Exact Bragg Condition Research Articles

Effect of the Diffraction Condition on the Mean Free Path of 50 kV Electron for Plasmon Excitation in Aluminium

The mean free path of high energy electrons for the plasmon excitation has been measured in a single crystal of aluminium by a Möllenstedt type energy analyser combined with an electron microscope. The mean free path of 50 kV electron is 1000±100Å when the crystal is far away from the exact Bragg condition to the incident electrons. When the crystal is near the exact Bragg condition to the incident electrons, an anomaly in the mean free path was observed. The mean free path was 900±100Å and 1100±100Å when W >0 and W <0 respectively, where W is a parameter showing the deviation from the exact Bragg condition. This result indicates that there are two mean free paths corresponding to the two Bloch waves, i. e. The Bloch wave on the branch-1 has the shorter mean free path than that on the branch-2.

Mean Free Path of Fast Electrons for Plasmon Excitation in a Single Crystal

The mean free path of 40–100 KeV electrons for plasmon excitation was measured by analysing energy spectra of bright field images of aluminum single crystal. Equal thickness fringes by (111) reflection were used to measure the specimen thickness. It was found that the mean free path slightly depends on the crystal orientation, and its voltage dependence at the exact Bragg condition agrees qualitatively well with Ferrell's theory (Phys. Rev. 101 (1956). 554).

The Effect of Systematic Reflections on the (110) Extinction Distance in Molybdenum

AbstractThe dependence of the (110) extinction distance in molybdenum on Δθ, the deviation from the exact Bragg condition, has been investigated. The results indicate that near the exact Bragg condition (0° &lt; Δθ &lt; 0.5°) the two‐beam theory is in good agreement with experiment. For larger values of Δθ the effects of systematic reflections become important. The agreement between the multi‐beam theory and experiment is excellent for values of Δθ greater than 1.25°. However, for intermediate values of Δθ where the depth periodicities are complex, neither the two‐ or multi‐beam theories give an adequate description of the experimental results obtained.

Applications of Kikuchi Line Analyses in Electron Microscopy

The usefulness of Kikuchi line diffraction patterns for electron microscopy experiments is demonstrated. Examples are given of the determination of exact foil orientation, the calibration of tilting stages, and the determination of the magnitude of the deviation parameter s from the exact Bragg condition.

Multiple Interference Fringes in Electron Micrographs of Wedge-Shaped Single Crystals

Multiple interference fringes have been observed in electron micrographs of wedge-shaped single crystals of poly-L-proline II. The interference fringes which occur when strong Bragg reflection is possible have been observed to split into two components as a result of secondary electron scattering and double refraction within the crystals. The separation of the fringe components is a function of the deviation of the incident electron beam from the exact Bragg condition for the reflection. The fringe contours are qualitatively interpreted using the dynamical theory of electron scattering.