Fast and slow relaxations in the free energy landscape

We present a phenomenological understanding of the fast and slow relaxations in super cooled liquids on the basis of the free energy landscape (FEL). The dynamics of a representative point in the FEL is assumed to obey the time-dependent Ginzburg–Landau type (TDGL) equation with the FEL as the driving potential. We analyze the dynamical structure factor for a toy model and demonstrate that the fast and slow relaxations are determined by jump motion among basins and stochastic motion within a basin, respectively and that the relaxation time of the fast process is determined by the curvature of the FEL around a local minimum.     

Breakdown of the fractional Stokes–Einstein relation in silicate liquids

The fractional Stokes–Einstein relation postulates a direct relationship between conductivity and shear flow. Like viscosity, the electrical resistivity of a glass-forming liquid exhibits a non-Arrhenius scaling with temperature. However, while both viscosity and resistivity are non-Arrhenius, here we show that these two properties follow distinct functional forms. Through analysis of 821 unique silicate liquids, we show that viscosity is best represented using the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) model, whereas the resistivity of the same compositions more closely follows the Avramov–Milchev (AM) equation. Our results point to two fundamentally different mechanisms governing viscous flow and conductivity and therefore cast doubt on the general validity of the fractional Stokes–Einstein relation.     

Marc有限元在Belt型两面顶模具应力分析中的应用

本文简要介绍了用于合成高品级金刚石工艺的Belt型两面顶装置的恶劣工作环境,以及模具的发展研究状况和相关技术瓶颈.简明概述了Marc软件强大的分析功能、程序结构特点以及接触问题的基本求解流程.以某一型号两面顶模具为例,利用Marc软件对其进行了建模计算,得到了模具的预应力分布,并采用Lame公式对计算结果进行了理论验证.     

Study of the kinetics of free volume in Zr45.0Cu39.3Al7.0Ag8.7 bulk metallic glasses during isothermal relaxation by enthalpy relaxation experiments

Enthalpy relaxation experiments were conducted to study the kinetics of free volume in Zr_45.0Cu_39.3Al_7.0Ag_8.7 bulk metallic glasses (BMGs) during isothermal relaxation using differential scanning calorimetry (DSC) at the temperature within the range from 648 to 684 K. Stretched exponential relaxation functions and the ?esták–Berggren SB (m, n) model were employed to analyze the kinetics of free volume. It is found that the relaxation time decreases from 2643.5 to 242.8 s while the Kohlrausch exponents increase from 0.717 to 0.892 in the investigated temperature range. The activation energy fluctuates slightly in the course of the relaxation process and its mean value is determined to be 239.7 kJ/mol. By fitting the first derivative of the conversion degree as a function of annealing time using the ?esták–Berggren SB (m, n) model, it is found that the values of m at all annealing temperatures are very small and can be approximated as zero. The values of the pre-exponential factors Z and the kinetic parameter n are found to be slightly varying with the annealing temperature, indicating the complexity of the kinetics of the isothermal relaxation. Finally, an approximate rate equation describing the kinetics of free volume during isothermal relaxation is proposed.     

Isobaric and isothermal glass transition of PMMA: pressure-volume-temperature experiments and modelling predictions

The scaling law for relaxation times, recently proposed by Casalini and Roland, is utilized in the framework of KAHR (Kovacs, Aklonis, Hutchinson, and Ramos) phenomenological theory. With this approach it is shown that the pressure, volume, and temperature (PVT) data obtained on Poly(methyl-methacrylate) (PMMA) can be reliably predicted, in the region of the alpha-relaxation, by using only two fitting parameters, namely: the relaxation time in the reference state, τ_g, and the fractional exponent, β, that describes the dispersion of the alpha-relaxation.     

Percolation of polar nanoregions: A dynamic approach to the ferroelectric phase transition

The percolative nature of the ferroelectric phase transition in a potassium tantalate niobate (KTN) crystal is studied using time domain dielectric spectroscopy. A relaxation process linked to the off-center niobium ions is observed. The dynamic nature of this relaxation shows well defined temperature regimes in which it progresses from independent (Arrhenius) to cooperative (Vogel–Fulcher–Tammann) behavior. A recursive fractal model was applied in order to interpret the data obtained from the dielectric measurements. The structural parameters, ν and μ, derived from the correlation functions, enable the investigation of the onset of the phase transition in terms of the fractal dimensions of the polarization excitation.     

掺铒PLZT电光陶瓷发光特性

测量并分析了Er3+∶PLZT电光陶瓷的吸收光谱和上转换光谱,利用Dexter理论和速率方程理论研究了该材料的发光特性.通过Dexter理论计算得到4I13/2+4I13/2→4I9/2+4I15/2( ET1)和4I11/2+4I11/2→ 4I15/2+4F7/2(ET2)能量传递过程的交叉驰豫几率分别为2.06×105 s-1和1.61 ×105 s-1.以此为基础,结合Er3+跃迁的动力学模型,利用速率方程讨论了交叉驰豫过程对4 I13/2,4I11/2,4I9/2能级上离子数的影响.通过分析可知,ET1和ET2交叉驰豫过程将会使4I13/2能级粒子数大幅度减少,不利于1550hm发光,而对800 nm的发光起到较大的促进作用.     

