Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Crystal structures of the copper and nickel complexes of RNase A: Metal-induced interprotein interactions and identification of a novel copper binding motif

We report the crystal structures of the copper and nickel complexes of RNase A. The overall topology of these two complexes is similar to that of other RNase A structures. However, there are significant differences in the mode of binding of copper and nickel. There are two copper ions per molecule of the protein, but there is only one nickel ion per molecule of the protein. Significant changes occur in the interprotein interactions as a result of differences in the coordinating groups at the common binding site around His-105. Consequently, the copper- and nickel-ion-bound dimers of RNase A act as nucleation sites for generating different crystal lattices for the two complexes. A second copper ion is present at an active site residue His-119 for which all the ligands are from one molecule of the protein. At this second site, His-119 adopts an inactive conformation (B) induced by the copper. We have identified a novel copper binding motif involving the α-amino group and the N-terminal residues.

Crystal structures of the trimeric human immunodeficiency virus type 1 matrix protein: implications for membrane association and assembly.

The human immunodeficiency virus type 1 (HIV-1) matrix protein forms a structural shell associated with the inner viral membrane and performs other essential functions throughout the viral life cycle. The crystal structure of the HIV-1 matrix protein, determined at 2.3 angstrom resolution, reveals that individual matrix molecules are composed of five major helices capped by a three-stranded mixed beta-sheet. Unexpectedly, the protein assembles into a trimer in three different crystal lattices, burying 1880 angstrom2 of accessible surface area at the trimer interfaces. Trimerization appears to create a large, bipartite membrane binding surface in which exposed basic residues could cooperate with the N-terminal myristoyl groups to anchor the protein on the acidic inner membrane of the virus.

The crystallography and morphology of Mo2C in ferrite

The orientation relationships between hexagonal Mo2C precipitates (H) in ferrite (B) have been determined by electron diffraction to an accuracy of +/-2degrees. With one exception, the 19 results are consistent with the previously reported Pitsch and Schrader (P/S) orientation relationship. However, these more accurate determinations show clearly that there is a systematic deviation of up to 5.5degrees from the exact P/S relationship and that this deviation consists of a small rotation about the parallel close packed directions-[100](B)//[2 (1) over bar(1) over bar0](H). The long direction of the Mo2C needles has been determined unequivocally in terms of the orientation relationship to be [100](B)//[2 (1) over bar(1) over bar0](H). Moire fringes between precipitate and matrix have been used to improve the accuracy of the orientation relationship results and to determine the lattice parameters of the carbide precipitates investigated. The Moire fringe analysis has shown small systematic departures from the exact parallelism between [100](B) and [2 (1) over bar(1) over bar0](H) along the length of Mo2C needles and a lowering of the carbide lattice parameter that is consistent with the replacement of Mo by Fe in the carbide. The orientation relationship results, including the observed systematic deviation from the exact P/S relationship, are shown to be consistent with the edge-to-edge model. (C) 2002 Kluwer Academic Publishers.

Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study

ic first-order transition line ending in a critical point. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling. In particular, the premartensitic transition occurs when such coupling is strong enough to freeze the involved mode phonon. The implication of the results in relation to the available experimental data is discussed.

Anharmonic Helmholtz free energy to O(lambdaâ ´) in the non- leading term approximation /|nby Leslie Wilk. -- 260 St. Catharines, Ont. : [s. n.],

Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study

ic first-order transition line ending in a critical point. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling. In particular, the premartensitic transition occurs when such coupling is strong enough to freeze the involved mode phonon. The implication of the results in relation to the available experimental data is discussed.

Lithium-lanthanum double chromates

Synthesis and crystallographic data are reported for low and high temperature forms of LiLa(CrO4)2. The compounds are closely related to lamellar rare earth phosphates and arsenates of sodium and to RbLu(CrO4)2. Lattice parameters of the orthorhombic (low temperature) and monoclinic (high temperature) forms are given. The low temperature form is moisture sensitive and Li+ ions are easily displaced by protons. Thermal decomposition takes place at 250 °C and results in the formation of LiCrO2, LaCrO4, LaCrO3 and Cr2O3. © 1993.

Anisotropy of crystallite growth during sintering of SnO2 xerogels

The crytallite and pore-size evolution during isothermal sintering (400 ≤ T ≤ 700°C) of SnO2 xerogels was studied by X-ray line broadening and nitrogen adsorption-desorption isotherms. The experimental results show a strong anisotropy of crystallite growth between [110] and [101] directions. The preferential growth at [101] is followed by an increase in the mean pore size, reduction of the specific surface area and invariance of total pore volume. This behaviour is typical of grain coalescence sintering. The kinetic analysis of experimental results suggests that the crystallite coalescence at [101] is governed by lattice diffusion. The strong anisotropy of the growth causes pore-size distribution broadening, hindering the macroscopic shrinkage of the compact during sintering. © 1996 Chapman & Hall.

Insulator-to-metal transition driven by clustering of solitons in polyacetylene

It's believed that the simple Su-Schrieffer-Heeger Hamiltonian can not predict the insulator to metal transition of transpolyacetylene (t-PA). The soliton lattice configuration at a doping level y=6% still has a semiconductor gap. Disordered distributions of solitons close the gap, but the electronic states around the Fermi energy are localized. However, within the same framework, it is possible to show that a cluster of solitons can produce dramatic changes in the electronic structure, allowing an insulator-to-metal transition.

Synthesis, characterization and spectroscopy of the europium doped lanthanum trimetaphosphate

Orthorhombic modification of europium doped lanthanum trimetaphosphate has been prepared. The compound was obtained by precipitation of rare earth chloride solution with trimetaphosphoric acid. The characterizations were made using X-ray diffractometry, chemical analysis and infrared spectroscopy. Excitation and emission spectra were recorded at liquid nitrogen and room temperatures. Assignments of the 5D0→7FJ (J=0, 1, 2, 3, 4, 5) transitions were made and an unusual high 5D0→7F4 transition intensity with six split lines has been observed. Structural distortion of the crystal lattice may be caused by the Eu3+ ion inclusion. The simple overlap model was applied for the calculation of the total splitting of the 5D0→7F1 transition, the 5D0→7F0/5D 0→7F2 transition intensity ratio and the Ωλ (λ=2.4) intensity parameters. Theoretical predictions showed to be in good accordance with the experimental data. © 1988 Elsevier Science S.A.

The substitution of cations by magnesium in the structure K3Ho(VO4)2

The cation substitutions in the crystal lattice of binary potassium-holmium vanadate (V) K3Ho(VO4)2 by magnesium have been studied using various types of chemical solid state reactions. It was shown that in the presence of the quasi-ternary system K3VO4-Mg3(VO4)2-HoVO 4 at 700°C there a compound defined as K3Ho(VO4)2 with a narrow homogeneity range where K and Ho are partially substituted by Mg in accordance with various schemes. © 1998 Published by Elsevier Science S.A.