PHASE DETERMINATION BY DUAL SPACE METHODS OF ELECTRON CRYSTALLOGRAPHY: A COMPARISON OF I23 & I2₁3 STRUCTURAL PHASES A. Schwartzman, P. Goodman,School of Physics, University of Melbourne, Parkville, Australia 3052, A.W.S.Johnson, E.M.Centre, University of Western Australia, Nedlands, W.A., Australia 6009.

No discussion on direct methods of structural phase determination can be considered complete without reference to the dual space methods of electron crystallography, whereby Fourier space and direct space data are collected by means of CBED and HREM respectively on the same sample. The method is based on the well-known relationship that phases in one space amount to displacements in the other. In this paper we illustrate this method by showing how the look-alike space group pairs I23/I2₁3 and I222/I2₁2₁2₁, commonly held to be indistinguishable since the space-group-forbidden reflections characterising the 2-fold screw axis are already extinguished by lattice centering, may be resolved in this way.

We present data on the crystal systems Bi₁₂GeO₂₄ (I23) and Ba₃Fe₂O₅Cl₂ (I2₁3). The former compound shows accurate 2-fold symmetry in the [001] CBED pattern, while the I2₁3 compound shows a weak departure from symmetry in the FOLZ reflections, due to 3-dimensional dynamic interaction. However distinction is much more unequivocal using dual space methods. High-resolution [001]-projection micrographs for Ba₃Fe₂O₅Cl₂ show a molecular structure as required by the projected horizontal 2₁ operators. Direct observation of this operation is possible in real space since this results in a unit-cell displacement, spatially distinct from the centering displacement caused by body centering.