Polyhedral Deformation Research Articles

Thermo-Statistical Effects of Inclusions on Vesicles: Division into Multispheres and Polyhedral Deformation.

The construction of simple cellular models has attracted much attention as a way to explore the origin of life or elucidate the mechanisms of cell division. In the absence of complex regulatory systems, some bacteria spontaneously divide through thermostatistically elucidated mechanisms, and incorporating these simple physical principles could help to construct primitive or artificial cells. Because thermodynamic interactions play an essential role in such mechanisms, this review discusses the thermodynamic aspects of spontaneous division models of vesicles that contain a high density of inclusions, with their membrane serving as a boundary. Vesicles with highly dense inclusions are deformed according to the volume-to-area ratio. The phase separation of beads at specific intermediate volume fractions and the associated polyhedral deformation of the membrane are considered in relation to the Alder transition. Current advances in the development of a membrane-growth vesicular model are summarized. The thermostatistical understanding of these mechanisms could become a cornerstone for the construction of vesicular models that display spontaneous cell division.

Crystal-field splitting of Ce3+ in narrow-band phosphor SrLiAl3N4

As a promising narrow-band phosphor, SrLiAl3N4 has a seemingly ultra-small total crystal-field splitting of only 2400 cm−1 with Ce3+ as dopant ions. This paper is devoted to unravel this anomalous phenomenon based on semi-quantitative crystal-field calculations. The results show that there may exist undetected excitation peaks immersed in the host excitation band, and the calibrated crystal-field splitting is 27000 cm−1, comparable to those of other Ce3+ doped phosphors. In the end the effect of polyhedral deformation on energy level is briefly discussed.

Raman spectroscopy of CaCoSi2O6–Co2Si2O6 clinopyroxenes

Raman spectra were collected on a set of synthetic clinopyroxenes along the series CaCoSi2O6–Co2Si2O6. Changes in peak position and peak width show: (1) evidence of a phase transition from C2/c to P21/c, at Ca0.4Co1.6Si2O6, in agreement with previous X-ray observations; (2) peak broadening for intermediate compositions, with sharper peaks close to the end members. The phase transition is revealed by a decrease or inversion in the slope of the peak position versus composition and by peak splitting of the peaks at 660 and 1,000 cm−1, related to Si–O bending and stretching modes within the tetrahedral chains, respectively. The observed changes with composition depend more on variation in bond lengths due to structural rearrangement with cation substitution, rather than by changes of the M2 cation mass. A comparison with the structurally analogous CaMgSi2O6–Mg2Si2O6 (Diopside-Estatite, Ca-Mg) series shows that one of the two splitted peaks is fainter than the Ca–Co pyroxenes. Therefore the frequency of the peak at about 1,000 cm−1 does not change for Ca–Mg substitution, whereas it shifts by as much as 20 cm−1 between CaCoSi2O6 and Co2Si2O6. Despite the mechanism of cation substitution is qualitatively similar in the two series, the effect of structural changes and polyhedral deformation on the Raman spectra appeared different. Peak broadening in samples with intermediate compositions could be interpreted as arising by compositional disorder, due to coexistence of local Ca-rich and Co-rich configurations which affect the short range interactions and therefore the Raman frequencies.

Ion substitutions and structural adjustment in Cr-bearing tourmalines

The geological settings of Cr-bearing tourmaline occurrences are reviewed and the crystal chemistry of Cr-bearing tourmalines is analysed on the basis of new X-ray single-crystal structure refinements ( R 0.019–0.025) of three crystals from the Ural deposits (Cr 2 O 3 content ~6 wt.%) and one from Umba Valley, Tanzania (~1 wt.% Cr 2 O 3 ) and published data (13 structures) on tourmalines from different deposits with Cr content up to 36 oxide wt.%. The boundary between the ordered and the disordered distribution of Cr between Y and Z octahedral sites is determined near 1.03 ± 0.27 Cr apfu and relationships between Cr content and structural parameters (unit-cell parameters, octahedral bond-lengths, charge of Y and Z sites and polyhedral deformation) are established. An increasing Cr content in tourmaline causes an increase of both lattice parameters, of and bond-lengths and a regular variation of the charge of the Y and Z octahedra. In general, the structure becomes less deformed by reducing the distortion of the octahedra and of the tetrahedral ring.

Deformation Techniques for Sparse Systems

We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system. This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration.

