EFFECT OF ATOMIC HETEROGENEITY ON SAYRE'S EQUATIONS Sabita Das, Victoria College, 78B Acharya Prafulla Chandra Road, Calcutta-700009, India and G.B. Mitra, Indian Association for the Cultivation of Science, Calcutta-700032, India.
An extension of Sayre's equation is developed for a structure formed by a single heavy atom and L number of equal and well resolved light atoms in the unit cell. Sayre's equation may be written as
for a squared structure of electron density [[rho]]2 (r). The structure factors corresponding to normal and squared atoms can be written as, respectively,
where the H stands for heavy atom and f(h) , g(h) being the atomic scattering factors of normal and squared atoms respectively. From equations (1) and (3), we get
Equations (4) give modified Sayre's equation for the direct determination of phases of light atoms, having the position of the heavy atom been pre-determined by Patterson or any other method.