Dynamical Theory of Kikuchi Electrons. Page: 4 of 9
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DYNAMICAL THEORY OF IKUCHI ELECTRONS UCRL-19631
T. Y. Tan
Inorganic Materials Research Division, Lawrence Radiation Laboratory,
Department of Materials Science and Engineering, University of California,
Berkeley, California 94720
In transmission electron microscopy it is generally believed that for the
pairs of Kikuchi lines resulting from inelastic scattering, the line nearer
the transmitted spot on the diffraction pattern should always be associated
with deficiency of electrons while the other should always contain excess
electrons. However, Thomas and Bell (1,) demonstrated experimentally that in
a case where the incident beam occurs at an exact Bragg angle, the intensities
of the lines in a pair reversed, depending only on foil thickness. This color
reversal of the Kikuchi line pair is associated with the dynamical behavior
of the Kikuchi electrons where crystal absorption plays an essential role.
Based on the two-beam dynamical theory for elastic electrons, a corresponding
(two-beam) theory on the fine structures of the Kikuchi electron intensity
distributions in relation to the various diffraction and absorption parameters
has been formulated (2). In this theory, the Kikuchi electrons were taken to
be those inelastic electrons generated in an infinitesimal thickness of the
specimen which subsequently underwent Bragg diffraction. The initial inelas-
tic electron wave amplitudes generated at any position inside the crystal
were obtained phenomenologically by considering the decrease in amplitude of
the elastic electrons due to absorption by the crystal. Appropriate scatter-
ing factors for the inelastic electrons were also phenomenologically intro-
duced for the proper Bragg diffractions being considered. A scattering matrik
similar to that used in dynamical scattering calculations (with absorption
included) was used to describe the effects upon these newly generated inelas-
tic electrons as they traveled through the crystal.
'It can be shown that the asymmetrical nature in angular distributions of the
Kikuchi electron intensities is due to anomalous absorption of the electrons
by the crystal. With correctly chosen absorption parameters, specimen thick-
ness, etc., the color reversal experiment of Thomas and Bell (1) can be
explained. It is well known that the intensity within the Kikuchi band, i.e.
the region bounded by the pair of Kikuchi lines, may change from a deficiency
to an excess of electrons when the energy of the incident electrons is
.increased or the crystal thickness decreased (3,4). This phenomenon can also
be explained in terms of the anomalous absorption of electrons.
Finally, and also contrary to general assumption, the angular separation
between the two lines of the Kikuchi pair has been shown to be thickness
dependent and therefore may be appreciable different from the observed line
spacing between the Kikuchi pair and the corresponding diffraction spot pat-
tern (figs. 1 and 2). This phenomenon is also associated with anomalous
absorption. Thus, the principal experimental behavior of Kikuchi electrons
is quite well explained by the theory.
The research is being performed in partial fulfillment of the Ph. D. degree,
University of California Berkeley, under the direction of Professor Gareth
Thomas. I acknowledge the contributions of Dr. W. L. Bell. This work is
supported by the U.S. Atomic Energy Commission through the Lawrence Radiation
1. G.Thomas and W.L. Bell, European Regional Conference on E.M. 283, 1968,Rome
2. Complete details of the theory are to be published, see T. Y. Tan, W.L. Bel.
and G. Thomas, UCRL-19020 (1970).
13. H. Boersch, Phys. Z. 38, 1000, 1937.
4. H. Pfister, Ann. Phys. Lpz. 11, 293, 1953.
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Tan, T. Y. Dynamical Theory of Kikuchi Electrons., report, January 1, 1970; [Berkeley, California]. (digital.library.unt.edu/ark:/67531/metadc871423/m1/4/: accessed August 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.