The shoving model for the glass-former LiCl·6H2O: A molecular dynamics simulation study

Molecular dynamics (MD) simulations of LiCl·6H₂O showed that the diffusion coefficient D, and also the structural relaxation time <τ>, follow a power law at high temperatures, D^?1 ∝ (T ? T_o)^?μ, with the same experimental parameters for viscosity (T_o = 207 K, μ = 2.08). Decoupling between D and <τ> occurs at T_x ～ 1.1T_o. High frequency acoustic excitations for the LiCl·6H₂O model were obtained by the calculation of time correlation functions of mass current fluctuations. The temperature dependence of the instantaneous shear modulus, G_∞(T), was considered in the shoving model for supercooled liquids [J.C. Dyre, T. Christensen, N.B. Olsen, J. Non-Cryst. Solids 352 (2006) 4635] resulting in a linear relationship log (D^?1) vs. G_∞/T.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

Aging of oriented polymer glasses

Dimensional (D) and enthalpy relaxation (ΔH) of oriented polymer glasses (PS and PC) have been studied as function of temperature, between T_g and T_g−20 °C, and aging time t, ranging to several weeks. The dimensional relaxation (shrinkage) and enthalpy relaxation curves verify the logarithm law D(t) ∼ H(t) ∼ log t, between an incubation τ_i and a final relaxation time τ_f. The time τ_f to reach the equilibrium (D and ΔH) follows the Vogel–Tamann–Fulcher (VFT) law. Enthalpy relaxation and shrinkage exhibit important differences. Enthalpy relaxation of oriented and isotropic polymers follows the same logarithm law, independent of the draw ratio λ and the mode of deformation, the relaxation time τ_f coincides with the relaxation time of the α segmental motions. Shrinkage depends on λ and the mode of deformation, the relaxation time τ_f is attributed to the normal mode, the relaxation time of the whole chain. Finally the shrinkages of PS and PC show some differences. PC at short aging times presents another type of dimensional relaxation which would be due to the β motions. This would be in close connection with the ductile (PC) and fragile (PS) behavior of these two polymers far below T_g.     

Positron annihilation and broadband dielectric spectroscopy: A series of propylene glycols

We report a thorough joint analysis of the behavior of the ortho-positronium lifetime as obtained from positron annihilation lifetime spectroscopy and of the dipolar relaxation spectra investigated by broadband dielectric relaxation spectroscopy in a series of glass-forming propylene glycols including propylene glycol, dipropylene glycol and tripropylene glycol. A number of empirical correlations between the temperature dependence of the ortho-positronium annihilation lifetime, τ₃(T), and the various spectral and relaxational quantities have been found. The phenomenological evaluation of the quasi-sigmoidal τ₃(T) dependence reveals three characteristic temperatures: T_g^PALS, T_b1 = (1.23 − 1.27)T_g^PALS and T_b2 = (1.46 − 1.53)T_g^PALS, which are found to decrease with increasing fragility. The slighter change of slope in the PALS response at T_b1 in this series of propylene glycols appears to be related to the crossover from the α-process to the excess wing or secondary relaxation, found in the dielectric spectra. The onset of the high-temperature plateau in the τ₃(T) plot at T_b2 occurs when τ₃ matches the average relaxation time of the primary α process. Moreover, the plateau region lies in the vicinity of the crossover in the dielectric parameters of the structural relaxation in all the samples, i.e. spectral width and relaxation strength. In addition it is approximately related to a crossover of the α relaxation time τ_α(T) from non-Arrhenius to Arrhenius regime. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in the series of propylene glycols.     

The order parameter model for structural relaxation in glass

The order parameter model assumes that the state of a glass or liquid depends on T, P and a number of order parameters Z_i. Structural relaxation is due to the kinetically impeded evolution of the order parameters following a rapid change in T or P. The linear relaxation function for the evolution of property Q (V or H) in response to a change in X (T or P) is of the form φ_QX = Σ_igⁱ_QX exp(?tτ_i). Expressions are derived for the qeighting coefficients gⁱ_QX in terms of the dependences of V and H on the various order parameters. It is shown that gⁱ_VT = gⁱ_HP and that gⁱ_VTgⁱ_HP/gⁱ_VPgⁱ_HT = II, where II is the Prigogine-Defay ratio. The corresponding relations among the relaxation functions are φ_VT = φ_HP and φ_VTφ_HP/φ_VPφ_HT ? II. The predictions of the order parameter model for structural relaxation are compared with and found generally to agree with existing literature data. A number of suggestions for future investigations to test this model are made.     

