Succession of stacking disorder in hard-sphere crystal under gravity by Monte Carlo simulation

We have performed Monte Carlo simulations of hard spheres under gravity. Vertical boundaries are hard walls, which are well separated with each other. On the other hand, the periodic boundary condition is imposed in the horizontal direction. While we previously reported enhancement of crystallinity as well as crystallization due to gravity, we present here the results that demonstrate the succession of a defect. In case that the crystal formed at the bottom of the system includes kinds of stacking disorders for the (0 0 1) growth, twin band structure develops as mediated by a stacking disorder succeeded in the crystal formed in the fluid region which lies on the bottom crystal. In case that the stacking structure along horizontal direction changes from the (1 1 1) stacking to the (0 0 1) stacking, twin band structure in the (0 0 1) stacking region develops as succeeded in the crystal transformed. The twin band structure also becomes large with its upward growth.     

Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

Untersuchungen im System LaI2/H2: Phasenverhältnisse und Fehlordnung

Investigation of the LaI₂/H₂ System: Phase Relations and Stacking Disorder Heating of LaI₂ under 1 bar hydrogen pressure to 650 °C leads to light gray LaI₂H_0.95(3), accompanied by a structural change from tetragonal to hexagonal. Sharp reflections in the XRD pattern can be indexed in P6₃/mmc with a = 4.2158(7)Å and c = 15.508(3)Å, however, diffuse reflections indicate the presence of stacking faults in the structure, which correspond to a polytypic intergrowth of MoS₂ and NbS₂ type structural fragments. Increasing the reaction temperature to 730 °C results in a better defined diffraction pattern with the peak positions close to those of the 2H‐NbS₂ structure type. An X‐ray powder study of the samples LaI₂H_n proved the miscibility gap between LaI₂ and LaI₂H_n (0 ≤ n ≤ 0.5) in agreement with previous results. With decreasing H‐content of the homogeneous phase the lattice parameters change in opposite direction, a increasing to 4.236(1)Å and c decreasing to 15.39(2)Å for the lower limit.     

Random walks on inhomogeneous lattices

For lattices with two kinds of points (black and white), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Novel random poly(propylene isophthalate/adipate) copolyesters: Synthesis and characterization

Poly(propylene adipate) (PPA) and poly(propylene isophthalate/adipate) (PPI-PPA) random copolymers of various compositions were synthesized in bulk and characterized in terms of chemical structure and molecular weight. Furthermore, the thermal behavior was examined by thermogravimetric analysis and differential scanning calorimetry. All the polymers showed a good thermal stability. At room temperature they appeared as semicrystalline materials, except the copolymers containing 20 and 30 mol% of PI units: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of melting temperature with respect to homopolymers. The crystalline phase of PPI and PPA was evidenced at high content of propylene isophthalate or propylene adipate units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g as the content of PI units is increased was observed. This behavior was explained as due to the stiff phenylene groups in the polymeric chain. The Wood equation was found to describe well T_g-composition data. Lastly, the presence of a rigid-amorphous phase was evidenced in the copolymers, differently from PPA homopolymer.     

A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO4 compounds

Electron diffraction and lattice dynamical calculations are used to investigate the unit cells, space group symmetries and inherent displacive flexibility of the room-temperature average structures of AlPO₄-8, AlPO₄-16 and AlPO₄-tridymite. The zero-frequency rigid unit modes (RUMs) of the idealized high-symmetry polymorphs thereof are also investigated along with their relationship to the lower-temperature polymorphism of these zeotypic aluminophosphates. The clear presence of satellite reflections in addition to the Bragg reflections (G) of the underlying Cmc2₁ parent structure in the case of AlPO₄-8 shows that the true unit cell of the room-temperature polymorph has a doubled c-axis due to a condensed RUM mode. Structured diffuse scattering is also observed which can be related to the thermal excitation of RUM modes. In the case of AlPO₄-tridymite, a complex F1 triclinic polymorph is observed and related to soft RUM modes while, in the case of AlPO₄-16, a soft q=0 RUM mode is shown to be responsible for an observed phase transition in the case of the all SiO₂ analogue of AlPO₄-16. A large number of additional zero-frequency RUM modes also exist in the case of AlPO₄-16.     

Structural Study of an Unusual Cubic Pyrochlore Bi1.5Zn0.92Nb1.5O6.92

Single-phase pyrochlore-type specimens of Bi_1.5Zn_0.92Nb_1.5O_6.92 were studied using combined electron, X-ray and neutron powder diffraction techniques. Rietveld refinements using neutron powder diffraction data confirmed an average pyrochlore structure A₂B₂O₆O′ (Fd&3macr;m, a=10.5616(1) Å) with both Bi and Zn mixed on the A-sites. However, refinements revealed significant local deviations from the ideal pyrochlore arrangement which were caused by apparent displacive disorder on both the A and O′ sites. The best fit was obtained with a disordered model in which the A-cations were randomly displaced by ∼0.39 Å from the ideal eight-fold coordinated positions. The displacements occur along the six 〈112〉 directions perpendicular to the O′-A-O′ links. In addition, the O′ ions were randomly displaced by ∼0.46 Å along all 12 〈110〉 directions. Crystal-chemical considerations suggest the existence of short-range correlations between the O′ displacements and both the occupancy of the A-sites (i.e., Bi or Zn) and the directions of the A-cation displacements. The combined A-cation and O′ displacements change the coordination sphere of the A-cations from 8 to (5+3); the resulting coordination environment of the A-cations bears similarities to that of the (5+1)coordinated Zn in zirconolite-like Bi₂Zn_2/3Nb_4/3O₇. The observed displacive disorder in the A₂O′ network of the Bi_1.5Zn_0.92Nb_1.5O_6.92 structure involves atoms associated with the lowest-frequency vibrational bending mode, and is likely responsible for both the high dielectric constant and the dielectric relaxation reported for this compound.