Treatment of small deformations of polyhedral shapes of functional group distributions in biomolecules

Polyhedral models of the distribution of the essential functional groups (the EFG polyhedra) within biomolecules provide simple tools for the study of small deformations affecting the mutual positioning of functional groups. In general, the relative locations of various functional groups may have an important role in determining the biochemical activities of biomolecules; the mere presence of functional groups is often insufficient to ensure a given biochemical effect linked to the functional group. Accessibility and the possibility of geometrically constrained, concerted action of several functional groups are of major importance in many instances. Often, small molecular deformations have a crucial role. In order to describe small deformations of biomolecules, two polyhedral deformation approaches are implemented for the entire electron density. The repositioning of essential functional groups generates a typically nonlinear deformation of the electron density that can be modeled by a nonlinear deformation of the entire three-dimensional space. These nonlinear deformations reproduce exactly the new locations of the reference points of the essential functional groups, and approximate the electron density of the new EFG polyhedron using either of two simple algorithms, the dimension expansion-reduction (DER) or the weighted affine transformation (WAT) algorithm. The adaptation of these two techniques to deformations defined in terms of the large scale EFG features of biomolecules is described. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 756–761, 2000

Structural variations induced by thermal treatment in lead feldspar (PbAl2Si2O8)

Other| February 01, 1998 Structural variations induced by thermal treatment in lead feldspar (PbAl 2 Si 2 O 8 ) Mario Tribaudino; Mario Tribaudino Dipartimento di Scienze Mineralogiche e Petrologiche, Turin, Italy Search for other works by this author on: GSW Google Scholar Piera Benna; Piera Benna Search for other works by this author on: GSW Google Scholar Emiliano Bruno Emiliano Bruno Search for other works by this author on: GSW Google Scholar American Mineralogist (1998) 83 (1-2): 159–166. https://doi.org/10.2138/am-1998-1-216 Article history first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Mario Tribaudino, Piera Benna, Emiliano Bruno; Structural variations induced by thermal treatment in lead feldspar (PbAl 2 Si 2 O 8 ). American Mineralogist 1998;; 83 (1-2): 159–166. doi: https://doi.org/10.2138/am-1998-1-216 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyAmerican Mineralogist Search Advanced Search Abstract Lead feldspar single crystals were annealed at T = 1050 and 1000 degrees C, starting from a disordered metastable configuration (PbF H , Q od = 0) and from an ordered configuration (PbF L , Q od = 0.89). Single-crystal data collection and refinement in space group I2/c show that the degree of Al-Si order increases to Q od = 0.42 after annealing the disordered PbF H at 1050 degrees C and decreases to Q od = 0.70 after annealing the ordered PbF L sample at 1000 degrees C. This suggests that the equilibrium Q od is between 0.70 and 0.42 for temperatures between 1000 and 1050 degrees C, where anorthite or strontium feldspar are almost completely ordered. A residual in the difference-Fourier map because of positional disorder was observed near the Pb site in all the refined crystals. The average y/b Pb coordinate changes with increasing Al-Si disorder, as Pb approaches the glide plane. A significant decrease in the intensity of b-type reflections was consequently observed. A spontaneous strain, with the main axis almost parallel to the a axis, is associated with Al-Si ordering. Pb polyhedral deformation related with Q od accounts for the observed strain. A calibrating equation, Q od = [(8.427(2)-a) / 0.048(3)] (super 1/2) , has been calculated and applied to the unit-cell parameters obtained from subsequent thermal treatments and from Bruno and Facchinelli (1972) to define the evolution of the Q od vs. the treatment temperature. The thermal behavior of the Q od could then be bracketed, suggesting T c between 1150 and 1200 degrees C for the I2/c-C2/m phase transition induced by the Al-Si order-disorder process. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Steric effects in heteroboranes. Part 7 : The synthesis and characterisation of arene-ruthenium complexes of C-substituted carbaboranes. Molecular structures of 1-Ph-3-(mes)-3,1,2- closo-RuC 2B 9H 10 (mes = C 6H 3-1,3,5) and 1-Ph-2-Me-3-( p-cym)-3,1,2- closo-RuC 2B 9H 9 ( p-cym = C 6H 4Me-1- iPr-4), the latter showing an incipient deformation

