Electron density modeling and reconstruction of infinite periodic minimal surfaces (IPMS) based phases in lipid-water systems. I. Modeling IPMS-based phases

This is the first of two papers dealing with the structural solution of physical systems based on infinite periodic minimal surfaces (IPMS), such as surfactant, lipid-water, and block copolymer systems. In the first paper, the mathematics of minimal surfaces is briefly reviewed and details of the construction of the associate D, P, and G IPMS are described. Electron density models of lipid-water systems based on these IPMS are then constructed. The resulting models are then Fourier transformed to calculate the amplitudes of the first few Fourier terms. These amplitudes are then used to reconstruct the electron density which is examined and discussed. The subsequent paper will utilize the modeling results to aid in solving the structure of several real physical systems based on the D surface. Received 15 January 1999 and Received in final form 20 October 1999     

Stability of inverse bicontinuous cubic phases in lipid-water mixtures

We investigate the stability of seven inverse bicontinuous cubic phases [ G, D, P, C(P), S, I-WP, F-RD] in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only G, D, and P are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acid/DLPC.     

The interplay between the surface band structure and possible surface reconstructions of Mo(112)

The experimental band structure of Mo(112) and the effects by temperature and adsorbate are presented. A surface resonance, identified as crossing the Fermi level at about 1/3 from to of surface Brillouin zone, was observed to be very sensitive to both contamination and temperature. We find evidence of adsorbate and temperature induced reconstruction of the Mo(112) surface. Examination of low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM) data provides evidence for an adsorbate induced reconstruction of the Mo(112) surface with periodicities consistent with the Fermi level crossing of the surface resonance. The reconstruction is found to occur at coverages as low as 0.03 Langmuirs of oxygen or carbon. The reconstruction and/or adsorbate affects the density of states and bands near the Fermi level of a ₁ symmetry. Received 3 March 1999 and Received in final form 1 October 1999     

Cubic phases of amphiphilic molecular aggregates

Stability and geometry of the lyotropic periodic cubic mesophases are considered in the framework of a general symmetry based phenomenological approach. A limited number of cubic structural types is shown to be formed by amphiphilic molecular aggregates due to the specific nature of self-organizing units. The related thermodynamic models predict topology of phase diagrams and specific features of transitions between isotropic, lamellar, cubic bicontinuous and cubic micellar phases. Received 25 February 1999 and Received in final form 29 June 1999     

Diamond-like phases prepared from graphene layers

The geometrically optimized structure of ten carbon diamond-like phases obtained by crosslinking graphene layers has been calculated using the density functional theory method and the structural parameters, densities, sublimation energies, and densities of electron states have been determined. Bulk moduli of diamond-like phases have been calculated using the PM3 semiempirical quantum-mechanical method. The X-ray powder diffraction patterns have been calculated based on structural parameters. These diffraction patterns can be used to identify new phases.     

Ripening of surface phases coupled with oscillatory dynamics and self-induced spatial chaos through surface roughening

Some pattern formation processes on single-crystal catalytic surfaces involve transitions between alternative surface phases coupled with oscillatory reaction dynamics. We describe a two-tier symmetry-breaking model of this process, based on nanoscale boundary dynamics interacting with oscillations of adsorbate coverage on microscale. The surface phase distribution oscillates together with adsorbate coverage, and, in addition, undergoes a slow coarsening process due to the curvature dependence of the drift velocity of interphase boundaries. The coarsening is studied both statistically, assuming a circular shape of islands of the minority phase, and through detailed Lagrangian modeling of boundary dynamics. Direct simulation of boundary dynamics allows us to take into account processes of surface reconstruction, leading to self-induced surface roughening. As a result, the surface becomes inhomogeneous, and the coarsening process is arrested way before the thermodynamic limit is reached, leaving a chaotic distribution of surface phases. (c) 1999 American Institute of Physics.     

The characterisation of iron-containing intermetallic phases within industrially cast aluminium

⁵⁷Fe conversion electron Mössbauer spectroscopy has been used to investigate the intermetallic phases near the surface of a D.C. cast aluminium ingot. The CEMS data is used with SAAES (selected area Auger electron spectroscopy) and SAXPS (selected area X-ray photoelectron spectroscopy) data to propose a model of the surface region above the grain boundaries.     