Dynamics of twin layer widening in In-Pb crystals

The authors studied mobility of boundaries of plane-parallel twin layers in In-0.2 wt.% Pb and In-2 wt.% Pb crystals in the temperature range 290–373 K when stresses are applied τ/G = (1.35 – 7) × 10⁻⁶ (G is the shear modulus). They found that lead concentration increase as well as dislocation structure deterioration result in lower boundary velocity for a constant stress. In In-2 wt.% Pb crystals, the boundary velocity is well describable as V_n = V₀(τ) × × exp [ − ΔH (τ)/kT] where V₀(τ) = Ae^ατ/G (A = 10⁻³ cm/s, α = 1.1 × 10⁶) τ ΔH(τ) is the activation energy depending on the stress, ranging under these circumstances from 0.33 to 0.43 eV. At present it is difficult to interpret the results at hand. The analysis allows only to assume that the change in the boundary movement activation energy for impure crystals as against that for pure ones can be associated with the impurity effect on the structure of the intermediate zone between the twin and the matrix. The dependence of the pre-exponential factor on the stress is probably due to the effect of the internal long-range stress field on sources of twinning dislocations. Comparison with data for calcite and pure indium shows that twin boundary mobility parameters and their dependence on the stress are governed by the crystal type and defect structure.     

Load relaxation of a flat rigid circular indenter on a gel half space

When a saturated elastic gel is suddenly indented to a fixed displacement, δ, by a flat circular rigid indenter, the solvent cannot escape immediately, this gives rise to a pressure gradient in the solvent and the solvent flows until the pressure in it goes to zero everywhere, and all the stresses are transferred to the elastic network. This load transfer process causes, the indenter load, F, to decrease with time t, with a characteristic time constant, τ, which is given by a²/D_c, where D_c is the cooperative diffusion coefficient and a is the radius of the circular punch. This load relaxation behavior can be used to extract the elastic moduli and the cooperative diffusion coefficient of the gel. A detailed finite element analysis shows the load relaxation as a function of normalized time (t/τ) and how it depends on the shear modulus G and the Poisson’s ratio ν of the drained gel. Using this result, we found that the energy release rate available for detaching the punch in a pull-off test can be estimated. It is found that the energy release rate decreases with time for a fixed displacement.     

Four solid-crystal forms of paraazoxyanisole and the thermodynamic relationships between them

It is shown that paraazoxyanisole has four solid-crystal forms. The heats and temperatures of melting and transition are related by the following five equations: Q _m(IV) = Q _m(II); Q _m(IV) = Q _m(I) + Q _m(III); T _m(IV) = T _m(III); T _tr(II–III) = T _m(I); and Q _tr(II–III) = Q _m(I), Q _m(SCIV) = 52.0 ± 0.3 kJ/mol. Earlier, similar relationships were established for the third homologue of paraazoxyanisole, Q _m[SCIV(C₃)] = 48.2 kJ/mol. It is found that for paraazoxyphenetole, Q _m[SCIV(C₂)] = 46.0 kJ/mol.     

