Direct methods (electron microscopy)

This article is about direct methods in electron diffraction. For X-ray diffraction direct methods, see Direct methods (crystallography).

In crystallography, direct methods is a set of techniques used for structure determination using diffraction data and a priori information. It is a solution to the crystallographic phase problem, where phase information is lost during a diffraction measurement. Direct methods provides a method of estimating the phase information by establishing statistical relationships between the recorded amplitude information and phases of strong reflections.

Background

Phase Problem

In electron diffraction, a diffraction pattern is produced by the interaction of the electron beam and the crystal potential. The real space and reciprocal space information about a crystal structure can be related through the Fourier transform relationships shown below, where $f({\textbf {r}})$ is in real space and corresponds to the crystal potential, and $F({\textbf {k}})$ is its Fourier transform in reciprocal space. The vectors ${\textbf {r}}$ and ${\textbf {k}}$ are position vectors in real and reciprocal space, respectively.

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