Ionic transports and optical spectra of 50Li2O–50B2O3 glass

The ionic and optical transports of 50Li₂O–50B₂O₃ glass were investigated. Time-resolved current spectra (TRCS) showed repetitions of typical charge and discharge processes. The model circuit and equation for the TRCS and the equation for the relation between the turning times of polarization (TTP) and configuration energy (CE) have also been suggested. Equations were satisfied by the experimental results, and the potential and temperature dependence of the configuration energy (CE) and the dipole length from the TTP were investigated in detail. Kink phenomena showed that three or more types of charges were involved in the polarizations. The bi-exponential conductivity equation was applied to obtain the temperature dependence of the ac conductivity (TDAC). Complex impedance spectra (CIS) consisted of a semi-arc and a spur due to the electrode-specimen polarization. The shift of inflection points and peak frequencies in complex modulus spectra (CMS) showed non-Debye type relaxations, and the activation energy for relaxation was consistent with the relaxation for the temperature dependence of the dc conductivity (TDC). The migration concept (MC) applied to the CMS was satisfied at the dispersion and peak region, but slightly swerved at the tail. The fractal dimensionality displayed a three-dimensional character. The band gap, Urbach energy and optical indexes were obtained from optical spectra using Kramers–Kronig analysis (KKA).     

Magnetization dynamics in Landau–Lifshitz–Gilbert formulation. FMR experiment modeling

A ferromagnetic resonance (FMR) spectrum of carbon coated magnetic nanoparticles in a non-magnetic elastic matrix has been investigated. The experimental absorption data have been compared with analogous data obtained with the help of the stochastic Landau–Lifshitz equation for the magnetic moment of a ferromagnetic single-domain nanoparticle and stochastic equations describing rotational oscillations of the polymer region containing a magnetic nanoparticle. We have shown that if polymer matrix anisotropies are blocking the rotational freedom of the easy axes direction of the magnetic nanoparticles, additional resonance peaks can appear in the FMR spectrum which are satellite peaks accompanying the main resonance peak. This is another mechanism for the appearance of additional peaks in the FMR spectra besides the spin-waves exchange mode in nanoparticles or inter-particle dipolar interactions. The compound Poisson process has been used to model this effect of additional correlations introduced on the motion of the particle’s magnetic moment.     

Hopping controlled time dependent reaction rates for the scavenging of electrons in glasses

Electron scavenging reactions in aqueous glasses are analyzed in a stochastic model and then compared with transient charge transport in thin film amorphous xerographic photo-conductors. In both systems time dependent rate constants need to be introduced which are related to the waiting time distribution governing single transitions. Evidence is presented suggesting that these transitions in at least some aqueous glasses are due to random walk hoppinh as opposed to tunnelling or trapping. A fractional power of an exponential decay law is derived which is consistent with the straight line experimental plots of log [N(0)/N(t)] versus logt, where N(t) is the number of reactants remaining at time t. Algebraic decay laws can also be derived which are related to the kinetics of xerographic photo-currents and to long lifetime phosphorescence.     

A Stochastic Model for Nucleation Kinetics Determination in Droplet-Based Microfluidic Systems

The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.     

Why the glass transition problem remains unsolved?

Glass-forming substances are made of units having nontrivial mutual interactions. Therefore, structural relaxation of glass-formers is a many-body relaxation problem, which unfortunately is still an unsolved problem in statistical mechanics. Conventional theories and models of glass transition bypass solution of this problem, and hence glass transition also remains an unsolved problem. There are plenty of experimental evidences for the many-body relaxation dynamics, and some examples are given. The Coupling Model of the author is not a full solution of the many-body relaxation problem either. Nevertheless, its predictions can explain the properties of structural relaxation originating from many-body relaxation and their relations to its precursor, namely the Johari–Goldstein secondary relaxation. A demonstration of the utility of the Coupling Model is given here by solving two problems in glass transition that involve many-body relaxation. The problems are: (1) the breakdown of Stokes–Einstein and Debye–Stokes–Einstein relations in neat molecular glass-formers and colloidal suspension, and (2) the component dynamics of polymer blends and mixtures of non-polymeric glass-formers.     

