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The electron-density map of an Si crystal is drawn by the maximum-entropy method (MEM) with 30 structure factors which were determined very accurately on an absolute scale by the Pendelli~sung method [Saka & Kato (1986). Acta Cryst. A42, 469-478]. It is shown that the following three beneficial points arise from the use of the MEM for accurate structure analysis. Firstly, a precise electron-density map can be obtained; the existence of bonding electrons is clearly visible in the maximum-entropy map, even though no forbidden reflections are included in the analysis. The structure factors calculated from the maximum-entropy map for the 222 and the 442 forbidden reflections show good agreement with those measured by different experiments. The final R factor was 0.05% as a consequence of the high accuracy of the measured structure factors. Secondly, there is no need to seek a better structural model which could be a complicated and time-consuming process in accurate structure analysis. Thirdly, the resolution of the maximum-entropy map is much higher than that of the map drawn by conventional Fourier transformation. It is also found in the case of silicon that phase information is not absolutely necessary because exactly the same density-distribution map can be obtained without any phase information as the map drawn with all the phase information.

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We report the direct observation of dioxygen molecules physisorbed in the nanochannels of a microporous copper coordination polymer by the MEM (maximum entropy method)/Rietveld method, using in situ high-resolution synchrotron x-ray powder diffraction measurements. The obtained MEM electron density revealed that van der Waals dimers of physisorbed O2 locate in the middle of nanochannels and form a one-dimensional ladder structure aligned to the host channel structure. The observed O-O stretching Raman band and magnetic susceptibilities are characteristic of the confined O2 molecules in one-dimensional nanochannels of CPL-1 (coordination polymer 1 with pillared layer structure).

Accurate charge-density distributions of cubic and tetragonal PbTiO3 and BaTiO3 have been obtained by the MEM(maximum entropy method)/Rietveld analysis using synchrotron-radiation powder data. The Pb-O bonds in tetragonal PbTiO3 show rather strong covalency, while those in cubic PbTiO3 are ionic. This is the clear evidence of the Pb-O hybridization in tetragonal PbTiO3, which has been theoretically predicted as a key factor of much larger ferroelectricity of this substance than that of BaTiO3. Tetragonal PbTiO3 forms a layered structure of a two-dimensional covalent-bonding network consisting of the Ti-O5 pyramid.

Carbonates are important constituents of marine sediments and play a fundamental role in the recycling of carbon into the Earth's deep interior via subduction of oceanic crust and sediments. Study of the stability of carbonates under high pressure and temperature is thus important for modelling the carbon budget in the entire Earth system. Such studies, however, have rarely been performed under appropriate lower-mantle conditions and no experimental data exist at pressures greater than 80 GPa (refs 3-6). Here we report an in situ X-ray diffraction study of the stability of magnesite (MgCO(3)), which is the major component of subducted carbonates, at pressure and temperature conditions approaching those of the core-mantle boundary. We found that magnesite transforms to an unknown form at pressures above approximately 115 GPa and temperatures of 2,100-2,200 K (depths of approximately 2,600 km) without any dissociation, suggesting that magnesite and its high-pressure form may be the major hosts for carbon throughout most parts of the Earth's lower mantle.

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