Determination of Crystal Structures by Means of Anomalously Scattered X-Rays

Abstract

is a better approximation for ,1 near the cell boundary than is the first term of equation (15). Series (24) involves quite a number of terms, but the magnitude of each term can be computed fairly accurately by the use of only a few F's. K This observation illustrates the differences and the relative advantages of the augmented-plane-wave method of computing st and the method discussed in the present paper. The quantities inside the braces in equation (24) can be considered as the unknown coefficients (the B's of equation [3 ]), and equation (5) can be integrated to produce a set of simultaneous equations4 for the B's which can be solved to find k2 and A1. Equation (5), however, involves the value and normal gradient of s1 at the surface of the sphere, where it can be represented by fewer terms in the expansion form (1) than by form (3). Therefore, the secular equation using the F's involves fewer terms than does that using the B's. Once the secular equation is solved, however, and the F's are obtained, to compute ,1 near the cell boundary it is often better to use series (24) than series (15).

Some New X-Ray and Neutron Studies of Hydrogen Bonding

“…A three-dimensional refinement of the structure of zinc aspartate trihydrate, in which the phase problem was solved by means of S the P,(2) function for anomalous scattering 2 , shows hydrogen positions, and reveals H-bonding which leads to an interesting ring structure and recalls the proposal of Steward and Thompson 3 for a cyclic structure for asparagine.…”

Nuclear Magnetic Resonance in Paramagnetic MnF2

“…sum extends over the three nearest Mn ++ neighbors of each F~ and (Si) 3 ' is the thermal average of S in the ith direction on the jth Mn ++ and where i runs over x, y, and z. The principal values of A along the x, y, and z directions we designate by Ai, A 2, and A3, respectively.…”

“…The protons may be thought of as noninteracting field probes in these compounds. If, however, one looks at the nuclear magnetic resonance of the nuclei of those nonmagnetic ions which are bonded to the paramagnetic ions [e.g., F 19 in MnF 2 , CI 35 -37 in CuCl 2 -2H 2 0], the effects of electron transfer will, as we shall see, cause relatively enormous shifts and splittings in the paramagnetic 3 Poulis, Hardeman, and Bolger, Physica 18, 429 (1952). 4 state, and, in the antiferromagnetic state, will result in a very high-frequency nuclear magnetic resonance even in the absence of an external magnetic field.…”

“…In the ordered state the NMR would be displaced by local fields of the order of ( M A 3 is the normalized Brillouin function which is unity at T-0 and vanishes at the transition temperature. Owing to the antiparallel ordering and the relative proximity of nuclei to a spin of a given orientation an additional splitting will, in general, occur.…”

The application of the anomalous scattering of X-rays to the solution of the crystal structure of (NH4)2.VO(NCS)4.5H5O

“…This effect has been used by Bijvoet, Peerdeman & van Bommel (1951) to determine absolute configuration, and by Pepinsky & Okaya (1956) to assist in the solution of Patterson functions. In this paper an alternative procedure is discussed for the use of anomalous scattering in the solution of centrosymmetric structures in cases where 2/~tK > 1.t The practical application of this method to the solution of the structure of diammonlum oxotetrakis(isothiocyanato)vanadate pentahydrate is described, this being a structure which had proved insoluble by other methods.…”