Application of the symbolic addition procedure in neutron diffraction for non-centrosymmetric crystals

Abstract

For non-centrosymmetric crystals containing both positive and negative scatterers of neutrons, the symbolic addition procedure has been tested as a means of obtaining phases of neutron reflexions. Test calculations were done for two structures, α-resorcinol and methyl GAG. 2HCl. H₂O, which have already been studied by neutron diffraction using conventional methods. It is found that this procedure yields the phase angles with reasonable accuracy. The average error in phases for α-resorcinol was 14° and the F_o Fourier synthesis with these phases revealed the position of all the positive scatterers and three out of six hydrogen atoms. The average error in methyl GAG. 2HCl. H₂O was 40° and only 10 positively scattering atoms out of 16 could be clearly seen in the Fourier map. For both the structures an F_o map was found to be superior to an E map. When the contribution of the negative scatterers to the total neutron scattering is less than 25%, it has been shown that the symbolic addition method will apply for crystals containing up to 100 atoms per unit cell.