Free induction decays in entangled polymer melts

The relaxation of the transverse magnetization components caused by both dipolar interactions between the spins of different polymer chains and the dipolar coupling between CH-protons on an isolated Kuhn segment along a single polymer chain have been calculated. Explicit expressions for the transverse relaxation function are given in terms of the absolute mean squared displacement of the Kuhn segment during melt g_r(t), the tangent vector dynamical correlation function 〈b_n(t)b(0)〉, the segmental relaxation time τ_s, the Kuhn segment length b, the bond length a₀, the internuclear distance d, and the spin number density ρ_s. It is shown that the functional dependence of the intramolecular relaxation function on 〈b_n(t)b(0)〉 is fairly weak. The time-dependence of the intramolecular contribution to the transverse relaxation function is dominated by the probability density distribution function of the end-to-end vector of the Kuhn segment. The long-time decay of the intramolecular contribution to the transverse relaxation function is found to scale as t^? 3/2 for τ_s < < t < < τ_max, where τ_maxis the maximum relaxation time of polymer chains in melts. For times much less than the spin–spin relaxation time, T₂ ≈ 10^? 3 ? 10^? 2s, we show that the intermolecular contribution to the relaxation function is given by the following expression: exp(? λ₁(b, τ_s, ρ_s)t²/g_r^3/2(t)). Both the numerical coefficient and the functional dependence of λ₁on b, τ_s and ρ_s reproduce the expression obtained from the frequently used second cumulant approximation. For longer times (T₂ ≤ t < < τ_max), the intermolecular contribution is determined by the following relation: exp(? λ₂(b, τ_s, ρ_s, t)g_r(t)). We show that λ₂ increases logarithmically with t. The molecular mass independence of λ₁and λ₂ shows that, in polymer melts with molecular masses M_w far above the critical value M_c, the relevant experimental window for the decay of the intermolecular relaxation function is connected with the anomalous diffusion regime. Comparison with the experimental data suggests that the intermolecular contribution plays a significant role in the NMR relaxation process in polymer systems close to the melting point.     

Stabilization of metallic glass studied by internal friction measurement

The internal friction Q^?1 and the oscillation frequency f of Zr–Ti–Cu–Ni–Be metallic glass specimens were measured using an inverted torsion pendulum with the free decay method. A single-roller melt-spinning apparatus was used for preparing the specimens. Isothermal annealing near the glass transition temperature T_g was performed to investigate the stabilization of the specimens. Q^?1 decreased with annealing time t due to the stabilization. Q^?1-vs-t was measured at various annealing temperatures T_a, and the values of relaxation time τ for the stabilization process were determined. The dependence of τ on T_a showed that the hydrodynamic behavior represented by the Vogel–Tammann–Fulcher form and the hopping behavior represented by the Arrhenius form were observed in high- and low-temperature regions, respectively. The crossover of the two behaviors was seen at a temperature near and somewhat higher than T_g. The result was discussed on the basis of the viscoelastic relaxation in glassy materials.     

Crystal structure of [{MoBr2(O){OPH(OPr i )2}2}2(μ-O)]

[{MoBr₂(O){OPH(OPr ⁱ )₂}₂}₂(μ-O)] (1) crystallizes in the monoclinic space group P2₁/n, with a = 13.063(17) Å, b = 11.818(14) Å, c = 15.889(17) Å, β = 90.30(1)°, Z = 2. The dimeric structure contains a bridging oxygen atom at a crystallographic center of symmetry. Each octahedral molybdenum center has trans-bromide ligands, and two cis-OPH(OPr ⁱ )₂ units, with a terminal oxygen atom trans to one of the OPH(OPr ⁱ )₂ units.     

Structure characterization of CVD amorphous Si3N4 by pulsed neutron total scattering

The structure factor S(Q) of chemically vapor-deposited (CVD) amorphous Si₃N₄ has been measured by pulsed neutron diffraction over the range of the scattering vector Q from 1–330 nm^?1. The oscillatory behavior in the S(Q) persists up to Q = 300 nm^?1 and there is appreciable small angle scattering intensity. The SiN bond length is l_SiN = 0.1729 nm, and its coordination numbers n_SiN and n_NSi are 3.70 and 2.78 respectively. The bond angles around a Si and a N atom are found to be 109.8 and 121°. Analysis of the small angle scattering intensity shows the existence of voids with an average diameter of about 1 nm and a volume fraction of about 4%, which may stabilize the amorphous structure of Si₃N₄ having rigid covalent bonds due to relaxing the strain energy accumulated in the matrix.     

