Crystallization Kinetics of Nucleated Polypropylene with Organic Phosphates

The crystallization kinetics of isotactic polypropylene (iPP) and nucleated iPP with two organic phosphates, sodium salt (NA7) and triglyceride ester (NA8) of 2,2'-methylene-bis(4,6-di-tert-butylphenyl) phosphoric acid, were investigated by means of a differential scanning calorimeter under isothermal and nonisothermal conditions. During isothermal crystallization, a modified Avrami equation was used to describe the crystallization kinetics. Moreover, kinetics parameters, such as the Avrami exponent, n, the crystallization rate constant, k, and the half-time of crystallization, τ_1/2, are compared. The results showed that a dramatic decrease of the half-time of crystallization, as well as a significant increase of the overall crystallization rate, were observed in the presence of the organic phosphates. During nonisothermal crystallization, the primary crystallization was analyzed using the Ozawa model, leading to similar Avrami exponents for iPP and iPP/NA7, which means simultaneous nucleation with three-dimensional spherulitic growth. However, for iPP/NA8, the Avrami exponent in nonisothermal crystallization is evidently different from that in isothermal crystallization, which would indicate a different mechanism of crystal growth. Adding the nucleating agent to iPP makes the overall crystallization activation energy increase.     

X-Ray kinetic study of glassy crystal formation in adamantane derivatives: TTT curves and crystal size effect

Abstract

The kinetics of polymorphic solid-state transformation in mixed adamantane compounds (CN_1?x Cl _x ADM: x = 0 and x = 0.25) have been studied by X-ray scattering. The classical form of the time-temperature-transformation TTT curves has been directly observed for the first time for the ordering supercooled plastic phases. For both compounds a considerable effect of crystal size on the kinetics has been observed. For x = 0.25 it leads to a continuous transition from Avrami to nucleation behaviour. These observations help us to understand the factors controlling nucleation and growth as well as to establish better operating conditions in order to form a glassy crystal.     

Pressure- and photo-induced phase transition in mixed-valence gold complexes

The pressure- and photo-induced phase transition in mixed-valence gold complexes of Cs₂Au₂X₆ (X = Cl, Br, and I) has been investigated by means of the Raman scattering. The Raman-active Au-X stretching modes were deactivated by the pressure, which indicates a pressure-induced phase transition from the mixed-valence (MV) state to the single-valence (SV) state. The electronic phase diagrams of Cs₂Au₂X₆ (X = Cl and Br) as a function of pressure and temperature have been derived. A photoinduced phase transition from the MV state to the SV state has been found for Cs₂Au₂Br₆. The observed time behavior accompanying this phase transition is successfully interpreted by the Avrami model, indicating the three-dimensional character of the MV cluster growth.     

Incommensurability and metastability problems in NH4HSeO4 and ND4DSeO4: A reinvestigation of phase diagrams

Abstract

X-ray and neutron diffraction results on NH₄HSeO₄ and ND₄DSeO₄ are reported. Direct evidence of an incommensurate phase sandwiched between the monoclinic high-temperature phase (space group B2) and the low-temperature ferroelectric lock-in phase k = ? (space group P1) has been obtained in NH₄HSeO₄. The phase situation is more complicated in ND₄DSeO₄, where an incommensurate phase is found sandwiched between the B2 phase and a lock-in phase k = ¼ and where a phase in which several modulations coexist has been discovered in between the two lock-in phases k = ¼ and k = ?. The non-equilibrium processes, also present in ND₄DSeO₄, have been identified. All these results have clarified the situation about the phase diagram.     

