Estimation technique of global fringe contrast using in interferometers with adjustable contrast

Observation of faint contrast at planar faults in alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108842 ◽

1978 ◽

Vol 36 (1) ◽

pp. 340-341

Author(s):

K. Kuroda ◽

Y. Tomokiyo ◽

T. Kumano ◽

T. Eguchi

Keyword(s):

Reciprocal Lattice ◽

Beam Theory ◽

Al Alloys ◽

Small Displacement ◽

Electron Microscopic ◽

Lattice Vector ◽

Fringe Contrast ◽

Planar Fault ◽

Lattice Displacement ◽

The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

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Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134144 ◽

1990 ◽

Vol 48 (2) ◽

pp. 110-111 ◽

Cited By ~ 1

Author(s):

F. Hasselbach ◽

A. Schäfer

Keyword(s):

Group Velocity ◽

Wave Packets ◽

Index Of Refraction ◽

Electron Wave ◽

Fringe Contrast ◽

Faraday Cage ◽

Optical Index ◽

Wien Filter ◽

Coherent Wave ◽

Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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Simulation and Contrast Analysis of tem Images of Cracks

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100181658 ◽

1990 ◽

Vol 48 (1) ◽

pp. 578-579

Author(s):

D. Goyal ◽

A. H. King

Keyword(s):

Displacement Vector ◽

Crack Tip ◽

Perfect Crystal ◽

Operating Conditions ◽

Displacement Fields ◽

Fringe Contrast ◽

Orthogonal Geometry ◽

Moire Fringe ◽

Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

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