Vaclav Petricek

The modulated structure of Ba0.39Sr0.61Nb2O6. I. Harmonic solution

The structure of a crystal of Sr(0.61)Ba(0.39)Nb(2)O(6) has been solved and refined as an incommensurate structure in five-dimensional superspace. The structure is tetragonal, superspace group P4bm(pp1/2,p - p1/2), unit-cell parameters a = 12.4566 (9), c = 7.8698 (6) A, modulation vectors q(1) = 0.3075 (6) (a* + b*), q(2) = 0.3075 (6) (a* - b*). The data collection was performed on a KUMA-CCD diffractometer and allowed the integration of weak first-order satellite reflections. The structure was refined from 2569 reflections to a final value of R = 0.0479. The modulation affects mainly the positions of the O atoms, which are displaced by as much as 0.5 A, and the site 4c that is occupied by Sr and Ba atoms. Only a simplified model, in which this atomic position is occupied by an effective atom Sr/Ba, could be refined from the data set. The modulation of displacement parameters has been used to account for the modulated distribution of Sr and Ba. The whole refinement uses only first-order modulation waves, but there are strong indications that for a complete solution the use of higher-order satellites and a more complicated model is necessary.

Refinement of the crystal structure of Cronstedtite-1T

The crystal structure of cronstedtite-2H2 was refined in a hexagonal cell, space group P63, Z = 2, using two acicular crystals from Wheal Maudlin, Cornwall, England, and from Pribram, Czech Republic. The Wheal Maudlin sample has the chemical composition

Hexagonal close-packed c60

\left( {{\rm{Fe}}_{2.291}^{2 + }{\rm{Fe}}_{0.709}^{3 + }} \right)\left( {{\rm{S}}{{\rm{i}}_{1.298}}{\rm{Fe}}_{0.707}^{3 + }{\rm{A}}{{\rm{l}}_{0.004}}} \right){{\rm{O}}_5}{\left( {{\rm{OH}}} \right)_4}

Sodium carbonate revisited

(Fe2.2912+Fe0.7093+)(Si1.298Fe0.7073+Al0.004)O5(OH)4 and the Příbram sample has the composition

Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs.

\left( {{\rm{Fe}}_{2.269}^{2 + }{\rm{Fe}}_{0.731}^{3 + }} \right)\left( {{\rm{S}}{{\rm{i}}_{1.271}}{\rm{Fe}}_{0.724}^{3 + }{\rm{A}}{{\rm{l}}_{0.005}}} \right){{\rm{O}}_5}{\left( {{\rm{OH}}} \right)_4}

Structures and phase transitions of the A7PSe6 (A = Ag, Cu) argyrodite-type ionic conductors. III. α-Cu7PSe6

(Fe2.2692+Fe0.7313+)(Si1.271Fe0.7243+Al0.005)O5(OH)4. The results of refinements are as follows: a = 5.500(1), c = 14.163(2) Å, V = 371.08(8) Å3, R = 3.83%, from 381 independent reflections, and a = 5.4927(1), c = 14.1481(2) Å, V = 369.70(4) Å3, R = 4.77%, from 1088 independent reflections for the Wheal Maudlin and Příbram samples, respectively. The best Fovs.Fc agreement was achieved when the structure was interpreted as merohedral twin; several possible twinning laws are discussed. The cronstedtite layer consists of one tetrahedral sheet and one octahedral sheet. There is one octahedral (M1) position, occupied by Fe only, and two tetrahedral (T1, T2) positions in the structure. Refinement of occupancy of tetrahedral sites led to values Si:Fe = 0.45:0.55(1) (Wheal Maudlin) and 0.432:0.568(8) (Příbram) in T1, and Si: Fe = 0.99:0.01(1) (Wheal Maudlin) and 0.888:0.112(7) (Příbram) in 72. Whereas the size of T1 is reasonable (average dT1-O = 1.693 Å (Wheal Maudlin), 1.691 Å (Příbram)), T2 is unusually large: (dT2-O= 1.740 Å (Wheal Maudlin), 1.737 Å (Příbram)) with respect to the small or almost zero Fe content. As an explanation, an alternative structure model comprising a certain amount of vacancies in T2 is presented. The tetrahedral rotation angle α is highly positive (+12.1° and +12.5° for the Wheal Maudlin and Příbram samples, respectively), and the layer belongs to the Franzini type A. Distortion parameters of octahedra and tetrahedra are given for both samples. One hydrogen atom engaged in the hydrogen bond was located in the Wheal Maudlin sample.

