Zone Axis Patterns Research Articles

Electron diffraction from anthracene

Collection of a three-dimensional data set from anthracene illustrates some of the difficulties which can be encountered. Since the crystals are grown from solution their orientation is not certain, and the crystals are very bendy, so a range of orientations is encountered at a given tilt setting. Anthracene is moderately labile to irradiation, so care must be taken to avoid radiation damage during data collection. Anthracene will sublime at room temperature under vacuum, so the data must be collected at reduced temperature. Flat, well-ordered areas of the crystals are rare, so collection of high-resolution data is time-consuming. The thickness of the crystals is difficult to control, so finding areas which have minimal multiple scattering is also formidable.The structure of anthracene is already known, so simulations of the diffraction patterns along various zone axes can be made. Cerius 2.0® was used to produce simulated zone axis patterns for all combinations of indices whose absolute values were 3 or less. The preferred orientation for the untilted grid is [102]. Scans of several preparations resulted in patterns which matched the simulation for [102]. The angles for each of the Miller planes with respect to [102] were calculated from the formula given by Dorset.

Measurement of low-order structure factors for silicon from zone-axis CBED patterns

The ability to acquire digitally collected, energy-filtered electron diffraction patterns has permitted the development of fully quantitative methods of pattern analysis based on fitting theoretical calculations to experimental intensities. We have developed a method of extracting accurate low-order structure factor information from zone-axis CBED patterns using an automated pattern matching technique. The feasibility of such an approach has already been established by fitting to simulated data-sets. Results are now presented from pattern matching calculations using energy-filtered Si [110] zone-axis patterns obtained with a serial EFLS detector attached to a Philips EM420 TEM. Fits to patterns at two different sample thicknesses (measured to be 2761 and 4092 Å) are discussed. The results show good agreement with the most accurate Si structure factors obtained from X-ray measurements.

What is the ultimate precision of CBED structure factor measurement? Application to Group IV and III-V semiconductors

We have previously demonstrated the feasibility of fitting calculated zone-axis Convergent Beam Electron Diffraction (CBED) patterns to zero-loss energy-filtered experimental data. The aim of this pattern matching procedure is to refine accurate low-order structure factors that can be used to reconstruct the bonding charge density. Initial tests on silicon [110] zone-axis patterns have shown that this new electron diffraction technique is capable of accuracies comparable with existing X-ray methods and that the results are in good agreement with solid state theory calculations. The general applicability of the CBED pattern matching technique is now investigated by studying the bond charge of two other Group IV materials, i.e. germanium and diamond, and the HI-V semiconductor GaAs.The (110) plane of the reconstructed bond charge density for each of the Group IV materials is shown in Figure 1. The agreement between these results and those predicted by solid state theory is excellent despite the use of only five independent Fourier components in the reconstruction.

Atomic String Potentials and the Form of [0001] Zone Axis Patterns of GaS, GaSe and InSe

The relationship between the form of hexagonal zone axis patterns and the projected atomic potential is explored as a method for polytype identification of GaS, GaSe and InSe. As the various known polytypes of these materials project to give unit cells with very different simple-string potentials this relationship may be exploited by making use of previous related work. It is found that this method is simple to apply and consistent with the results of more conventional analyses based on the symmetry of convergent beam electron diffraction patterns. Growth faults could, however, cause ambiguities in the method of analysis. Microsc. Microana 1. Microstruct.

Benefits of energy filtering for advanced convergent beam electron diffraction patterns

Energy filtering is well known to have a dramatic effect on the appearance of standard, zone-axis convergent beam electron diffraction patterns. In this paper, the effects of energy filtering on some less-common types of CBED patterns are shown. In particular, the (002) and (402) quasi-forbidden reflections in silicon are investigated, and the effects of energy filtering demonstrated. The filtering of HOLZ excess lines in large-angle zone-axis patterns is shown, as these patterns are of interest for Debye-Waller factor determination. Filtered and unfiltered bright-field large-angle CBED (LACBED) patterns of aluminum are presented along with EELS spectra to demonstrate the partial removal of inelastically scattered electrons due to the LACBED geometry.

Local internal stress characterization in a tensile-deformed copper single crystal by convergent-beam electron diffraction

Abstract Convergent-beam electron diffraction (CBED) was used to measure localized lattice distortions in single-crystal copper deformed in tension. Local lattice parameters were determined by comparison of experimental zone-axis patterns with computer-simulated patterns employing a kinematical approximation. The observed non-cubic distortions are discussed in terms of residual elastic stresses left in the material after external deformation as a result of the formation of a heterogeneous dislocation microstructure. These internal stresses are modelled semiquantitatively using a composite approach, wherein dislocation cell walls constitute a hard phase and dislocation cell interiors a soft phase. The CBED results support the model's predictions of resultant long-range internal stresses that develop as a consequence of maintaining compatibility between the two deforming phases. Aspects of lattice parameter determination with 〈001〉 zone-axis patterns are also discussed.

