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2000, Journal of Applied Physics
The field of viscous liquid and glassy solid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg, and a fourth dealing with “short time processes.” The first part tackles the high temperature regime T>Tg, in which the system is ergodic and the evolution of the viscous liquid toward the condition at Tg is in focus. The second part deals with the regime T∼Tg, where the system is nonergodic except for very long annealing times, hence has time-dependent properties (aging and annealing). The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for “superionic” conductivit...
Physics-Uspekhi, 2018
Relaxation theories of the glass transition and viscous flow of glass-forming melts are presented. The focus is on modern representations of the glass transition equation qs g dT g that describes the appearance of a glassy state during cooling. Here, q dTadt is the temperature change rate during melt cooling and s g is the relaxation time at the glass transition temperature T g. Various methods for calculating the characteristic temperature band dT g during the liquid±glass transition are considered. The generalized equation for the dependence of T g on the melt cooling rate is derived. Based on the model of delocalized atoms, a modified kinetic glass transition criterion is discussed. A generalized viscosity equation for glass-forming liquids is derived.
The European Physical Journal E, 2012
Recently, Mallamace et al. (Eur. Phys. J. E 34, 94 (2011)) proposed a crossover temperature, T(×), and claimed that the dynamics of many supercooled liquids follow an Arrhenius-type temperature dependence between T(×) and the glass transition temperature T(g). The opposite, namely super-Arrhenius behavior in this viscous regime, has been demonstrated repeatedly for molecular glass-former, for polymers, and for the majority of the exhaustively studied inorganic glasses of technological interest. Therefore, we subject the molecular systems of the Mallamace et al. study to a "residuals" analysis and include not only viscosity data but also the more precise data available from dielectric relaxation experiments over the same temperature range. Although many viscosity data sets are inconclusive due to their noise level, we find that Arrhenius behavior is not a general feature of viscosity in the T(g) to T(×) range. Moreover, the residuals of dielectric relaxation times with respect to an Arrhenius law clearly reveal systematic curvature consistent with super-Arrhenius behavior being an endemic feature of transport properties in this viscous regime. We also observe a common pattern of how dielectric relaxation times decouple slightly from viscosity.
Physica B-condensed Matter, 2017
A short review on relaxation theories of glass transition is presented. The main attention is paid to modern aspects of the glass transition equation qτ g = C, suggested by Bartenev in 1951 (qcooling rate of the melt, τ gstructural relaxation time at the glass transition temperature T g). This equation represents a criterion of structural relaxation at transition from liquid to glass at T = T g (analogous to the condition of mechanical relaxation ωτ = 1, where the maximum of mechanical loss is observed). The empirical parameter С = δT g has the meaning of temperature range δT g that characterizes the liquid-glass transition. Different approaches of δT g calculation are reviewed. In the framework of the model of delocalized atoms a modified kinetic criterion of glass transition is proposed (q/T g)τ g = C g , where C g ≅ 7•10 −3 is a practically universal dimensionless constant. It depends on fraction of fluctuation volume f g , which is frozen at the glass transition temperature C g = f g /ln(1/f g). The value of f g is approximately constant f g ≅ 0.025. At T g the process of atom delocalization, i.e. its displacement from the equilibrium position, is frozen. In silicate glasses atom delocalization is reduced to critical displacement of bridge oxygen atom in Si-O-Si bridge necessary to switch a valence bond according to Muller and Nemilov. An equation is derived for the temperature dependence of viscosity of glass-forming liquids in the wide temperature range, including the liquid-glass transition and the region of higher temperatures. Notion of (bridge) atom delocalization is developed, which is related to necessity of local low activation deformation of structural network for realization of elementary act of viscous flowactivated switch of a valence (bridge) bond. Without atom delocalization ("trigger mechanism") a switch of the valence bond is impossible and, consequently, the viscous flow. Thus the freezing of atom delocalization process at low temperatures, around T g , leads to the cease of the viscous flow and transition of a melt to a glassy state. This occurs when the energy of disordered lattice thermal vibrations averaged to one atom becomes equal or less than the energy of atom delocalization. The Bartenev equation for cooling rate dependence of glass transition temperature T g = T g (q) is discussed. The value of f g calculated from the data on the T g (q) dependence coincides with result of the f g calculation using the data on viscosity near the glass transition. Derivation of the Bartenev equation with the account of temperature dependence of activation energy of glass transition process is considered. The obtained generalized relation describes the T g (q) dependence in a wider interval of the cooling rate compared Bartenev equation. Experimental data related to standard cooling rate q = 3 K/min were used in this work.
