Kinetics Of Structural Relaxation Research Articles

How to Distinguish Nonexponentiality and Nonlinearity in Isothermal Structural Relaxation of Glass-Forming Materials.

The nonexponentiality and nonlinearity are two essential features of the structural relaxation in any glass-forming material, which seem to be inextricably bound together by the material time. It is shown that the temperature down-jump and up-jump experiments of the same magnitude ΔT = T0 - T to the same temperature T provide a clue for their separation. The isothermal structural relaxation can be quantified using the stabilization period on the logarithmic time scale log(tm/t0). It is described as the sum of the nonexponentiality term 1.181/ß and the nonlinearity term (σ/2.303)ΔT for the temperature down-jump, and as their difference for the temperature up-jump. The material parameter σ = -(∂lnτ/∂Tf)i quantifies variation of the relaxation time with structural changes at the inflection point of the relaxation curve and is formulated for the most widely used phenomenological models. The asymmetry of approach to equilibrium after the temperature down-jump and up-jump was first described by Kovacs in 1963. A detailed analysis of this asymmetry is provided, and a simple method for the estimation of the parameters characterizing the nonexponentiality (ß) and nonlinearity (σ) is proposed. The applicability of this method is tested using previously reported isothermal experimental data as well as calculated data for aging of polymers and other glass-forming materials. This concept illuminates differences in structural relaxation kinetics in a simple and consistent way that can be useful in the design of novel materials and the evaluation of their physical aging treatment.

Glass transition and crystallization of Se95Te5 chalcogenide glassy semiconductor

The study is dedicated to the investigation of thermo-physical characteristics of Se95Te5 chalcogenide glassy semiconductor during its glass formation and crystallization processes, employing various scanning rates of 5, 10, 15 and 20 K/min in non-isothermal modes through DSC measurement. Analysis of the structural relaxation kinetics involves the Kissinger’s, Augis and Bennett's, as well as Matusita’s approaches. Experimental data yield contains the determination of crucial parameters such as glass transition (𝑇𝑇𝑔𝑔), crystallization(𝑇𝑇𝑐𝑐), and melting temperatures alongside factors like reduced temperature of glass transition (𝑇𝑇𝑟𝑟𝑟𝑟), Hruby’s parameter (𝐾𝐾𝑔𝑔𝑔𝑔), fragility index (𝐹𝐹𝑖𝑖), Avrami exponents (n, m), glass transition (140.24 kJ/mol) and crystallization (Ec = 95.11 kJ/mol) energies, respectively. The results confirm that Se95Te5 chalcogenide system as an efficient glass former. Matusita’s method reveals that the crystallization mechanism (n = 2.51, m = 1.9) corresponds to volumetric nucleation with two-dimensional growth.

Unveiling crystallization and relaxation dynamics interplay in a deeply supercooled glass

Crystallization in glasses below their transition range (Tg) is crucial for understanding material stability and performance. However, data on the time evolution of crystallized fractions in this temperature range is scarce. This study investigates the interplay between structural relaxation and crystallization kinetics in a model silicate glass (5BaO·8SiO2) below Tg. Analyzing the number of crystals, their size, and the crystallized volume as a function of the treatment time, we demonstrate that a single parameter accounting for structural relaxation effectively describes these three crystallization processes. Notably, we found that glasses prone to rapid crystallization below Tg can fully crystallize before reaching complete structural relaxation. These findings highlight the complex interplay between relaxation dynamics and crystallization in deeply supercooled glasses, with implications for understanding and controlling these processes in various materials.

Nonadiabatically Driven Subcritical Crack Nucleation in Solids

This paper discusses a subcritical crack nucleation mechanism in a brittle solid within a real range of applied stress. A medium deformed by uniaxial tension is considered as an open nonequilibrium system of nuclei and electrons. Structural relaxation of the medium begins with the excitation of dynamic displacements during nonadiabatic Landau–Zener transitions. Dynamic displacements induce the instability of the medium to the longitudinal displacement wave. The kinetics of structural relaxation is described by two nonlinear parabolic kinetic equations for dynamic order parameters. Conditions are derived for the existence of localized solutions (autosolitons). The excitation of autosolitons leads to local elongation and cross-sectional reduction of the specimen. The resulting neck is a subcritical crack.

