Analysis of incoherent channelling patterns formed by X-ray emission from host lattice species and interstitial Cr in mullite

The position of Cr cations within a mullite lattice has recently been determined by analysis of contrast in two-dimensional incoherent channelling patterns (ICPs), obtained from variations in characteristic X-ray emission rate with electron beam orientation, near low index zone axis orientations. In previous work a thermally smeared δ-function was assumed as the interaction potential from which ICPs were calculated. Comparison with experiment yielded the position of Cr in mullite as the interstitial site <010>/4. In this paper, ICP analysis is extended to account for interaction delocalization and X-ray absorption, and to predict the extent to which delocalized oxygen ionization events may contribute to ICP contrast from mullite. It is shown how calculated variations in ICP contrast for a test site, systematically scanned across the projected unit cell, are necessary to facilitate unequivocal identification of the Cr site. Effects of Cr-doping of the mullite structure on convergent beam electron diffraction (CBED) contrast are also discussed. It is shown that ICP analysis is relatively robust in that overall ICP contrast changes little with small variations in lattice structure, unlike contrast in CBED patterns which, depending on beam index, may be extremely sensitive to small changes in overall lattice structure or composition.