Direct Methods and Anomalous Dispersion (Nobel Lecture)

Todays triumphant advance of X‐ray structure analysis is due in large part to the development of the “direct methods” by Herbert Hauptman and Jerome Karle . Previously, it was generally assumed to be impossible to determine a structure directly from the diffraction pattern of a crystal, for a normal diffraction experiment afforded only amplitudes, but no phases of the diffraction maxima. This phase problem was overcome in a series of steps that involved recognition that the required phase information was contained in the measured intensities, the derivation of a foundation mathematics that displayed relationships between phases and magnitudes and even among phases alone and, finally, the development of practical methods for structure determination, strategies that brought together in a more or less optimal fashion the mathematical relationships with suitably adjusted and refined experimental data.