3D shape reconstruction of parabolic trough collector from gradient data based on slope stitching approach

A method based on slope stitching for measurement of a large off-axis parabolic trough collector is proposed and applied to the surface shape reconstructed from the gradient data acquired by using the reverse Hartmann test.The entire reflector is divided into three sections with overlapping zones along the concentration direction.A mathematical model for the slope stitching algorithm is developed.An improved reconstruction method combining Zernike slope polynomials iterative fitting with the Southwell integration algorithm is utilized to recover the real three-dimensional(3 D) shape of the collector.The efficiency and validity of the improved reconstruction method and the stitching algorithm are experimentally verified.     

Crystal-chemical features of phases with the A15 structure

Since Hume-Rothery factors are important in the stability of bounded and unbounded solid solutions and many ordered and intermediate phases, an attempt has been made to study the effect of the size factor and the electron density on the range of binary phases with the A15 structure. It has been found that a ±10% deviation of the atomic radii is predominant and the electron concentration is limited, its value depending on the electron configurations of the constituent components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 85–88, December, 1991.     

Phase transitions between orthogonal and tilted hexatic phases

Tilt-driven phase transitions between hexatic smectic phases: SmF-HexB and reversed HexB-SmF have been studied in compounds belonging to two enaminoketone derivative homologue series. The tilt angle order parameter has been measured and its temperature dependence near the phase transition point has been described by applying mean-field model. For both phase sequences the tricritical points have been observed on phase transition lines in binary mixtures of respective materials having first and second order phase transitions between hexatic phases. Received 21 June 1999     

Electric quadrupole interactions and the γ–α phase transition in Ce: the role of conduction electrons

We present a theoretical model of the “isostructural" - phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. The latter are treated in tight-binding approximation. The - transition is described as an orientational ordering of quadrupolar electronic densities in a structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the - transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the structure. Received 21 September 1999 and Received in final form 2 May 2000     

Electron density and electron redistribution in alloys—II: Electron density in alloys and intermetallic phases

Electron density for alloys which have close-packed metallic structures is calculated by assigning valence electrons to octahedral and tetrahedral interstices, a method which has been previously used for elemental metals. Some localization of electron density is proposed for β -phases when there is considerable difference in ion core sizes. This method of characterizing electron density in alloys can be used to derive structures with the amount of electron transfer if an assumption is made for the volume fraction occupied by each component of the alloy. In general, the electronic structure of intermetallic phases appears to be dominated by the correspondence of a definite number of valence electrons with the number of interstices in the metallic structure (the Hume-Rothery $\text{e}\text{a}$ ratios). The model used can also accommodate electron distributions which include both ionic and covalent components of electron density. This is the case for Laves phases and the metallic A-15 compounds. There is a preponderance of intermetallic phases where one component is a d-shell metal. Evidence is presented that in several such alloys there is a change in d-shell configuration of the elemental metal which serves to minimize size differences of the ion cores of the alloy.     

In-vivo fluorescence molecular tomography based on optimal small animal surface reconstruction

Accurate small animal surface reconstruction is important for full angle non-contact fluorescence molecular tomography （FMT） systems. In this letter, an optimal surface reconstruction method for FMT is proposed. The proposed method uses a line search method to minimize the mismatch between the reconstructed three- dimensional （3D） surface and the projected object silhouette at different angles. The results show that the mean mismatches of the 3D surfaces generated on three live anesthetized mice are all less than two charge coupled device （CCD） pixels （0.154 mm）. With the accurately reconstructed 3D surface, in-vivo FMT is also performed.     

Novel twist grain boundary smectic-C phases

Several new kinds of smectic-C twist grain boundary phases (TGBC) have been observed during the last few years. These pure compounds or mixtures exhibit unusual textures with polygonal lattices (square or hexagonal grids) in the plane normal to the TGB helix. The structure of these new phases seems to be complex and different from reported and predicted TGBC phases. In this article, we review the main results obtained on these different new phases, and we propose new TGBC structures based on the well-known splayed polarization --twisted director structures adopted by chiral smectic-C's in planar aligned (bookshelf) cells. The observed square or hexagonal lattices are made of superimposed pairs of unwinding lines due to the suppression of the helix within smectic-C blocks by the grain boundaries (unwinding walls). A lattice-free TGBC occurs if the helix within smectic-C blocks is suppressed completely. Received 15 March 2001     

Characterisation of phases in nanostructured, multilayered titanium alloys by analytical and high-resolution electron microscopy

