On the accurate measurement of low-order structure factor amplitudes and phases by quantitative CBED

Abstract

Over the past four years we have developed the software and computer control of electron microscope data acquisition needed for quantitative electron crystallography. CBED patterns in the systematics orientation (see Fig. 1) are scanned over the slit of a Gatan Model 607 ELS unit, and the energy filtered elastic scattering rocking curves compared with the results of theoretical calculations (see Figs. 2 and 3). The calculations are based on the Bloch wave method, and treat three-dimensional dynamical diffraction from a non-centrosymmetric crystal with absorption and inclined boundary conditions. The Fortran source code has been published, and is available by Bitnet from ZALUZEC @ANLMST. High voltage, sample thickness, absorption coefficients Vg and selected low order structure factors Vg are adjusted(using the most sensitive portion of the pattern for each)for best fit. The resulting Fourier coefficients of crystal potential may be used (via the Mott Formula) to obtain a charge density difference map, which reveals the distribution of valence electrons involved in bonding, as shown for GaAs in figure 4.The partially ionic character of the bond is seen. We find V(111)1/V(111) = 0.05, V1 (220)/V(220) = 0.035, V1 (400)/V (400) = 0.07 and V1 (333)/V(333)=0.08. Results for work on MgO in progress are shown in figs. 2 and 3.