Higher-order Laue Zone Lines Research Articles

Using the Hough transform for HOLZ line identification in convergent beam electron diffraction.

The Hough transform as a means for automatic line detection is applied for higher order Laue zone (HOLZ) line identification in convergent beam electron diffraction. The HOLZ line positions are commonly used to measure the strain state in the investigated material. Besides the automation, a very important aspect is the accuracy of the detected line positions. The limits are determined by the amount of noise in the pattern relative to the contrast of the HOLZ lines and the line width. Our investigations show that sub-pixel resolution can be achieved routinely. We have also developed a new strain analysis procedure in which the dynamical shift of each individual line can be taken into account using a model based on several Ewald spheres with different radii. In comparison to the effective high voltage method, finer details of the dispersion surface can be considered, which increases the accuracy of the strain analysis. A measurement of the thermal expansion of aluminium is presented as a model experiment. The lattice constants were determined with an accuracy of about 10-4.

Determination of bulk mismatch values in transmission electron microscopy cross-sections of heterostructures by convergent-beam electron diffraction

Abstract The relaxation which occurs along the thinning direction of transmission electron microscopy (TEM) cross-sections of heterostructures is still poorly known. This has so far prevented the accurate determination of the corresponding bulk mismatch values from convergent-beam electron diffraction (CBED) patterns. In this paper it is demonstrated that, by using elasticity theory, it is possible to deduce a simple relationship for (001) heterostructures which relates the latice mismatches along the different crystallographic directions of the TEM specimen, as deduced from a single CBED pattern, to the bulk value. Both 〈001〉 and 〈110〉 orientations of the TEM cross-sections are considered. However, to obtain accurate results, the validity of the kinematical approach used to deduce mismatches from high-order Laue zone line patterns must be critically checked; it depends on the crystallographic projection, on the beam voltage and, in the case of Si1−xGex heterostructures, on the Ge concentration. It is found that the best results are obtained at 100kV, working in the 〈013〉 projection, and for Ge concentrations up to 20 at.%. The method has been applied to both uniform and graded Si1−xGe/x/Si heterostructures, as well as to a B+ -implanted, epitaxially regrown Si wafer. Good agreement is found between the CBED results and the bulk values obtained from double-crystal X-ray diffractometry.

Determination of bulk mismatch values in trasmission electron microscopy cross-sections of heteostructures by convergent-beam electron diffraction

Abstract The relaxation which occurs along the thinning direction of transmission electron microscopy (TEM) cross-sections of heterostructures is still poorly known. This has so far prevented the accurate determination of the corresponding bulk mismatch values from convergent-beam electron diffraction (CBED) patterns. In this paper it is demonstrated that, by using elasticity theory, it is possible to deduce a simple relationship for (001) heterostructures which relates the latice mismatches along the different crystallographic directions of the TEM specimen, as deduced from a single CBED pattern, to the bulk value. Both 〈001〉 and 〈110〉 orientations of the TEM cross-sections are considered. However, to obtain accurate results, the validity of the kinematical approach used to deduce mismatches from high-order Laue zone line patterns must be critically checked; it depends on the crystallographic projection, on the beam voltage and, in the case of Si1−xGex heterostructures, on the Ge concentration. It is found that the best results are obtained at 100kV, working in the 〈013〉 projection, and for Ge concentrations up to 20 at.%. The method has been applied to both uniform and graded Si1−xGe/x/Si heterostructures, as well as to a B+ -implanted, epitaxially regrown Si wafer. Good agreement is found between the CBED results and the bulk values obtained from double-crystal X-ray diffractometry.

Strain Measurements in Thin Film Structures by Convergent Beam Electron Diffraction

The Convergent Beam Electron Diffraction technique (CBED) has been applied to determine the lattice strain in Si 1-x Ge x /Si heterostructures and below patterned films on silicon substrates. The well known problem of the stress relaxation which occurs in thinned TEM samples has been overcome, in the case of the heterostructures, by applying the isotropic elasticity theory to the lattice constants measured along different crystallographic directions through the shift of the High Order Laue Zone (HOLZ) lines in the central disk of the CBED patterns. In this way bulk strain values have been obtained, in good agreement with values deduced from independent techniques. In patterned structures, the high spatial resolution of the CBED technique has been applied to determine the distribution of the components of the strain tensor induced into oxidized silicon substrates by Si 3 N 4 stripes. A good agreement with the results obtained using numerical computations has been found.