Surface processing of a Ti-6Al-4V alloy led to a complex multilayered microstructure containing several phases of the Ni-Ti-P-Al-O system, which improves the mechanical and tribological surface properties. The microstructure, chemical and phase compositions of the hard layer formed on the surface were investigated by LM, XRD, SEM as well as analytical/high-resolution TEM, STEM, EDS, electron diffraction and FIB. Phase identification based on electron diffraction, HRTEM and EDS microanalysis revealed the presence of several binary and ternary phases in the system Ti-Ni-P, sometimes with partial substitution of Ti by Al. However some phases, mainly nanoparticles, still remain not identified satisfactorily. Electron microscopy techniques used for identification of phases present in surface multilayers and some practical limits to their routine application are reminded here.     

Boerdijk-Coxeter helix and biological helices

Helices and dense packing of spherical objects are two closely related problems. For instance, the Boerdijk-Coxeter helix, which is obtained as a linear packing of regular tetrahedra, is a very efficient solution to some close-packing problems. The shapes of biological helices result from various kinds of interaction forces, including steric repulsion. Thus, the search for a maximum density can lead to structures related to the Boerdijk-Coxeter helix. Examples are presented for the -helix structure in proteins and for the structure of the protein collagen, but there are other examples of helical packings at different scales in biology. Models based on packing efficiency related to the Boerdijk-Coxeter helix, explain, mainly from topological arguments, why the number of amino acids per turn is close to 3.6 in -helices and 2.7 in collagen. Received 26 November 1998 and Received in final form 12 April 1999     

Carbon phases on nickel surfaces

The conditions of the formation of different carbon surface phases on nickel substrates by the example of a planar Ni( 110) surface and a stepped Ni(771 ) surface similar in structure were determined. The structure of the phases was investigated by means of scanning tunneling microscopy (STM), and the influence of carbon on the structure of the nickel surface was demonstrated. The process of graphene synthesis by propylene cracking is described. A method for forming graphene islands on nickel is proposed. A variety of phase transitions between the carbon surface phases (e.g., surface carbide, graphene, and graphene islands) and the reasons for their irreversibility are discussed. The relation between the structures of the surface carbide phases and the crystal structures of the initial surfaces for two different substrates is shown.     

Vacant-site octahedral tilings on SrTiO(3) (001), the (sqrt[13]×sqrt[13])R33.7° surface, and related structures

The structure of the SrTiO(3) (001) (sqrt[13]×sqrt[13])R33.7° surface reconstruction has been determined using transmission electron diffraction combined with direct methods and density functional theory. It has a TiO(2)-rich surface with a 2D tiling of edge or corner-sharing TiO(5)□ octahedra. Additionally, different arrangements of these octahedral units at the surface, dictated by local bond-valence sums, form 2D networks that can account for many ordered surface reconstructions as well as disordered glasslike structures consistent with the multitude of structures observed experimentally, and potentially other materials and interfaces.     

Self-consistent interpretation of the 2D structure of the liquid Au82Si18 surface: bending rigidity and the Debye-Waller effect

The structural and mechanical properties of 2D crystalline surface phases that form at the surface of liquid eutectic Au82Si18 are studied using synchrotron x-ray scattering over a large temperature range. In the vicinity of the eutectic temperature the surface consists of a 2D atomic bilayer crystalline phase that transforms into a 2D monolayer crystalline phase during heating. The latter phase eventually melts into a liquidlike surface on further heating. We demonstrate that the short wavelength capillary wave fluctuations are suppressed due to the bending rigidity of 2D crystalline phases. The corresponding reduction in the Debye-Waller factor allows for measured reflectivity to be explained in terms of an electron density profile that is consistent with the 2D surface crystals.     

Surface photovoltage in semiconductors under sub-band-gap illumination: continuous distribution of surface states

Surface photovoltage spectra in semiconductors are analyzed when the sub-band-gap illumination induces the electron transitions from surface states to the conduction band under the assumption that distribution of surface states is continuous. From analysis performed it follows that the fictitious densities of surface states can be induced due to the wavelength dependence of the photoionization capture cross-section of surface states for electrons and by the electron recombination capture cross-section of surface states which depends on the energy position of surface states in the energy gap. The high illumination intensity (laser illumination), which makes completely empty the surface states, can eliminate the fictious surface states when the density of surface states is not very large, the temperature of measurements is low, and the surface potential barrier is high. Received: 24 June 1998 / Accepted: 29 March 1999 / Published online: 14 June 1999