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Hexagonal ferrites represent an extensive family of mixed-layer magnetic materials with periods up to 1500 Å along the stacking direction, probably constituting the largest unit cells in the inorganic realm. The (TS) nT subfamily includes and structures that can be derived from Y ferrite Ba2 M2Fe12O22 ( M = Zn, Fe, Co, Mg, Mn) by introducing stacking faults. A unified (3 + 1)-dimensional superspace model is proposed for all members of the (TS) nT family. The model belongs to the superspace group with , , has a unit cell of the basic structure with a = 5.88, c = 4.84 Å and modulation vector , where n is rational for periodic structures and irrational for the aperiodic ones. The model was tested on calculated data of one of the principal members of the (TS) nT family, the Y ferrite ( ). The fit obtained with the superspace model was excellent. The model allowed a reduction of refinable parameters by 19% with respect to the ordinary refinement without a significant increase of the refinement R values. [ABSTRACT FROM AUTHOR]

Co-crystals of hexamethylenetetramine and resorcinol were investigated by X-ray diffraction. The structure was refined in the superspace group , . In the average structure the resorcinol molecules are disordered between two orientations. The main effect of the modulation in the structure is a harmonic modulation of the occupation probabilities of the two orientations of the resorcinol molecule. However, the modulated order is not perfect and the resorcinol molecules remain partially disordered. Below 270 K the crystal undergoes a phase transition to a commensurately modulated structure with modulation vector and superspace group . The structure of the low-temperature phase could not be determined owing to the poor quality of the crystals affected by the reconstructive phase transition. [ABSTRACT FROM AUTHOR]

3,4-Diphenyl-2a,5a,6,7,8,8a,8b-heptahydro-furo[4,3,2- de]chromen-2-one (1) was prepared as part of a project aimed at the synthesis of polycyclic natural-product-like scaffolds. X-ray analysis of crystals grown from ethanol revealed an incommensurately modulated structure. Data include main and satellite reflections up to second order. The modulation vector was refined using the NADA program. The modulated character of the structure of the organic compound C22H20O3 is interpreted in terms of the intermolecular C—H⋯O hydrogen bonds and close-contact approximation. [ABSTRACT FROM AUTHOR]

Based on the structural data of phases α (hexagonal; 756–972 K), β (monoclinic; 605–751 K), γ (incommensurate, monoclinic; 295 K) and δ (lock-in, monoclinic; 110 K) of sodium carbonate, Na2CO3, we could draw a parallel between the phase transitions and the evolution of the second coordination sphere of the C atoms. The temperature-dependent structures observed in the β phase are reproduced in the incommensurate γ phase as a modulation wave, which relates to the content of the symmetrically equivalent {110} lattice planes in the α phase. By decreasing the temperature, the phase transitions are associated with a stepwise increase in the number of Na ions participating in the second coordination sphere of the C atoms. Over the full temperature range, this number increases from 3 to 7. The C—O distances and the mobility of the O atoms depends on the number of Na ions in the vicinity of the C atoms. [ABSTRACT FROM AUTHOR]

Based on the structural data of phases α (hexagonal; 756–972 K), β (monoclinic; 605–751 K), γ (incommensurate, monoclinic; 295 K) and δ (lock-in, monoclinic; 110 K) of sodium carbonate, Na2CO3, we could draw a parallel between the phase transitions and the evolution of the second coordination sphere of the C atoms. The temperature-dependent structures observed in the β phase are reproduced in the incommensurate γ phase as a modulation wave, which relates to the content of the symmetrically equivalent {110} lattice planes in the α phase. By decreasing the temperature, the phase transitions are associated with a stepwise increase in the number of Na ions participating in the second coordination sphere of the C atoms. Over the full temperature range, this number increases from 3 to 7. The C—O distances and the mobility of the O atoms depends on the number of Na ions in the vicinity of the C atoms. [ABSTRACT FROM AUTHOR]

The incommensurate palmierite-like structure of β-K5Yb(MoO4)4, potassium ytterbium tetramolydate, has been refined in the (3 + 1)-dimensional monoclinic superspace group X2/ m(0ρ0)00, with X = [0 0 0 0; ½½ 0 0; 0 0 ½½; ½½½½] and the unit-cell parameters a = 10.4054 (16), b = 6.1157 (12), c = 19.7751 (18) Å, β = 136.625 (10)°; q = 0.6354 (30) b*. The occupations of the K and Yb atomic positions are described by crenel functions. The structure model reveals a balanced interaction between the atoms of the first and second coordination spheres. It is shown that the third coordination sphere should not be neglected in studies of modulated structures. The ordering of the K and Yb atoms appears to be the driving force for the modulation of all the other atoms. [ABSTRACT FROM AUTHOR]