Application of microdiffraction to crystal structure identification

In a previous paper by J.P. Morniroli and J.W. Steeds [Ultramicroscopy 45 (1992) 219] it was shown that microdiffraction patterns obtained with a nearly parallel electron beam and a small spot size can be used to identify and to characterize crystal structures. A systematic method was proposed to deduce, via the Buerger extinction symbol, the space group or a set of consistent space groups. In order to illustrate how this method can be applied experimentally, three examples concerning the σ, X and R intermetallic phases are detailed. Experimental solutions are given to overcome difficulties connected with the frequent absence of high-order Laue zone reflections on high-symmetry zone axis patterns. The possibility to identify the Buerger extinction symbol from a unique zone axis pattern is also explored.

Convergent-beam thickness determination: The advantages of digital imaging

Convergent-beam electron diffraction (CBED) patterns contain an immense amount of information relating to the structure of the material from which they are obtained. The analysis of these patterns has progressed to the point that under appropriate, well specified conditions, the intensity variation within the CBED discs may be understood in a quantitative sense. Rossouw et al for example, have produced numerical simulations of zone-axis CBED patterns which show remarkable agreement with experimental patterns. Spence and co-workers have obtained the structure factor parameters for lowindex reflections using the intensity variation in 2-beam CBED patterns. Both of these examples involve the use of digital data. Perhaps the most frequent use for quantitative CBED analysis is the thickness determination described by Kelly et al. This analysis has been implemented in a variety of different ways; from real-time, in-situ analysis using the microscope controls, to measurements of photographic prints with a ruler, to automated processing of digitally acquired images. The potential advantages of this latter process will be presented.

Accurate methods for crystal structure determination using aspects of dynamical diffraction theory

An approach to the solution of crystal structures has been developed over the past ten years which is based on the intensities of high order Laue zone (HOLZ) fine structure lines present in zone axis patterns. It is a common observation that when the individual reflections in a HOLZ ring are studied in detail, several individual excess lines are observed. These individual lines are directly related to the excited branches of the dispersion surface, created by the two dimensional dynamical diffraction which occurs in the zero order Laue zone (ZOLZ). They may either directly correspond to a single branch of the dispersion surface (a unique Bloch state) or else to a cluster of close branches (a small number of distinct Bloch states). It is often the case that the intensities of these lines may be derived from a pseudo-kinematical theory, which greatly simplifies the process of deducing atomic positions from the experimental data.

The evolution of structural order in rapidly solidified Au-Ti alloys

Abstract Rapidly solidified alloys of Au-2wt%Ti, Au-3 wt% Ti and Au-5wt% Ti have been examined using transmission electron microscopy in order to investigate both the nature of structural order induced by rapid solidification and the evolution of long-range order during post-solidification heat-treatment. 〈1½0〉 special-point order is identified as a feature of the as-solidified microstructures and an intermediate state of order, incorporating both elements of the long-range-ordered (D1a) structure and elements of 〈1½0〉 special-point order, is observed to be stable up to the nucleation temperature of the equilibrium (D1a) Au4Ti phase in Au-3 wt% Ti. The evidence from electron diffraction patterns is discussed and interpreted by considering the nature and distribution of the three-dimensional diffuse streaking observed in zone-axis patterns from a variety of different orientations. The compositions examined demonstrate that these materials are members of the ‘special-point’ family of alloys and that incorpo...

The crystal structure of eugaAl

A polycrystalline specimen of nominal formula EuGaAl with unknown crystal structure was investigated by various electron microscope techniques; EDS-, SED-, and CBED data were taken on a Philips 400 electron microscope operated at 100kV, HREM data on a Hitachi 9000 microscope operated at 300kV. The EDS data confirmed the composition for the bulk of the material but, in addition, revealed particles with other fractions of the elements. Only the EuGaAl particles were further investigated. The unit cell was determined to be orthorhombic with a ratio: a/b=0.969(2) , a/c=0.234(2) and b/c=0.234(2). The lattice constants are a=4.54(5)Ȧ, b=4.68Ȧ and c=19.97(20)Ȧ. Based on systematic extinctions for hkl reflections with h+l=2n+l, the unit cell was found to be b-centered. CBED patterns of the [001], [100], and [010] zone axes are shown in Fig. 1. The zone axis patterns are in agreement with the above stated data except for diffused (2m+l,2n+l,0)- reflections, not compatible with the above stated systematic absences. But these occurred only occasionally in conjunction with a complicated noncommensurate superlattice pattern.

