Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tc = 348° ± 15°K, is a tungsten bronze-type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024 ± 0.00002 and c = 3.91341 ± 0.00001 Å at 298°K, space group P4bm, and five formulas in the unit cell. The integrated intensities of 6781 structure factors were measured with PEXRAD, 875 symmetry-independent structure factors being significantly above background. The metal-atom positions were determined from the three-dimensional Patterson function and the oxygen atoms from subsequent Fourier series. The final agreement factor between measured and calculated structure factors is 0.0508. The structure consists of close-packed slightly puckered layers of oxygen atoms separated by nearly c / 2. The Nb atoms are slightly displaced from one layer, the Ba and Sr atoms from the other and in the same sense. The oxygen atoms in the Ba and Sr layer are disordered. Neither of the two independent sites occupied by the Ba and Sr atoms is fully filled. The 2a site is preferred by Sr, which is in distorted cubo-octahedral coordination; the Sr–O distances range from 2.547 ± 0.008 Å to 2.919 ± 0.008 Å. The 4c site, occupied by Ba and Sr, has distorted tricapped trigonal prismatic symmetry; the Ba/Sr–O distances range from 2.604 ± 0.009 Å to 3.035 ± 0.010 Å. The two independent Nb atoms fully occupy the 2b and 8d sites and are each in relatively regular octahedral coordination. The 2b site has Nb–O distances ranging from 1.92 ± 0.03 Å to 2.03 ± 0.03 Å; the 8d-site Nb–O distances range from 1.88 ± 0.03 Å to 2.11 ± 0.03 Å. A ferroelectric mechanism is proposed in which the metal atoms in the 2a, 2b, and 4c sites move, at the Curie temperature, into the oxygen layers. These metal atoms then acquire 4̄,222, or 2 point symmetry, respectively, as the space group transforms to P4̄b2. The remaining Nb atoms, in the 8d position, also rearrange so as to have half above and half below the oxygen layer. The absolute displacements of the metal atoms from their nearest mean planes of oxygen atoms, in space group P4̄bm, are directly related to the ferroelectric polarization sense.

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Normal probability plot analysis is applied to independent sets of crystallographic structure factor measurements (F) and the derived coordinates (p). Differences between corresponding pairs of structure factors (AF) in the two sets are examined in terms of their pooled standard deviations (oF) by plotting the ordered statistic tim = AF/aF against the expected normal distribution. Differences between pairs of coordinates (zip) are similarly examined in afp= Ap/ap half-normal probability plot. Both plots result in linear arrays of unit slope and zero intercept, for normal error distribution in the experiment and the model and correctly assigned standard deviations. Analysis of departures from this ideal, especially when both plots are considered together, provides detailed information of the kinds of error in fm and in fp. By inference, the kinds of error in F and trF as well as in p and ap can be deduced. The normal probability plot fiR= IFmeasl-IFeaael/aFmeas should ideally also be linear, with unit slope and zero intercept. Deviations from ideal provide considerably more information than the conventional R values. Analysis of fiR in combination with fm plots allows further specification of the error distribution. Examples using these plots are given and discussed, based both on real and on simulated data.

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