The Journal of Chemical Physics, 1995
Calculations have been presented for the intermediate scattering function, dynamic structure factor, and dynamic susceptibility of a complex correlated system undergoing relaxation with independent vibrations. The vibrational contribution was approximated by a Debye spectrum, smoothed at high frequency, while the coupling model was used to describe the relaxation. This model asserts for nonpolymeric glass-forming liquids a crossover at a microscopic time from intermolecularly uncorrelated relaxation at a constant rate to intermolecularly coupled relaxation with a time-dependent, slowed-down rate. Although the model has previously been employed to successfully predict and otherwise account for a number of macroscopic relaxation phenomena, critical phenomena are not included in, and cannot be addressed by, the coupling model. Notwithstanding an absence of any change in transport mechanism for the supercooled liquid at a critical temperature, the coupling model data, when analyzed in t...
Physical Review E, 2015
Analysis of temperature dependence of structural relaxation time τ(T) in supercooled liquids revealed a qualitatively distinct feature-a sharp, cusp-like maximum in the second derivative of log τ α (T) at some T max. It suggests that the super-Arrhenius temperature dependence of τ α (T) in glass-forming liquids eventually crosses over to an Arrhenius behavior at T<T max , and there is no divergence of τ α (T) at non-zero T. T max can be above or below T g , depending on sensitivity of τ(T) to change in liquid's density quantified by the exponent γ in the scaling τ α (T) ~ exp(A/Tρ-γ). These results might turn the discussion of the glass transition to the new avenue-the origin of the limiting activation energy for structural relaxation at low T.
2013
We present a study of the atomic dynamics in a Mg 65 Cu 25 Y 10 metallic glass former both in the deep glassy state and in the supercooled liquid phase. Our results show that the glass transition is accompanied by a dynamical crossover between a faster than exponential shape of the intermediate scattering function in the glassy state and a slower than exponential shape in the supercooled liquid. While the crossover temperature is independent on the previous thermal history, both the relaxation rate and the shape of the relaxation process depend on the followed thermal path. Moreover, the temperature dependence of the the structural relaxation time displays a strong departure from the Arrhenius-like behavior of the corresponding supercooled liquid phase, and can be well described in the Narayanaswamy-Moynihan framework with a large non-linearity parameter.
2010
As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassy solids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solid glass ͑in common with crystalline states͒ has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solid glasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.
2017
Many glass-formers exhibit phase transitions between two distinct liquid states. For some metallic glass-formers, the liquid-liquid transition is experimentally found in the supercooled liquid at intermediate temperature between the melting point and the glass transition temperature Tg. We report here on a liquid-liquid transition in an ultra-viscous metallic glass-former, accessed during long-time annealing. This study is conducted on the Au49Cu26.9Si16.3Ag5.5Pd2.3 composition with a liquid-liquid transition temperature slightly lower than Tg. The consequence is that the high-temperature kinetically fragile liquid freezes into the glass during conventional processing and the underlying liquid-liquid transition is thus accessed by the system during annealing below Tg. Upon reheating, the reverse transformation is observed by calorimetry. This conclusion is supported by a broad collection of complementary laboratory and synchrotron-based techniques, such as differential- and fast- sc...
Journal of Physics: Condensed Matter, 1998
This paper discusses the isothermal pressure behaviour of the relaxation times for supercooled glass-forming liquids. Analysis based on reference data and the authors' measurements of dielectric relaxation is carried out for both strong and fragile glass formers. All of the experimental relaxation times clearly exhibit a non-Arrhenius behaviour well reproduced by a function τ = τ 0p exp(C p P /(P 0 -P )) or τ = τ 0 exp(CP 0 /(P 0 -P )), giving the same estimates of the ideal glass transition pressure P 0 . Experimental data indicate that fragile materials show a more rapid increase of the relaxation time with rise of pressure than the strong ones.
