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A detailed synchrotron X‐ray diffraction (XRD) study performed with a single crystal of BaVS3 (barium vanadium trisulfide) in the temperature range between 10 and 295 K is reported. Aside from the known tetragonal–orthorhombic (240 K) and orthorhombic–monoclinic (69 K) phase transitions, in the 130 < T ≤ 295 K range the overall structure can be viewed as a host–guest (H–G) composite. The BaS3 matrix is the host, while the V‐chains form the guest. The two subsystems lock in at TLOCK = 130 ± 20 K. This temperature is marked by a symmetry change from orthorhombic to monoclinic. This results in the formation of twins, implying a structural phase transition identified here for the first time. From the refined structural data, it is possible to follow, starting already at 295 K downwards, the stepwise transformation of VS6 octahedra into VS5 tetragonal pyramids as the origin of the structure evolution. The new findings will yield a better understanding of the complex electronic phase diagram of BaVS3. [ABSTRACT FROM AUTHOR]

Hydrothermally synthesized dipotassium gallium {hydrogen bis[hydrogenphosphate(V)]} difluoride, K2Ga[H(HPO4)2]F2, is isotypic with K2Fe[H(HPO4)2]F2. The main features of the structure are ([Ga{H(HPO4)2}F2]2−) n columns consisting of centrosymmetric Ga(F2O4) octahedra [average Ga—O = 1.966 (3) Å and Ga—F = 1.9076 (6) Å] stacked above two HPO4 tetrahedra [average P—O = 1.54 (2) Å] sharing two O-atom vertices. The charge-balancing seven-coordinate K+ cations [average K—O,F = 2.76 (2) Å] lie in the intercolumn space, stabilizing a three-dimensional structure. Strong [O...O = 2.4184 (11) Å] and medium [O...F = 2.6151 (10) Å] hydrogen bonds further reinforce the connections between adjacent columns. [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]

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]

4-benzoylpyridine thiosemicarbazone (H4Bz4DH) and N(4′)-phenyl-4-benzoylpyridine thiosemicarbazone (H4Bz4Ph) were obtained and fully characterized by infrared, UV and NMR spectroscopies. The assignment of the NMR signals was made by using DEPT135 and the HMQC heteronuclear correlation technique. X-ray diffraction studies have shown the presence of a water molecule in the crystal structure of both compounds as well as the protonation of the pyridine nitrogen. Moreover, a Cl− counter-ion was evidenced in the crystal structure of H4Bz4DH and an HSO4− ion in the structure of H4Bz4Ph. Refined structures of both compounds are included and the X-ray crystallographic studies can be summarized as follows: H4Bz4DH+Cl−·H2O crystallizes with triclinic symmetry, space group P1, with a=9.159(2), b=9.749(2) and c=17.787(4) A˚, α=81.75(3), β=81.24(3) and γ=69.41(3)° and Z=4. H4Bz4Ph+HSO4−·H2O crystals have monoclinic symmetry, space group C2/c, with a=32.767(7), b=10.149(2) and c=12.763(3) A˚, β=99.23(3)° and Z=8. [Copyright &y& Elsevier]

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.

The incommensurately modulated structure of the mineral natrite has been refined for the first time. Two single-crystal grains, Lv and Kh, from two different occurrences [Mt. Karnasurt, Lovozero massif (Lv), Kola peninsula, Russia, and the pegmatite of Mt. Koashva, Khibiny massif (Kh)], have been investigated at 293 and 120 K using synchrotron X-ray data. The average structures of both minerals are identical and the basic features of the structural modulations are similar to the synthetic γ-Na2CO3 phase previously published. The γ (incommensurate) → δ (lock-in) phase transition reported at low temperature for the synthetic compound was not observed down to 120 K in natural natrite. Crystal-chemical aspects, especially about the second coordination sphere for the carbon atoms, are examined to explain the different structural behaviors observed at low temperature. The possible role played by the minor isomorphous substitutions in natural natrite specimens is also discussed. [ABSTRACT FROM AUTHOR]

Hydrothermally synthesized dipotassium gallium {hydrogen bis[hydrogenphosphate(V)]} difluoride, K2Ga[H(HPO4)2]F2, is isotypic with K2Fe[H(HPO4)2]F2. The main features of the structure are ([Ga{H(HPO4)2}F2]2−) n columns consisting of centrosymmetric Ga(F2O4) octahedra [average Ga—O = 1.966 (3) Å and Ga—F = 1.9076 (6) Å] stacked above two HPO4 tetrahedra [average P—O = 1.54 (2) Å] sharing two O-atom vertices. The charge-balancing seven-coordinate K+ cations [average K—O,F = 2.76 (2) Å] lie in the intercolumn space, stabilizing a three-dimensional structure. Strong [O...O = 2.4184 (11) Å] and medium [O...F = 2.6151 (10) Å] hydrogen bonds further reinforce the connections between adjacent columns. [ABSTRACT FROM AUTHOR]

Obituary for Dieter Schwarzenbach.

