Multiple magnetic-phase transitions and critical behavior of charge-density wave compound TbTe3.

We report multiple magnetic phase transitions and critical behavior of the 2D charge-density wave compound TbTe3 studied by µSR measurements and dc magnetization measurements. Zero-field µSR has shown three magnetic transitions below 7 K. The longitudinal field measurements under 50 G has confirmed the first transition at T N = 6.3 K. Scaling analysis from above T N gives the critical exponent w = 0.63(5), suggesting the Ising 3D antiferromagnetic nature of the ordering, which is likely mediated by the 2D correlations. However, the obtained w = 0.81(5) below T N indicates the ferromagnetic phase, which arises over the multiphase transitions at lower temperatures. Temperature-dependent transverse frequency shift gives a relatively smaller exponent γ = 1.0(1) than the Ising 3D model. The different transitions were also observed by dc magnetization measurements, suggesting two magnetic transitions at 7.4 K and 3.1 K, which correspond to the antiferromagnetic and ferromagnetic phases respectively.

The role of magnetic order in VOCl.

VOCl and other transition metal oxychlorides are candidate materials for next-generation rechargeable batteries. We have investigated the influence of the underlying magnetic order on the crystallographic and electronic structure by means of density functional theory. Our study shows that antiferromagnetic ordering explains the observed low-temperature monoclinic distortion of the lattice, which leads to a decreased distance between antiferromagnetically coupled V-V nearest neighbors. We also show that the existence of a local magnetic moment removes the previously suggested degeneracy of the occupied levels, in agreement with experiments. To describe the electronic structure, it turns out crucial to take the correct magnetic ordering into account, especially at elevated temperature.

Phase-channel dynamics reveal the role of impurities and screening in a quasi-one-dimensional charge-density wave system.

Charge density waves (CDWs), i.e. the periodic spatial modulation of coupled electronic and lattice density, are ubiquitous in low-dimensional conductors and have taken on renewed relevance due their role in state-of-the-art materials, e.g. high-T c superconductors, topological insulators and low-dimensional carbon. As CDWs are described by a complex order parameter to represent both the amplitude and phase, they are formally analogous to BCS superconductors and spin-waves, providing a prototype of collective phenomena for the further development of field theories and ab-initio calculations of complex solids. The low-energy excitations are mixed electron-phonon quanta which ideally separate into an amplitude and phase channel, and provide a sensitive probe of the ground state and non-equilibrium dynamics, including ultrafast photoinduced phase transitions. While recent studies of the amplitude modes have brought substantial progress aided by a phenomenological Ginzburg-Landau framework, we focus here on the phase modes using ultrafast terahertz spectroscopy. Experiments on K0.3MoO3 provide a more complete picture, and reveal a high sensitivity to interactions with impurities and screening effects from photogenerated carriers, both of which can be accounted for by generalizations of the model. Moreover, our considerations emphasize the need to revisit the treatment of inherent electronic damping in quantum-mechanical CDW theories.

Superhard semiconducting optically transparent high pressure phase of boron.

An orthorhombic (space group Pnnm) boron phase was synthesized at pressures above 9 GPa and high temperature, and it was demonstrated to be stable at least up to 30 GPa. The structure, determined by single-crystal x-ray diffraction, consists of B12 icosahedra and B2 dumbbells. The charge density distribution obtained from experimental data and ab initio calculations suggests covalent chemical bonding in this phase. Strong covalent interatomic interactions explain the low compressibility value (bulk modulus is K300=227 GPa) and high hardness of high-pressure boron (Vickers hardness HV=58 GPa), after diamond the second hardest elemental material.

Bulk modulus and non-uniform compression of Nb3Te4 and InxNb3Te4 (x < 1) channel compounds.

