catalyst systems. A large number of surface characterization techniques have been used to determine the atomic structure of the cleaved (100) surface. Clean surfaces have been produced either by cleaving MgO crystals in-situ under ultra-high vacuum (UHV) conditions, or more frequently, by cleaving in air and subsequent annealing in UHV. A wide variety of annealing temperatures and times have been used by different researchers, the upper limit on the temperature being set at ≈900°C to avoid segregation of Ca to the surface. Calcium is the main impurity in even the purest MgO crystals and a few studies have dealt with the structure of the Ca-rich (100) surface of MgO. All of the existing studies have used diffraction and spectroscopy techniques without imaging of the surface. It is the purpose of this work to study the topography of the UHV-annealed (100) surface by reflection electron microscopy (REM).

High resolution secondary electron (SE) images can be obtained in a scanning transmission electron microscope (STEM) by collecting the type I secondary electrons generated directly by the incident electron beam. The high resolution SE signal is, in general, localized to about 1 nm in the generation process. The escape depth of the secondary electrons, however, varies from about 1 nm for most metals to about 10 nm for some insulating materials. Surface steps can be imaged by collecting high resolution secondary electrons Among other possible contrast mechanisms for SE imaging of surface steps, topographic contrast plays an important role. The topographic contrast of surface steps depends on: (1) the incident electron probe size; (2) step height to SE escape depth ratio; (3) localization of the generated SE signals and (4) the incident beam angle relative to the specimen surface.In our UHV STEM (MIDAS) instrument, both the entrance and exit surfaces of the sample can be imaged by collecting secondary electrons. For thin samples, the resolution is < lnm for SE images of entrance and exit surfaces but for thicker samples the resolution of the SE image obtained from the exit surface will be degraded by the beam broadening effects. For studying steps on thick or bulk crystal surfaces, secondary electrons emitted from the entrance surfaces are, in general, collected to form images with high contrast and high resolution. In this report, all the SE images are obtained, in MIDAS, by collecting secondary electrons emitted from the entrance surfaces of the samples. Figure 1 is a SE image of a MgO smoke crystal revealing the surface growth steps with high contrast. The parallel straight steps, along directions, constitute the edges of unfinished atomic planes on the MgO {100} crystal surfaces. This image indicates that the {100} surfaces of MgO smoke crystals are flat surfaces. Figure 2 shows a SE image of a MoO3 crystal with surface growth steps spiraling from an end-on screw dislocation (the black dots in the SE image represent electron beam induced reduction products). The dark lines (indicated by D) represent up-steps and the bright lines (indicated by B) represent down-steps. It is interesting to note that the two-dimensional crystal growth around the dislocation is anisotropic, forming terraces with long edges parallel to [010] direction.

The structures and properties of the prismatic faces and of as-grown single-crystal sapphire are still not well understood. Known information have been limited to calculated surface energies and TEM characterization . The TEM characterization has been limited to identification of the orientation of the structures. For better understanding of the behavior of these surfaces, the use of the RHEED and REM techniques, which have proved their value for purely surface analysis, is necessary. In this paper we report the characterization of these surfaces by the RHEED and REM techniques.The sapphire ribbons were purchased, as-grown, from Saphikon, Inc.. The method of preparation of the REM samples has been reported. The samples were oxygen-annealed for 3 6h at 1500°C. The experiments were performed in a Philips 400T TEM with a vacuum pressure of 10-6 Torr.Fig. 1(a) is a REM image showing the structural features that characterize the surface in the beam direction. The surface can be seen to exhibit periodic bright and dark domains, with parallel small steps (S) in average direction oriented 7° from the (after de-foreshortening). The appearence of two domains may be due to a difference in termination of the lattice at the surface. The THREED pattern (insert) shows the specular reflection used for imaging. Fig. 1(b) shows the structural features on the surface in the beam direction. Two domains (grey, G and white, W) can also be seen here, and may be attributed to the same effect. A well defined step can be seen at the boundary of the two domains. The faceted steps in the white domain can be seen to adopt average direction oriented 5° from the . Strain field of dislocation (D) can be seen to run across the steps, and is displaced at the steps. The RHEED pattern (insert) shows the specular spot used for imaging. Fig. 2 shows the structural features on the surface in the beam direction, with the spot (insert) used for imaging. Emerging dislocation (D) can be seen terminating at kink of the large step.

Franckeite (˜FeSn3Pb5Sb2Si14) has a complex modulated structure containing alternating layers of different composition. The complex composition and structure, lack of a well-defined unit cell, incommensurate character, and poor quality of crystals has made it difficult to study by standard X-ray and electron-diffraction methods. High-angle annular dark-field (HAADF) STEM imaging provides a way of mapping the compositional distributions directly and with atomic resolution. For thin regions of the sample, the intensity of the electrons scattered at high angles depends strongly on the atomic number of the scatterer. This unique property makes HAADF imaging powerful for studying compositional modulations on the atomic scale. By comparing the structure as viewed by high-resolution imaging to the compositional information provided by the HAADF technique, we have been able to obtain an improved understanding of crystal structures with displacive and compositional modulations, such as franckeite. We use the HAADF technique to test the assumption that in franckeite two kinds of layers (SnS2 and PbS) are stacked along the a axis with a 1.73 nm repeat, and that Sb and Fe produce structural modulations in the c direction.