Simulation of surface structural relaxation kinetics in silica glass accelerated by water vapor

It is known that surface structural relaxation of silica glass takes place more rapidly than bulk structural relaxation, especially in the presence of water vapor. The effect of water vapor pressure, heat-treatment temperature and initial fictive temperature on the surface structural relaxation kinetics in silica glasses was investigated by measuring the change of the surface fictive temperature determined from the IR reflection peak shift of silica structural bands. The superimposed component of bulk structural relaxation was subtracted from the measured surface structural relaxation data to isolate the true surface structural relaxation kinetics. The obtained surface structural relaxation data as a function of fictive temperature, heating temperature and water vapor pressure were simulated with a model based on the diffusion equation with time-dependent surface concentration. The simulation model was used to predict the surface structural relaxation kinetics of the optical fiber having a high fictive temperature of ～ 1650 °C at 950 °C under 355 torr of water vapor, and it was confirmed that the present model can simulate surface structural relaxation of the fiber reasonably well.     

Interpretation of the Ni K-edge EXAFS in nanocrystalline nickel oxide using molecular dynamics simulations

Analysis of atomic structure at the nanoscale is a challenging task, complicated by relaxation phenomena and thermal disorder. In this work, the x-ray absorption spectroscopy at the Ni K-edge was used to address this problem in nanocrystalline NiO (nano-NiO) at 300 K. The analysis of the first two coordination shells using conventional two-shell single-scattering approximation allowed us to determine the expansion of the average lattice but contraction of the Ni―O bonds in the first coordination shell in nano-NiO in comparison with the bulk nickel oxide. The EXAFS signal generated within the first six coordination shells (up to ~ 6.5 Å) was successfully interpreted using classical molecular dynamics and ab initio multiple-scattering EXAFS theory. We found that simple rigid-ion force-field model is able to describe the structure relaxation and dynamics in both bulk and nano-NiO. Such approach requires less parameters than conventional EXAFS analysis and allows accounting explicitly for thermal effects and many-atom distribution functions. Finally, we showed that the EXAFS signal is rather sensitive to small variations of the force-field model and, thus, the agreement between the experimental and calculated EXAFS signals can be used for the force-field model optimization.     

Asymptotic behavior for linear and nonlinear elastic waves in materials with memory

In this review, we study the Cauchy problem associated to the equation of linear and nonlinear viscoelasticity with memory.Our first point is the study of dispersive properties of the solution to the linear equation of viscoelasticity with memory. The decay estimates obtained in this first part are important to treat the corresponding nonlinear Cauchy problem.The key novelty is the fact that we admit algebraic singularities and decay at infinity for the time dependent functions in the memory kernel. This fact enables one to include models different from the classical viscoelasticity problem, where this kernel is smooth and exponentially decaying in time.     

Spinodal decomposition in amorphous systems

The theory of spinodal decomposition in amorphous systems is extended to include the effect of internal stress due to coherency strain. A quantitative treatment is developed for the kinetics of internal stress relaxation via plastic deformation. The general solution for the evolution of the composition and internal stress distributions during the early stage of spinodal decomposition is derived for a system obeying the visco-elastic constitutive relations of a Maxwell solid. A kinetic equation for the structure factor is obtained for the limiting case in which coherency strain is relatively large. In this case, it is found that plastic deformation to relieve internal stress can become the rate-limiting step in the evolution of Fourier components having large wavenumbers. The predicted shape of the structure factor as a function of wavenumber, time, and temperature can be very different from that obtained when the kinetics of internal stress relaxation are neglected. The theory is expected to be particularly applicable to amorphous systems in which the species of interest have very different mobilities, and can explain the discrepancies found in previous analyses of scattering data for the lead-aluminum-borate system and alkali-silicate systems.     

Temperature dependence of lattice parameters of SBN single crystals in the vicinity of their structural phase transitions

Changes of lattice parameters of Sr_xBa_1‒xNb₂O₆ (0.35 < x < 0.72) solid solution single crystals were measured as a function of temperature. The X‐ray Bond’ method was used to carry out very precise measurements of the lattice parameters. Fine correlations between values of the lattice parameter and the Sr concentration in the solid solution of Sr_xBa_1‒xNb₂O₆ single crystals are found. A conventional analysis of lattice parameter data in terms of spontaneous strain and strain/order parameter coupling shows that a normal structural phase transition does occur. While the ferroelectric system (SBN26) displays a nearly tricritical behavior, β ≈ 0.20, the relaxor one (SBN61) complies with the two‐dimensional Ising‐model‐like criticality, β ≈ 0.17.     

Atomic‐scale study of vapour growth morphology of crystalline urea

The role of surface relaxation on habit controlling energetics and growth morphology are investigated within the framework of Burton‐Cabrera‐Frank (BCF) and Hartman‐Perdok (HP) models. The habit controlling energetics has been calculated using first principles method. The growth morphology obtained using BCF theory shows that the structural relaxation has considerable effect on growth morphology. The relaxed growth morphology obtained using BCF model match with the experimental result from vapour phase. On the other hand the shape obtained using HP model does not correspond with the experimental shape. Observed polar growth morphology of urea crystal has been discussed particularly in the context of different atomic environments of (111) and (111) faces. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)