A Method for Measuring Film Thickness by Zone Axis Contrast of TEM Image

The thickness of a bending thin film was determined by the comparison of the observed contrast of zone axis patterns with the calculated contrast based on a dynamical electron diffraction theory. This method allows us to measure the film thickness nondestructively at the symmetry Bragg reflection position where crystal lattice images appear clearly. Therefore, it seems to be a useful technique for high resolution electron microscopy. The estimation of the film thickness can be easily performed if the contrast of the patterns has been calculated once as a function of thickness

The HOLZ lines in Si[111] zone axis patterns

High order Laue zone (HOLZ) lines in the high symmetry zone axis of Si[111] have been carefully examined theoretically and experimentally. The dependences of the displacement of HOLZ lines in Si[111] zone axis patterns on the incident electron energy and on the lattice parameter were studied using computer simulations based on the Bloch wave many beam theory. Thus, the angular displacement of HOLZ lines was found to vary with voltage at a rate of 0.24 mrad/kV at about 100 kV The HOLZ lines (5, 5, 11), (5, 11, 5) and (11, 5, 5) were found to coincide at an incident electron energy of 103.15 ke V. Experimental convergent beam electron diffraction (CBED) patterns obtained using an electron microscope equipped with either a field emission gun (FEG) or an energy filter are compared with computer simulations. Good agreement between experimental and simulated patterns is found if the electron energy is adequately corrected for materials with known lattice parameters. The high precision of lattice parameter determinations using the coincidences of X-rays from lattice sources according to Walther Kossel and the accurate material analysis using Castaing’s microprobe are mentioned in this context.

Prospects for convergent beam electron diffraction with a 200kV cold field-emission transmission electron microscope

We review the analytical powers which will become more widely available as medium voltage (200-300kV) TEMs with facilities for CBED on a nanometre scale come onto the market. Of course, high performance cold field emission STEMs have now been in operation for about twenty years, but it is only in relatively few laboratories that special modification has permitted the performance of CBED experiments. Most notable amongst these pioneering projects is the work in Arizona by Cowley and Spence and, more recently, that in Cambridge by Rodenburg and McMullan.There are a large number of potential advantages of a high intensity, small diameter, focussed probe. We discuss first the advantages for probes larger than the projected unit cell of the crystal under investigation. In this situation we are able to perform CBED on local regions of good crystallinity. Zone axis patterns often contain information which is very sensitive to thickness changes as small as 5nm. In conventional CBED, with a lOnm source, it is very likely that the information will be degraded by thickness averaging within the illuminated area.

Precipitation of gold into metastable gold silicide in silicon.

We report a detailed investigation of the precipitation behavior of gold in float-zone silicon from a highly supersaturated solution. Nucleation, morphology, and crystallography as well as the decomposition of the solution were examined using high-resolution electron microscopy, selected area diffraction combined with tilting experiments, Hall-effect measurements, and energy dispersive x-ray spectroscopy. After in-diffusion of gold at 1275 {degree}C annealing experiments were performed at 850 {degree}C for durations ranging from 5 min up to 35 d. It is shown that gold precipitates in small spherical particles (diameter: 10--20 nm) consisting of a metastable gold silicide. By means of selected area diffraction combined with a special tilting procedure, the unit cell is proved to be orthorhombic with lattice parameters {ital a}=0.971 nm, {ital b}=0.768 nm, and {ital c}=0.703 nm. Systematic absence of reflections in several precipitate zone-axis patterns reveals the space group of the silicide to be {ital Pnma} or {ital Pn}2{sub 1}{ital a}. According to Hall-effect measurements the concentration of substitutional gold decreases to a few percent within 5 min annealing at 850 {degree}C. Only a part of it has precipitated in gold silicide particles, which are found at small extrinsic stacking faults. The stacking faults represent a density of self-interstitialsmore » Si{sub {ital i}} of about 10{sup 18} cm{sup {minus}3}, which according to control experiments is about a factor of 50 above the equilibrium concentration of Si{sub {ital i}} at 1274 {degree}C. As annealing proceeds the stacking faults disappear, and gold is finally found in spherical particles embedded stress-free into the silicon matrix.« less

Simultaneous Identification of the Bravais Lattice and Glide Planes From Microdiffraction Patterns: Deduction of the Possible Space Groups

