Absorption in high-energy electron diffraction from non-centrosymmetric crystals

Measurements of the phase (and amplitude) of the 00.2 structure factor of BeO are reported. These were obtained by applying an automated least-squares refinement method to experimental convergent-beam transmission electron diffraction data, collected from sub-micrometer single-crystal regions of two different thicknesses. Multiple-scattering effects were included, using the Bloch-wave method. Perturbation methods were used to include weak beams and to estimate errors. After conversion to X-ray structure factors, it was found that ~0x(00.2)=-1.190 (9)rad. The same value was found, within experimental error, using data collected from a region of different thickness. New single-crystal X-ray results are also reported, which are in good agreement with the electron diffraction results. Phases derived from multipole refinement using X-ray data are about fifty times less accurate than the electron results. This electron diffraction technique may be the most accurate method for the measurement of low-order structurefactor phases from acentric crystals with small unit cells. The method may therefore allow the extension of previous highly accurate studies of charge density in silicon to acentric materials from which large single crystals cannot be grown.1989; Hiimmer et al., 1990).

supporting

confidence: 62%

“…In X-ray diffraction, this effect is known as anomalous dispersion. Its effects in electron diffraction were pointed out by Bird (1990) and have also been observed in electron-energy-loss spectroscopy (Taftgt, 1987). The effect allows the phase of the absorption coefficient to be measured from a comparison of the g and -g rocking-curve intensities.…”

mentioning

confidence: 74%

Measurement of individual structure-factor phases with tenth-degree accuracy: the 00.2 reflection in BeO studied by electron and X-ray diffraction

Zuo¹,

Spence²,

Downs³

1993

“…Our results are similar to his, which is surprising given that his azimuthal integration is performed incorrectly. Table 1 also shows that the Buxton & Loveluck (1977) parameterization of f'~(s) does not provide a particularly good approximation to the full integral, particularly for large g. Further discussion on the absorptive potential, including its ratio to the elastic potential, its variation with g and its temperature dependence may be found in the following paper (Bird, 1990). However, the primary purpose of this work is not to calculate the absorptive potential for certain special cases, but to provide the means of constructing it for any material.…”

Section: Interpolationmentioning

confidence: 99%

“…One example of this is for non-centrosymmetric crystals where both Vg and Vg have an amplitude and a phase. The 10% rule assumes that the phases of the two are the same, but there is no reason in principle why this should be the case, and a phase difference can lead to interesting and observable effects (Gevers, Blank & Amelinckx, 1966;Bird, James & King, 1989;Bird, 1990). With electron microscopy becoming increasingly quantitative, both in high-resolution imaging (e.g.…”

Section: )Vgmentioning

confidence: 99%

Absorptive form factors for high-energy electron diffraction

Bird¹,

King²

1990

Self Cite

257

102

The thermal diffuse scattering contribution to the absorptive potential in high-energy electron diffraction is calculated in the form of an absorptive contribution to the atomic form factor. To do this, the Einstein model of lattice vibrations is used, with isotropic Debye-Waller factors. The absorptive form factors are calculated as a function of scattering vector s and temperature factor M on a grid which enables polynomial interpolation of the results to be accurate to better than 2% for much of the ranges 0-< Ms 2<-6 and 0_< M_<2/~2. The computed values, together with an interpolation routine, have been incorporated into a Fortran subroutine which calculates both the real and absorptive form factors for 54 atomic species.

“…If absorption is included exactly (not using perturbation theory), then small differences appear between the g and -g rocking curves in two-beam theory. These are responsible for asymmetries in Kikuchi lines (Allen & Rossouw, 1989;Bird, 1990;Bird & Wright, 1989) and on inner-shell energy-loss spectra (Tafto, 1987), both of which may also be used to determine the polarity of acentric crystals. (Energy 'absorbed' by inelastic processes from the elastic 'channel' makes a positive contribution to peaks in the energy-loss spectrum.…”

Section: F/ Lmentioning

confidence: 99%

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

Spence¹

1993

138

A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1 °. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting K_ikuchi-and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.