Moire Fringes on Precipitates in Quenched and Aged Beryllium

A number of investigators have examined moire patterns on precipitate particles in various age-hardening alloys. For example, Phillips has analyzed moire fringes at cobalt precipitates in copper and Von Heimendahl has reported on moire fringes in the system Al-Au. Recently, we have observed moire patterns on impurity precipitates in beryllium quenched in brine from 1000°C and aged at various temperatures in the range of 500-800°C. This heat treatment of beryllium rolled from vacuum cast ingots produces the precipitation of both an fee ternary phase, AlFeBe4, and an hcp binary phase, FeBe11. However, unlike a typical age-hardening alloy, the solute content of this material is low (less than 1000 ppm of Fe and 600 ppm of Al) and hence the total volume fraction of precipitates is small. Therefore there is some difficulty in distinguishing the precipitates and their orientation relationships with the beryllium matrix since the weak precipitate spots generally do not appear on the diffraction patterns.

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The Use of Moiré Patterns in TEM Images to Measure Precipitate Composition in Al-Si-Ge Alloys

Microscopy and Microanalysis ◽

10.1017/s1431927600027264 ◽

2001 ◽

Vol 7 (S2) ◽

pp. 238-239

Author(s):

V. Radmilovic ◽

D. Mitlin ◽

S. Hinderberger ◽

U. Dahmen

Keyword(s):

Elastic Interaction ◽

Lattice Parameter ◽

Multiphase System ◽

Orientation Relationships ◽

Precipitate Crystal ◽

Large Matrix ◽

Moiré Fringes ◽

Moire Patterns ◽

Lattice Images ◽

Moiré Patterns

Moiré patterns are commonly formed in multiphase system when diffracting planes of similar spacing and orientation lead to interference effects. They can be used experimentally to evaluate the stress distribution in materials [1], to analyze orientation relationships and latttice strain in diffraction contrast microscopy, or, combined with the related geometrical phase technique, to analyze displacements in high resolution lattice images [2,3]. The interpretation of moiré fringes is often not straightforward due to the elastic interaction between the crystals at the interface and the dynamical nature of electron diffraction [4]. However, if the two lattices are fully relaxed, or if a small precipitate crystal is embedded in a large matrix, moiré patterns can give a simple and direct measure of orientation and lattice constants. in the present work, the moiré technique has been applied to the quantitative analysis of lath-shaped Ge or Ge-Si precipitates in Al with the aim to determine the composition (the Si:Ge ratio) from the lattice parameter indicated by the moiré fringes.

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Direct imaging of order-disorder and antiphase domain structures in Ti3Al intermetallic compound

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175533 ◽

1990 ◽

Vol 48 (4) ◽

pp. 480-481

Author(s):

H. Q. Ye ◽

T.S. Xie ◽

D. Li

Keyword(s):

Intermetallic Compound ◽

Volume Fraction ◽

Fundamental Problem ◽

Antiphase Domain ◽

Atomic Scale ◽

Orientation Relationships ◽

Domain Structures ◽

Α Phase ◽

Diffraction Patterns ◽

Two Phases

The Ti3Al intermetallic compound has long been recognized as potentially useful structural materials. It offers attractive strength to weight and elastic modulus to weight ratios. Recent work has established that the addition of Nb to Ti3Al ductilized this compound. In this work the fundamental problem of this alloy, i.e. order-disorder and antiphase domain structures was investigated at the atomic scale.The Ti3Al+10at%Nb alloys used in this study were treated at 1060°C and then aged at 700°C for 2 hours. The specimens suitable for TEM were prepared by standard jet electrolytic-polishing technique. A JEM-200CX electron microscope with an interpretable resolution of about 0.25 nm was used for HREM.The [100] and [001] projections of the α2 phase were shown in Fig.l.The alloy obtained consist of at least two phases-α2(Ti3Al) and β0 structures. Moreover, a disorder α phase with small volume fraction was also observed. Fig.2 gives [100] and [001] diffraction patterns of the α2 phase. Since lattice parameters of the ordered α2 (a=0.579, c=0.466 nm) and disorder α phase (a0=0.294≈a/2, c0=0.468 nm) are almost the same, their diffraction patterns are difficult to be distinguished when they are overlapped with epitaxial orientation relationships.

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Analysis of moiré patterns in images of thin YBa2Cu3O7-δ films on MgO

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121582 ◽

1992 ◽

Vol 50 (1) ◽

pp. 236-237

Author(s):

M. Grant Norton ◽

C. Barry Carter

Keyword(s):

Metal Films ◽

Double Diffraction ◽

Bright Field ◽

Small Deviations ◽

Moiré Fringes ◽

Moire Patterns ◽

Interfacial Strain ◽

Fringe Patterns ◽

Moiré Patterns ◽

Scattered Beam

Moiré fringes arise from the interference between diffracted beams from two overlapping crystals (double diffraction) and in the bright-field case the forward scattered beam. The fringe patterns act as magnifiers of lattice imperfections and small deviations from perfect crystallographic orientation and symmetry. Moiré patterns have been used previously to study, for example, the growth of metal films on substrates such as molybdenum disulfide—which can easily be prepared to electron transparency. Moiré patterns can be used to identify microstructural defects in epitactic deposits. For example, the presence of rotationally misaligned grains, the presence of dislocations, and residual interfacial strain will be revealed in the fringe pattern.