Structure of complexes of uranyl succinate with carbamide and dimethylurea

Three new succinate-containing complexes of uranyl with carbamide (Urea) and N,N'-dimethylurea (s-Dmur) are synthesized and studied by IR spectroscopy and X-ray diffraction. Structures of the same type, [UO₂(Urea)₄(H₂O)][(UO₂)₂(C₄H₄O₄)3] · 3H₂О and [UO₂(Urea)₄(H₂O)][(UO₂)₂(C₄H₄O₄)3] · 2Urea contain two sorts of uranium-containing complex groups, namely, mononuclear [UO₂(Urea)₄(H₂O)]²⁺ cations and two-dimensional [(UO₂)₂(C₄H₄O₄)₃]^2– anions described by crystal-chemical formulas AМ ₅ ¹ and A ₂ Q ₃ ⁰², respectively (A = UO₂ ²⁺, M ¹ = Urea or H₂O, Q ⁰² = C₄H₄O₄ ^2-), and differ only in the nature of noncoordinated molecules—water and carbamide. The main structural groups of the [(UO₂)₂(C₄H₄O₄)₂(s-Dmur)₃] crystals are [(UO₂)₂(C₄H₄O₄)₂(s-Dmur)₃] chains belonging to the А ₂ Q ₂ ⁰² M ₃ ¹ (A = UO₂ ²⁺, Q ⁰² = C₄H₄O₄ ^2-, M ¹ = s-Dmur) crystal-chemical group. Specific features of intermolecular interactions in the crystal structures are revealed using the Voronoi–Dirichlet method of molecular polyhedra.     

High-temperature in situB NMR study of network dynamics in boron-containing glass-forming liquids

In situ high-temperature nuclear magnetic resonance (NMR) spectroscopy can be very useful for probing changes in structure and dynamics in glass-forming liquids, and is a unique method for observing chemical exchange among structural species (e.g. BO₃–BO₄, Qⁿ–Qⁿ⁺¹, and NBO–BO) at the seconds to microseconds time scales. High-temperature ¹¹B MAS NMR line shape measurements were made at about 100 K above the glass transitions on (Na₂O)_0.3(B₂O₃)_0.7 and (Na₂O)_0.2(B₂O₃)_0.21(Al₂O₃)_0.08(SiO₂)_0.51 glass-forming liquids. BO₃ and BO₄ groups are well resolved in ¹¹B MAS NMR spectra at 14.1 T with sample spinning at 5000 Hz. At higher temperatures, partial peak coalescence occurred due to exchange of BO₃ and BO₄. Temperature effects on borate speciation were also determined by varying the fictive temperature (T_f) of glasses, where T_f estimated from differential scanning calorimetry measurements. We combined these complementary data sets to model structural exchange in the liquid state. The time scale of BO₃–BO₄ exchange from NMR data, τ_NMR, appears to be “decoupled” from that of the macroscopic shear relaxation process τ_s derived from the viscosity, however, at higher temperatures, τ_s approaches τ_NMR. The “decoupling” at lower temperature may be related to intermediate-range compositional heterogeneities, and/or fast modifier cation diffusivities which trigger “unsuccessful” network exchange events.     

Universal critical-like scaling of dynamics in plastic crystals

Many theoretical models for the glassy dynamics have been proposed so far describing the changes in molecular dynamics along the extraordinary slowing down in the vitrification process of a disordered phase on cooling. Many of these theories share the concept of cooperative rearranging regions firstly proposed by Adam and Gibbs. Among them, the dynamical scaling model (DSM) is based on the random diffusion of free volume which creates random walking clusters formed by cooperatively rearranging entities.Within this framework a critical phenomenon relating a hidden phase transition at T_C (below T_g) implies the divergence of the relaxation time (τ) or viscosity (η) τ, η ∝ (T − T_C) ^− ? with a universal scaling exponent φ → 9. In this work we apply the DSM model to orientational glasses, obtained from the quenching of orientationally disordered phases (plastic crystals) via the application of the linearized derivative-based transformation of dielectric spectroscopy τ(T) data.     

Relaxations in polystyrene below the glass transition studied by viscosity measurement

The shear viscosity of organic glass polystyrene has been determined under pure shear deformation mode from room temperature up to the glass transition temperature. A mechanical model of series connection of anelasticity and viscosity was used to determine the viscosity of the material. Relaxation time for the viscous flow was determined as a function of temperature. The relaxation was composed of two thermal-activation type relaxation processes: the high temperature relaxation (HTR) and the low temperature relaxation (LTR). In both relaxations the relaxation time was represented as τ=τ_o exp(E/k_BT), and the values of τ₀ and E were different in specimens treated differently – aged, loaded, and annealed. The observed τ₀ and E were not independent of each other but a compensation effect, a linear decrease of logτ₀ with increased E, was seen. The results were explained using the idea of cooperative relaxations of relaxing elements. HTR and LTR were considered to correspond to the structural and the slow relaxations, respectively, and the relaxing elements could respectively be a single atom or molecule and a segment in molecular chains.     

