ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

The solution of the phase problem in isomorphous series

F. Hanic

Institute of Inorganic Chemistry, The Slovak Academy of Sciences, Bratislava

Abstract: It is possible, for isomorphous centrosym. structures, to det. directly the signs of the structure factors from the diffraction data if the positions of the isomorphously substituted atoms NI and NII are known. With pairs of zerointensity reflections with identical indexes for both I and II structures, it is possible to det. the position of the isomorphous pair or limit its selection. For reflections of the type F(hkl)I = F(hkl)II = O, this equation is valid: δF = F(hkl)II-F(hkl)I = 2(fII - fI)cos2π(hx1 + ky1 + lz1) = 0 (1), where x1,y1, x1 are the coordinates of the isomorphous atoms NI and NII, FI and FII are the structure factors of the isomorphous structures I and II and fI and fII are at. scattering factors. An infinite no. of solutions exists for the relation (1), but it is limited if several pairs of zero reflections are present. The possible positions of the substituted atoms can be graphically detd. in the chosen projection by the point of intersection of the lines which are represented by the zero solution of relation (1). If the detns. are carried out with Beevers-Lipson strips, the possible positions of the isomorphous atoms are indicated by the zero points or by those of min. value, if the intensities of the zero reflections differ slightly from zero or if the structures are not strictly isomorphous. The detns. are further limited by the fact that some reflections possess, in the chosen projection, intensities different from zero only for 1 structure, for which an equation is presented. Isomorphous structures MgSO4.6H2O and MgSeO4.6H2O are given as examples.

Full paper in Portable Document Format: 183a161.pdf (in Slovak)

Chemical Papers 18 (3) 161–171 (1964)