Comparative study of the high-pressure behavior of As,Sb, and Bi

The high-pressure behavior of the heavier group 15 elements As, Sb, and Bi was investigated by means of ab initio density functional calculations employing pseudopotentials and a plane wave basis set. The high-pressure structural sequence of these elements is distinguished by the occurrence of the Bi-III structure, which is a complex, incommensurately modulated, host-guest structure. We approximated this structure by a supercell which reproduced the experimentally established pressure stability ranges of the host-guest structure for the different elements extremely well. With pressure we find an increasing admixture of d states (s-d hybridization) in the occupied levels of the electronic structure of As, Sb, and Bi. However, the s-d mixing remains at a low level. Thus, the emergence of a complex intermediate pressure structure cannot be explained by a pressure-induced altered valence state for these elements. Instead, it is argued that the Bi-III structure is a consequence of a delicate interplay between the electrostatic and the band energy contribution to the total energy. In the intermediate pressure range of heavier group 15 elements, both important parts of the total energy account equally for structural stability.     

Simulation of ordered packed beds in chromatography

A computer simulation of chromatographic dispersion in an ordered packed bed of spheres is conducted utilizing a detailed fluid flow profile provided by the Lattice Boltzmann technique. The ordered configurations of simple cubic, body-centered cubic, and face-centered cubic are employed in these simulations. It is found that zone broadening is less for the fcc structure than the sc and bcc structures and less than a random packed bed analyzed in a previous study in the low flow velocity region used for experimental chromatography. The factors which contribute to the performance of the ordered pack beds are analyzed in detail and found to be dependent both on the nearest surface to surface distance and on the distribution of velocities found in the various packing geometries. The pressure drops of the four configurations are compared and contrasted with the pressure drop from monolithic columns.     

Numerical investigation into the effects of ordered particle packing and slip flow on the performance of chromatography

The pressure drop and the plate height of chromatography columns packed with particles in the face‐centered cubic, the body‐centered cubic and the simple cubic configurations are calculated by a volume averaging method model. It is found that the Kozeny‐Carman equation provides a reasonable prediction of the pressure drop when particles are in the face‐centered cubic configuration, but overestimates the pressure drop when particles are in the body‐centered cubic and the simple cubic configurations. The face‐centered cubic configuration has the advantage to provide a smaller longitudinal dispersion coefficient than the body‐centered cubic, the simple cubic, and the random configurations. The pressure drop and the plate height for slip flow through particles in the face‐centered cubic configuration are lower than that for no‐slip flow. The values of the smallest reduced plate height of columns packed with particles in the face‐centered cubic configuration for no‐slip flow and slip flow are about 0.084 and 0.059, respectively. The plate height of the ordered particle packing structures is smaller and the effect of slip flow on the plate height is less remarkable than results reported in literature.     

Phase behavior of a thermotropic cubic mesogen 4'-n-hexadecyloxy-3'-nitro- biphenyl-4-carboxylic acid under pressure

The phase behavior of an optically isotropic cubic mesogen 4'-n-hexadecyloxy-3'-nitrobiphenyl-4-carboxylic acid (ANBC-16) was investigated under hydrostatic pressures up to 200 MPa using a high-pressure DTA, a polarizing optical microscope equipped with a high-pressure hot-stage and a wide-angle X-ray diffractometer equipped with a high-pressure vessel. In the T vs. P phase diagram constructed in the heating mode, a triple point exists at 54±1 MPa and 205±1°C for the SmC, cubic, and SmA phases. A new mesophase, denoted here as X, appears in place of the cubic phase under pressures above about 60 MPa, while the X phase appears on cooling in the whole pressure region studied. Thus the X phase is a monotropic (metastable) phase between the SmA and Cub phases in the low pressure region, while being an enantiotropic phase between the SmA and SmC phases in the high pressure range. The X phase exhibits broken-fan or sand-like textures under pressure and a spot-like diffraction pattern, indicating the birefringent feature and no layered structure. It is suggested that the X phase is tetragonal or hexagonal columnar phase. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure and phase transitions of the lanthanide metals

The structures and phase transitions of the lanthanide metals can be related to f orbital contributions to the bonding. With increasing availability of the f orbitals the structure sequence hexagonal closest packed, double hexagonal closest packed, δ-samarium, cubic closest packed, and body-centered cubic is observed. Increases in temperature and/or pressure result in an increased availability of the f orbitals resulting in predictable phase transitions.     

A reactive force field simulation of liquid-liquid phase transitions in phosphorus

A force field model of phosphorus has been developed based on density functional (DF) computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact (simple cubic) structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P(4)) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric (gel) state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic (A17) structure observed in the solid state, and also corresponds to a semiconductor to metal transition.     

