Orbital ordering in LaMnO₃: estimates of structure factors and comparison of measurement methods

Abstract

This paper shows that the phenomenon of orbital ordering should be detectable by energy-®ltered quantitative convergent-beam electron diffraction (QCBED). The structure factors of LaMnO 3 crystals are calculated using a non-spherical atomic scattering model of the Mn 3+ ion. Several low-order electron structure factors showed pronounced change with orbital ordering, in which the e 1 g electron orders in the 3d(3z 2 À r 2 ) orbital leaving the 3d(x 2 À y 2 ) unoccupied. In contrast, the X-ray structure factors showed very small change. Orbital order is important in transition-metal oxides, including colossal magnetoresistive manganite oxides. The calculations show that by using QCBED it is possible to measure the subtle changes in electron structure factors due to orbital ordering of the e 1 g electron of the Mn 3+ ion in an LaMnO 3 crystal. A comparison of methods for structure-factor measurement is given, including Bragg X-ray and -ray diffraction, X-ray Pendello È sung and critical-voltage methods. New measurements by QCBED of structure factors in rutile are compared with the Bragg X-ray values. These show that QCEBD can provide an accurate extinction-free measurement of low-order structure factors, which is extremely dif®cult or perhaps impossible when using other methods applied to real crystals.

Precession technique and electron diffractometry as new tools for crystal structure analysis and chemical bonding determination

“…Indeed, electron scattering factors are much more sensitive to atomic bonding variations than equivalent X-ray scattering factors. For example, in LaMnO 3 a change of 1.45% in electron structure factors amplitudes of the strongest reflections (detectable by quantitative convergent beam electron diffraction-QCBED) account for a change of 0.26% or less for equivalent X-ray structure factors, which is hardly detectable [2]. Considerable progress on resolving crystal bonding in atoms has been reported recently with QCBED using an energy filter and a CCD camera [3].…”

“…The Vincent-Midgley technique originally stemmed from studies of HOLZ reflections in CBED patterns, where precession was a logical extension. 2 The geometry of precession can be seen at Fig. 1 [21] where the beam is rocked in a conical fashion with a wide symmetrical tilt above the specimen.…”

Crystal structure refinement using Bloch-wave method for precession electron diffraction

“…Nevertheless, if all experimental conditions (with possible source of errors) are well under control, is possible then that the final reduced parameters would be of high accuracy, as was shown in Ref. [12].…”

“…[12], extinction parameter has been used. At present is impossible to have a strict theoretical account of all experimental features that may influence our experiment, therefore for compensation of differences between experimental and calculated dynamical intensities refinement of phenomenological extinction parameter has been used.…”

“…As has been shown in Ref. [12] such measurement errors should be evaluated statistically after repeating several measurements of those parameters; those error values should not be estimated through refinement, as their magnitude could be 10-100 times less in relation with statistical errors. Is important that experimental data have to be corrected from all type of errors (including possible systematic errors), otherwise all reduced parameters will be distorted after refinement.…”