Microdiffraction experiments obtained with a small spot size and a nearly parallel electron beam are well-adapted to most specimens and especially to small particles. They are particularly useful when Convergent Beam Electron Diffraction (CBED) patterns do not give the 2D and 3D information required to identify the point and the space groups. They can also be used to start the identification or the determination of a crystal structure. Specific and simplest CBED experiments are later realized to remove left ambiguities.The microdiffraction Zone Axis Patterns (ZAP) are composed of sharp reflections whose high angular resolution helps to appreciate the shifts and the periodicity differences between the Zero (ZOLZ) and First (FOLZ) Order Laue Zones reflection nets. Observations of thin areas at low temperature are recommended in order to produce many well visible FOLZ reflections.It was already indicated that the crystal system and the Laue class are deduced from observation of the whole pattern symmetry of the reflections.

Identification by Electron Microdiffraction of Intermetallic Phases in a Duplex Stainless Steel

2D and especially 3D symmetry information required to determine the crystal structure of four intermetallic phases present as small particles (average size in the range 100-500nm) in a Fe.22Cr.5Ni.3Mo.0.03C duplex stainless steel is not present in most Convergent Beam Electron Diffraction (CBED) patterns. Nevertheless it is possible to deduce many crystal features and to identify unambiguously these four phases by means of microdiffraction patterns obtained with a nearly parallel beam focused on a very small area (50-100nm).From examinations of the whole pattern reduced (RS) and full (FS) symmetries the 7 crystal systems and the 11 Laue classes are distinguished without ambiguity (1). By considering the shifts and the periodicity differences between the ZOLZ and FOLZ reflection nets on specific Zone Axis Patterns (ZAP) which depend on the crystal system, the centering type of the cell and the glide planes are simultaneously identified (2). This identification is easily done by comparisons with the corresponding simulated diffraction patterns.

Structural Analysis of a Metastable Al-Ge Phase Using CBED

With standard x-ray diffraction it is often impossible to solve structures in multi-phase materials. Electron probes offer diffraction from micron-sized areas though dynamical effects will be present. Here we describe a structural analysis using electron diffraction from a metastable phase in the Al-Ge system. Preliminary analysis had provided a trial structure, that is summmarised here. This phase, found in recrystallised, amorphous equiatomic Al-Ge films, was body centred tetragonal with space group I/4mcm and a=6.26Å; c=5.0Å, which was consistent with the C16 structure. To confirm the structure a set of medium order intensities was obtained from LACBED zone axis patterns around [001]. On a zone axis we find annuli filled with a network of non-systematic HOLZ reflections from a single layer in the reciprocal lattice. Thus for thin, strain-free crystals, their intensities can approach the kinematic limit. Conditional Patterson transforms of the intensities for both hkl and hk2 reflections gave peaks corresponding to inter-string vectors in agreement with the C16 structure.

TEM study of lanthanum aluminate

Lanthanum aluminate(LaAlO3) single crystal as a substrate for high Tc superconducting film has attracted attention recently. We report here a transmission electron microscopy(TEM) study of the crystal structure and phase transformation of LaAlO3 by using Philips EM420 and EM430 microscopes. Single crystals of LaAlO3 were investigated first by optical microscope. Stripe-shaped domains of mm size are clearly seen(Fig.1a), and 90° domain boundary is also obvious. TEM specimens were prepared by mechanical grinding and polishing followed by ion-milling.Fig.lb shows μm size stripe domains of LaAlO3. Convergent beam electron diffraction patterns (CBED) from single domain were taken.Fig. 2a and Fig. 2c are [001] zone axis patterns which show a 4mm symmetry, and the (200) dark field of this zone axis gives 2mm symmetry(fig.2b). Therefore the point group of this crystal is either 4/mmm or m3m. The projection of the first order Laue zone(FOLZ) reflections on zero layer (fig. 2c) shows that the unit cell is face centered. A tetragonal unit ceil is chosen, with a=0.532nm and c=0.753nm, c being determined from the FOLZ ring diameter.

CBED measurement of lattice mismatch for sub-micron quaternary structures grown on indium phosphide substrates

The positions of HOLZ lines in CBED zone axis patterns, taken from heteroeptaxial thin films, are influenced by both dynamical diffraction and strain effects. Rather than relying on a priori calculations for extracting the lattice mismatch from HOLZ line positions for sub-micron quaternary (InGaAsP) structures grown on InP, however, we have chosen to calibrate HOLZ line positions using X-ray lattice parameter measurements which were obtained from planar quaternary layers grown on InP substrates. For the active quaternary region of an electro-optical device structure, it is shown that this approach may be sensitive to a relative change in the lattice parameter as small as ±2 parts in 10 4 .