410 THE CORRECTION OF MEASURED INTEGRATED BRAGG INTENSITIES 0( 4 is the corresponding value calculated for the finite aperture (0-20 scan) and it can be seen that the approximation of an intinite slit in this case gives an error of the order of 300/0 in the TDS contribution to the peak scan. The values obtained for a spherical volume (~5) are in this case also quite good approximations for 0 > 40 °; the effective scan range being + 1-47 °. A sphere of equal volume would give an effective scan range of + 1.43 ° resulting in values of 7 30/0 lower than ~5. These effective scala ranges may be compared with the true scan range of + 1.2 °; a spherical volume using the true scan range would thus give values of c~ of the order of 20% too small in this case. The error in the intensities resulting from ignoring the TDS correction would again be less than about 1% with a corresponding error in the mean temperature factor. The relative agreement between the various ~ values is also illustrated in Fig. 2.We have also estimated the 'mosaic spread' effect for the barium fluoride measurements. The full width at half height of the mcasured peaks varied from 0.2 ° up to 0.8 ° resulting in a reduction of the TDS correction between 1% and 10%. This can therefore be an important factor particularly if the width of the measured peaks changes rapidly with the scattering angle and passes through a focusing position. The structures of thiourea, SC(NH2)~,, and deuterated thiourea, SC(ND2)2, have been determined at room and liquid nitrogen temperatures from three-dimensional neutron diffraction data. No significant structural change on deuteration has been found. N-H.--S hydrogen bonds occur in both materials at both temperatures with N-S distances of 3.35-3-43/~ and N-H-S angles of 169-171 ° and, apart from these hydrogen atoms, the molecules are planar to within 0-010/~. An analysis of the thermal parameters of the atoms in each molecule in terms of rigid vibration parameters shows that at liquid nitrogen temperature the molecules are fairly rigid whereas at room temperature there are serious deviations from rigidity. Excellent agreement has been found between the thermal vibrations of the molecules at room temperature and the observed structure change to the lower ferroelectric state. A qualitative theory of the fcrroelectric nature of thiourea is proposed which explains the observed temperature variation of the spontaneous polarization and coercive field in the lower ferroelectric region, in terms of a variable molecular orientation and a single hydrogen bond which is switched from one sublattice to the other during ferroelectric reversal.

It is shown that quantitative X‐ray powder diffraction analyses using full profile multiphase refinement should include corrections for the Brindley particle absorption contrast effect. This is demonstrated with synthetic mixtures of the highly contrasting phases LiF and Pb(NO3)2 (μ/ρ = 20 and 231 cm−1 for Co Kα). With contrast corrections, the only parameter which needs to be input is an effective particle radius R for each phase. For mixtures of LiF and Pb(NO3)2 over the whole composition range, quantification is achieved, under the present specimen preparation method, with an effective particle radius of 51 μm for both phases, giving analyses correct to within 1 percentage point. Without Brindley corrections, the analysis is grossly in error.

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The crystal structure of thorium nitrate pentahydrate, Th(NO3)4.5H20, has been determined by neutron diffraction. It is orthorhombic, space group Fdd2, with a = 11.191 + 0.007/~,, b = 22-889 + 0.015/~ and c= 10.579+0.007/~,. A total of 1642 independent reflections with 20 < 122 ° 0~= 1.065/~) were used. The structure was solved from the three-dimensional Patterson function and refined by the full-matrix least-squares method to R = 4.3 % with the use of a statistical weighting scheme.Eleven oxygen atoms are bound to the thorium atom, eight being from four bidentate nitrate groups and the other three from water molecules. The Th-O (water) distances, 2-438 and 2.473/~,, are shorter than the Th-O (nitrate) distances, 2-528 to 2.618/1. The nitrate groups are planar and the N-O distances are found to be significantly different within the group. The structure is tied together by a simple hydrogen-bond scheme in which the hydrogen bonds are either 'strong' water-water hydrogen bonds (2-70/~) or 'weak' water-nitrate oxygen hydrogen bonds (2.90-2.95 •).

Coordination polyhedra in crystals are identified by matching interbond angle matrices for observed and ideal polyhedra. An algorithm for permuting the N vertices of the observed polyhedron is described in which not all of the N! combinations are examined. The method has been used to identify a number of higher-coordination polyhedra.

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