Amorphous silicon hexaboride at high pressure

ABSTRACT

We investigate the pressure-induced structural phase transformation of amorphous silicon hexaboride (a-SiB₆) using a constant pressure first principles approach. a-SiB₆ is found to undergo a gradual phase transformation to a high-density amorphous phase (HDA) in which the average coordination number of both B and Si atoms is about 6. The HDA phase consists of differently coordinated motifs ranging from 4 to 8. B₁₂ icosahedra are found to persist during compression of a-SiB₆ and the structural modifications primarily occur around Si atoms and in the regions linking pentagonal pyramid-like configurations to each other. Upon pressure release, an amorphous structure, similar to the uncompressed one, is recovered, indicating a reversible amorphous-to-amorphous phase change in a-SiB_6. When the electronic structure is considered, the HDA phase is perceived to have a wider forbidden band gap than the uncompressed one.     

Effect of uniaxial stress on the dielectric properties of BaTiO3+0.1wt.%Eu2O3 ceramics

ABSTRACT

BaTiO₃+0.1wt.%Eu₂O₃ ceramics were prepared by a solid-state reaction method. The dielectric behavior of these ceramics as a function of uniaxial pressure has been systematically studied. The external stress showed obvious effects on these properties. An increase of the Curie point (T_c) and decrease of the Curie–Weiss temperature (T₀) was observed with increasing pressure, resulting in an increase in the first-order nature of the phase transformation (T_c–T₀ increases). Broadening and flattening of the permittivity versus temperature curves near their maximum was found. The pressure behavior of thermal hysteresis and the ??/?T vs. T plot suggests that the phase transition changes to second-order type with increasing pressure. Furthermore, the Curie–Weiss constant obtained from a modified Curie–Weiss law strongly decreases with increasing pressure, suggesting that the mechanism of phase transition is going to order–disorder type.     

New types of phase behaviour in binary mixtures of hard rod-like particles

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters D_i and lengths L_i (i = 1,2). The aspect ratios k_i = L_i/D_i of the components are kept fixed (with values of k ₁ = 15 and k ₂ = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D ₁/D ₂. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.     

High-pressure phases of plutonium monoselenide studied by X-ray diffraction

Abstract

Plutonium monoselenide was studied under high pressure up to 47 GPa, at room temperature, using a diamond anvil cell in an energy dispersive X-ray diffraction facility. At ambient pressure, PuSe has the NaC1-type (B1) structure. The compound has been found to undergo a second-order crystallographic phase transition at around 20 GPa. This phase can be described as a distorted B1 structure, with a rhombohedral symmetry. PuSe transforms to a new phase at around 35 GPa, which can be indexed in the cubic CsCl-type (B2). The volume collapse at this phase transition is 11%. When releasing pressure, we observed a strong hysteresis to the inverse transformation down to 5 GPa. From the pressure-volume relationship, the bulk modulus has been determined to B ₀ = 98 GPa and its pressure derivative as B ₀ = 2.6. These results are compared to those obtained with other actinide monmictides and monochalcogenides.     

Phase transformations in calcite from electrical impedance measurements

The phase transformation in calcite I-IV-V and calcite ? aragonite have been characterized by electrical impedance measurements at temperatures 600–1200°C and pressures 0.5–2.5?GPa in a piston cylinder apparatus. The bulk conductivity σ has been measured from Argand plots in the frequency range 10⁵–10^?2?Hz in an electric cell representing a coaxial cylindrical capacitor. The synthetic polycrystalline powder of CaCO₃ and natural crystals of calcite were used as starting materials. The transformation temperature T_c was identified from resistivity-temperature curves as a kink point of the activation energy. At pressure above 2?GPa in ordered phase calcite I, the activation energy E _σ is c. 1.05?eV, and in disordered phase calcite V E _σ is c. 0.75?eV. The pressure dependence of T_c for the rotational order–disorder transformation in calcite is positive for pressures <1?GPa and negative for pressures >1?GPa. The transformation boundary of calcite 1–IV is observed only during first heating in samples after a long annealing at low temperatures. The activation energy of calcite I???IV decreases gradually from 1.8 to 1.05?eV with the pressure increase from 0.5 to 2?GPa. The kinetics of calcite ? aragonite transformation has been monitored by measuring a time-variation of the electrical resistance of a calcite sample at 10³?Hz in the stability P-T field of aragonite. The variation of the impedance correlates with the degree of phase transformation, estimated from X-ray powder diffraction studies on quenched products of experiments. The kinetics of calcite ? aragonite transformation may be fitted to the Avrami kinetics with the exponent m???1–1.5.     

