Aspherical form factor

As a test, the standard aspherical form factors in their proper orientations were applied in a refinement of both room temperature and low temperature (125 K), accurate, but low-resolution, data ( 0.7 A -1) on the tripeptide pGlu-Phe-D-Pro-0[CN4]-Me (PPP). The improvements on introduction of the aspherical scattering factors are dramatic, the /(-factors being reduced by 30-40% without the introduction of additional variables. Significant adjustments in the anisotropic... 

The analysis of the polarised neutron experiment on K2NaCrFe (Fig. 9) has been completed< >. The aspherical form factor component/4(0 was shown to be particularly sensitive to the covalent spin distribution, and the shape of fi Q) supported the inference for eg spin polarization drawn from the comparison of powder neutron diffraction data and resonance data (Section VI. B). A preliminary report of the form factor determination for both tetra-hedrally and octahedrally coordinated Fe + in YaFesOis by polarized neutrons has been given ). The form factors are not the same and that for tetrahedral Fe + is contracted relative to that for octahedral Fe +, which follows closely the calculated free-ion curve. The ligand forward peak (Section VI. B) has been directly observed ) in a measurement of the critical scattering of neutrons by ferromagnetic K2CUF4. 

Two advanced techniques have been proposed and applied to some crystal structures (Section IV,C), in which aspherical distributions of valence electrons around an atom are directly taken into account in the least-squares calculations. Aspherical atomic form factors are introduced in the least-squares refinement in the first method (29, 38, 80) and multipole parameters describing the aspherical valence distributions are used in the second method (31, 34, 46). 

Fig. 30. The form factor for Cu t in K2CUF4 [after Ref. (47)]. The broken curve is the theoretical form factor for isolated Cu t taking into account tlie asphericity in the 00 direction. This curve is renormalized so as to give the reduction factor given by the NMR data for fa and / ...

A slightly different type of form-factor measurement was performed by Felcher et al. (1976) who performed an experiment to look specifically at the aspherical component of the form factor of Ho. (The measurements were performed both for a pure Ho crystal and a H00.9SC0.1 alloy.) They showed that for a spiral magnetic structure of ions having aspherical magnetization distributions, the form factor for ions in the /th layer at a given Q was given by... 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

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