Through the years, mineralogical studies have produced a tremendous amount of data on the atomic arrangement and mineral properties. Quite often, structural analysis has led to elucidate the role played by minor components, giving interesting insights into the physico-chemical conditions of mineral crystallization and allowing the description of unpredictable structures that represented a body of knowledge critical for assessing their technological potentialities. Using such a rich database, containing many basic acquisitions, further steps became appropriate and possible, into the directions of more advanced knowledge frontiers. Some of these frontiers assume the name of modularity, complexity, aperiodicity, and matter organization at not conventional levels, and will be discussed in this review.

The host-guest structures of elements at high pressure discovered a decade ago still leave many open questions due to the lack of precise models based on full exploitation of the diffraction data. This concerns in particular Ba IV, which is stable in the range 12-45 GPa. With the example of phase Ba IVb, which is characterized here for the first time, a systematic analysis is presented of possible host-guest structure models based on high-quality single-crystal diffraction data obtained with synchrotron radiation at six different pressures between 16.5 and 19.6 GPa. It is shown that a new incommensurately modulated (IM) structure model better fits the experimental data. Unlike the composite models which are commonly reported for the Ba IV phases, the IM model reveals a density wave and its pressure-dependent evolution. The crucial role played by the selected model in the interpretation of structure evolution under pressure is discussed. The findings give a new experimental basis for a better understanding of the nature of host-guest structures.

An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be derived. Euclidean symmetry operations associated with the tangent bundle are generalized and their usefulness for the determination of the intrinsic translation part in helicoidal axes and glide planes is illustrated. Finally, a novel representation of space groups is shown to be independent of any origin point.

Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the manifold. Manifold theory proves particularly powerful as a unified formalism describing symmetry operations of conventional as well as modulated crystals without requiring a higher-dimensional space. We show, in particular, that a modulated structure recovers a three-dimensional periodicity in any tangent space and that its point group consists of linear applications.

The incommensurately modulated scheelite-like KSm(MoO(4))(2) structure has been refined in the monoclinic superspace group I2/b(alphabeta0)00 by the Rietveld method on the basis of synchrotron radiation powder diffraction data. The systematic broadening of satellite reflections has been accounted for by applying anisotropic microstrain line-broadening. The microstructure has been studied by transmission electron microscopy (TEM). The partial disorder of the K and Sm cations in the A position is best approximated by a combination of harmonic and complex crenel functions with (0.952Sm + 0.048K) and (0.952K + 0.048Sm) atomic domains. This combination yields a compositional wave distribution from {KMoO(4)} to {SmMoO(4)} observed in the ab structure projection along q. The specific features of KSm(MoO(4))(2) and degree of the A-cation ordering are discussed in comparison with the previously reported structure of KNd(MoO(4))(2).

The previously reported incommensurately modulated scheelite-like structure KNd(MoO(4))(2) has been exploited as a natural (3 + 1)-dimensional superspace model to generate the scheelite-like three-dimensional structure family. Although each member differs in its space-group symmetry, unit-cell parameters and compositions, in (3 + 1)-dimensional space, they share a common superspace group, a common number of building units in the basic unit cell occupying Wyckoff sites with specific coordinates (x, y, z) and specific basic unit-cell axial ratios (c/a, a/b, b/c) and angles. Variations of the modulation vector q, occupation functions and t(0) are exploited for the derivation. Eight topologically and compositionally different known structures are compared with their models derived from the KNd(MoO(4))(2) structure in order to evaluate the capabilities and limitations of the incommensurately modulated structure to act as a superspace generating model. Applications of the KNd(MoO(4))(2) structure as a starting model for the refinement and prediction of some other modulated members of the family is also illustrated. The (3 + 1)-dimensional presentation of the scheelite-like structures reveals new structural relations, which remain hidden if only conventional three-dimensional structure descriptions are applied.