Scanning transmission electron microscopy (STEM) offers a powerful extension to the conventional transmission electron microscopy (TEM) by combining high resolution microanalysis with a variety of imaging and diffraction modes. Bright-field (BF) and dark-field STEM imaging (with or without energy filtering) can be used to obtain structural images or to locate small particles and other inhomogeneous sample areas for microanalysis. The microdiffraction technique can provide crystallographic information on nanometer-scale small particles. Secondary electron (SE) images with a resolution approaching the probe size (0.5 nm) can be obtained in STEM instruments, providing topographic information on the samples studied. High-angle annular dark field (HAADF) imaging is also available in dedicated STEM instruments. The intensity of high-angle scattered electrons depends strongly on the atomic number (Z). This unique property makes the HAADF imaging a powerful microscopic technique in characterizing supported catalyst systems which often comprize high atomic number particles supported on low atomic number substrates.

The bright-field and dark-field electron microscope images expected for [100] split interstitials in thin crystals of gold and aluminum without and with lattice relaxation have been calculated by the method of periodic continuation including full n-beam dynamical interactions of both the Bragg reflections and the diffuse scattering. The advantage of using 1 MeV rather than 100 keV electrons is demonstrated in that, even with the same nominal resolution, the 1 MeV electrons give images in which the defect structure is more readily recognized. The conditions have been determined for which the defect images have high contrast and provide clear representations of the atom configurations.

Kinematical diffraction from a crystal having planar faults is described by a systematic writing of the Patterson function and its Fourier transform for the general case of an arbitrary number of different kinds of layer, describing the faults in terms of a fault vector plus an addition, or subtraction, of scattering matter. The general series expression is readily simplified to deal with a wide variety of special cases. Particular examples include Wadsley-type shear faults associated with non-stoichiometry of oxides and the deformation and growth faults of simple close-packed structures.

It has been previously established that calculations of intensity distributions in high-resolution electron-microscope images of crystal structures can reproduce the experimental observations. The use of comparisons Of observed and computed images for structure analysis has been extended for the first time to the refinement of a defect structure in the case of crystals of nominal composition 'GeNb9O25. The results show that previously proposed models for the disordered atom configurations around 'tetrahedral' sites are not completely correct. A new model is proposed which shows good agreement between computed and observed images. This model suggests an interpretation for observations on other related structures in terms of a new type of defect.

Some of the most important applications of STEM depend on the variety of imaging and diffraction made possible by the versatility of the detector system and the serial nature, of the image acquisition. A special detector system, previously described, has been added to our STEM instrument to allow us to take full advantage of this versatility. In this, the diffraction pattern in the detector plane may be formed on either of two phosphor screens, one with P47 (very fast) phosphor and the other with P20 (high efficiency) phosphor. The light from the phosphor is conveyed through a fiber-optic rod to an image intensifier and TV system and may be photographed, recorded on videotape, or stored digitally on a frame store. The P47 screen has a hole through it to allow electrons to enter a Gatan EELS spectrometer. Recently a modified SEM detector has been added so that high resolution (10Å) imaging with secondary electrons may be used in conjunction with other modes.

Dynamical diffraction calculations have been made by use of the periodic-continuation assumption for the diffuse scattering in electron diffraction patterns and for electron microscope images of single split interstitials in gold crystals for thicknesses up to 200 A in order to demonstrate the strong fluctuations of scattering with thickness. The diffuse scattering from distributions of defects in crystals, described in terms of correlation functions, can be written in terms of 'dynamical factors' for each type of individual defect. These dynamical factors multiply the same Fourier transforms of correlation functions as are used in kinematical theory to give the effect of dynamical scattering on the diffraction intensities. Calculations of dynamical factors have been made by multi-slice dynamical diffraction methods for unit changes in atomic scattering factors and for atom displacements in gold and aluminum crystals in [001] orientation for thicknesses up to 100 A. With increasing thickness the dynamical factors show rapidly reducing fluctuations with crystal thickness and become more nearly isotropic except for the effects of Kikuchi bands which are seen to develop.

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 general theory for kinematical diffraction from crystals having planar faults is applied to the case of microtwinning and the related cases occurring in some minerals where there is a disordered sequence of two types of structure having small differences in composition, unit-cell dimensions and axial orientations. It is shown that, if intensities are measured for unresolved or partially resolved pairs of diffraction spots using conventional techniques, errors may well arise if the measurements are interpreted on the usual assumption that the intensities from the different crystal regions are summed incoherently. Calculations for representative cases suggest that errors, due to the neglect of the spreading of intensity maxima into continuous streaks, may amount to 20 or 30% when overlapping diffraction spots have structure amplitudes of opposite sign, but are usually much smaller, especially if the structure amplitudes are of the same sign.

