LACBED measurement of the chemical composition of a thin In(x)Ga(1-x)As layer buried in a GaAs matrix.

Large angle convergent beam electron diffraction (LACBED) observations are used to determine the x indium content of a thin In(x)Ga(1-x)As quantum well buried in a GaAs matrix. The method consists in a quantitative analysis of the Bragg line intensities lying in the central disc of any LACBED pattern. This analysis makes it possible to determine the displacement vector R introduced, between the two parts of the GaAs matrix, by the deformation of the quantum well and consequently to determine the x indium content. This indium content is found to be consistent with the value expected from the molecular beam epitaxy growth conditions.     

Effect of sample bending on diffracted intensities observed in CBED patterns of plan view strained samples

Convergent beam electron diffraction is used to study the effect of the sample bending on diffracted intensities as observed in transmission electron microscopy (TEM). Studied samples are made of thin strained semiconductor Ga(1-)(x)In(x)As epitaxial layers grown on a GaAs substrate and observed in plan view. Strong variations of the diffracted intensities are observed depending on the thinning process used for TEM foil preparation. For chemically thinned samples, strong bending of the substrate occurs, inducing modifications of both kinematical and dynamical Bragg lines. For mechanically thinned samples, bending of the substrate is negligible. Kinematical lines are unaffected whereas dynamical lines have slightly asymmetric intensities. We analyse these effects using finite element modelling to calculate the sample strain coupled with dynamical multibeam simulations for calculating the diffracted intensities. Our results correctly reproduce the qualitative features of experimental patterns, clearly demonstrating that inhomogeneous displacement fields along the electron beam within the substrate are responsible for the observed intensity modifications.     

Trace analyses from LACBED patterns

Trace analysis is of major interest in transmission electron microscopy since the identification of the (h k l) indices of lattice planes or the [uvw] indices of lattice directions is required for the complete analysis of crystal defects (stacking faults, dislocations, etc). It is usually carried out from observations of micrographs and corresponding selected area electron diffraction patterns. The main difficulty comes from the rotation occurring between the image and the diffraction pattern. Therefore, the method requires a careful calibration of this rotation. The LACBED patterns have a unique property: they display information connected both with the direct and the reprocal lattices. The shadow image of the illuminated area of the specimen (direct lattice) is superimposed with the LACBED pattern composed of Bragg lines (reciprocal lattice). Since this shadow image is not rotated (or rotated by 180 degrees C) with respect to the diffraction pattern, LACBED patterns can be conveniently used to identify planes and directions. Several experimental methods are described. Most of them require observation of Bragg lines which are parallel or perpendicular to the trace of the analysed plane or direction.     

A quantitative procedure to probe for compositional inhomogeneities in InxGa1-xN alloys

The distribution of indium in a GaN/InxGa1-xN/AlyGa1-yN quantum well with x+/-Deltax=0.24+/-0.07 is quantitatively investigated by extraction of displacement fields from lattice images. Simulations accurately describe the measured strain relaxation across a wedge-shaped sample for a sample thickness up to 150nm. The proportionality between indium concentration and resulting lattice constant cx is approximated by cx=0.5185+0.111xnm. In general, it is challenging to discriminate the effects of random alloying against clustering. In InxGa1-xN this is particularly true at low indium concentrations x<0.2. For an accurate quantitative analysis, sample preparation and imaging were developed such that radiation damage can be recognized if present. Further, an analysis of detection limits and knowledge of the sample thickness are crucial for obtaining reproducible results. Data averaging is necessary to reach sufficient precision. Consequently, the size of the indium-rich clusters is poorly known if x is small. Beyond the interest in physical properties of InxGa1-xN alloys, the analysis of strain and its relaxation exemplifies how quantitative analysis is possible at an atomic level and is in excellent agreement with theoretical predictions.     

Effects of 10 MeV electron irradiation at high temperature of a Ni-Mo-based Hastelloy

A Hastelloy alloy was irradiated with 10 MeV electrons at 650 degrees C for 700 h to a total dose of 2 x 10(-3) displacements per atom (dpa). The microstructure of irradiated and non-irradiated specimens of this alloy were investigated by transmission electron microscopy (TEM). The non-irradiated specimens were analyzed by 3-D atom probe tomography (APT) in a local-electrode atom-probe (LEAP). TEM analysis before the irradiation detects small precipitates with a mean diameter of 22 nm, which are coherent with the FCC matrix. The number density of these precipitates is approximately 7 x 10(18) m(-3). Electron diffraction patterns from these precipitates exhibit superlattice reflections corresponding to the L1(2) ordered structure. The chemical composition of the precipitates, as measured by APT, is around 75 at% Ni with additions of Al, Ti and Mo. After electron irradiation, small precipitates with an irregular morphology are observed. The number density of these new precipitates about 10(20) m(-3) is greater than that of the L1(2) ordered precipitates before irradiation. The L1(2) superlattice reflections disappear completely, instead diffuse diffraction spots are observed at 1(1/2)0(FCC), which is attributed to compositional short-range order (SRO). The results are discussed with respect to the influence of the electron irradiation on the morphology and structure of the ordered precipitates.     