Hexagonal ferrites represent an extensive family of mixed-layer magnetic materials with periods up to 1500 A along the stacking direction, probably constituting the largest unit cells in the inorganic realm. The (TS)(n)T subfamily includes P3m1 and R3m structures that can be derived from Y ferrite Ba(2)M(2)Fe(12)O(22) (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)(n)T family. The model belongs to the superspace group X3m1(00gamma) with X = {(1/3, 2/3, 0, 1/3), (2/3, 1/3, 0, 2/3)}, has a unit cell of the basic structure with a = 5.88, c = 4.84 A and modulation vector q = 4n+3/9n+6 c*, 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)(n)T family, the Y ferrite (n = infinity). 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.

Hydrothermally synthesized dipotassium gallium {hydrogen bis[hydrogenphosphate(V)]} difluoride, K(2)Ga[H(HPO(4))(2)]F(2), is isotypic with K(2)Fe[H(HPO(4))(2)]F(2). The main features of the structure are ([Ga{H(HPO(4))(2)}F(2)](2-))(n) columns consisting of centrosymmetric Ga(F(2)O(4)) octahedra [average Ga-O = 1.966 (3) Angstrom and Ga-F = 1.9076 (6) Angstrom] stacked above two HPO(4) tetrahedra [average P-O = 1.54 (2) Angstrom] sharing two O-atom vertices. The charge-balancing seven-coordinate K(+) cations [average K-O,F = 2.76 (2) Angstrom] lie in the intercolumn space, stabilizing a three-dimensional structure. Strong [O...O = 2.4184 (11) Angstrom] and medium [O...F = 2.6151 (10) Angstrom] hydrogen bonds further reinforce the connections between adjacent columns.

Co-crystals of hexamethylenetetramine and resorcinol were investigated by X-ray diffraction. The structure was refined in the superspace group Xmcm(0beta0)s0s, X=(1/2 1/2 0 1/2). 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 q=(0 1/2 1/4) and superspace group X2/m(0betagamma)0s. 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.

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 C(22)H(20)O(3) is interpreted in terms of the intermolecular C-H...O hydrogen bonds and close-contact approximation.

The structure of room-temperature ZrP2O7 is shown to be orthorhombic by a combination of high-resolution synchrotron powder diffraction and single-crystal synchrotron diffraction data. Small nontwinned single crystals were obtained by synthesizing the compound using solvothermal methods at temperatures below the cubic to orthorhombic phase transition. The average P-O-P angle is 146 degrees. DFT calculations (B3LYP/AUG-cc-pVDZ) on the isolated P2O7(4-) anion yield a P-O-P angle of 153.42 degrees and indicate that the barrier to inversion is of the order 3.6 kJ mol(-1).

A method based on the superspace approach is presented with the aim of generating a family of modular structures from a single incommensurately modulated structure. This approach based on the variation of the modulation vector q is applied to the generation of the K5Yb(MoO4)4, potassium ytterbium tetramolybdate, family of modular structures. The beta coefficient of the modulation vector q = betab* is a temperature-dependent variable which determines the modification. Our method gives a unified frame to describe and explain the three temperature-dependent phases of K5Yb(MoO4)4. Phase beta can be represented as a polytypic modification with 1/2b* < or = q < or = 2/3b*; phases gamma (q = 1/2b*) and alpha (q = 1b*) are the lowest and the highest temperature members of the K5Yb(MoO4)4 family, respectively.

Based on the structural data of phases alpha (hexagonal; 756-972 K), beta (monoclinic; 605-751 K), gamma (incommensurate, monoclinic; 295 K) and delta (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 beta phase are reproduced in the incommensurate gamma phase as a modulation wave, which relates to the content of the symmetrically equivalent {110} lattice planes in the alpha 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.

The incommensurate palmierite-like structure of beta-K5Yb(MoO4)4, potassium ytterbium tetramolydate, has been refined in the (3 + 1)-dimensional monoclinic superspace group X2/m(0rho0)00, with X = [0 0 0 0; (1/2) (1/2) 0 0; 0 0 (1/2) (1/2); (1/2) (1/2) (1/2) (1/2)] and the unit-cell parameters a = 10.4054 (16), b = 6.1157 (12), c = 19.7751 (18) A, beta = 136.625 (10) degrees ; 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.

