DIRECT DETERMINATION OF PHASE FROM THREE BEAM CONVERGENT BEAM DIFFRACTION PATTERNS OF CENTROSYMMETRIC CRYSTALS. J. Etheridge, A. F. Moodie and C. J. Humphreys, Dept of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, U.K

The symmetries of three beam diffraction from a centrosymmetric crystal are such that the distribution of scattered intensity uniquely determines both the phase and the magnitude of the three structure amplitudes. In particular, the phase can be read directly from convergent beam diffraction patterns where the three beam approximation retains some validity, whilst the magnitudes can be determined from three distances measured on these patterns. Technically, this result derives from the fact that orientations can be found along which the general symmetry of the special unitary group, SU(3), factors into three subgroups in SU(2). This result is independent of thickness. The experimental conditions under which these results can be exploited are discussed quantitatively. Experimental convergent beam electron diffraction patterns are used to illustrate the method.