Electron diffraction study of MgOh00-systematic interactions

Abstract

An investigation was made of the MgO h00-systematic interactions using the experimental method of fine-focus convergent beam electron diffraction. The experimental data were compared directly with intensity distributions computed from assumed MgO structure factors by multiple-beam diffraction theory.The investigation showed that close agreement could be obtained between calculation and experiment provided specific values were chosen for the scattering potentials and the crystal thickness. Close agreement was found with a value of V200 = 6"92 volt. This value is appreciably lower than the value of 7"29 volt derived from the Hartree-Fock calculations for neutral atoms, but is in agreement with the scattering curve derived by Tokonami using a model for the O2-ion recently developed by Yamashita.A form of distribution was found for the absorbing potential (leading to a Borrmann effect) which i was close to that of 6 functions located at the atom sites. The value obtained for V20o, 0.14 volt, was considerably lower than that estimated in some earlier investigations. Experimental and theoretical reasons for this difference are given. It was apparent that study of a more strongly interacting reflexion set than the MgO h00-systematics would give more precision in the potential determination. In fitting the calculated and experimental curves the crystal thickness was determined to within one unit cell or with an accuracy of 0.5 ~o for the crystals studied. IntroductionMany studies have been made in the past of dynamic effects in diffraction patterns from magnesium oxide. Recently single wedge-crystals have been examined, both in a diffraction camera (Lehmpfuhl & Moli6re, 1961, 1962, and in the electron microscope (Kamiya, 1963;Uyeda & Nonoyama, 1965) to obtain values of Vh and V~,, the Fourier coefficients of the elastic and inelastic scattering potential. Mostly the two-beam approximation of Bethe has been used for these determinations. From the magnitude of the term (V gig z) implicit inBethe's derivation for addition-potentials, the importance of the higher order interferences can be estimated in each case. It is expected that this systematic interference effect will be more important for the 200 reflexion than for example for the 220 and 420 reflexions.Estimates made for 11200 and V~0o from the two-beam ealculati0n will be in error from this effect. Corrections for the weak beams in the form of addition-potentials can be applied from Bethe's theory under ":ertain conditions, namely when the excitation error for the main beam is very small and the excitation errors of all other reflexions appearing in the correction terms are large. However, this correction gives no solution for the weak beams, nor for the main beams far from the Bragg position. On the other hand as has been pointed out by Howie & Whelan (1960), when n-beam theory is used the systematic effect itself can lead to a better determination of the scattering potentials, and in particular of the absorption factors, provided the experimental data are adequat...

Numerical evaluations ofN-beam wave functions in electron scattering by the multi-slice method

“…As examples we refer to Goodman & Lehmpfuhl (1967), (1968) Lynch & O'Keefe (1972). In addition two further examples are included in order to show how particular features of the multi-slice method may be exploited.…”

“…The solution itself is not suited to direct numerical evaluation, but a numerical method based on the finite-slice approximation (Moodie, 1965) called here the multi-slice method, was tested by Goodman & Lehmpfuhl (1967) and has been since greatly expanded and applied to a large range of problems, including the study of large and complicated unit cells by Lynch & O'Keefe (1972). Most, if not all, published calculations made for comparison with experimental work have used either this method, or Bethe's eigenvalue method (recent examples of the latter: Lehmpfuhl, 1972;Ayroles & Mazel, 1970;Lally, Humphreys, Metherell & Fisher, 1972).…”

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

“…For reviews of this work, see Cowley (1967) and Goodman (1978). Typical of this approach are the papers of Goodman & Lehmpfuhl (1967) Ishizuka & Taft0 (1984) for ZnS, Kreutle & Meyer-Ehmson (1969) for Si, , Shishido & Tanaka (1976) for Ge, Smart & Humphreys (1978) for Cu, Smith & Lehmpfuhl (1975), Steeds & Mansfield (1984), Terasaki, Watanabe & Gj0nnes (1979) for Si and Gjonnes, Gjonnes, Zuo & Spence (1988) and Zuo, Spence & O'Keefe (1988) for GaAs.…”

Point-group determination by convergent-beam electron diffraction

“…The diffracted intensity in a disk can be compared with that calculated on the basis of the dynamical theory of electron diffraction. Goodman & Lehmpfuhl (1967) applied CBED to the precise measurement of the low-order structure factors of MgO. When their work is checked from the viewpoint of diffraction symmetry, an important symmetry is found in the 200 diffraction disk: that is, the intensity distribution in the disk is symmetric with respect to the Bragg position.…”