On the relationship between projected crystal potential and the form of certain zone axis patterns in high energy electron diffraction

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Abstract
An investigation of the form of electron diffraction zone axis patterns has been made for zone axes where the projected potentials may be regarded as arrays of identical, approximately cylindrically symmetric, potential wells. Close-packed, approximately close-packed, square and rectangular arrangements of the potential wells are considered (such as occur for the 〈111〉, 〈110〉 and 〈100〉 axes of f.c.c. and b.c.c. crystals for example). The observed patberns are interpreted in terms of dispersion surfaces obtained by matrix calculations. A simple development of the patterns is observed in the first Brillouin zones if the patterns are arranged according to their proximity to the second critical voltage. A method for measuring the second critical voltage is described and discussed and the importance of diagonalizing complex matrices near this degeneracy is emphasized. The previously reported approximate equivalence of small voltage and thickness changes to zone axis patterns (Tatlock and Steeds 1973) is investigated.