Structural stability analysis of Wigner crystal with Gaussian and Yukawa‐type positive background

Calculations of the ground‐state energies of Wigner crystals having simple cubic (sc), body‐centered cubic (bcc), face‐centered cubic (fcc), diamond, and perovskite structures and (hence) the analysis of relative stability of Wigner crystals of various different structures are reported. The positive background is represented by a periodic array of Gaussians and Yukawa‐type distribution. The effects on stability of the perturbation due to the underlying lattice have been demonstrated. Among the structures, the bcc lattice still remains the most stable known arrangement and the Yukawa‐type background leads to a lower ground state energy value compared to a Gaussian type. The calculations are done for the range of the density parameter r_s corresponding to low densities for the above two cases. The range of low‐density region favorable for Wigner crystallization is found to be above r_s=20. The role of correlation energy is suitably taken into account. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

Interlayer Bond Formation in Black Phosphorus at High Pressure

Black phosphorus was compressed at room temperature across the A17, A7 and simple‐cubic phases up to 30 GPa, using a diamond anvil cell and He as pressure transmitting medium. Synchrotron X‐ray diffraction showed the persistence of two previously unreported peaks related to the A7 structure in the pressure range of the simple‐cubic phase. The Rietveld refinement of the data demonstrates the occurrence of a two‐step mechanism for the A7 to simple‐cubic phase transition, indicating the existence of an intermediate pseudo simple‐cubic structure. From a chemical point of view this study represents a deep insight on the mechanism of interlayer bond formation during the transformation from the layered A7 to the non‐layered simple‐cubic phase of phosphorus, opening new perspectives for the design, synthesis and stabilization of phosphorene‐based systems. As superconductivity is concerned, a new experimental evidence to explain the anomalous pressure behavior of T_c in phosphorus below 30 GPa is provided.     

Potassium under pressure: Electronic origin of complex structures

Recent high-pressure X-ray diffraction studies of alkali metals revealed unusual complex structures that follow the body-centred and face-centred cubic structures on compression. The structural sequence of potassium under compression to 1 Mbar is as follows: bcc–fcc–h-g (tI19*), hP4–oP8–tI4–oC16.We consider configurations of Brillouin-Jones zones and the Fermi surface within a nearly-free-electron model in order to analyze the importance of these configurations for the crystal structure stability. Formation of Brillouin zone planes close to the Fermi surface is related to opening an energy gap at these planes and reduction of crystal energy. Under pressure, this mechanism becomes more important leading to appearance of complex low-symmetry structures. The stability of the post-fcc phases in K is attributed to the changes in the valence electron configuration under strong compression.     

Elongated silica nanoparticles with a mesh phase mesopore structure by fluorosurfactant templating

Mesoporous silica materials with pore structures such as 2D hexagonal close packed, bicontinuous cubic, lamellar, sponge, wormhole-like, and rectangular have been made by using surfactant templating sol-gel processes. However, there are still some "intermediate" phases, in particular mesh phases, that are formed by surfactants but which have not been made into analogous silica pore structures. Here, we describe the one-step synthesis of mesoporous silica with a mesh phase pore structure. The cationic fluorinated surfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride (HFDePC) is used as the template. Like many fluorinated surfactants, HFDePC forms intermediate phases in water (including a mesh phase) over a wider range of compositions than do hydrocarbon surfactants. The materials produced by this technique are novel elongated particles in which the layers of the mesh phase are oriented orthogonal to the main axis of the particles.     

Ab initio molecular dynamics simulation of pressure-induced phase transition in MgS

Pressure-induced phase transition in MgS is studied using a constant pressure ab initio molecular dynamics method, and a solid evidence of existence of its high-pressure phase is provided. As predicted by total energy calculations, MgS undergoes a structural phase transformation from the rocksalt structure to a CsCl-type structure under hydrostatic pressure. The transformation mechanism is characterized, and two intermediate phases having P4/nmm and P2₁/m symmetries for the rocksalt-to-CsCl-type phase transformation of MgS are proposed, which is different from the previously proposed mechanisms. We also study this phase transition using the total energy calculations. Our predicted transition parameters and bulk properties are in good agreement with the earlier first principle simulations.     