Structure analysis of embedded nano-sized particles by precession electron diffraction. eta'-precipitate in an Al-Zn-Mg alloy as example

The Vincent-Midgley precession technique has been used to collect three-dimensional electron diffraction intensity data from a dispersion of coherent precipitates in a matrix. In order to suppress severe effects from multiple diffraction via matrix reflections, a fairly large precession (tilt) angle had to be used. This implied a high background from the surrounding matrix, and limited the number of reflections that could be measured from patterns on image plates. The heavily faulted hexagonal eta'-precipitates (a = 0.496 nm, c = 1.405 nm) with thickness 3-5 nm occur in four equivalent orientations relative to the aluminium matrix; with frequent overlap of reflections. A model of the average structure in the space group P6(3)/mmc with assumed composition Mg(2)Zn(5-x)Al(2+x), have been derived by Patterson analysis and intensity comparisons.     

Low-dose performance of parallel-beam nanodiffraction

We evaluate the low-dose performance of parallel nano-beam diffraction (NBD) in the transmission electron microscope as a method for characterizing radiation sensitive materials at low electron irradiation dose. A criterion, analogous to Rose's, is established for detecting a diffraction spot with desired signal-to-noise ratio. Our experimental data show that a dose substantially lower than in high-resolution bright-field imaging is sufficient to determine structure and orientation of individual nanoscale objects embedded in amorphous matrix. In an instrument equipped with a cold field-emission gun it is possible to form a probe with sub-3 nm diameter and sub-0.3 mrad convergence angle with sufficient beam current to record a diffraction pattern with less than 0.2 s acquisition time. The interpretation of NBD patterns is identical to that of selected area diffraction patterns. We illustrate the physical principles underlying good low-dose performance of NBD by means of a phase grating. The electron irradiation dose needed to detect a diffraction peak in NBD is found proportional to 1/N2, where N is the number of lattice planes contributing to the peak.     

The quantitative characterization of SiGe layers by analysing rocking profiles in CBED patterns

Convergent beam electron diffraction is used for the quantitative determination of layer thickness, composition and strain in pseudomorphic Si/SiGe two- and three-layer systems grown by molecular beam epitaxy. By using plan-view specimens, we are able to avoid the influence of surface relaxation which generally complicates the determination of strains in cross-sectional specimens. For quantitative strain determination, rocking curves of Bragg lines in energy-filtered convergent beam electron diffraction patterns are analysed. The experimentally obtained rocking curves are compared with kinematical calculations by a computerized fit procedure. The resulting layer parameters are then further refined by a dynamical simulation. Results for the strains obtained with this technique are in good agreement with theoretical values. With this method layer thickness is measured down to monolayer precision. The accuracy of the strain analysis depends on the sequence and thickness of the layers.     

HANSIS software tool for the automated analysis of HOLZ lines

A software tool, named as HANSIS (HOLZ analysis), has been developed for the automated analysis of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns. With this tool, the angles and distances between the HOLZ intersections can be measured and the data can be presented graphically with a user-friendly interface. It is capable of simultaneous analysis of several HOLZ patterns and thus provides a tool for systematic studies of CBED patterns.     

Crystal structure determination by direct inversion of dynamical microdiffraction patterns

The intensity at points where coherent convergent-beam transmission diffraction discs overlap is shown to be described by interference between elements of the same row but different columns of the dynamical scattering matrix for an axial orientation. These intensities are used as the basis for an exact, nonperturbative inversion of the multiple electron scattering problem, allowing crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. Eigenvectors of the structure matrix are obtained using coherent CBED patterns from many crystal orientations. Unique eigenvalues are obtained from these patterns recorded at two accelerating voltages. The inevitable variation in electron probe position at different crystal tilts is considered. The analysis applies to centrosymmetric crystals with anomalous absorption, to centrosymmetric projections of acentric crystals and to acentric crystals if the mean absorption potential only is included. The method would allow the direct synthesis of charge-density maps of unknown crystal structures at high resolution from multiple scattering data, using a scanning transmission electron microscope (STEM). The resolution of this map may be much higher than the first-order d -spacing; however, the STEM need only be capable of resolving this first-order spacing. Such a charge-density map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X-ray powder patterns obtained or analysed. In summary, we solve the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the nonrelativistic Schrödinger equation, in which the scattering is given as a function of some parameter, and the potential sought.     

A practical method to detect and correct for lens distortion in the TEM

A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images. The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry.     