Structural relaxation dynamics of a silicate glass probed by refractive index and ionic conductivity

AbstractRelaxation occurs spontaneously in all glasses and is a fundamental step of important technological processes, such as annealing, crystal nucleation, and chemical strengthening by ion exchange. Despite extensive studies over the past decades, there are still conflicting results on whether the kinetics of structural relaxation depends on the analyzed property. Thus, in this study, we used a lithium disilicate glass as a model composition to determine the structural relaxation kinetics during physical aging experiments by measuring the time evolution of the refractive index and ionic conductivity down to 35 K below the initial fictive temperature. In all cases, variations in these properties were adequate to capture the structural changes throughout the aging experiments. At each temperature, the experimental relaxation data fit quite well with the classical stretched exponential relation. We also found that the relaxation process starts faster when probed by ionic conductivity than by refractive index; however, they show similar average relaxation times. These very small structural rearrangements are always the same, but ionic conductivity changes faster than refractive index at the beginning of the process. Our comprehensive results strongly indicate that relaxation dynamics is indeed dependent on the analyzed property.

Dynamic Heterogeneity and Kovacs’ Memory Effects in Supercooled Water

Understanding the properties of supercooled water is important for developing a comprehensive theory for liquid water and amorphous ices. Because of rapid crystallization for deeply supercooled water, experiments on it are typically carried out under conditions in which the temperature and/or pressure are rapidly changing. As a result, information on the structural relaxation kinetics of supercooled water as it approaches (metastable) equilibrium is useful for interpreting results obtained in this experimentally challenging region of phase space. We used infrared spectroscopy and the fast time resolution obtained by transiently heating nanoscale water films to investigate relaxation kinetics (aging) in supercooled water. When the structural relaxation of the water films was followed using a temperature jump protocol analogous to the classic experiments of Kovacs, similar memory effects were observed. In particular, after suitable aging at one temperature, water's structure displayed an extremum versus the number of heat pulses upon changing to a second temperature before eventually relaxing to a steady-state structure characteristic of that temperature. A random double well model based on the idea of dynamic heterogeneity in supercooled water accounts for the observations.

NONADIABATICALLY DRIVEN SUBCRITICAL CRACK NUCLEATION IN SOLIDS

This paper discusses a subcritical crack initiation mechanism in a brittle solid within a real range of applied stress. A medium deformed by uniaxial tension is considered as an open nonequilibrium system of nuclei and electrons. Structural relaxation of the medium begins with the excitation of dynamic displacements during nonadiabatic Landau-Zener transitions. Dynamic displacements induce the instability of the medium to the longitudinal displacement wave. The kinetics of structural relaxation is described by two nonlinear parabolic kinetic equations for dynamic order parameters. Conditions are derived for the existence of localized solutions (autosolitons). The excitation of autosolitons leads to a local elongation and cross-sectional reduction of the specimen. The resulting neck is a subcritical crack.

Structural relaxation in chalcogenide glasses

AbstractThe structural relaxation of chalcogenide glasses is discussed within Tool–Narayanaswamy–Moynihan (TNM) formalism. The TNM parameters for more than 70 different glassy compositions are compared on the basis of the relaxation rate defined as Rf(ΔT) = −(dTf/dlogt)i at the inflection point of the isothermal relaxation curve plotted on a logarithmic timescale. The Rf(ΔT) depends on the TNM parameter ß and the parameter σ, combining the nonlinearity parameter x, the effective activation energy h* or the fragility m. It is shown that Rf(10) estimated at 10 K below Tg is useful for the prediction of structural relaxation kinetics in different amorphous materials. The chalcogenide glasses are, for example, compared with oxide glasses and organic polymers. For all these materials, the Rf(10) versus σ plot shows a well‐defined pattern that is thoroughly discussed.

