Volume 221, Issue 9

The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ( r ) REF ]. The Fourier coefficients of ρ( r ) REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ( r ) MEM ] and ρ( r ) REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs, on the basis of a set of observed structure factors. We have carried out our study varying the number of observed structure factors [ i.e. sin (θ)/λ cut-off], the nature of the prior -density [uniform density and procrystal-like model] and the way in which the prior -density is treated during MEM maximization [fixed or free to change]. We observe that (i) it is recommendable to use the prior -density as a start point only, and allow it to change during maximization; (ii) the closer is the prior -density to ρ( r ) REF , the easier one attains by MEM a correct ED; (iii) if the prior -density is varied and a sufficient large number of observed structure factors used, then MEM tends to yield converging EDs, regardless of the prior -density chosen as a start point.

In this article, we show how the mathematical concept of a deformed model set can be used to gain insight into the diffraction pattern of quasicrystalline structures. We explain what a deformed model set is, what its characteristic features are and how it relates to certain disorder phenomena in solids. We then apply this concept to distorted Penrose tilings, i.e. , Penrose tilings where we apply size-effect-like distortions. While the size effect in crystals only operates on the diffuse scattering, there is also an intensity transfer on the Bragg peaks in distorted Penrose tilings. The persistence of pure point diffraction in distorted Penrose tilings can be explained by interpreting such tilings as deformed model sets.

The non-centrosymmetric materials Zn(IO 3 ) 2 , Mn(IO 3 ) 2 , Co(IO 3 ) 2 , Mg(IO 3 ) 2 and β-Ni(IO 3 ) 2 have been synthesised by evaporation of nitric acid solutions of metal salts and lithium iodate. All these compounds are isostructural and their structures were characterised both by X-ray diffraction on powder and single crystals. They crystallise in the monoclinic crystal system, space-group type P 2 1 (no. 4) with a pseudo-hexagonal lattice, as shown by the lattice parameters of Mn(IO 3 ) 2 for example: a = 11.247(1) Å, b = 5.045(1) Å, c = 11.246(1) Å, β = 120.02(1)°, V = 552.5(1) Å 3 , Z = 4. This monoclinic symmetry with a ∼ c and β ∼ 120° leads to a three-individual pseudo-hexagonal twin by pseudo-merohedry. The structure reveals a three-dimensional network in which each octahedrally coordinated cation is linked to ten others via iodate bridges. All these metal iodates generate second harmonics.

The mineral bicchulite, |Ca 8 (OH) 8 |[Al 8 Si 4 O 24 ]- SOD , has sodalite-(SOD)-type structure. It is one of the few minerals contradicting Loewenstein’s rule, as it contains twice as much Al as Si at the topologically unique tetrahedrally coordinated position, with both species being randomly distributed. The solid solution series |(Eu x Ca 2– x ) 4 (OH) 8 |[(Al 2+ x Si 1– x ) 4 O 24 ]- SOD with 0 ≤ x ≤ 1 and Δ x = 0.125, was synthesized in order to clarify, whether the continuous violation of Loewenstein's rule is possible in an aluminosilicate framework structure like SOD, or whether the reported examples of SOD-type compounds with an Al : Si-stoichiometry of 2 : 1 represent a preferred composition on the tetrahedrally coordinated site of the structure. Here, we report on the variation of the lattice parameter and of some structural parameters in the series, determined by X-ray powder diffraction and results of 27 Al MAS NMR spectroscopy. We found Loewenstein's rule to be systematically and continuously violated in this series. The observed structural variations mainly reflect stronger electrostatic interactions between the cage cations and the sodalite framework with increasing (Al + Eu)-content. While the evaluation of the X-ray diffraction data indicate a global adaptation of the sodalite framework to the cage guest size, the significant line-broadening of the NMR spectra with increasing (Al + Eu)-content points towards local adaptations of the framework to the shape of the cage guests.

New ethylenediammonium diphosphates (NH 3 (CH 2 ) 2 NH 3 ) 2 [ Me (HP 2 O 7 ) 2 · 2 H 2 O] [ Me = Co ( 1 ), Ni ( 2 )] have been synthesized and investigated by single-crystal X-ray diffractometry. The two structures resulted to be isostructural within triclinic space group P -1. The unit-cell parameters are: a = 7.5211(6) Å, b = 7.5574(3) Å, c = 9.7689(7) Å, α = 103.6(1)°, β = 111.14(1)°, γ = 98.04(1)°, V = 486.9(1) Å 3 ( 1 ) and a = 7.4631(15) Å, b = 7.5274(12) Å, c = 9.743(3) Å, α = 104.28(2)°, β = 110.75(2)°, γ = 97.50(2)°, V = 481.4(2) Å 3 ( 2 ). The three-dimensional network is built up by discrete Me (HP 2 O 7 ) 2 · 2 H 2 O moieties, which, via strong O—H … O bonds, form layers parallel to ab plane. Ethylenediammonium groups are located between such layers, stabilizing the framework via N—H … O bonds. The hydrogendiphosphate group presents bent eclipsed conformation, while the Me ion lies on inversion centre. The structural data, as the bent POP configuration, have been confirmed by the Raman and infrared spectra of the title compounds. In particular, the non-coincidence between the infrared and Raman bands supports the centrosymmetric structure of the investigated crystals.

The experimental charge density and related atomic and bond topological properties of an L-phenylalanine formic acid complex were derived from a high resolution X-ray data set (sin θ/λ = 1.18 Å –1 / d = 0.42 Å) measured at 25 K. The complex consists of a zwitterionic and a cationic phenylalanine molecule with formate as counterion. Special focus was directed on the density distribution in the region of a strong O—H ·· O hydrogen bond (O ·· O = 2.491(1) Å) which is formed between the two phenylalanine units. The obtained results are compared with the 15 previously derived experimental amino acid charge density data, with various theoretical calculations at experimental geometries and with the complete set of topological descriptors based on ab initio calculations of the neutral forms of all 20 amino acids published recently in the literature. A comparison of all available data in this biologically important class of compounds gives an impression about the significance of the quantitative results from experimental and theoretical charge density determinations.