Modeling Thermal Diffuse Scattering in Electron Diffraction InvolvingHigher-Order Laue Zones

The importance of thermal diffuse scattering (TDS) in electron diffraction contrast is well known. Experiments involving higher-order Laue-zone (HOLZ) reflections are highly sensitive to variations in the TDS form factors. The Einstein model for TDS gives excellent agreement with experimental convergent-beam electron diffraction (CBED) patterns containing HOLZ lines provided that the absorption coefficients are not calculated using perturbative methods but instead are evaluated exactly. This is in contrast to absorption potentials determined from experiments sensitive to beams in the zero-order Laue zone (ZOLZ) only, the use of which can be inconsistent with data sensitive to HOLZ beams. Here the features of the Einstein model important for the correct interpretation of the experimental data are analyzed and why it is inadequate to treat HOLZ beams perturbatively is discussed.

Higher-Order Laue Zone (HOLZ) Line Patterns and their Applications in Determining Microstructures in Barium-Titanate-Based Ceramics

In this paper, main higher-order Laue zone (HOLZ) lines over a cubic orientational triangle range in barium titanate (BaTiO3) ceramics are obtained by theoretical simulation as well as experimental observation. The tiny difference of the lattice parameters between the pure BaTiO3 and Sn-substituted Ba(Ti, Sn)(3) ceramics has been observed in nanometer-sized areas. The preliminary results show that these HOLZ line patterns are useful tools in studying the microstructural fluctuations in microareas of special ceramics.

Structural Transformation of Immiscible Metals Induced by Mechanical Alloying

In this paper, main higher-order Laue zone (HOLZ) lines over a cubic orientational triangle range in barium titanate (BaTiO3) ceramics are obtained by theoretical simulation as well as experimental observation. The tiny difference of the lattice parameters between the pure BaTiO3 and Sn-substituted Ba(Ti, Sn)(3) ceramics has been observed in nanometer-sized areas. The preliminary results show that these HOLZ line patterns are useful tools in studying the microstructural fluctuations in microareas of special ceramics.

On the measurement of lattice mismatch between γ and γ′ phases in nickel-base superalloys by CBED technique

Nickel base superalloys are strengthened by ordered {gamma}{prime} precipitates of L1{sub 2} structure, which are coherently embedded in the {gamma} matrix (fcc). The mismatch in lattice parameter ({delta}) between the {gamma} and the {gamma}{prime} phases influences the mechanical properties of these alloys. The value and the sign of {delta} also control the morphological changes in {gamma}{prime} (rafting), which occur during deformation at high temperatures and at low strain rates. Recently, Convergent Beam Electron Diffraction (CBED) has emerged as a powerful method for lattice parameter measurements and has been used to measure lattice constants in cubic systems including superalloys. In the CBED technique, the lattice constants are determined by analyzing the High Order Laue Zone (HOLZ) line patterns present in the transmitted beam of the CBED pattern. The symmetry and position of the HOLZ lines are very sensitively dependent on the lattice constants, the orientation and the thickness of the specimen as well as on the microscope operating conditions. By comparing the experimental HOLZ line patterns with computer simulated patterns from a known crystal, one can determine the lattice constants very accurately (comparable to X-ray measurements).

Bulk mismatch values of heterostructures as determined from convergent beam electron diffraction on thin cross sections

High order Laue zone lines present in the central disk of convergent beam electron diffraction patterns have been used to determine the bulk mismatch in thinned, cross-sectioned heterostructures, where a relaxation occurs along the thinning direction. The position of these lines is sensitive to lattice parameters along different crystallographic directions, so that information on the residual strain along the growth and the thinning directions can be extracted from a single diffraction pattern. This information has been properly combined using the isotropic elasticity theory to give the bulk mismatch. The results are in good agreement with independently obtained bulk measurements.

The Determination of Arsenic Atom Concentration in Arsenic-Doped Silicon by Using HOLZ Analysis

Higher-order Laue zone (HOLZ) disk patterns obtained from arsenic-doped and undoped silicon are investigated under the exact [011] zone axis orientation at 100 kV. For this orientation, the fine HOLZ structure consists mainly of two bright lines produced from the intersections of a HOLZ reflection with two branches associated with atomic and tunneling sites of the zeroth-layer dispersion surfaces. The arsenic atom concentration and its strain contribution can be visibly detected by comparison of the two HOLZ lines on doped silicon with those on the undoped one. It is revealed that the position for these lines is not sensitive to the crystal thickness, Debye-Waller factors, and absorption potential but to the impurity concentration and accelerating voltage. The simple fitting between experiment and dynamical simulation permits a reasonable estimation of the arsenic atom concentration.

