X-ray data on silicon, tetracyanoethylene, p-nitropyridine N-oxide and ammonium thiocyanate are refined with a generalized aspherical-atom formalism as introduced by Stewart, but modified to have a spherical valence more similar to the unperturbed HF valence shell. Several types of radial dependences of the multipole functions are tested and criteria are developed for judging the adequacy of the aspherical-atom refinement. The aspherical-atom model leads to a significant decrease in the least-squares error function, a reduction of features in the residual map, and an improvement in thermal parameters when comparison is made with the neutron results or when the rigid-bond postulate proposed by Hirshfeld is applied. Positional parameters are often improved except in the case of terminal atoms for which discrepancies, attributed to correlation between dipole-population and positional parameters, are sometimes observed. Deformation maps based on the aspherical-atom least-squares parameters contain less noise than X --N maps and benefit from inclusion of calculated values of weak structure amplitudes in the summation. In the cases studied, deformation maps including terms beyond the experimental resolution do not yield additional information.

The electron density distribution and 3d-orbital electron occupancies for the Fe atom in synthetic triphylite, LiFePO4, have been analysed using single-crystal X-ray diffraction data measured at T= 298 K with Mo Ka (3. =0.71069 ,~) radiation to a resolution corresponding to (sinOmax/3.)= 1.078 ,~-~. Measurements of 3265 reflections gave 944 unique data [Rint(I) = 0.036] with I > 2o,(1). For an atomic multipole density model fitted by least-squares methods R(F) = 0.0174 for all unique reflections. The Fe atom 3d-orbital occupancies have been derived from the multipole population coefficients using point-groupspecific relations. The asphericity of the electron deformation density around the Fe atom is discussed using crystal-field theory and magnetic properties of triphylite. Crystal data: lithium iron(II) phosphate, IntroductionThe crystal structure of LiFePO4, which has been studied by Yakubovich, Simonov & Belov (1977) and described in more detail by Yakubovich, Belokoneva, Tsirelson & Urusov (1990), has an olivine-type structure with a distorted hexagonal * Author to whom correspondence should be addressed. Present address: Crystallography Centre, University of Western Australia, Nedlands, Western Australia 6009, Australia.0108-7681/93/020147-07506.00 anion close packing, where the cations occupy three different positions: a tetrahedral (P) site and two octahedral sites. An ORTEP (Johnson, 1965) plot showing the cation coordination is given in Fig. 1. One octahedral site lies at the inversion centre and the other is in the mirror plane. As usual in olivinetype structures the former octahedral site is occupied by cations with smaller charge (Li) and the latter by cations with larger charge (Fe). The main feature of the LiFePO4 crystal structure consists of olivine-type ribbons extending along the b crystal axis. The Li octahedra protrude from the olivine ribbon and are connected along their edges and with the larger Fe © 1993 International Union of Crystallography 148 LiFePO4 octahedra. PO4 tetrahedra have three of the six edges in common with the cation octahedra. These edges have the shortest lengths and differ significantly from the other O---O distances.The magnetic structure of LiFePO4 has been determined by Santoro & Newnham (1967) from neutron diffraction data. Below the N~el temperature TN = 50 K, the spin vectors associated with these Fe-atom positions are antiparallel and align in an antiferromagnetic array collinear with the b axis. The magnetic space group is Pnma'. AS has been shown (Santoro & Newnham, 1967), the only Fe O---Fe superexchange interactions give rise to antiferromagnetic puckered planes orthogonal to a. There are no direct or superexchange linkages between these planes, and long-range interactions, such as Fe---O---P--O--Fe triple exchange, have been suggested.The present paper describes a study of the electron deformation density in synthetic crystalline triphylite, LiFePO4. A multipole refinement of the X-ray diffraction data has been carried out using different approxim...

The structure of a crystal of Sr0.61Ba0.39Nb2O6 has been solved and refined as an incommensurate structure in five-dimensional superspace. The structure is tetragonal, superspace group P4bm(\,pp1/2,p - p1/2), unit-cell parameters a = 12.4566 (9), c = 7.8698 (6) Å, modulation vectors q 1 = 0.3075 (6) (a* + b*), q 2 = 0.3075 (6) (a* − b*). The data collection was performed on a KUMA-CCD diffractometer and allowed the integration of weak first-order satellite reflections. The structure was refined from 2569 reflections to a final value of R = 0.0479. The modulation affects mainly the positions of the O atoms, which are displaced by as much as 0.5 Å, and the site 4c that is occupied by Sr and Ba atoms. Only a simplified model, in which this atomic position is occupied by an effective atom Sr/Ba, could be refined from the data set. The modulation of displacement parameters has been used to account for the modulated distribution of Sr and Ba. The whole refinement uses only first-order modulation waves, but there are strong indications that for a complete solution the use of higher-order satellites and a more complicated model is necessary.

The refinement of electron-density distributions for noncentrosymmetric crystals from X-ray diffraction data may lead to a very good fit between model and data but to totally meaningless electron densities. This is to a large extent because varying certain parameters, or combination of parameters, in the model mainly leads to a change in the phases of the structure factors. A formal analysis of why this happens, when using multipole models, is given as well as specific examples using real data: the contributions of odd-order multipoles, which are invariant under crystal-class symmetry operations, are poorly determined. The importance of applying constraints on the models is stressed. The conclusions of this analysis can be carried over to refinements of anharmonic atomic vibrations.

A detailed account of X-ray diffraction measurements on single crystals of KTiOPO4 (potassium titanyl phosphate) is given. The experiments were carried out at room temperature and the data were used for the analysis of the electron-deformation density. We have been confronted with difficulties in obtaining a correct description of the electron density owing to the noncentrosymmetry of the crystal structure and the probable anharmonic thermal motion or local disorder of the potassium ions. The electron density indicates the presence of a strong covalent bond between Ti 4' and 0 2 ions. The possibility of relating the electron density to the high second-order electronic electric susceptibility of KTiOPO4 has previously been discussed by Hansen,