The crystal structures of Nb3Te4 and InxNb3Te4 [x = 0.539 (4)] are reported for a series of pressures between 0 and 40 GPa. Both compounds crystallize in space group P6(3)/m with a = b = 10.671 and c = 3.6468 A for Nb3Te4, and a = b = 10.677 and c = 3.6566 A for InxNb3Te4 at ambient conditions. Phase transitions were not observed. High-pressure X-ray powder diffraction was measured using a diamond anvil cell and synchrotron radiation. Full Rietveld refinements provided the values of the lattice parameters and the values of the atomic coordinates at each pressure. The bulk modulus is found as K(0) = 70 (5) GPa for Nb3Te4 and as K(0) = 73 (4) GPa for InxNb3Te4. The analysis of the pressure dependences of the detailed crystal structures shows that the compression along c involves the folding up of the quasi-one-dimensional zigzag chains of Nb. The compression perpendicular to c is entirely due to the reduction of the diameter of the channels. The presence of intercalated In atoms is found to have hardly any influence on the compression behaviour up to 40 GPa.

Disordered crystal structure of pentamethylcyclopentadienylsodium as seen by high-resolution X-ray powder diffraction.

The crystal structure of pentamethylcyclopentadienylsodium, [NaC10H15] (NaCp*), has been determined from high-resolution X-ray powder diffraction. The compound crystallizes in space group Cmcm with lattice parameters a = 4.61030 (3), b = 16.4621 (3), c = 14.6751 (2) A, V = 1113.77 (4) A(3) (Z = 4). NaCp* forms polymeric multidecker chains along the a axis. The Rietveld refinement (R(p) = 0.050 and R(F) = 0.163) shows that the Cp* moieties occupy, with disorder, two different orientations rotated away from the eclipsed conformation by +/-13.8 degrees.

Structural basis for the phase transitions of Cs2HgCl4.

The a(0) x b(0) x 2c(0) twofold superstructure of dicaesium mercury tetrachloride, Cs(2)HgCl(4), at T = 120 K has been determined by single-crystal X-ray diffraction using synchrotron radiation. Lattice parameters were found as a = 9.7105 (2), b = 7.4691 (1), c = 26.8992 (4) A, and beta = 90.368 (1) degrees with the supercell space group P2(1)/c. Refinements on 1828 observed unique reflections converged to R = 0.053 (wR = 0.057) using anisotropic temperature factors for all atoms. This phase is the stable phase of Cs(2)HgCl(4) below 163 K. A quantitative comparison is made of the distortions of the 2c(0) superstructure with the undistorted phase that is stable at room temperature, and with the 3c(0) and 5a(0) superstructures that are stable at temperatures between 163 K and room temperature. The principal difference between the 2c(0) superstructure and all other phases of Cs(2)HgCl(4) is that the Cs cations are displaced away from the centers of their coordination polyhedra in the 2c(0) superstructure. The structural basis for the driving force of the series of phase transitions in this compound is found in the variations of the environments of Cs atoms and in the variations of the distortions of the HgCl(4) tetrahedra.

Charge-density-wave transitions in the local-moment magnet Er5Ir4Si10

We report the observation of a new type of charge-density wave (CDW) in the large magnetic-moment rare-earth intermetallic compound, Er5Ir4Si10, which then orders magnetically at low temperatures. Single crystal x-ray diffraction shows the development of a 1D incommensurate CDW at 155 K, which then locks into a purely commensurate state below 55 K. The well-localized Er3+ moments are antiferromagnetically ordered below 2.8 K. We observe very sharp anomalies in the specific heat at 145 and 2.8 K, signifying the bulk nature of these transitions. Our data suggest the coexistence of strongly coupled CDW with local-moment antiferromagnetism in Er5Ir4Si10.

Discrete Fourier transform in arbitrary dimensions by a generalized Beevers-Lipson algorithm

The Beevers-Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in n-dimensional space would lead to n nested loops over the n coordinates, respectively, and different computer code is required for each dimension. An algorithm is proposed based on the generalization of the Beevers-Lipson procedure towards transforms in n-dimensional space that contains the dimension as a variable and that results in a single piece of computer code for arbitrary dimensions. The computational complexity is found to scale as N log(N), where N is the number of pixels in the map, and it is independent of the dimension of the transform. This procedure will find applications in the evaluation of Fourier maps of quasicrystals and other aperiodic crystals, and in the maximum-entropy method for aperiodic crystals.