Indomethacin: The Interplay between Structural Relaxation, Viscous Flow and Crystal Growth.

Non-isothermal differential scanning calorimetry (DSC) was used to study the influences of particle size (daver) and heating rate (q+) on the structural relaxation, crystal growth and decomposition kinetics of amorphous indomethacin. The structural relaxation and decomposition processes exhibited daver-independent kinetics, with the q+ dependences based on the apparent activation energies of 342 and 106 kJ·mol−1, respectively. The DSC-measured crystal growth kinetics played a dominant role in the nucleation throughout the total macroscopic amorphous-to-crystalline transformation: the change from the zero-order to the autocatalytic mechanism with increasing q+, the significant alteration of kinetics, with the storage below the glass transition temperature, and the accelerated crystallization due to mechanically induced defects. Whereas slow q+ led to the formation of the thermodynamically stable γ polymorph, fast q+ produced a significant amount of the metastable α polymorph. Mutual correlations between the macroscopic and microscopic crystal growth processes, and between the viscous flow and structural relaxation motions, were discussed based on the values of the corresponding activation energies. Notably, this approach helped us to distinguish between particular crystal growth modes in the case of the powdered indomethacin materials. Ediger’s decoupling parameter was used to quantify the relationship between the viscosity and crystal growth. The link between the cooperativity of structural domains, parameters of the Tool-Narayanaswamy-Moynihan relaxation model and microscopic crystal growth was proposed.

Формирование нерегулярного паттерна локализованной пластичности на стадии перехода от линейного к стадии параболического упрочнения

During the transition from the stage of linear to the stage of parabolic hardening, the formation of an irregular pattern is experimentally observed. The reasons and conditions for the formation of such a pattern are considered. A deformable medium is considered as a non-linear system with a continuously changing structure on two spatial and temporal scales. Kinetics of structural relaxation of a deformable medium. is described by a system of two nonlinear equations of parabolic type for dynamic order parameters. Based on the analysis of the solutions of the kinetic equations, it is shown that the solutions of the equations at the intermediate stage are static autosolitons.

Relaxation dynamics in multicomponent glass formers with adjustable concentration fluctuations

Here, we study the structural relaxation kinetics in modified binary (i.e., ternary) mixtures with strong concentration fluctuation imposed by a polar picoline and an apolar triphenylethylene by adding a surfactant phenanthridine. The dielectric and enthalpy relaxation measurements are applied to monitor the dynamic properties aiming at distinguishing various effects of the concentration fluctuation. It is found that the strong concentration fluctuations are largely suppressed by adding the surfactant molecule. However, compared with the binary mixtures, a larger difference in the glass transition temperatures determined by the dielectric and enthalpy methods is observed in some of the ternary mixtures. Another unusual behavior in the ternary mixtures is that the enthalpy relaxation produces higher non-exponential factor β than the dielectric relaxation. The comparison of various parameters confirm that the reduced glass transition width is more suitable for characterizing the strength of concentration fluctuations in multi-component systems.

Is the structural relaxation of glasses controlled by equilibrium shear viscosity?

AbstractKnowledge of relaxation processes is fundamental in glass science and technology because relaxation is intrinsically related to vitrification, tempering as well as to annealing and several applications of glasses. However, there are conflicting reports—summarized here for different glasses—on whether the structural relaxation time of glass can be calculated using the Maxwell equation, which relates relaxation time with shear viscosity and shear modulus. Hence, this study aimed to verify whether these two relaxation times are comparable. The structural relaxation kinetics of a lead metasilicate glass were studied by measuring the refractive index variation over time at temperatures between 5 and 25 K below the fictive temperature, which was initially set 5 K below the glass‐transition temperature. Equilibrium shear viscosity was measured above and below the glass‐transition range, expanding the current knowledge by one order of magnitude. The Kohlrausch equation described very well the experimental structural relaxation kinetics throughout the investigated temperature range and the Kohlrausch exponent increased with temperature, in agreement with studies on other glasses. The experimental average structural relaxation times were much longer than the values computed from isostructural viscosity, as expected. Still, they were less than one order of magnitude higher than the average relaxation time computed through the Maxwell equation, which relies on equilibrium shear viscosity. Thus, these results demonstrate that the structural relaxation process is not controlled by isostructural viscosity and that equilibrium shear viscosity only provides a lower boundary for structural relaxation kinetics.

