An Elementary Introduction to Direct Methods

Abstract

In a diffraction experiment intensities I_hkl are measured whereas F_hkl = |F_hkl|exp(i _φhkl) are necessary to image the electron density. Now |F_hkl| can be calculated straightforward from I_hkl but the relative phases _φhkl are lost in the experiment and cause the so called phase problem. Direct methods try to evaluate phases _φhkl “directly” from the measured diffraction intensities I_hkl by using relationships among the phases, relationships, whose values are based on the intensities only. Roughly it can be stated that, since the crystal structure can be described by a limited number of parameters (the positions of the atoms) and since many more intensities can be measured, relationships among the structure factors F_hkl, and thus among the phases _φhkl, must exist. Direct Methods identify and use these phase relationships to solve the phase problem.