Jerome Karle

Jerome Karle (1918–2013) was an American physical chemist who developed direct methods for solving crystal structures from X-ray diffraction data. He shared the 1985 Nobel Prize in Chemistry with Herbert A. Hauptman.

X-ray crystallography: A method for determining atomic structures by measuring how crystals diffract X-rays. Karle developed mathematical methods for extracting structures from its diffraction data.
Direct methods: Crystallographic techniques that derive phase information from measured diffraction intensities and statistical relationships. Karle and Herbert A. Hauptman established the approach that became central to his scientific work.
Herbert A. Hauptman: An American mathematician and crystallographer who developed direct methods with Jerome Karle. Hauptman’s mathematical partnership with Karle led to their Nobel-recognized work.
1985 Nobel Prize in Chemistry: The Nobel Prize awarded to Jerome Karle and Herbert A. Hauptman for developing direct methods to determine crystal structures. The award recognized the scientific contribution most closely associated with Karle.
X-ray diffraction: The scattering of X-rays by matter, producing patterns that reveal the arrangement of atoms. These measurements supplied the intensities used in Karle’s structure-solving methods.
Karle–Hauptman equations: Mathematical inequalities relating crystal structure factors and constraining their unknown phases. These equations provided a foundation for the direct methods Karle and Hauptman developed.
Isabella Karle: An American crystallographer who developed experimental methods for determining molecular structures. Karle’s wife and collaborator, she applied crystallographic techniques to complex molecules.
Small-molecule crystallography: The determination of atomic structures of relatively small crystalline compounds using diffraction methods. Direct methods made many small-molecule structures solvable without heavy-atom models.
Crystallography phase problem: The loss of phase information when diffraction intensities are measured, complicating reconstruction of a crystal’s structure. Direct methods infer missing phase information from relationships among diffraction measurements.
Symbolic addition procedure: A direct-methods procedure that uses known phase relationships to assign additional crystallographic phases. Karle helped turn phase relationships into a practical route for solving structures.

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