Controlling the Curie temperature in amorphous glass coated microwires by heat treatment

In amorphous ferromagnetic alloys the Curie temperature (Tc) can be changed by modifying the short-range ordering between 3d-atoms, and the kinetics of this change depends on the details of structural relaxation. In the present work, isothermal annealing was used to control Tc in amorphous Fe3.9Co64.82B10.2Si12Cr9Mo0.08 and Fe5Co27.4B12.26Si12.26Ni43.08 microwires with a relatively low Curie point in as-quenched state of 61.5 °C and 48 °C , respectively. The kinetics of structural relaxation in the first alloy appears to result in stronger antiferromagnetic coupling of Cr–Fe and Cr–Co, which lowers Tc down to 53.5 °C on annealing with a temperature of 350 °C during 10 min. Annealing the Ni-based alloys produces a continuous increase in Tc with time and annealing temperatures up to high annealing temperatures near the onset of crystallization. Partial crystallization at higher annealing temperature may also contribute to Tc- change. We demonstrated the controllable change in the Curie temperature in these wires in the range of 53.5–68°C for Cr-containing alloy and 48–72°C for Ni-containing alloys. Fine tuning of the critical temperature can be used in a variety of sensing applications in the important industrial temperature range.

Understanding aging in chalcogenide glass thin films using precision resonant cavity refractometry

Chalcogenide glass (ChG) thin films have a wide range of applications in planar photonics that rely on the stability of their optical properties. However, most methods do not provide quantitative optical property data at sufficiently high resolution. We have employed a resonant cavity refractometry technique capable of detecting refractive index changes down to 10−6 refractive index unit (RIU) to study the aging, or sub-Tg structural relaxation kinetics, of Ge23Sb­7S70 ChG. Our study reveals that the refractive index (RI) change due to aging tends to follow stretched exponential behavior, with stretch exponents and rate of index change dependent on initial glass treatment. Thermally annealed devices show the best stability, suggesting that thermal annealing is the appropriate post-deposition treatment method for obtaining stable ChG films.

Kinetics of the Structural Relaxation in Borosilicate Melts

The kinetics of structural relaxation in oxide systems containing complexing elements—boron and silicon— was studied by the potentiometric method. The effect of the nature and composition of the oxide electrolyte and the quenching temperature on the kinetic parameters of the anionic polymerization process was uncovered. Modeling of the relaxation processes in liquid borosilicates was conducted. Two kinetic schemes of structural relaxation, taking account of the slowness of the depolymerization of silicon oxide complexes and change of the coordination of boron, are examined. The influence of different physical and chemical factors on the rate of the relaxation processes and the equilibration time are analyzed.

Correlation between the structure and structural relaxation data for (GeSe2)y(Sb2Se3)1-y glasses

Combined calorimetric and structural study, employing the techniques of differential scanning calorimetry and Raman spectroscopy, was performed to describe the enthalpy relaxation processes in the (GeSe2)y(Sb2Se3)1-y chalcogenide glasses. The full glass forming compositional region (y = 0.3–0.9) was explored. The enthalpy relaxation was described in terms of the phenomenological Tool-Narayanaswamy-Moynihan model. Compositional evolution of the glass transition temperatures and relaxation activation energies was explained based on the changing average bond energies and overall interconnectivity of the glassy matrices. Resemblance between the activation energies of the relaxation processes and viscous flow was confirmed for all studied glasses. Non-linearity and non-exponentiality of the enthalpy relaxation were found to be invariant with composition. The structural relaxation kinetics as well as kinetic fragilities determined for the present (GeSe2)y(Sb2Se3)1-y glassy system were very similar to the results obtained earlier for the (GeS2)y(Sb2S3)1-y glasses, which can be attributed to the similarly constrained topology of the pseudo-binary compositional lines.

