Accurate Structure-Factor Phase Determination by Electron Diffraction in Noncentrosymmetric Crystals

Abstract

A solution to the phase problem is described which gives the phase invariant $\ensuremath{\Psi}=2{\ensuremath{\varphi}}_{h}\ensuremath{-}{\ensuremath{\varphi}}_{g}$ for electron structure factors with phases ${\ensuremath{\varphi}}_{h}$ and ${\ensuremath{\varphi}}_{g}$ in noncentric crystals. The method exploits the high-voltage dependence of a minimum in convergent-beam transmission-electron-diffraction patterns in the systematics three-beam geometry. For CdS, with $h=(00\overline{2})$ and $g=(00\overline{4})$ we find $\ensuremath{\Psi}=54.4\ifmmode^\circ\else\textdegree\fi{}+0.9\ifmmode^\circ\else\textdegree\fi{}$. The error in the derived ($00\overline{2}$) x-ray structure-factor phase is 0.069\ifmmode^\circ\else\textdegree\fi{}. The method is accurate enough to provide information on the bonding charge distribution in noncentric crystals.