Group-theoretical analysis of possible structural phase transitions in the high-temperature superconductors

A group-theoretical analysis is performed for the complete condensation of order parameters at structural phase transitions (SPT's) in the high-temperature superconductors belonging to the D ¹⁷ _4h -14/mmm space group in the high-symmetry phase. As a rule, such transformations are due to a successive softening of phonons with wave vectors k ₁ = 1/2 b ₃ and k ₂ = 1/2 (b ₁ - b ₃) belonging to the K13(X) star of the Brillouin zone of a tetragonal body-centered Bravais cell. SPT's in system La_2-x Ba _x CuO₄ are considered in detail.     

An approximate expression for the galvanomagnetic tensor

Using the iterative solution to the Boltzmann equation for electrons in d.c. electric and magnetic fields, an expression for the resistivity tensor can be obtained in the form of an infinite series. This series can be approximated by retaining only the first two terms. In the cases where relaxation times exist — in the sense that the collision term in the Boltzmann equation can be written asg(k)/τ(k), whereτ(k) is the relaxation time, andf (k) = f _E(ɛ k) + [∂f _E(εk)/∂ε]·g(k) the distribution function for electrons with wavevectork — this approximation is exact. For polyvalent metals in the one-OPW approximation, the complete galvanomagnetic tensor can be obtained using this approximation and the result differs from that obtained by using a time of relaxation given by an expression suggested byZiman. A calculation for a simple model Fermi surface, with screened Coulomb scattering, is carried out and the results compared with those of the relaxation time approximation.     

Investigation of phase transformation in an Al-0.58 wt% Fe alloy by Mössbauer spectroscopy

Phase transformation of the metastable Al₆Fe intermetallic phase to Al₃Fe in an Al-0.58 wt% Fe alloy was investigated by Mössbauer spectroscopy. The kinetics of the process was estimated by the Avrami equation. The activation energy of the over-all process was 3.33±0.47 eV. A simple model suggested for the mechanism of the transformation proved that this process was interface controlled between 635 and 580°C.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.     

The effect of the heating rate on the phase transition

ABSTRACT

The simple cubic spin-1 Ising model exhibits the ferromagnetic (F)–ferromagnetic (F) phase transition in the low temperature region for the interval 1.40 < d = D/J < 1.48 at k = K/J = –0.5. The degree of the F-F phase transition determines the special point on the (k_BT/J, d) phase diagram. In this paper, the critical behavior of the F-F phase transition was investigated for different heating rates using the cellular automaton heating algorithm. The universality class and the type of F-F phase transition were analyzed using the finite-size scaling theory and the power law relations. The results show that the F-F phase transition may be the second order, the first order or the weak first order depending on the heating rate in the interval 1.40 < d < 1.48 for k = –0.5.     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Precise in situ study of the kinetics of pressure-induced phase transition in CaF<Subscript>2</Subscript> including initial transformation stages

The kinetics of room-temperature phase transition in fluorite (CaF₂) single crystals under hydrostatic pressure up to 9 GPa was studied in situ by means of strain gauge compressibility measurements. Initial stages of the pressure-induced first-order phase transition kinetics (corresponding to less than 1% content of the new phase) were studied for the first time. In a broad range of concentrations of the new phase (5–20%), the transformation kinetics is well described within the framework of the classical Kolmogorov-Avrami-Mehl-Johnson model. The laws governing the initial and late stages of the transformation are more complicated and do not conform to the classical model. The initial stages involve avalanche growth in the nucleation rate corresponding to giant values of the Avrami exponent (n ≈ 20). At large concentrations of the new phase (above 30%), the transformation rate significantly decreases (saturation) as a result of the formation of a rigid cellular structure of the new phase.     