Journal of Physics: Condensed Matter, 2008
This preface focuses on the importance of pressure studies for explaining the glass transitions puzzle. Subsequently, some issues related to the European Science Foundation Exploratory Workshop (ESF EW) Glassy Liquids Under Pressure: Fundamentals and Applications (Ustroń, Poland, 10-12 October 2007) are recalled. Most liquids crystallize on 'normal' cooling at the melting temperature T m . However, some liquids can skip crystallization and undergo supercooling down to glass temperature T g . Turnbull proposed an empirical link between these temperatures indicating good glass forming ability (GFA) for T g /T m 2/3. Values of the GFA factor T g /T m → 1/2 were suggested for 'poor' glass formers, where crystallization is difficult to avoid. Recently, the significance of the pressure dependence of the GFA factor was also noted . Reaching the glass transition is associated with a series of phenomena, namely [3]: (i) the thermal expansion coefficient at constant pressure changes smoothly from values common for a liquid to those of a crystal, showing anomalous behaviour near T g , (ii) viscosity reaches a value of η = 10 13 P and the structural relaxation time τ ≈ 100 s, (iii) the specific heat drop occurs, giving rise to the famous Kauzmann paradox. On cooling towards glass transition, the 'pretransitional' behaviour can be observed for dynamic properties even well above T g + 100 K [3]. This includes the non-Arrhenius evolution of such magnitudes as viscosity, primary (structural-, α-) relaxation time, electric conductivity or diffusion coefficient associated with increasingly non-Debye distribution of relaxation times . Such behaviour is associated with short-time scale relaxation processes. The most characteristic is the secondary (β-) relaxation which merges with the 'structural' dynamics near τ (T B ) = 10 -7±1 s, the hypothetically universal (magic) time-scale . Below T B the split in the evolution of the translation and orientation related properties occurs . It is worth stressing that these features seem to be universal, shared by various systems, despite their fundamentally different microscopic basis . It is probable that the latter fact caused the long-standing interest in glass transition phenomenon. It can be said that the puzzling artifacts matched with the intuitive hypothetical universality of the given phenomenon have always attracted the attention of researchers. The modern concept of critical phenomena, developed three to four decades ago, serves as an excellent example . Society-relevant applications of the knowledge gained from studies on the vitrification phenomenon are of great significance for material engineering such as rewritable data storage, pharmacy industry, geophysics, biotechnology, etc . Glass transition physics also constitutes one of the reference points for the novel category of complex liquids/soft matter systems .
Scientific Reports, 2016
While lots of measurements describe the relaxation dynamics of the liquid state, experimental data of the glass dynamics at high temperatures are much scarcer. We use ultrafast scanning calorimetry to expand the timescales of the glass to much shorter values than previously achieved. Our data show that the relaxation time of glasses follows a super-Arrhenius behaviour in the high-temperature regime above the conventional devitrification temperature heating at 10 K/min. The liquid and glass states can be described by a common VFT-like expression that solely depends on temperature and limiting fictive temperature. We apply this common description to nearly-isotropic glasses of indomethacin, toluene and to recent data on metallic glasses. We also show that the dynamics of indomethacin glasses obey density scaling laws originally derived for the liquid. This work provides a strong connection between the dynamics of the equilibrium supercooled liquid and non-equilibrium glassy states.
Unifying Concepts in Granular Media and Glasses, 2004
Recent numerical simulations of a disordered system [5] have shown the existence of two different relaxational processes (called stimulated and spontaneous) characterizing the relaxation observed in structural glasses. The existence of these two processes has been claimed to be at the roots of the intermittency phenomenon observed in recent experiments. Here we consider a generic system put in contact with a bath at temperature T and characterized by an adiabatic slow relaxation (i.e. by a negligible net heat flow from the system to the bath) in the aging state. We focus on a simplified scenario (termed as partial equilibration) characterized by the fact that T = 0 (where only the spontaneous process is observable) and whose microscopic stochastic dynamics is ergodic when constrained to the constant energy surface. Three different effective temperatures can be defined: a) from the fluctuation-dissipation theorem (FDT), T FDR eff , b) from a fluctuation theorem describing the statistical distribution of heat exchange events between system and bath, T FT eff and c) from a set of observable-dependent microcanonical relations in the aging state, T MR eff. In a partial equilibration scenario we show how all three temperatures coincide reinforcing the idea that a statistical (rather than thermometric) definition of a non-equilibrium temperature is physically meaningful in aging systems. These results are explicitly checked in a simple model system.
Entropy
Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section disc...
arXiv: Soft Condensed Matter, 2016
We use relaxation data taken out of equilibrium on glasses of different stability and equilibrium relaxation times from the supercooled liquid to propose a common description for both liquid and glass states. Using ultrafast scanning calorimetry, the accessible timescales of the glass are expanded to much shorter values than previously achieved. Our data show that the relaxation time of glasses follows a super-Arrhenius behaviour in the high-temperature regime above the conventional devitrification temperature heating at 10 K/min. Surprisingly, both the liquid and glass states can be described by a common VFT-like expression that solely depends on temperature and limiting fictive temperature. We apply this common description to nearly-isotropic glasses of indomethacin, toluene and to recent data on metallic glasses. We also show that the dynamics of indomethacin glasses obey density scaling laws derived for the liquid. This work provides a strong connection between the glass and liq...
