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One of the classical problems in the application of the maximum-entropy method (MEM) to electron-density reconstructions is the uneven distribution of the normalized residuals of the structure factors [|F(obs)(H)|-|F(calc)(H)|]/sigma(H) of the resulting electron density. This distribution does not correspond to the expected Gaussian distribution and it leads to erroneous features in the MEM reconstructions. It is shown that the classical chi(2) constraint is only one of many possible constraints, and that it is too weak to restrict the resulting distribution to the expected Gaussian shape. It is proposed that constraints should be used that are based on the higher-order central moments of the distribution of the structure-factor residuals. In this work, the influence of different constraints on the quality of the MEM reconstruction is investigated. It is proposed that the use of a combined constraint on more than one central moment simultaneously would lead to again improved results. Oxalic acid dihydrate was chosen as model structure, from which several data sets with different resolutions and different levels of noise were calculated and subsequently used in the MEM. The results clearly show that the use of different constraints leads to significantly improved results.

The modulated structures of incommensurate composite crystals (La(0.912)S)(1.13)TaS(2) at room temperature and of (La(0.949)S)(1.14)NbS(2) at T = 115 K are refined against high-resolution X-ray data. The compounds are isostructural with superspace group F'm2m(alpha,0,0)00s. For (LaS)(1.13)TaS(2), lattice parameters of the first subsystem TaS(2) were obtained as a = 3.2922 (1), b = 5.7776 (2) and c = 23.013 (2) A. For the second subsystem LaS, the same b and c parameters were found, but a = 5.8090 (8) A. Refinements led to a final structure model with R = 0.036 for 4767 observed unique reflections (R = 0.023 for 2147 main reflections, R = 0.099 for 1554 first-order satellites and R = 0.112 for 1042 second-order satellites). The final model includes modulation parameters up to the second-order harmonics for the displacements of the atoms, for the occupational parameters and for the temperature parameters. A clear correlation is found between the relative positions of the subsystems, the displacement modulation, the occupational modulation and the modulation of the temperature parameters. The analysis shows that the variations in environments are resolved by correlated variations in the temperature factors. For (LaS)(1.14)NbS(2), lattice parameters at T = 115 K of the NbS(2) subsystem were obtained as a = 3.3065 (4), b = 5.7960 (5) and c = 22.956 (3) A. For the LaS subsystem, the same values for b and c were obtained, but a = 5.7983 (7) A. Refinements led to a final structure model with R = 0.048 for 5909 observed unique reflections (R = 0.034 for 2528 main reflections, R = 0.092 for 2171 first-order satellites and R = 0.113 for 1103 second-order satellites). The final structure model is similar to that of (LaS)(1.13)TaS(2). In particular, it is found that the values of the modulation parameters are almost equal and it is concluded that the modulations are independent of the temperature and the replacement of Ta with Nb, and thus represent a general mechanism of resolving the strain between the mutually incommensurate layers.

The compounds tetrakis(trimethylstannyl)germane, Ge(SnMe3)4 (1), and tetrakis(trimethylstannyl)silane, Si(SnMe3)4 (2), have crystal structures with the quasispherical molecules in a closed-packed stacking. At room temperature both structures have the space group P1 (Z = 2) with a = 9.94457 (5), b = 14.52927 (8), c = 9.16021 (5) A, alpha = 90.53390 (30), beta = 111.73080 (30), gamma = 90.0049 (4) degrees, and V = 1229.414 (12) A3 for (1) and a = 9.92009 (7), b = 14.51029 (11), c = 9.13585 (7) A, alpha = 90.4769 (4), beta = 111.6724 (4), gamma = 89.9877 (6) degrees, and V = 1222.037 (16) A3 for (2). The molecules are found to be ordered as a result of steric interactions between neighboring molecules, as shown by analyzing the distances between the atoms. Upon heating, both compounds undergo a first-order phase transition at temperatures T(c) = 348 +/- 5 K, as characterized by a relative jump of the lattice parameter of approximately 16%. At 353 K, both structures have the space group P1 (Z = 4), with a = 14.2037 (2) A, and V = 2865.52 (7) A3 for (1) and a = 14.1346 (2) A, and V = 2823.90 (7) A3 for (2). Rietveld refinements were performed for the low-temperature phases measured at T = 295 K [R(wp) = 0.0844 for (1), R(wp) = 0.0940 for (2)] and for the high-temperature phases measured at T = 353 K [R(wp) = 0.0891 for (1), R(wp) = 0.0542 for (2)]. The combination of high-resolution X-ray powder diffraction measurements and variable-temperature magic-angle-spinning 13C, 29Si and 119Sn NMR experiments demonstrates low crystallographic and molecular (C1) symmetries for the low-temperature phases of (1) and (2) at temperatures T < 348 +/- 5 K and high crystallographic symmetry due to rotational disorder for the high-temperature phases at temperatures T > 348 +/- 5 K.

The crystal structure of the ambient-pressure phase of vanadyl pyrophosphate, (VO)2P2O7, has been precisely determined at 120 K from synchrotron X-ray diffraction data measured on a high-quality single crystal. The structure refinement unambiguously establishes the orthorhombic space group Pca2(1) as the true crystallographic symmetry. Moreover, it improves the accuracy of previously published atomic coordinates by one order of magnitude, and provides reliable anisotropic displacement parameters for all atoms. Along the a axis, the structure consists of infinite two-leg ladders of vanadyl cations, (VO)2+, which are separated by pyrophosphate anions, (P2O7)4-. Parallel to the c axis, the unit cell comprises two alternating crystallographically inequivalent chains of edge-sharing VO5 square pyramids bridged by PO4 double tetrahedra. No structural phase transition has been observed in the temperature range between 300 and 120 K.