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An electron microscope study of synthetic graphite

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0202 ◽

1959 ◽

Vol 253 (1274) ◽

pp. 390-402 ◽

Cited By ~ 27

Keyword(s):

Electron Diffraction ◽

Electron Micrographs ◽

Stacking Faults ◽

Grain Structure ◽

Thin Sections ◽

Average Value ◽

Moire Patterns ◽

Synthetic Graphite ◽

Diffraction Patterns ◽

Moiré Patterns

The ultra-microtome has been used to obtain thin sections of synthetic graphite blocks. The thickness of the sections was measured by shadowcasting and measuring the shadow length at appropriate edges. An average value of 150 Å was obtained. Transmission electron micrographs of thin sections showed moire patterns and the interrelation of these moire patterns revealed a characteristic grain structure in graphite akin to that seen in metals but with component microcrystals of smaller dimensions. The area of the individual micro - crystals forming the grain structure was measured and was found to be 0·11 + 0·074μ 2 . The boundary between neighbouring microcrystals was narrow and of around 50 A in width. Pores were visible at the junction of three or more contiguous microcrystals and were of diameter 400 to 800 Å. The selected-area electron diffraction technique was used to determine the orientation of individual microcrystals in the graphite sections. It was found that the hexagonal layer net planes were lying parallel or at a very small angle to the plane of the section. The electron diffraction patterns were also used to correlate the layer stacking faults in individual microcrystals both by counts of individual reflexions on the (1120) diffraction ring and by counts of the extra reflexions due to the long spacings between successive displaced layers. The average value of 13 Å found for the distance between successive stacking faults is equivalent to the distance between four hexagonal layer net planes. The moire patterns in the electron micrographs could be related to the long spacings in the electron diffraction patterns. It was possible to calculate the angle of twist between successive stacking faults from the long spacing or from the moire pattern. Dislocations were seen in many of the thin sections and were observed as extra terminating half-lines in the moire patterns; these dislocations were present in the hexagonal layer net planes themselves and indicated that there was in this region a considerable deformation of the benzenoid structure of the hexagonal layer nets. The measured frequency for their occurrence was 3·3 x 10 7 /cm 2 . Slip planes were also detected in some specimens.

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Shear and rotation moiré patterns obtained by spatial filtering of diffraction patterns

Journal of Strain Analysis ◽

10.1243/03093247v062134 ◽

1971 ◽

Vol 6 (2) ◽

pp. 134-142 ◽

Cited By ~ 8

Author(s):

J A Clark ◽

A J Durelli ◽

V J Parks

Keyword(s):

Diffraction Pattern ◽

Spatial Filtering ◽

Circular Ring ◽

Fourier Optics ◽

Fraunhofer Diffraction ◽

Diametral Compression ◽

Moire Patterns ◽

Diffraction Patterns ◽

Indicial Equation ◽

Moiré Patterns

Two superposed gratings can produce many other moiré patterns in addition to the pattern commonly observed. They correspond to different forms of the indicial equation employed in parametric descriptions of moiré phenomena. An analysis of the Fraunhofer diffraction pattern of two superposed gratings by the methods of Fourier optics shows that the different moiré patterns can be separately observed by spatial-filtering techniques. Examples of additive and subtractive moiré patterns obtained individually over the whole field of two superposed gratings are presented. This method is combined with a previously developed method for obtaining partial derivatives from deformed gratings as a direct moiré pattern (rather than as moiré of moiré) to determine experimentally the whole field of cartesian shears and rigid rotations. The method is applied to a circular ring subjected to diametral compression.

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Moiré fringes of higher-order harmonics versus higher-order moiré patterns

Applied Optics ◽

10.1364/ao.57.009777 ◽

2018 ◽

Vol 57 (33) ◽

pp. 9777 ◽

Cited By ~ 1

Author(s):

Mohammad Yeganeh ◽

Saifollah Rasouli

Keyword(s):

Higher Order ◽

Moiré Fringes ◽

Moire Patterns ◽

Moiré Patterns

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The coprecipitation of Cr3P and Cr in Cu

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100105886 ◽

1988 ◽

Vol 46 ◽

pp. 764-765

Author(s):

M.J. Witcomb ◽

U. Dahmen ◽

K.H. Westmacott

Keyword(s):

Orientation Relationship ◽

Interface Structure ◽

Model System ◽

Relative Orientation ◽

Age Hardening ◽

Precipitation Behavior ◽

Solution Treated ◽

Small Needle ◽

Diffraction Patterns ◽

Interface Structures

Cu-Cr age-hardening alloys are of interest as a model system for the investigation of fcc/bcc interface structures. Several past studies have investigated the morphology and interface structure of Cr precipitates in a Cu matrix (1-3) and good success has been achieved in understanding the crystallography and strain contrast of small needle-shaped precipitates. The present study investigates the effect of small amounts of phosphorous on the precipitation behavior of Cu-Cr alloys.The same Cu-0.3% Cr alloy as was used in earlier work was rolled to a thickness of 150 μm, solution treated in vacuum at 1050°C for 1h followed by quenching and annealing for various times at 820 and 863°C.Two laths and their corresponding diffraction patterns in an alloy aged 2h at 820°C are shown in correct relative orientation in Fig. 1. To within the limit of accuracy of the diffraction patterns the orientation relationship was that of Kurdjumov-Sachs (KS), i.e. parallel close-packed planes and directions.

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