AIP Advances, 2019
The presence of fluctuating local relaxation times, τ r (t) has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent τ r (t) from experimental or numerical data. Here we report on a new method for determining a local phase field, φ r (t) ≡ ∫ t dt τ r (t ) from snapshots { r(t i )} i=1...M of the positions of the particles in a system, and we apply it to extract φ r (t) and τ r (t) from numerical simulations. By studying how this phase field depends on the number of snapshots, we find that it is a well defined quantity. By studying fluctuations of the phase field, we find that they describe heterogeneities well at long distance scales.
Ceramics
The glass transition is described as a time- and history-independent singular event, which takes place in an interval dependent on the distribution width of molecular vibration amplitudes. The intrinsic glass transition is not seen as a relaxation phenomenon, but is characterized by a fixed volumetric state at the glass temperature Tg0. The relaxation behavior of the transport properties depends on the distance to Tg0. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into condensed matter and the resulting combined interactions between the vibration elements. This creates vacancies between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such apertures depend on the size and axis orientation and do not require further energetic activation. After a displacement, additional volume is created by delays in occupying abandoned positio...
Journal of Non-Crystalline Solids, 2009
The structural relaxation dynamics of two molecular glass forming systems have been analyzed by means of dielectric spectroscopy, under cooling and compression conditions. The relation of the dynamic slowing down with the reduction of the configurational entropy, S C , as predicted by Adam and Gibbs (AG), was also investigated. As S C is not directly accessible by experiments, it was estimated, following a common procedure in literature, from the excess entropy S exc of the supercooled liquid with respect to the crystal, determined from calorimetric and expansivity measurements over the same T-P range of dynamics investigation. The AG relation, predicting linear dependence between the logarithmic of structural relaxation time and the product of temperature with configurational entropy, was successfully tested. Actually, a bilinear relation between S exc and S C was found, with different proportionality factors in isothermal and isobaric conditions. Using such results, we derived an equation for predicting the pressure dependence of the glass transition temperature, in good accordance with the experimental values in literature.
The glass transition is described as a time-and history-independent singular event, which takes place in an interval dependent on the distribution width of the molecular vibration amplitudes. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into the condensed matter and the resulting combined interactions between the vibration elements. This creates vacancies between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such gaps depend on the size and axis orientation and do not require further energetic activation. After a displacement additional volume is created by delays in occupying abandoned positions and restoring the energetic equilibrium. The different possibilities of axis orientation in space result in different diffusive behavior of simple molecules and chain molecules, silicate network formers and associating liquids. Glass transformation takes place at a critical volume Vg 0 when the cross-section of the apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg 0 is assigned to Vg 0 and is therefore independent of molecular relaxation processes. Tg 0 is well above the Kauzmann and Vogel temperatures, usually just a few degrees below the conventionally measured glass temperature Tg(qT). The specific volume at the two temperatures mentioned above cannot be achieved by a glass with an unordered structure but only with aligned molecular axes, i. e. in the crystalline state. Simple liquids consisting of non-spherical molecules additionally alter their behavior above Vg 0 at Vg l where the biggest gaps are as small as the largest molecular diameter. Tg l is located in the region of the crystalline melting point Tm. Both regions, above and below Tm, belong to different physical states and have to be treated separately. In the region close to Vg 0 resp. Tg 0 the distribution of vibration amplitudes has to be taken into account. The boundary volume Vg 0 and the creation of apertures larger than the cross-section of the vibrating elements or parts thereof, in conjunction with the distribution width of the molecular vibrations approaching Vg 0 and the molecular axis orientation, is the key to understanding the glass transition.
The Journal of Chemical Physics, 2013
At temperatures moderately below their glass transition temperature, the properties of many glassforming materials can evolve slowly with time in a process known as physical aging whereby the thermodynamic, mechanical, and dynamic properties all drift towards their equilibrium values. In this work, we study the evolution of the thermodynamic and dynamic properties during physical aging for a model polymer glass. Specifically, we test the relationship between an estimate of the size of the cooperative rearrangements taking the form of strings and the effective structural relaxation time predicted by the Adam-Gibbs relationship for both an equilibrium supercooled liquid and the same fluid undergoing physical aging towards equilibrium after a series of temperature jumps. We find that there is apparently a close correlation between a structural feature of the fluid, the size of the string-like rearrangements, and the structural relaxation time, although the relationship for the aging fluid appears to be distinct from that of the fluid at equilibrium.
2008
We propose that there exists a generic class of glass forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where ageing, relaxation and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to ageing occur where the local shear modulus is low (even negative), and result in an increase in the size of local patches of relative order. We examine the ageing events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass forming systems to the reduction in relative volume of the amorphous material which is liquid-like. While we agree with the well known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulae that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most super-exponentially when the temperature is lowered.
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