N-Salicylideneaniline (SA), C13H11NO, belongs to the large family of aromatic Schiff bases. It is of particular importance owing to its reversible photoreactivity. SA forms two photochromic polymorphs, both with two non-coplanar benzene rings. In addition, we have recently discovered a planar polymorph, named the beta-polymorph, which will be discussed in a subsequent paper. We report here the structure of the alpha2-polymorph in the orthorhombic crystal system. This compound exhibits a strong intramolecular O-H...N hydrogen bond and the dihedral angle between the two rings varies with temperature.

In order to apply the molecular dynamics (MD) method to simulate modulated phases in organic materials, a compensating external pressure tensor is proposed to compensate for the deficiencies of the force field applied in the simulation. MD can well reproduce modulated phases that have been measured by diffraction. Mechanisms of incommensurate modulation are revealed from the simulations. Details of the structures relating to the origins and mechanisms giving rise to the formation of modulated phases are presented.

To investigate the mechanism of structural changes of a peptide nanotube and water confined inside the channel, the helical peptide tryptophylglycine monohydrate (WG.H2O) was studied by molecular dynamics (MD) simulations using the three-dimension parallel MD program ddgmq (software package) and a consistent force field. Simulations were performed on both the water-containing system and a model system without water molecules. The details of the structural behavior with temperature are investigated for the entire simulated temperature range. Phase transitions were obtained at 115, 245, 270, 310, and 385 K, due to the contributions of both the peptide and the confined water subsystems. The crystalline, amorphous, liquidlike, liquid, and superheated phases of water were observed in the temperature ranges 40-115, 115-245, 245-310, 310-385, and >385 K, respectively. At 300 K, the diffusion constant of the confined water is 0.46 x 10-5 cm2 s-1, a value comparable to that of other peptide nanotubes. The empty peptide system melts at 440 K. Mechanisms of the negative thermal expansion (NTE) along the tube axis were investigated for different temperature ranges. The contraction of the crystalline water (or amorphous water) draws also the tube walls in and leads to NTE below 245 K. The other NTEs appear to be connected to the collapse of the ice network or the solid peptide network between 245 K and room temperature or from 310 to 440 K, respectively.

The thermotropic phase diagram of 1:1 co-crystals of hexamethylenetetramine and pimelic acid (heptanedioic acid) is investigated. Three crystalline phases are identified at ambient pressure. Phase I is disordered, as revealed by diffuse rods in its diffraction pattern. When the temperature is lowered the diffuse streaks disappear in Phase II, but superstructure reflections emerge indicating an ordering process of the structure through a non-ferroic, or at least non-ferroelastic, phase transition. Phase II is mainly characterized by an unusual distribution of its reflection intensities. Phase III is reached through a ferroelastic phase transition that induces twinned domains. A model based on the stacking of an elementary layer is proposed with the aim of describing the structures in a unified framework. Depending on the value of the unique stacking parameter eta, each of the different structures observed can be reproduced by this model. Its validity is then tested by a series of simulations reproducing the main features of the diffraction patterns such as the diffuse scattering streaks, the occurrence of superstructure peaks at lower temperature and twinning.

The single-crystal investigation of the self-hosting sigma-structure of beta-tantalum (beta-Ta) at 120 K (low-temperature, LT, structure) and at 293 K (RT-I before cooling and RT-II after cooling and rewarming; RT represents room temperature) shows that this 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 sigma-structure can be described as [H: P4(2)/mnm; G: P4/mbm (c(G) = 0.5c(H)); composite: P4(2)/mnm]. A complete analysis of possible symmetries is presented in the Appendix. In beta-Ta, two components modify their symmetry during the thermal process 293 K (RT-I)=> 120 K (LT)=> 293 K (RT-II): [H: P(-)42(1)m; G: P(-)42(1)m; composite: P(-)42(1)m]=> [H: P(-)4, G: P4/mbm (c(G) = 0.5c(H)), composite: P(-)4]=> [H: P(-)42(1)m, G: P4/mbm (c(G) = 0.5c(H)), composite: P(-)42(1)m]. Thus, the phase transition is reversible with respect to H and irreversible with respect to G.

HMT-C11 belongs to the family of adducts formed by the co-crystallization of N(4)(CH(2))(6) molecules (hexamethylenetetramine or HMT) and aliphatic dicarboxylic acids HOOC(CH(2))(n - 2)COOH with 5

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 incommensurately modulated structure of K(3)In(PO(4))(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(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(4) units follows the cations in order to stabilize the InO(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(3)In(PO(4))(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(3)InP(2), alpha- and beta-Na(3)In(PO(4))(2), Na(3)Fe(PO(4))(2) and Rb(3)In(PO(4))(2).