Mineralogical applications of electron diffraction. 1. Theory and techniques

The small wavelengths used in electron-diffraction experiments and the thinness of the crystals necessary for the transmission of the electron beam combine to require a somewhat different diffraction geometry for the interpretation of electron-diffraction patterns than is used in the interpretation of X-ray diffraction patterns. This geometry, based on the reciprocal lattice concept and geometrical construction of Ewald, needed for the interpretation.
of transmission electron-diffraction single-crystal patterns is here reviewed.

Transmission electron-diffraction single-crystal patterns of two monoclinic
substances, colemanite [CaB₃O₃(OH)₃•H₂O] and potassium chlorate (KC10₃), are examined and the .theory necessary for their interpretation is given in
detail. The study of these patterns furnishes a basis for the interpretation
of single-crystal patterns of materials belonging to any crystal system. It
is shown that useful unit-cell data, accurate to a few tenths of a percent,
can be obtained from the patterns of colemanite and KClO₃. A method of
evaluating unit-cell data from measurements of such single-crystal patterns
is given.

The transmission electron-diffraction powder pattern obtained from an
oriented aggregate of thin crystals gives the same unit-cell data as are
given by the electron-diffraction single-crystal pattern obtained from one
crystal of the aggregate., A graphical method is given for precisely evaluating
unit-cell constants from measurements of such a powder pattern.