letters to the editor
Xray structure of barium titanate – missed opportunities
^{a}School of Physics, Madurai Kamaraj University, Madurai 625021, India
^{*}Correspondence email: saravana@pronet.net.in
Anomalous Xray scattering effects are quite extensive in the noncentrosymmetric ferroelectric structure of barium titanate, and typical estimates for three published Xray diffraction experiments are computed. These data show that the Bijvoet pairs should not be averaged before leastsquares
for this polar crystal with small atomic displacements from a higher symmetric space group.In the tetragonal ferroelectric structure of barium titanate, the heavy atoms have the dispersive components f′_{Ba} = −0.613, f′′_{Ba} = 2.28, f′_{Ti} =0.28 and f′′_{Ti} = 0.446 (International Tables for Xray Crystallography, 1974) for Mo K Xrays used in three extensive structure analyses, namely Evans (1961), Harada et al. (1970; HPB) and recently Buttner & Maslen (1992; BM). For the 4mm, any reflection with l 0 can exhibit a Bijvoet difference = 0.5(I − )/(I + ) between the intensities of inverse reflections.
In Table 1, our estimated dispersive effects for a few reflections are displayed for the above three reported structures. The structure magnitudes F_{+}, F_{−}, the phase angles _{+}, _{−} and the values are listed along with F_{c} and (F_{o}), as reported by the above three authors. () can be up to four times larger than (F_{o}) and therefore such dispersive scattering estimates should have been measurable.

We have in fact computed the F_{+}, F_{−} and values at ambient temperature for all reflections up to Å^{−1} for the BM (1992) structure. The trends are summarized in Table 2.
Evans (1961) measured approximately 350 h0l reflections using a fitted to a Weissenberg instrument and Mo K Xrays up to Å^{−1}. He reported an `impasse' in the even with residuals as low as 0.03, owing to parameter interaction in the leastsquares refinements with such a polar deviating by small atomic displacements from a higher symmetric In a discussion we pointed out (Chandrasekaran & Mohanlal, 1965) our estimates of the very appreciable values for a large number of reflections. In a rejoinder Evans (1966) stated that his raw expermental data for h0l, 0l and h0 , 0 had not shown any such differences, which he attributed to `antiparallel with l_{+} and l_{−} intensities tending to average out. In HPB (1970) a single C domain crystal was used for the Xray studies; dispersive scattering effects were noticed in that only the refinements using an l index of positive sign yielded the best standard errors for the parameters with low residuals.
BM (1992) recorded two independent sets of measurements on the same sample with 3500 data in each set, up to 1.08 Å^{−1} for Mo K. They stated that `Friedel pairs were averaged and merged even in case 3 (the correct noncentrosymmetric P4mm structure), because the effects of are very small (Buerger, 1960)'. It is not clear to us from this quote whether they had sought to measure Bijvoet differences at all in their experiment or merely cited the text (Buerger, 1960) to justify their merging and averaging of the Friedel pairs. Also, BM (1992) had probably taken the magnitudes f + f′ + if′′ for the atomic scattering factors, which procedure would eliminate any values in the structurefactor calculations and, in addition, lead to large errors in the structurefactor magnitudes and phases. Furthermore, Buerger (1960) devotes four pages to with Argand diagrams for F_{+} and F_{−}, a table for f′ and f′′ for different targets and several examples of the actual experimental measurement of Bijvoet differences.
The leastsquares and Fourier procedures for noncentrosymmetric structures with appreciable dispersive scattering have been extensively discussed in a previous review (Srinivasan, 1972) and an International Conference Report (Ramaseshan & Abrahams, 1974). Here, therefore, we only cite Ibers & Hamilton (1964), who recommend that Friedel pairs should be treated independently in the least squares, using the actual observed values and corresponding calculated values F_{+}(H) and F_{−}(H). For the effects of domains in BaTiO_{3}, tending to average out l_{+} and l_{−} intensities, the Flack enantiopole parameter (Flack, 1983), namely F()^{2} = (1 − x) F(h)^{2} + xF(−h)^{2}, is called for to account for the intensities, with x as a parameter for refinement.
Footnotes
‡Present address: The Madura College, Madurai 615011, Tamil Nadu, India.
Acknowledgements
One of us (KSC) wishes to dedicate this work to the memory of the late Professor M. Buerger, with whom he had a pleasant personal acquaintance and another (RS) acknowledges the CSIR for financial assistance.
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