Synthesis and structure of zirconium and 3d-transition metal phosphates M 0.5Zr2(PO4)3(M = Mn, Co, Ni, Cu, Zn)

Double zirconium and 3d-transition metal phosphates of the compositions M 0.5Zr2(PO4)3[M = Mn (I), Co (II), Ni (III), Cu (IV), Zn (V)] have been synthesized and the types of their structures have been refined. Compounds I, II, III, IV, and V are all monoclinic (sp. gr. P2₁/n, Z = 4) and have the unit cell parameters a = 12.390(3), 12.389(3), 12.385(3), 12.389(3), 12.389(2) Å; b = 8.931(4), 8.928(3), 8.924(4), 8.925(4), 8.929(3) Å; c = 8.843(3), 8.840(2), 8.840(3), 8.841(3), 8.842(2) Å, β = 90.55(1), 90.54(1), 90.53(1), 90.53(1), 90.54(1)°; V = 978.5, 977.7, 977.0, 977.4, 978.1 ų, respectively. All the structures have the {[Zr₂(PO₄)₃]^?}3_∞-type frameworks. The crystallographic data for 3d-transition and alkali earth metal phosphates described by the general formula M _0.5Zr₂(PO₄)₃ are compared.     

Structural features of 3d metal compounds with 1-hydroxyethylidenediphosphonic acid

Structural features of 3d metal complexes with anions of 1-hydroxyethylidenediphosphonic acid (HEDP, H₄ L), in which the M: HEDP ratios are equal to 1: 2, 1: 1, 3: 2, and 5: 2, are discussed. The Cu(II): HEDP = 1: 2 complexes are characterized by five types of structures: monomeric structures trans-[Cu(H_{4 ? n} L)₂(H₂O)₂]^{2 ? 2n} , cis-[Cu(H_{4 ? n} L)₂(H₂O)₂]^{2 ? 2n} , and [Cu(L)₂]^6?; the dimeric structure { [Cu(H₂ L)(H₂O)]₂(μ ₂-H₂ L)₂}^4? ; and the polymeric chain structure {[Cu(μ ₂-H₂ L)₂]^2?}_∞. Six coordination modes exhibited by HEDP in the Cu(II) compounds are described.     

Complete normalizer for a direct product of three-dimensional rotation groups

A normalizer of the symmetry group defined on a three-dimensional sphere S ³ of rotation is considered in the four-dimensional Euclidean space E ⁴. The sphere S ³ is treated as the first approximation of the three-dimensional crystallographic space. The analysis of the normalizer N of the direct product G = G ₁ × G ₂ of space crystallographic rotation groups G ₁ and G ₂ is reduced to the study of transformations characterized by the positive determinants of the subgroups N ⁺ (G ₁ and N ⁺(G ₂). These subgroups correspond to the Euclidean normalizers N = N ⁺ (G ₁) × N ⁺(G ₂) of the components of the direct product. We derived a table including the groups of automorphisms induced by the transformations corresponding to the normalizers under study. Analyzing the general operation of multiplication of three-dimensional rotations in E ⁴, we refined the distribution of the supersymmetry operators of the three-dimensional sphere of rotations, S ³, for the symmetry groups considered earlier.     

Effect of structural relaxation on helium diffusion and solubility in vitreous B2O3

Helium permeation, diffusion, and solubility in vitreous B₂O₃ were measured as a function of thermal history and as a function of time at constant temperature. Volume relaxation measurements were also made on similar specimens. The correspondence between the effective relaxation times for gas mobility and molar volume suggests that the changes observed in both properties results from the same changes in the glass structure. This relaxation mechanism is described by the expression τ′ = 10^?4 exp(-18 000/RT), where τ′ is in seconds and the activation energy is in cal/mole. It is concluded that helium mobility is a function of the molar volume of the glass.