Effect of Nonmagnetic Substituents Mg and Zn on the Phase Competition in the Multiferroic Antiferromagnet MnWO4

CeO crystals were grown from purified powder material with a multiple sublimation technique. In addition to crystals with a cubic close-packed (ccp ) arrangement, crystals were found with a hexagonal close-packed (hcp ) structure. Detailed crystallographic evidence is given, including complete refinements, of the room-temperature structures of both polytypes. The radius of the CsO molecule was determined as 3.54 1 ( 1) A, and was found to be equal for both ccp and hcp crystals.

Hexamethylenetetramine Sebacate, an Incommensurate Structure With Large Nonsinusoidal Modulations - Comparison of Two Refinement Strategies

We present the structure of anhydrous sodium carbonate at room temperature (phase gamma) and 110 K (phase delta) based on single-crystal X-ray diffraction data. The incommensurate phase gamma was determined almost 30 years ago in the harmonic approximation using one modulation wave and first-order satellites. In our work we use satellites up to fifth order and additional harmonic waves to model the anharmonic features of the structure. The commensurate phase delta is presented for the first time. Using the superspace approach, both phases are compared in order to find common trends in the whole range of the sodium carbonate phases. We present arguments supporting the hypothesis that the driving force of the phase transitions may originate in the unsaturated bonding potential of one of the Na ions.

The description and analysis of composite crystals

Sr(14/11)CoO(3) (i.e. Sr(14)Co(11)O(33), tetradecastrontium undecacobalt tritriacontaoxide), a new phase in the hexagonal perovskite Sr(x)CoO(3) system, has been prepared and its structure solved from single-crystal X-ray data within the (3 + 1)-dimensional formalism. Sr(14/11)CoO(3) crystallizes in the trigonal symmetry, R3;m(00gamma)0s superspace group with the following lattice parameters: a(s) = 9.508 (2), c(s) = 2.5343 (7) Å, q = 0.63646 (11)c(*) and V(s) = 198.40 (13) Å(3). With the commensurate versus incommensurate test not being conclusive, the structure was considered as commensurate (P32 three-dimensional space group), but refined within the (3 + 1)-dimensional formalism to a residual factor R = 0.0351 for 47 parameters and 1169 independent reflections. Crenel functions were used for the oxygen and cobalt description and a Gram-Charlier expansion up to the third order of the atomic displacement parameter was employed for one Co atom. The structure is similar to that of Sr(6/5)CoO(3), but with a different sequence of the octahedra and trigonal prism polyhedra along the [CoO(3)] chains. An interesting feature evidenced by the non-harmonic expansion is the displacement of the prismatic Co atoms from the site center, towards the prism rectangular faces.

Superspace-symmetry determination and multidimensional refinement of the incommensurately modulated structure of natural fresnoite

The crystal structure of the third polymorph of the Cu(7)PSe(6) argyrodite compound, alpha-Cu(7)PSe(6), heptacopper phosphorus hexaselenide, is determined by means of single-crystal diffraction from twinned crystals and X-ray powder diffraction, with the help of extensive NMR measurements. In the low-temperature form, i.e. below the last phase transition, alpha-Cu(7)PSe(6) crystallizes in orthorhombic symmetry, space group Pna2(1), with a = 14.3179 (4), b = 7.1112 (2), c = 10.1023 (3) A, V = 1028.590 (9) A(3) (deduced from powder data, T = 173 K) and Z = 4. Taking into account a twinning by reticular merohedry, the refinement of the alpha-Cu(7)PSe(6) structure leads to the residual factors R = 0.0466 and wR = 0.0486 for 127 parameters and 3714 observed, independent reflections (single-crystal data, T = 173 K). A full localization of the Cu(+)d(10) element is reached with one twofold-, one threefold- and five fourfold-coordinated Cu atoms. The observation of two phase transitions for Cu(7)PSe(6), to be compared with only one for Ag(7)PSe(6), is attributed to the d(10) element stability in a low coordination environment, copper being less prone to lower coordination sites than silver, especially at low temperature.