STRUCTURE DETERMINATION OF A RHOMBOHEDRAL AL-GE PHASE BY CBED AND X-RAY-POWDER DIFFRACTION

A new approach to the problem of crystal structure determination by el ectron diffraction is described based upon the intensities of higher-o rder Laue-zone (HOLZ) reflections in convergent-beam electron diffract ion (CBED) patterns. Along a major zone axis, a subset of symmetry-rel ated atoms may project into separate string potentials associated with localized Bloch states. In a quasi-kinematic limit, the amplitudes of HOLZ excess lines diffracted from the Bloch states are proportional t o the partial structure factors for these atoms. If a structure is unk nown, the Bloch states cannot be calculated but it is shown that the c onditional Patterson transform of the HOLZ intensities around suitable axes may include narrow correlation peaks that identify interatomic v ectors. This approach was tested by analysis of a metastable AI-Ge pha se with space group R $($) over bar$$ 3c. A transform of HOLZ intensit ies measured around the c axis showed peaks displaced by only 0.21 Ang strom from the screw axes, consistent with Ge atoms in the 18(e) posit ions. Although Al atoms were not visible in the Patterson maps, the cr ystal structure with nominal composition Al6Ge5 was identified as isos tructural with the Zn4Sb3 phase by comparison of observed and calculat ed X-ray powder intensities.