The synthesis and characterization of Tl 2[7-Ph-7,8- nido-C 2B 9H 10], 3-( p-cym)-3,1,2- closo-RuC 2B 9H 10 ( 1), 1-Ph-3-(mes)-3,1,2- closo-RuC 2B 9H 10 ( 2), 1-Ph-3-( P-cym)-3,1,2- closo-RuC 2B 9H 10 ( 3) and 1-Ph-2-Me-3-( p-cym)-3,1,2- closo-RuC 2B 9H 9 ( 4) are reported. The ruthenium-containing species are obtained from the reactions between the appropriate [(arene)RuCl 2] 2 and either Tl 2[7,8- nido-C 2B 9H 11], Tl 2[7-Ph-7,8- nido-C 2B 9H 10] or Tl 2[7-Ph-8-Me-7,8- nido-C 2B 9HP 9]. Crystallographic studies on 2 and 4 reveal that whereas the former contains an essentially undistorted {RuC 2B 9} framework, there is some indication that in the latter, a polyhedral deformation from closo towards pseudocloso has just begun. This idea gains support from comparison of the 11B NMR shifts for 1, 3 and 4 with those for reference carbaboranes.

Structure of 7,8-Ph2-10-endo-PPh3Hg-7,8-nido-C2B9H9 methylene chloride solvate

Diphenyl-10-endo-(triphenylphosphino mercury)-7,8-dicarba-nido-undecaborane(9) methyl- ene chloride solvate, C32H34B9HgP.CH2C12, Mr = 832.41, monoclinic, P2~, a= 10.9534(15), b= 13.274 (3), c = 11.5283 (17) A,/3 = 90.074 (12) °, V= 1676.1 flk 3, Z ~--- 2, Dx = 1.649 Mg m- 3, ,~(Mo Ka) = 0.71069A, /z =4.82mm-1, F(000)=816, T= 185 (1) K, R = 0.0214 for 2656 independent observed reflections. The Hg atom is slipped by 1.1 A away from the C(cage) atoms and the cage-bound phenyl groups are cooperatively twisted about their C(cage)--C(aryl) bonds by an average of 29.1 ° as the result of Ph3P'Ph intramolecular crowding. The C(7)--C(8) connectivity, 1.589(9) A, the shortest C(cage)--C(cage) distance yet recorded in a diaryl- carbaborane, is a direct consequence of the twisting of the phenyl groups. Introduction. In the two preceding papers (Lewis & Welch, 1993; Cowie, Donohoe, Douek & Welch, 1993), we describe the molecular structures of 1,2-Ph2-1,2-closo-C2BloHlo and (7,8-Ph2-7,8-nido- C2B9HIo)-. These studies were stimulated by our previous observation (Lewis & Welch, 1992) of an unusual polyhedral deformation in 1,2-Ph2-3-(r/-

Petrology and mineralogy of dredged gabbro from Gettysburg Bank, eastern Atlantic

Gabbros have been dredged from Gettysburg Bank, 110 km west of Portugal on the Azores/Gibraltar fracture zone. Primary minerals in olivine, pyroxene and brown hornblende gabbros are partially replaced by metamorphic minerals. Igneous textures are inhomogeneously overprinted by a granular polyhedral deformation and a cataclastic deformation. Amphiboles show characteristics which indicate a transition from crystallisation in a magma chamber to formation of amphibole in solid gabbro under metasomatic conditions. Of the amphiboles analysed, chlorine was present in the green amphiboles but below 0.05% in the brown suggesting the penetration of sea water after the formation of the brown amphibole but during the formation of the green.

Polyhedral deformations in olivine-type compounds and the crystal structure of Fe2SiS4 and Fe2GeS4

Fe2SiS4 and Fe2GeS4 have the olivine structure with space group Pnma. Cell dimensions are a= 12.407 (2), b=7.198(1), c= 5.812(1) /~ for Fe2SiS4 and a= 12.467(2), b=7.213(1), c= 5.902(1) /~ for Fe2GeS4. The crystal structures were refined by least squares to final values of R=0.052 and 0044 respectively for Fe2SiS4 and Fe2GeS4. The distortions of the coordination octahedra and tetrahedra in the sulfide olivines are smaller than in the oxide and fluoride olivines. The distortion indices (relative deviations from the mean) of the edges of the octahedra and tetrahedra in accurately determined olivines are linear functions of the parameter DI(AB) which measures the misfit of the sizes of the octahedra to the tetrahedra. The adjustment stresses between polyhedra of different dimensions are more important contributors to polyhedral deformation than electrostatic forces. A computer simulation of olivines with varied sizes for the octahedral cations supports this interpretation.