How does the s(E + N) equation work? Comparisons with a modified Swain–Scott equation (E + sN) and revision of the N1 scale of solvent nucleophilicity

Modifications of the Swain–Scott equation (log k/k₀) = sn) give an equation log k₁ = (E + sN₁′); k₁ is the rate constant, E is an electrophilicity parameter, N₁′ is a solvent nucleophilicity parameter and s is an electrophile‐specific sensitivity parameter. The equation is tested using over 300 published first‐order rate constants (k₁) for decay of a range of benzhydrylium cations in various solvents, on which the published N₁ scale of solvent nucleophilicity is based (S. Minegishi, S. Kobayashi and H. Mayr, J. Am. Chem. Soc. 2004, 126, 5174–5181) using the alternative equation log k = s(E + N₁), in which s is a nucleophile‐specific parameter. The modified (E + sN₁′) equation provides a revised N₁′ scale of solvent nucleophilicity, and a more precise fit, with less than half the number of adjustable parameters. It is found that the sensitivities of the benzhydrylium cations to changes in solvent nucleophilicity decrease slightly as reactivity increases, in contrast to s(E + N) equations, which show no trends in s values. It is proposed that more reliable N scales can be defined using (E + sN), because N is determined directly from definitions, and residual errors (e.g. experimental or due to solvation effects) can be incorporated into the slope and intercept. The complex reasons for the success of equations of the type log k = s(E + N) are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Decomposition of nitromethane in shock waves: The primary stage and the kinetics of decomposition at pressures of about 40 atm

The kinetics of nitromethane (NM) decomposition and the observed rate constant of the process were measured behind reflected shock wave using absorption spectroscopy at λ = 230 nm, temperatures of 1060 to 1350 K, pressure of ∼40 atm, and initial reactant concentration within 30–100 ppm. It was observed that, at the initial stage, nitromethane decomposes exponentially, without autoacceleration. The results of numerical simulations with the help of three most known kinetic schemes of nitromethane decomposition proved to be in close to agreement with our experimental data over the entire temperature range covered. It was demonstrated that the measured rate constant is identical to the rate constant of the dissociation CH₃NO₂ → CH₃ + NO₂. The temperature dependence of k ₁ was approximated by the Arrhenius formula k ₁ = 2.57 × 10¹⁴ exp(−52.85/RT) s⁻¹ (activation energy in kcal/mol), which suggests that the nitromethane dissociation proceeds in the falloff pressure region.     

Stimulated polariton-polariton scattering and dynamic Bose-Einstein condensation of polaritons in GaAs microcavities under excitation near the exciton resonance

The dynamics of formation of the macroscopically occupied polariton mode at the bottom of the polariton band E _LP(k = 0) and its spin polarization under the quasiresonant pulse excitation of excitons (E = E _X ) with large values of quasi-momentum have been studied in planar GaAs microcavities. It has been found that the growth in the depth E _X − E _LP(k = 0) of the polariton band leads to the change in the formation mechanism for the k = 0 condensate state from the direct parametric decay of the photoexcited mode (due to the polariton-polariton interaction) to the dynamic condensation of polaritons, which results from the multiple scattering of polaritons by both phonons and polaritons. At the same time, in microcavities with E _X − E _LP(k = 0) > 3.5 meV, the direct decay of the photoexcited mode does not disappear, becoming an efficient mechanism for the filling of the states located at the k-space ring, corresponding to the energies E _LP(k) ≈ E _X − 2.6 meV.     

The phase statistics of a multichannel radar interferometer

Abstract

The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σ_k=1 ^N S_k(t) S_k*(t+Δt) where, for example, the signals from each antenna in the kth pair are S_k(t) and S_k(t+Δt).

The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible to measure the phase of the coherence function of an electromagnetic wave field scattered from a randomly moving extended object (such as the ocean surface) using such a multichannel radar. This phase is related to asymmetry of the Doppler power spectrum. Furthermore, if this asymmetry is a result of surface currents on the ocean interacting with the surface waves which cause the electromagnetic scattering, then the surface currents may be measured in some sense.