Bragg diffraction using a 100 ps 17.5 keV x-ray backlighter and the Bragg diffraction imager

A new diagnostic for measuring Bragg diffraction of petawatt-generated high-energy x rays off a laser-compressed crystal was designed and tested successfully at the Omega EP laser facility on static Mo and Ta (111) oriented single crystal samples using a 17.5 keV Mo?Kα backlighter. The Bragg diffraction imager consists of a heavily shielded enclosure and a precisely positioned beam block attached to the enclosure by an aluminum arm. Fuji image plates are used as the x-ray detectors. The diffraction from Mo and Ta (222) crystal planes was clearly detected with a high signal-to-noise. This technique will be applied to shock- and quasi-isentropically loaded single crystals on the Omega EP laser.     

Lost in reciprocal space? Determination of the scattering condition in spot profile analysis low-energy electron diffraction

The precise knowledge of the diffraction condition, i.e., the angle of incidence and electron energy, is crucial for the study of surface morphology through spot profile analysis low-energy electron diffraction (LEED). We demonstrate four different procedures to determine the diffraction condition: employing the distortion of the LEED pattern under large angles of incidence, the layer-by-layer growth oscillations during homoepitaxial growth, a G(S) analysis of a rough surface, and the intersection of facet rods with 3D Bragg conditions.     

Electron diffraction in porous silicon

Electron diffraction patterns, obtained in a high-voltage electron microscope (HVEM), of silicon containing a high density of small pores (diameter ca. 5 nm) produced by anodic etching show an enhancement of high-order Bragg reflections at the expense of low-order Bragg reflections. A theory of this effect is developed based on multiple scattering of Bloch waves at the pores. The theory allows the determination of the volume fraction of the pores from quantitative diffraction data. The results of this analysis are in good agreement with those obtained from HVEM images.     

Visualization and electron diffraction on cryosections of stratum corneum: a utopia?

The skin acts as an effective barrier to protect the body against penetration of substances from the environment and against desiccation. The main barrier function resides in the stratum corneum, and more specifically in the intercellular lipid domains. Several techniques have been used to elucidate the local lipid crystal arrangements in these domains, but they either needed an extensive pretreatment of the skin with the risk of damaging the native structure, or were not suited to obtain local structure information as bulk quantities of stratum corneum were required. In this paper a method of performing local structure analysis (electron diffraction) on cryo-fixed specimens is described. Therefore a cold chain procedure was used to obtain cryosections of stratum corneum. On these sections visualization and electron diffraction at low temperature were carried out.
Using a so-called tape sandwich method, cryosections were prepared in which corneocytes and lipid matrix could easily be distinguished. Moreover, detailed cellular components such as desmosomes and intracellular lipid domains were observed. However, probably due to the limited amount of intercellular lipids in the stratum corneum, electron diffraction on cryosections did not result in diffraction patterns that were undoubtedly originating from the intercellular lipids. In the electron diffraction patterns of a skin lipid model system reflections were present that were indicative of hexagonal and orthorhombic sublattices. The d-spacings of these reflections were similar to the spacings of the high-intensity reflections of the X-ray diffraction pattern of the same mixture. This showed agreement between a bulk and a local technique, X-ray and electron diffraction.     

Symmetry in electron diffractions from helical structures

In this work, we elucidate the regular rule of the symmetry in electron diffraction patterns from helical structures. It is affected by the value of the dominating Bessel function orders for the layer lines and relative orientation of the samples with respect to the electron beam. For Single-Walled Carbon nanotubes (SWCNTs), we use analytic analysis and computer simulations to demonstrate that the 2mm symmetry of the electron diffraction may break down not only from an achiral SWCNT, but also from a chiral SWCNT. Also, the simulation work for B-DNA is presented to corroborate the theoretical analysis.     

Characterization of the diffraction properties of quantum-dot-array diffraction grating

A new dispersive element named as quantum-dot-array diffraction grating [L. F. Cao, China patent No. 200410081499 (August 10, 2004)] for visible light has been developed and characterized experimentally. A large number of quantum dots distributed on a substrate as sinusoidal function can be used to diffract x rays without higher-order diffraction. The experimental patterns show that the higher-order diffractions which inevitably exist in the spectrum recorded using traditional diffraction gratings can be eliminated effectively by this newly designed element. It indicates that quantum-dot-array diffraction grating could be an attractive alternative of presently used diffraction grating in soft x-ray spectroscopy application to get rid of the higher-order diffraction distortions.     

Statistical analysis of atom probe data: Detecting the early stages of solute clustering and/or co-segregation

Statistical analysis of atom probe data has improved dramatically in the last decade and it is now possible to determine the size, the number density and the composition of individual clusters or precipitates such as those formed in reactor pressure vessel (RPV) steels during irradiation. However, the characterisation of the onset of clustering or co-segregation is more difficult and has traditionally focused on the use of composition frequency distributions (for detecting clustering) and contingency tables (for detecting co-segregation).