Inversion of the phase sequence between the cubic and smectic C phases under pressure

The phase behaviour of a thermotropic cubic mesogen of 1,2-bis(4′-n-tetradecyloxybenzoyl)hydrazine BABH-14 was studied under hydrostatic pressure using a polarising optical microscope equipped with a high-pressure optical cell, and the P–T phase diagram was constructed. BABH-14 shows the Cr–Cub–I transition sequence under atmospheric and lower pressures, but the Cub phase is replaced completely by the high-pressure SmC, SmC(hp), phase under higher pressures. There is a narrow intermediate-pressure region between the low- and high-pressure regions, in which the Cr–SmC(hp)–Cub–I phase sequence is recognised. The SmC(hp)–Cub transition line has a positive slope with pressure and there are two triple points: one is for the Cr, Cub and SmC(hp) phases and the other is for the I, Cub and SmC(hp) phases. Comparing the phase sequence of BABH-14 with those for BABH-8 and -10, the pressure-induced inversion of the phase sequence between the cubic and SmC phases occurs in the BABH-n homologous compounds. Another new phenomenon is the formation of the monotropic cubic phase on cooling in the intermediate- and high-pressure regions, and an intriguing phenomenon of the cubic phase appearing twice, i.e. I–Cub–SmC(hp)– Cub–Cr phase transition, occurs in the intermediate-pressure region.     

Self-Reaction of HO2 and DO2: Negative temperature dependence and pressure effects

The negative temperature dependence, pressure dependence, and isotope effects of the self-reaction of HO₂ are modeled, using RRKM theory, by assuming that the reaction proceeds via a cyclic, hydrogen-bonded intermediate. The negative temperature dependence is due to a tight transition state, with a negative threshold energy relative to reactants, for decomposition of the intermediate to products. A symmetric structure for this transition state reproduces the observed isotope effect. The weak pressure dependence for DO₂ self-reaction is due to the approach to the high-pressure limit. Addition of a polar collision partner, such as ammonia or water vapor, enhances the rate by forming an adduct that reacts to produce deexcited intermediate. A detailed model is presented to fit the data for these effects. Large ammonia concentrations should make it possible to reach the high-pressure limit of the self-reaction of HO₂.     

Phase behaviour of the thermotropic cubic mesogen 1,2-bis-(4- n -octyloxybenzoyl)hydrazine under pressure

The phase transition behaviour of an optically isotropic, thermotropic cubic mesogen 1,2-bis-(4- n -octyloxybenzoyl)hydrazine, BABH(8), was investigated under pressures up to 200 MPa using a high pressure differential thermal analyser, wide-angle X-ray diffraction and a polarizing optical microscope equipped with a high pressure optical cell. The phase transition sequence, low temperature crystal (Cr 2 )-high temperature crystal (Cr 1 ) - cubic (Cub)-smectic C (SmC)-isotropic liquid (I) observed at atmospheric pressure, is seen in the low pressure region below about 30 MPa. The cubic phase disappears at high pressures above 30-40 MPa, in conjunction with the disappearance of the Cr 1 phase. The transition sequence changes to Cr 2 -SmC-I in the high pressure region. Since only the Cub-SmC transition line among all the phase boundaries has a negative slope (d T /d P ) in the temperature-pressure phase diagram, the temperature range for the cubic phase decreases rapidly with increasing pressure. As a result, a triple point was estimated approximately as 31.6 ±2.0 MPa, 147.0 ±1.0°C for the SmC, Cub and Cr 1 phases, indicating the upper limit of pressure for the observation of the cubic phase. Reversible changes in structure and optical texture between the Cub and SmC phases were observed from a spot-like X-ray pattern and dark field for the cubic phase to the Debye-Sherrer pattern and sand-like texture for the SmC phase both in isobaric and isothermal experiments.     

Kinetics of lamellar-to-cubic and intercubic phase transitions of pure and cytochrome c containing monoolein dispersions monitored by time-resolved small-angle X-ray diffraction