A high-resolution image may be derived from a large number of `dark-field' images of normal resolution, obtained by varying the angle of incidence of the electron beam in a standard electron microscope. The intensity distribution in each dark-field image is multiplied by an appropriate cosine function. Summing gives the function, for one dimension, C(x) = ∫ V(X) G(-X) V(X + x) G(x - X) dX where V(x) is the potential distribution in the specimen and G(x) defines the loss of resolution due to lens imperfections in normal micrographs. From this, V(x) may be derived. The practical applications of the method are limited by requirements of specimen and instrumental stability.

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.

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.

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 theoretical and experimental investigation of Fourier images, described in Parts I and II, is extended to the case of finite sources. The Fourier images produced by a pair of point sources, a rectangular source and a Gaussian source are considered in detail. The dependence of focus on source dimensions for the first two of these cases is confirmed experimentally with light optics. From the results obtained for these idealized sources, the contrast and resolution of Fourier images from experimentally realizable sources is deduced. The possibility is considered of an improvement in resolution in the electron microscopy of thin crystals when the first stages of magnification are performed by forming magnified Fourier images. It is shown that the resolution that can be attained depends on the sharpness with which the boundaries of the source are defined. In particular, if the effective source is formed by using electron lenses to demagnify a larger source, the resolution may be improved by a factor of 2-1/2.

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.

The theoretical and experimental investigation of Fourier images described in Part I is extended to the patterns on planes other than focal planes. The theory is developed from a new statement of the diffraction equations correct to the Fresnel approximations, and experimentally observed patterns are shown to be in good agreement with the results of the theory. It is concluded that, at least within the angular range of the experiments, some fifteen degrees, the Fresnel approximation gives an adequate description of the phenomenon.

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.

High-resolution electron micrographs of crystal lattices showing a recognizable correlation of intensity with atom positions are normally obtained only for very thin crystals (less than about 100 A thick). For some crystals of niobium and titanium-niobium oxides, it has been observed that this thin-crystal contrast is repeated for thicknesses of the order of 1000 A. This is regarded as evidence that under conditions of high symmetry of excitation, the wave field in the crystal is essentially periodic with distance in the beam direction if a particular relationship exists between the structure amplitudes and the excitation errors for the diffraction process. This is confirmed by calculations made for f.c.c. lattices with Cu, CuAu3, or Au atoms and for a range of wavelengths.

Simple expressions are derived for the form of the intensity distributions in high-resolution dark-field electron micrographs of thin specimens for which the phase-object approximation may be applied. For cases in which the phase change of the electron wave can be assumed to be small it is shown that there is an optimum defocus value which gives the best, interpretable resolution. For dark-field images obtained either with a central beam stop or with a tilted incident beam, the image intensity is shown to depend on the square of the deviation of the projected potential from an average value. The further complications resulting when the phase change cannot be assumed small are discussed and illustrated by means of a simple example.

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.

A new approach to the kinematical theory has been developed for the case of binary alloy solid solutions with short-range ordering of the atoms and displacements of the atoms from the average lattice sites due to departures of the effective atomic radii from the average for the alloy. Both the pseudo-temperature factor on the Bragg reflexions and the diffuse scattering intensity are shown to depend on summations over higher-order correlation parameters, defined in terms of the probabilities that groups of three, four or more sites should be occupied in specific ways. Expressions involving these parameters, and the usual short-range order parameters, αi, are derived with terms of up to the second order in the displacement parameters for the Huang scattering around the fundamental Bragg reflexions, for the short-range order diffuse peaks, and for additional diffuse scattering depending on higher-order correlation parameters only. Special cases of practical significance are explored, and some estimates are made of the relative magnitudes of the terms not included in previous treatments of this problem.

The problem of designing a light or electron optical system specifically for the imaging of periodic objects, such as real crystals, is discussed. A qualitative appeal to communication theory suggests that it should be possible to devise systems of higher efficiency than the conventional microscope by using the a priori knowledge of periodicity. The possibility of deforming the incident wavefront in such a way that the periodic object acts as its own imaging system is considered and a formalism is set up. The particular case of the spherical wavefront is then examined in detail and it is predicted that a new type of image should be formed on certain planes. Since this image is in many ways analogous to the Fourier projection of crystallography, and since it can only be formed by periodic objects, it is named the Fourier image. Fourier images produced experimentally with light optics are presented and shown to be in agreement with theoretical predictions. Patterns on planes other than Fourier image planes are described briefly, but detailed treatment is deferred until Part II. The possibility of application to the imaging of crystal lattices by electron optics is discussed, but a quantitative treatment of the crucial problems of finite source size and coherence are deferred until Part III.

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.