Higher-order Laue zone contrast from arsenic-doped silicon

Higher-order Laue zone (HOLZ) disc patterns obtained from As-doped and undoped Si have been examined under the exact 011 zone axis orientation at 100 kV. For this orientation, two lines in the HOLZ disc are produced from the intersections of HOLZ reflections, with two branches corresponding to atomic and tunnelling sites of the zeroth-layer dispersion surface. The As atom concentration and its strain contribution can be visibly detected by comparison of the two HOLZ line positions. A simple fitting between experiment and simulation permits a reasonable estimate of the As atom concentration.

Effect of Mn doping on charge density in γ-TiAl by quantitative convergent beam electron diffraction

Abstract The intermetallic compound TiAi with and without 5 at.% manganese, has been studied by energy filtered convergent beam electron diffraction (CBED) in a transmission electron microscope. The addition of Mn is known to be beneficial for the mechanical properties of this material. The aim has been to investigate whether this effect is followed by detectable changes in electronic structure, with the focus on bonding. From the positions of high-order Laue zone lines in the centre disc, the lattice tetragonality is found to decrease with the addition of Mn. By ALCHEMI studies, Mn is found to substitute randomly on Ti and Al sites. The structure factors are determined using multiparameter least-square minimization based on fitting between experimental and calculated intensity profiles. The X-ray structure factors for the nine lowest order reflections have been derived for doped and undoped material. The uncertainty is typically 0·3%, and is best for the strong, lowest order reflections. The electron def...

Contrast of HOLZ lines in energy-filtered convergent-beam electron diffraction patterns from silicon

Higher-order Laue-zone (HOLZ) lines were investigated in convergent-beam electron diffraction patterns from silicon near the low-indexed zone axes [100], [110] and [111]. The visibility of these lines depends on the effective structure potentials of the reflections from the first Laue zone depending on their Debye–Waller factor. The contrast of the HOLZ lines is strongly reduced by inelastically scattered electrons. They can be excluded by an imaging Ω filter for energy losses above 2 eV. The diffraction patterns were compared with many-beam calculations. Without absorption, an excellent agreement could be achieved for the [111] and [100] zone axes, while the simulation of the [110] zone-axis pattern needed a calculation with absorption. The reason for this observation is explained in the Bloch-wave picture. Calculations with absorption, however, lead to artefacts in the intensity distribution of the [100] HOLZ pattern. In order to obtain agreement with the experiment, the Debye–Waller factor had to be modified in different ways for the different zone axes. This corresponds to a strong anisotropy of the Debye–Waller factor. To confirm this observation, the temperature dependence of the intensity distributions of the HOLZ patterns was investigated between 50 and 680 K. At room temperature, the parameter D in the Debye–Waller factor exp(−Ds2) was determined as 0.13, 0.26 and 0.55 Å2 for the zone axes [100], [111] and [110], respectively. The reliability of the conclusions is discussed.

Strain Distribution Measurement in Stainless Steels by Convergent-Beam Electron Diffraction

A convergent-beam electron diffraction technique was utilized to measure local strain distributions in stainless steels. Electron beams were focused into {210} crystal planes and the higher order Laue zone (HOLZ) lines diffracted from {375} and {119} planes were characterized by measuring the distances between the intersections of these HOLZ lines. Four parameters, including strains in three directions and one magnification factor, were calculated based on the least squares method. Strain distributions near a chromium carbide precipitate were measured in sensitized SUS 304 and it was confirmed that parallel tensile strain and vertical compressive strain to the edge of the precipitate existed and that they decreased with the distance from the edge of precipitate.

Determination of Bulk Mismatch Values in Heterostructures” by TEM/CBED

AbstractUsing isotropic elasticity theory it is possible to determine the bulk mismatch in thinned, cross-sectioned heterostructures, where a relaxation occurs along the thinning direction. This is accomplished by measuring, in the central disk of a single Convergent Beam Electron Diffraction (CBED) pattern, the position of the High Order Laue Zone lines, which are sensitive to lattice parameters along different crystallographic directions. The results obtained in both uniform and graded Sil-xGex/Si heterostructures are in good agreement with bulk values deduced from independent techniques.