We investigated the effect of incorporation of a small aqueous peripheral membrane protein (cyt c) into the three-dimensional periodic nanochannel structures formed by the lipid monoolein (MO) on its rich phase behavior as a function of temperature, pressure, and protein concentration using synchrotron X-ray small-angle diffraction. By simultaneous use of the pressure-jump relaxation technique and time-resolved synchrotron X-ray diffraction, we also studied the kinetics of various lipid mesophase transformations of the system for understanding the mechanistic pathways of their formation influenced by the protein-lipid interactions. Cyt c incorporated into the bicontinuous cubic phase Ia3d of MO has a significant effect on the lipid structure and the pressure stability of the system already at low protein concentrations. Concentrations higher than 0.2 wt % of cyt c led to an increase in interfacial curvature due to interaction of the protein with the lipid headgroups. This promotes the formation of a new, probably partially micellar cubic phase of crystallographic space group P4(3)32. Upon pressurization, the P4(3)32 phase undergoes a phase transition to a cubic Pn3m phase with smaller partial specific volume. Increase in protein concentration increases the pressure stability of the P4(3)32 phase. The formation of this phase from the cubic phase Pn3m is a slow process taking many seconds and having a time lag in the beginning. It seems to occur as a two-state process without ordered intermediate states. At temperatures above 60 degrees C, the P4(3)32 phase is unable to accommodate the unfolded protein and transforms to a bicontinuous cubic Ia3d phase. Time-resolved small-angle X-ray scattering studies show that the L(alpha) --> Ia3d transition in pure MO dispersions under limited hydration conditions occurs within a time interval of 1 s at 35 degrees C preceded by a lag phase of 1.5 s. The Ia3d cubic phase initially forms with a much larger lattice constant due to hydration and experiences an initially lower curvature that relaxes within about 1 s. Interestingly, no other cubic phases are involved as intermediates in the transition, i.e., the gyroid cubic phase is able to form directly from the L(alpha) phase. The mechanism behind the L(alpha) --> Ia3d transition in pure MO dispersions has been discussed within the framework of recent stalk models for membrane fusion. In the presence of cyt c, the L(alpha) --> Ia3d transition is much slower. The rather long relaxation times of the order of seconds are probably due to a kinetic trapping of the system and limitation by the transport and redistribution of water and lipid in the evolving new lipid phases. We also studied the transition from the pure lamellar L(alpha) phase to the Ia3d-P4(3)32 two phase region and observed a rather complex transition behavior with transient lamellar and cubic intermediate states.     

Coordinated and clathrated guests in the 3infinity[Hg6As4]4+ bicompartmental framework: synthesis,crystal and electronic structure,and properties of the novel supramolecular complexes [Hg6As4](CrBr6)Br and [Hg6As4](FeBr6)Hg0.6

Two new supramolecular complexes [Hg(6)As(4)](CrBr(6))Br (1) and [Hg(6)As(4)](FeBr(6))Hg(0.6) (2) have been prepared by the standard ampoule technique and their crystal structures determined. Both crystallize in the cubic space group Pa$\bar 3$ with the unit cell parameter a=12.275(1) (1) and 12.332(1) A (2), and Z=4. Their structures consist of bicompartmental, three-dimensional [Hg(6)As(4)](4+) frameworks with cavities of two different sizes occupied by guest anions of different type. The bigger cavities are filled with the octahedral MBr(6) (n-) ions (M=Cr or Fe; n=3 or 4), whereas the smaller cavities trap either Br- ions (1) or Hg(0) (2). The analysis of the host-guest contacts has allowed a classification of the octahedral guests as coordinated and the monatomic guests as clathrated. Magnetic measurements and ESR spectroscopy data have given information about the interaction between the host and guests. Band structure calculations (HF and hybrid DFT level) indicate that both 1 and 2 are non-metallic, with a band gap of approximately 1.5 eV (B3LYP), and that the interaction between the host and guests is of predominantly electrostatic character. It is shown that though the electrostatic host-guest interaction is weak it plays an important role in assembling the perfectly ordered supramolecular architectures.     

From the two-component system CBrCl3+CBr4 to the high-pressure properties of CBr4

The experimental phase diagram of the CBrCl3+CBr4 system has been determined by means of X-ray powder diffraction and thermal analysis techniques from 200 K to the liquid state. Before melting, the two components have the same orientationally disordered (OD) face-centered cubic phase, and solid-liquid equilibrium is explained by simple isomorphism. The application of multiple crossed isopolymorphism formalism to the low-temperature solid-solid equilibria has enabled the inference of an OD rhombohedral metastable (at normal pressure) phase for CBr4. Experimental determination of the pressure-volume-temperature and construction of the pressure-temperature phase diagrams for CBr4 reveal the existence of a high-pressure phase, the rhombohedral symmetry of which is inferred by means of the thermodynamic assessment of the experimental phase diagram and demonstrated by means of high-pressure neutron diffraction measurements. The procedure used in this work confirms the connection between the appearance of metastable phases at normal pressure and their existence at high-pressure.     

On the lattice stability of metals

The success of perturbation calculations of second order for the NFE (“Nearly Free Electron”) metals and that of the two-parameter model of Pettifor for the transition elements show that the lattice-stability of the metals has simple physical reasons. Using the results of Harrison, Heine and Weaire, Deegan, and Pettifor, a model is developed which allows to explain the stability of the three metal lattices in terms of differences in the potentials. Only those potential differences are considered which are caused by the different packing of the lattices. With the aid of the virial theorem the band structure energy is connected with the potential bandstructure energy. The sequence of stability is predicted to be body centered cubic (bcc), hexagonal close packed (hcp), face centered cubic (fcc) with increasing valence electron concentration. The ranges of stability can be expressed in simple numbers. This simple model holds in principle for NFE as well as for transition metals because it contains no assumptions restricted to only one of these metal types. Deviations of the observed lattice stability from the model can be understood from the approximations involved.