Reduction in internal friction in silica glass with high OH content

AbstractThe aim of this article was to investigate processes occurring during annealing of silica glass classified as being of type III (J Non Cryst Solids. 1970;5(2):123‐75). This is an inexpensive silica glass produced by many manufacturers across the globe. However, it can be successfully used for fabrication of high‐Q mechanical resonators. The relationship between residual internal stress and internal friction is elucidated. Quantitative analysis of the structural relaxation kinetics is presented. The influence of the cooling process for structural transformation is also discussed. On the basis of our results, we suggest optimal annealing conditions for minimizing internal friction type III silica glass. The results will be useful for further improvement of the Q‐factor of mechanical resonators, including the test masses of the next generation of gravitational wave detectors. Our approach might, in addition, be used for studying the modification of atomic structure in multicomponent glasses.

Collective Structural Relaxation in Phase‐Change Memory Devices

AbstractPhase‐change memory devices are expected to play a key role in future computing systems as both memory and computing elements. A key challenge in this respect is the temporal evolution of the resistance levels commonly referred to as “resistance drift.” In this paper, a comprehensive description of resistance drift as a result of spontaneous structural relaxation of the amorphous phase‐change material toward an energetically more favorable ideal glass state is presented. Molecular dynamics simulations provide insights into the microscopic origin of the structural relaxation. Based on those insights, a collective relaxation model is proposed to capture the kinetics of structural relaxation. By linking the physical material parameters governing electrical transport to such a description of structural relaxation, an integrated drift model that is able to predict the current–voltage characteristics at any instance in time even during nontrivial temperature treatments is obtained. Accurate quantitative matching with experimental drift measurements over a wide range of time (10 decades) and temperature (160–420 K) is demonstrated.

Chirality impact on physical ageing: An original case of a small organic molecule

The purpose of this paper is to investigate the structural relaxation of N-acetyl-α-methylbenzylamine (Nac-MBA), a chiral organic molecule, through the study of the glass transition temperature Tg and the well-known physical ageing, occuring at temperatures lower than Tg. The influence of the enantiomeric excess (ee) on the structural relaxation kinetics is highlighted through standard differential scanning calorimetry (DSC) and fast scanning calorimetry (FSC) investigations. This original work evidences that even if the enthalpy loss to reach equilibrium remains globally the same whatever the ee, the structural relaxation kinetics are clearly slowed down when ee is increased.

Physical aging of shape memory polymers based upon epoxy-thiol “click” systems

The physical aging behaviour of two epoxy-thiol shape memory polymers has been studied: diglycidyl ether of bisphenol-A cross-linked with pentaerythritol tetrakis, denoted 4-thiol, with a calorimetric glass transition temperature, Tg, of 51 °C; and the same system modified with tri (2,3-epoxypropyl)isocyanurate in a 30 wt% proportion, denoted 4-thiol-30%iso, with Tg = 63 °C. The aging of both polymers has been measured by torsional creep for aging temperatures between room temperature and the Tg of each polymer. The creep behaviour of each polymer is characterised by a discrete distribution of relaxation times, which shifts with aging time according to a double logarithmic aging rate, μ, and with aging temperature according to an activation energy. The distribution of creep relaxation times for 4-thiol is rather symmetrical, and slightly narrower than that for 4-thiol-30%iso, which is also skewed to longer times. The dependence of μ on temperature displays a peak as the aging temperature reduces below Tg, and is sharper for 4-thiol, in accordance with the narrower distribution, as predicted by a theoretical model based upon structural relaxation kinetics. The other parameters defining the aging behaviour, namely the reduced activation energy (Δh*/R = 92 kK for 4-thiol and 82 kK for 4-thiol-30%iso) and the non-linearity parameter of structural relaxation (x = 0.35 for 4-thiol and 0.25 for 4-thiol-30%iso), have been determined experimentally and are compared with the predictions of the theoretical model. These parameters can be used to predict the effects of physical aging on the shape memory response.