Bulk modulus and high-pressure crystal structures of tetrakis(trimethylsilyl)methane C

The pressure dependence of the crystal structure of cubic tetrakis(trimethylsilyl)methane C[Si(CH3)3]4 (TC) (P < 16.0 GPa, T = 298 K) is reported using high-resolution angle-dispersive X-ray powder diffraction. The compound has crystal structures with the molecules in a cubic-close-packed (c.c.p.) arrangement. It shows three phase transitions in the measured pressure range. At ambient conditions, TC has space group Fm3m (Z = 4) with a = 12.8902 (2) A, V = 2141.8 (1) A3 (phase I). Between 0 and 0.13 GPa TC exhibits a first-order phase transition into a structure with space group Pa3 (phase II). A second first-order phase transition occurs between 0.2 and 0.28 GPa into a structure with space group P2(1)3 (phase III). Under non-hydrostatic pressure conditions (P > 10 GPa) a transformation is observed into a c.c.p. structure that is different from the face-centred-cubic structure at ambient conditions. A non-linear compression behaviour is observed, which could be described by a Vinet relation in the range 0.28-4.8 GPa. The extrapolated bulk modulus of the high-pressure phase III was determined to be K0 = 7.1 (8) GPa. The crystal structures in phase III are refined against X-ray powder data measured at several pressures between 0.49 and 4.8 GPa, and the molecules are found to be fully ordered. This is interpreted to result from steric interactions between neighbouring molecules, as shown by analysing the pressure dependence of intramolecular angles, torsion angles and intermolecular distances. Except for their cell dimensions, phases I, II and III are found to be isostructural to the corresponding phases at low temperatures.

Crystal structures and thermotropic properties of alkyl alpha-D-glucopyranosides and their hydrates.

Thermotropic properties and crystal structures of alkyl alpha-D-glucopyranosides and their hydrates were estimated by X-ray, DSC and thermogravimetric measurements (TGA). Monohydrates rapidly lose their crystal water several degrees below the melting point of the anhydrous glucopyranosides. The melting points of the monohydrates measured in DSC pressure cells (chain length longer than seven) are lower, and the clearing points higher than those of the anhydrous glucosides. Layer distances of smectic and crystalline phases of anhydrous compounds were established. Melting points, densities and layer distances of the crystalline anhydrous glucopyranosides display strong even-odd effects. The strong decrease of these effects in the case of the monohydrates can be elucidated by the results of X-ray crystal structure analysis.

The morphology of quasicrystals, incommensurate composite crystals and modulated crystals derived from the broken-bond model.

The broken-bond model for the surface free energy of crystals is considered. The consequences are derived for the morphology of periodic crystals, quasicrystals, incommensurately modulated crystals and intergrowth compounds. It is found that low-index facets on periodic crystals and quasicrystals are the result of finding an optimized position along the vector normal to the surface of the surface plane. The same principle explains the normal facets on modulated crystals and intergrowth crystals. The so-called satellite facets are the result of surface pinning of the phase of the modulated wave. On intergrowth compounds, facets may be found that are stabilized by a combination of both mechanisms. It is shown that the most stable facets on intergrowth crystals are the normal facets that are common to the subsystems, independent of the details of the structure.

Disorder determined by high-resolution powder diffraction: structure of pentamethylcyclopentadienyllithium.

The crystal structure of pentamethylcyclopentadienyllithium, [Li(C(10)H(15))] (LiCp*), has been determined from a high-resolution powder pattern by modelling and the maximum entropy method (MEM). The compound crystallizes in space group R3m with lattice parameters a = b = 14.7711 (5), c = 3.82206 (6) Å and V = 722.19 (4) Å(3) (Z = 3). LiCp* forms polymeric 'multidecker' chains along the c axis. The pentamethylcyclopentadienyl anions are coplanar with each other and show threefold rotational disorder. The MEM calculations did not only confirm the structural model and the type of disorder, but also discovered additional symmetry compared with the Rietveld analysis. This is the first solid-state structure of a Lewis-base-free alkali metal Cp* compound.

Modulated structures of Cs2HgCl4: the 5a superstructure at 185 K and the 3c superstructure at 176 K.

