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

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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Moire Fringes on Precipitates in Quenched and Aged Beryllium

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100101888 ◽

1968 ◽

Vol 26 ◽

pp. 426-427

Author(s):

F. J. Fraikor ◽

A. W. Brewer

Keyword(s):

Ternary Phase ◽

Volume Fraction ◽

Age Hardening ◽

Orientation Relationships ◽

Solute Content ◽

Moiré Fringes ◽

Moire Patterns ◽

Total Volume Fraction ◽

Diffraction Patterns ◽

Moiré Patterns

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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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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Dynamical theory of electron diffraction for the electron microscopic image of crystal lattices II. Image of superposed crystals (moiré pattern)

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1961.0007 ◽

1961 ◽

Vol 253 (1033) ◽

pp. 490-516 ◽

Cited By ~ 19

Keyword(s):

Electron Diffraction ◽

Present Theory ◽

Dynamical Theory ◽

Bragg Angle ◽

Electron Microscopic ◽

Microscopic Images ◽

Electron Microscopic Image ◽

Moire Patterns ◽

Lattice Images ◽

Moiré Patterns

The dynamical theory of electron diffraction is applied to the interpretation of electron microscopic images of moire patterns. Two cases often observed are treated. One is the case where two plate-shaped crystals are superposed closely without a vacuum layer between them and another is the case where two crystals are superposed with a vacuum layer between them. Resolved lattice images of two superposed crystals are also interpreted. The intensity profiles of the images vary with the thicknesses of the crystals and vacuum layer and with the deviation from the Bragg angle. The shifts of the fringes and anomalies of the contrast which are expected from the present theory were observed in the electron microscopic images of moire patterns of cupric sulphide, palladiumgold and platinum-phthalocyanine. The relation between moiré patterns and crystal structure is also discussed.

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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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What can be inferred from moiré patterns? A case study of trimesic acid monolayers on graphite

Faraday Discussions ◽

10.1039/c7fd00113d ◽

2017 ◽

Vol 204 ◽

pp. 331-348 ◽

Cited By ~ 5

Author(s):

Saskia Spitzer ◽

Oliver Helmle ◽

Oliver Ochs ◽

Joshua Horsley ◽

Natalia Martsinovich ◽

...

Keyword(s):

Self Assembly ◽

Lattice Parameter ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

Trimesic Acid ◽

Moire Pattern ◽

Porous Networks ◽

Moiré Pattern ◽

Moire Patterns ◽

Moiré Patterns

Self-assembly of benzene-1,3,5-tricarboxylic acid (trimesic acid – TMA) monolayers at the alkanoic acid–graphite interface is revisited. Even though this archetypal model system for hydrogen bonded porous networks is particularly well studied, the analysis of routinely observed superperiodic contrast modulations known as moiré patterns lags significantly behind. Fundamental questions remain unanswered such as, are moiré periodicity and orientation always the same, i.e. is exclusively only one specific moiré pattern observed? What are the geometric relationships (superstructure matrices) between moiré, TMA, and graphite lattices? What affects the moiré pattern formation? Is there any influence from solvent, concentration, or thermal treatment? These basic questions are addressed via scanning tunneling microscopy experiments at the liquid–solid interface, revealing a variety of different moiré patterns. Interestingly, TMA and graphite lattices were always found to be ∼5° rotated with respect to each other. Consequently, the observed variation in the moiré patterns is attributed to minute deviations (<2°) from this preferred orientation. Quantitative analysis of moiré periods and orientations facilitates the determination of the TMA lattice parameter with picometer precision.

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