Dynamical diffraction effect on HOLZ-pattern geometry in Si-Ge alloys and determination of local lattice parameter

Higher-order Laue zone (HOLZ) patterns are observed in convergent-beam electron diffraction (CBED) patterns of Si-Ge alloys and the dynamical effect on HOLZ lines is discussed in relation to the kinematical approximation to simulate the HOLZ lines. Double lines often appear from one HOLZ reflection due to the excitation of the first and second branches of the zeroth-layer dispersion surface. The magnitude of the systematic line shift from the line positions predicted by the kinematical simulation changes sensitively with specimen thickness and alloy composition depending on which branch is dominantly excited. The kinematical simulation is applicable to accurate determination of lattice parameters with a proper correction δ E: a difference between the effective electron energy and the actual microscope operating voltage. Usefulness of the kinematical simulation is demonstrated in the investigation of the segregation in a Si-Ge alloy.

Preliminary studies of the interface strain field in an Al-Al2O3 composite by means of convergent-beam electron diffraction

Various kinds of composite materials have been extensively studied concerning their manufacture processing and applications in recent years. Among them, metallic composite materials have drawn extensive attention, because they can offer selected physical, chemical and mechanical properties which cannot be obtained with traditional alloys, ceramics or organic matrix composites. The interfaces in the composites play an important role in the properties of the composite. Up to now, the studies on the interfaces have been mainly limited in the interface morphologies, interfacial reaction products and orientation relationship between the reinforcing phase, crystalline reaction products and the matrix. However, differences in thermal expansion between the reinforced phase and the matrix, generate residual stresses which may affect the aging characteristics of the matrix and the mechanical properties of such composites. Efforts have been made to measure the local lattice strain in the vicinity of the interface, quantitatively by contrast simulation and by detecting the movements of the higher order Laue zone (HOLZ) lines in conventional convergent-beam electron diffraction (CBED). As the electron probe is very close to the interface, HOLZ lines often become obscure or even split. In such cases, it is very difficult to measure the movements of HOLZ lines. Nevertheless, itmore » is possible to measure the strain by matching a dynamical simulation to the experimental splitting of HOLZ lines. Large-angle CBED (LACBED) combines real space and reciprocal space information. A single LACBED pattern shows directly the spatial variation of the lattice strain. The purpose of the present work is to explore the possibility of studying the interface strain field in composite materials according to the shifts and splittings of HOLZ lines by means of improved LACBED technique.« less

A Cbed Procedure for Determining Local Residual Stresses from Nanoscale Areas in Cermets

ABSTRACTA convergent beam electron diffraction method was used in a transmission electron microscope to determine residual thermal stresses from nanometer-scale areas in a ceramic-metal (cermet) composite material. It is demonstrated that the method is simple, but requires a standard sample for each of the phases in the composite. The principle of the technique is that the stresses are determined by comparing higher order Laue zone line shifts, due to lattice strain, in high-symmetry zone-axis electron diffraction patterns recorded under the same experimental conditions from the unknown phases and the standards. The application of the method to composite systems containing dissimilar phases, such as ceramic-metal composite systems, demonstrates the universality of the technique in obtaining local structural information of anisotropic strain unambiguously with a high accuracy. The procedure involved is described in detail with application to B4C-AI, a three-dimensional intertwined ceramic-metal composite.

Dynamical treatment of the splitting of higher-order-Laue-zone lines induced by dislocations in an icosahedral quasicrystal

The dynamical theory of electron diffraction for quasicrystals (QCs) was used to treat the splitting behaviour of higher-order-Laue-zone (HOLZ) lines induced by dislocations in icosahedral quasicrystals (IQCs). The influences of some parameters on the splitting of HOLZ lines were calculated. On the basis of this calculation, several experimental convergent-beam electron diffraction patterns from the aluminium–copper–iron IQC were simulated. Good agreement between the experiment and the simulation confirms the correctness of the dynamical theory of electron diffraction for QCs.

New method of Bravais lattice determination

A new method of Bravais lattice determination from a single convergent beam electron diffraction (CBED) pattern is proposed. The method is based on the principle that a primitive reciprocal lattice cell can be measured accurately from the deficiency line of medium or high order reflections or high order Laue zone (HOLZ) line positions within the central disk of a single CBED pattern taken near an arbitrary zone axis. This primitive cell can be reduced to the unique Niggli cell and thus the Bravais cell by Krivy and Gruber reduction procedures. This method could be very useful in identifying phase of mixed phase materials or as the first step toward determination of a new structure or as an automated procedure of indexing diffraction patterns of known structure.