Quininium (R)-mandelate, C20H25N2O2+·C8H7O3-,is an organic salt with an incommensurately modulated structure. The superspace approach is required for a precise description of the structure at room temperature. In addition to the main reflections, the diffraction pattern also exhibits higher-order satellite reflections. The large number of first- and second-order satellite reflections with relatively strong intensities indicates a significant modulation. No average structure solution could be obtained on the basis of the main reflections only and hence the structure solution was performed in two suitable superstructure approximations, including satellite intensities. Positional modulation functions and modulation functions for the anisotropic atomic displacement parameters were introduced. The modulation originates from a competition between intramolecular and intermolecular forces, which is reflected, in the superspace formalism, in the modification of hydrogen bonds along the internal space variable t. [ABSTRACT FROM AUTHOR]

Focuses on structural phases of hexamethylenetetramine-pimelic acid (1/1): a unified description based on a stacking model. Number of crystalline phases identified at ambient pressure; Form of crystal growth and caloriemetric compounds; Basic entity of the model.

We present the structure of anhydrous sodium carbonate at room temperature (phase γ) and 110 K (phase δ) based on single-crystal X-ray diffraction data. The incommensurate phase γ was determined almost 30years 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 theanharmonic features of the structure. The commensurate phase δ 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 transition may originate in the unsaturated bonding potential of one of the Na ions. [ABSTRACT FROM AUTHOR]

The single crystal investigation of the self-hosting a σ-structure of β-tantalum (β-Ta) at 120 K (low-temperature, LT, structure) and at 293 K. (RT-1 before cooling and RT-II after cooling and rewarming; Rt represents rm temperature) shows that his structure is indeed a specific two-component composite where the components have the same (or an integer multiple) lattice constants but different space groups. The space groups of both host (H) and guest (G) components cause systematic absences, which result from their intersection. The highest symmetry of a σ-structure can be described as [H: P4[SUB2]mnm; G: P4/mbm (c[SUBG]=0.5c[SUBH]); composite: P4[SUB2]/mnm]. a complete analysis of possible symmetries is presented in the Appendix: In β-Ta, two components modify their symmetry during the thermal process 293 K (RT-1), ⇒ 120 K (LT) ⇒ 293 K (RT-II): [H: P42[SUB1]m; G: P42[SUB1]m; composite: P42[SUB1]m] ⇒ [H: P4, G: P4/mbm (c[SUBG]= 0.5c[SUBH]), composite P4] ⇒ [H: P42[SUB1]m, G: P4/mbm (c[SUBG] = 0.5 c[SUBH], composite: P42[SUB1]m], Thus, the phase transition is reversible with respect to H and irreversible with respect to G. [ABSTRACT FROM AUTHOR]

HMT-C11 belongs to the family of adducts formed by the cocrystallization of N[SUB4](CH[SUB2])[SUB6] molecules (hexamethylenetetramine or HMT) and aliphatic dicarboxylic acids HOOC(CH[SUB2])[SUBn - 2]COOH with 5 ≤ n ≤ 13 (Cn). The adducts exhibit a layered structure in which the packing between HMT and Cn is determined by strong hydrogen bonds. The compounds in this family studied so far present thermotropic structural phase transitions and, depending on the chain length, disordered, twinned and modulated phases. The structure refinement of HMT-C11 based on X-ray diffraction experiments indicates three distinct phases from the melting point down to liquid nitrogen temperature: phase I is not crystalline: phase II is isordred (stacking fault) and its average structure is described in space group Bmmb: phase III is partially disordered and its symmetry is P2[SUB1]/c. The systematic study of the structure evolution of phase III upon cooling revealed that the disorder has a dynamic character (anharmonicity). The main structured change observed from 293 K down to 93 K is the increase of the tilting angle of the C11 chains relative to the layer plane and the rotation of the HMT molecules. Both HMT and C11 behave like rigid bodies in the temperature range investigated. The quality of the refinements leads to a conclusive model for the O-H&ellips;N hydrogen bonds linking HMTand C11. [ABSTRACT FROM AUTHOR]

The incommensurately modulated structure of K[sub 3]In(PO[sub 4])[sub 2] has been solved and refined. The origin of the modulation relates to the ordering of K cations within the hexagonal close packing of the PO[sub 4] anions. The driving forces for the modulation of the other cations are In-P and K-P interactions. The modulation of O atoms of rigid PO[sub 4] units follows the cations in order to stabilize the InO[sub 6] octahedron. It is shown that the previously published three-dimensional structure refined from powder diffraction data obtained at room temperature is an average structure. Therefore the incommensurately modulated phase of K[sub 3]In(PO[sub 4])[sub 2] is the only one that has been unequivocally identified at room temperature. The origin of the modulation is discussed in comparison with the structures of Na[sub 3]InP[sub 2], α- and β-Na[sub 3]In(PO[sub 4])[sub 2], Na[sub 3]Fe(PO[sub 4])[sub 2] and Rb[sub 3]In(PO[sub 4])[sub 2]. [ABSTRACT FROM AUTHOR]

Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T[sub h] > 0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a[sub o] ... 4.7, b ... 26.1 and c ... 14.4 Å. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a[sub 1] = 2a[sub o], b[sub 1] = b, c[sub 1] = c and space group Pcc2 is begun (at ∼301 K). The superposition structure of the OD system, at T = 286 (1)K with space group Bmmb and cell â = 2a[sub o], &bcirc; = b and ĉ = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a[sub m] = -a[sub o] +c/4, b[sub m] = b, c[sub m] = -2(a[sub o] + c/2), space group P2[sub 1]/c, spontaneous deformation ~2°, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At ∼233 K, the system reaches its ground state (cell a[sub M] = a[sub m], b[sub M] = b, c[sub M] = c[sub m] and space group P2[sub 1]/c) via an irreversible transition. The phase... [ABSTRACT FROM AUTHOR]

The structure of a crystal of Sr[sub 0.61]Ba[sub 0.39]Nb[sub 2]O[sub 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) Å, modulation vectors q[sub 1] = 0.3075 (6) (a[sup *] + b[sup *]), q[sub 2] = 0.3075 (6) (a[sup *] - b[sup *]). 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 Å, 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. [ABSTRACT FROM AUTHOR]

Using electrodeposition from a bath of molten fluorides single crystals of tetragonal β-tantalum have been obtained for the first time at normal pressure; The unit-cell parameters a = 10.211 (3), c = 5.3064 (10) Å, space group P&macr4;21m. The β-Ta structure belongs to the σ-type Frank-Kasper structures which are typical for binary intermetalliccompounds and β-U. In comparison to the σ-type, additional intercalated Ta atoms (population factor ∼0.01) have been detected between the atoms located in the channels of the structure. The shorter interatomic distances observed between the channel atoms in comparison with the atoms of the framework justify the 'self-hosting' characteristic. β-Ta exhibits common features with the complex tetragonal structures of the high-pressure phases for the elements Rb, Ba, Sr, Bi and Sb. [ABSTRACT FROM AUTHOR]

Reports on the solution and refinement of the structure of a crystal of natural melilite from San Venanzo, Umbria, Italy, as an incommensurate structure in five-dimensional superspace. Description of the structure; Modulations of the atomic positions as well as modulations of thermal parameters.

Discusses a study on the perovskite-type crystal structure of the colourless transparent crystals potassium tantalate, with a high degree of precision. Type of structure of the new cubic potassium tantalate; Differences in the properties; Ability of potassium tantalate to maintain its dielectric properties.

An La2Co1.7 crystals was investigated by single-crystal neutron and X-ray diffraction. The neutron measurement was performed with a Laue white-beam technique at 15 K and room temperature, using a large position-sensitive detector. The X-ray measurements were obtained at room temperature from a CCD detector. The average structure of La2Co1.7 is hexagonal with cell parameters a = 4.885 (1), c = 4.273 (2) Å and space group P63/mmc. The satellites are located at the vertices of small hexagons perpendicular to the c axis. The modulated crystal was indexed assuming a sixfold twinned 3 + 1 dimensional structure with q = (α, 0, γ). The structure was solved in the pseudoorthorhombic cell, with a = 8.461 (1), b = 4.885 (1), c = 4.273 (2) Å, in the superspace group C2/m(α, 0, γ). Owing to space requirements, the Co atoms cannot fit precisely into the octahedral sites of the La h.c.p. (hexagonal close packing). Instead, the Co atoms adopt a different periodicity, which is not commensurate with the periodicity of the La atoms. Two structure models have been refined in order to describe this behavior, one using the sawtooth function for the positional modulation of cobalt and the other describing the structure as a composite system. The chemical composition calculated from the composite model is La2O1.8 (1) with the estimated standard deviation arising from the variation of q for different samples. In both models lanthanum is incommensurately modulated, while the position of cobalt seems not to be affected by any relative periodic displacement. [ABSTRACT FROM AUTHOR]

The structural phases observed in LiKSO4 crystals due to thermotropic transitions have been studied for more than a century. Nowadays many different phases are referenced, but some of the results are still controversial. Structural studies by single-crystal X-ray diffraction from room temperature to 803 K are presented here. Phase II (708 < T < 943 K) is extensively discussed on the basis of ordered and disordered models, using harmonic and anharmonic atomic displacements, and considering a twinned crystal composed of three orthorhombic domains Analyses of the same phase at different temperatures determine the best structure model. [ABSTRACT FROM AUTHOR]

3,4-Diphenyl-2a,5a,6,7,8,8a,8b-heptahydro-furo[4,3,2- de]chromen-2-one (1) was prepared as part of a project aimed at the synthesis of polycyclic natural-product-like scaffolds. X-ray analysis of crystals grown from ethanol revealed an incommensurately modulated structure. Data include main and satellite reflections up to second order. The modulation vector was refined using the NADA program. The modulated character of the structure of the organic compound C22H20O3 is interpreted in terms of the intermolecular C—H⋯O hydrogen bonds and close-contact approximation. [ABSTRACT FROM AUTHOR]