Crystalline dicaesium mercury tetrachloride (Cs(2)HgCl(4)) is isomorphous with beta-K(2)SO(4) (space group Pnma, Z = 4) in its normal phase at room temperature. On cooling a sequence of incommensurate and commensurate superstructures occurs, below T = 221 K with modulations parallel to a*, and below 184 K with modulations along c*. The commensurately modulated structures at T = 185 K with q = (1/5)a* and at T = 176 K with q = (1/3)c* were determined using X-ray scattering with synchrotron radiation. The structure at T = 185 K has superspace group Pnma(alpha,0,0)0ss with alpha = 0.2. Lattice parameters were determined as a = 5 x 9.7729 (1), b = 7.5276 (4) and c = 13.3727 (7) Å. Structure refinements converged to R = 0.050 (R = 0.042 for 939 main reflections and R = 0.220 for 307 satellites) for the section t = 0.05 of superspace. The fivefold supercell has space group Pn2(1)a. The structure at T = 176 K has superspace group Pnma(0,0,gamma)0s0 with gamma = 1/3. Lattice parameters were determined as a = 9.789 (3), b = 7.541 (3) and c = 3 x 13.418 (4) Å. Structure refinements converged to R = 0.067 (R = 0.048 for 2130 main reflections, and R = 0.135 for 2382 satellite reflections) for the section t = 0. The threefold supercell has space group P112(1)/a. It is shown that the structures of both low-temperature phases can be characterized as different superstructures of the periodic room-temperature structure. The superstructure of the 5a-modulated phase is analysed in terms of displacements of the Cs atoms, and rotations and distortions of HgCl(4) tetrahedral groups. In the 3c-modulated phase the distortions of the tetrahedra are relaxed, but they are replaced by translations of the tetrahedral groups in addition to rotations.

Order-disorder phenomena determined by high-resolution powder diffraction: the structures of tetrakis(trimethylsilyl)methane C

The compounds tetrakis(trimethylsilyl)methane C[Si(CH(3))(3)](4) (TC) and tetrakis(trimethylsilyl)silane Si[Si(CH(3))(3)](4) (TSi) have crystal structures with the molecules in a cubic closed-packed (c.c.p.) stacking. At room temperature both structures have space group Fm{\bar 3}m (Z = 4) with a = 13.5218 (1) Å, V = 2472.3 (1) Å(3) for TSi, and a = 12.8902 (2) Å, V = 2141.8 (1) Å(3) for TC. X-ray scattering data can be described by a molecule with approximately sixfold orientational disorder, ruling out a structure with free rotating molecules. Upon cooling, TSi exhibits a first-order phase transition at T(c) = 225 K, as is characterized by a jump of the lattice parameter of Deltaa = 0.182 Å and by an exothermal maximum in differential scanning calorimetry (DSC) with DeltaH = 11.7 kJ mol(-1) and DeltaS = 50.0 J mol(-1) K(-1). The structure of the low-temperature phase is refined against X-ray powder data measured at 200 K. It has space group P2(1)3 (Z = 4), a = 13.17158 (6) Å and V = 2285.15 (2) Å(3). The molecules are found to be ordered as a result of steric interactions between neighboring molecules, as is shown by analyzing distances between atoms and by calculations of the lattice energy in dependence on the orientations of the molecules. TC has a phase transition at T(c1) = 268 K, with Deltaa(1) = 0.065 Å, DeltaH(1) = 3.63 kJ mol(-1) and DeltaS(1) = 13.0 J mol(-1) K(-1). A second first-order phase transition occurs at T(c2) = 225 K, characterized by Deltaa(2) = 0.073 Å, DeltaH(2) = 6.9 kJ mol(-1) and DeltaS(2) = 30.0 J mol(-1) K(-1). The phase transition at higher temperature has not been reported previously. New NMR experiments show a small anomaly in the temperature dependence of the peak positions in NMR to occur at T(c2). Rietveld refinements were performed for the low-temperature phase measured at T = 150 K [space group P2(1)3, lattice parameter a = 12.609 (3) Å], and for the intermediate phase measured at T = 260 K [space group Pa{\bar 3}, lattice parameter a = 12.7876 (1) Å]. The low-temperature phase of TC is formed isostructural to the low-temperature phase of TSi. In the intermediate phase the molecules exhibit a twofold orientational disorder.