Ewald, Peter Paul

The sums may be carried out with respect to the atomic positions in direct (real) space or to lattice planes in reciprocal space, an approach introduced in 1913 by Paul Peter Ewald (1888-1985), a doctoral student under Arnold Sommerfeld (Ewald, 1913). In reciprocal space, the structures of crystals are described using vectors that are defined as the reciprocals of the interplanar perpendicular distances between sets of lattice planes with Miller indices (hkl). In 1918, Erwin Rudolf Madelung (1881-1972) invoked both types of summations for calculating the electrostatic energy of NaCl (Madelung, 1918). 

Max von Laue was a Privatdozent and Paul Peter Ewald was a doctoral student at the University of Munich in 1912 when Ewald told Laue about his thesis on crystal modek. In what he later called the bluest mistake of hk scientific fife, Ewald did not realize that the spacings between layers of hk model su ested the possibility of X-ray diffiaction, which Laue quickly went on to discover and prove. 

Peter Paul Ewald (1888-1985) uses reciprocal lattice vectors to interpret the diffraction patterns by orthorhombic crystals and later generalized the approach to any crystal class. 

Peter Paul Ewald (1888-1985). German physicist, whose work [P.P. Ewald, Das reziproke Gitter in der Strukturtheorie, Z. Kristallogr. 56, 129 (1921)] is considered a landmark in using reciproeal lattice in x-ray diffraction. 

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