Non-equilibrium entropy of glasses formed by continuous cooling

We propose a generalized definition of entropy accounting for the continuous breakdown of ergodicity at the laboratory glass transition. Our approach is applicable through all regimes of glass forming, from the equilibrium liquid state through the glass transition range and into the glassy state at low temperatures. The continuous loss of ergodicity during the laboratory glass transition is accompanied by a loss of entropy as the system gradually becomes trapped in a subset of the configurational phase space. Using a hierarchical master equation approach, we compute the configurational entropy of selenium, a simple but realistic glass-former, for cooling rates covering 25 orders of magnitude, viz., 10^?12 to 10¹² K/s. In all cases, the entropy of glass is zero in the limit of absolute zero temperature, since here the system is necessarily confined to a single microstate.     

Composition dependence of the glass transition temperatures of PdNiP and PtNiP glasses

Thermal properties of glassy PdNiP and PtNiP alloys have been measured as a function of the concentration of transition metals. The glass transiion temperature, T_g, of these alloys glasses exhibits a negative linear deviation with transition metal content - which is in contrast to the increasing T_g of binary glassy alloys with increasing metalloids.It is suggested that the suppression of the glass transition temperature of these glassy alloys may be attributed to the excess configurational entropy of disorder associated with a mixture of hard spheres differing in radius. In contrast, the increasing T_g of binary glassy alloys with the metalloid content may be associated with the short-range order resulting from strong interactions between metal and metalloid atoms.     

Vibrational entropy near glass transition in a chalcogenide glass and supercooled liquid

Raman spectroscopic measurements have been performed on Ge₂₀Se₈₀ glass and supercooled liquid at temperatures ranging between 298 and 500 K. Temperature dependent softening of vibrational mode frequencies has been used in conjunction with the available vibrational density of states data at ambient temperature to estimate the relative contributions of vibrational and configurational entropies across glass transition. Nearly 20% of the additional entropy above glass transition is estimated to be vibrational. Thermal expansion effect on vibrational mode softening is found to be insufficient to account for the anharmonic component of vibrational entropy implying possible coupling between the vibrational and configurational entropies at temperatures above T_g. These results may have important consequences in shaping our understanding of various aspects of glass transition.     

Relationship between viscous dynamics and the configurational thermal expansion coefficient of glass-forming liquids

We propose a model to describe the relationship between the viscosity of a glass-forming liquid and its configurational contribution to liquid state thermal expansion. The viscosity of the glass-forming liquids is expressed in terms of three standard parameters: the glass transition temperature (T_g), the liquid fragility index (m), and the extrapolated infinite temperature viscosity (η_∞), which are obtained by fitting of the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) expression to measured viscosity data. The model is tested with experimental data for 41 different glass-forming systems. A good correlation is observed between our model viscosity parameter,h(T_g, m, η_∞), and the configurational coefficient of thermal expansion (i.e., the configurational CTE). Within a given class of glass compositions, the model offers the ability to predict trends in configurational CTE with changes in viscosity parameters. Since viscosity is governed by glass network topology, the model also suggests the role of topological constraints in governing changes in configurational CTE.     

Experimental evidence against the existence of an ideal glass transition

The absolute liquid heat capacity of poly(α-methyl styrene) was determined at temperatures far below T_g and T_K in previous work by use of pentamer/polymer athermal mixtures. Here the data is compared to data compiled by Wunderlich and coworkers from 0 K to above T_g in order to obtain the absolute entropy for the polymer in its equilibrium state at temperatures as much as 180 K below the glass temperature or 130 K below the Kauzmann temperature. The results provide no evidence of a second-order transition or of a smeared transition in the entropy. In addition, we find no evidence that the entropy would become negative at a finite temperature.     

Structural behavior of amorphous and liquid metallic alloys at elevated temperatures

The thermal behavior of the short-range order of Pd₄₀Cu₃₀Ni₁₀P₂₀ bulk metallic glasses has been investigated in situ by means of high-temperature X-ray synchrotron diffraction. The dependence of the X-ray structure factor S(q) of the glassy state on temperature follows the Debye theory up to the glass transition. Above the glass transition temperature T_g, the temperature dependence of S(q) is altered toward a continuous development of structural changes in the liquid state with temperature. The behavior of the structure factor during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at the caloric glass temperature.     

Unusual Glassy Smectic-G Liquid Crystal: Heat Capacity of N-p-n-Pentyloxybenzylidene-p'-n-butylaniline between 11 and 393 K

Abstract

The heat capacities of the title compound (C₃H₁₁,O—C₆H₄,- CH=N—C₆H₄,—C₄H₉, abbreviation 5O ? 4) with a purity of 99.92 mole percent have been measured with an adiabatic-type calorimeter between 11 and 393 K. The transition temperature and the enthalpy and entropy of phase transition for stable crystal → S_G, S_G → N and N → isotropic liquid were T _c = 299.69 K/ΔH = 22.68 kJ mol^?1/ΔS = 75.70 JK^?1 mol^?1, 325.72/7.11/21.79 and 342.48/1.78/5.22, respectively. The crystal which melts at 285.5 K is a metastable modification. The S_A phase hitherto reported in between S_G and N does not exist. The glassy So state was realized by rapid cooling of the specimen from the So phase. The molar enthalpy of the glassy S_G state at 0 K was by (10.1±0.1) kJ mol^?1 higher than that of the stable crystalline state and the residual entropy of the glassy state was (9.40±0.83) JK^?1 mol^?1. The relaxational heat-capacity anomaly was observed from as low as 100 K and double glass transition phenomenon occurred around 200 K; a quite unusual phenomenon which has never been observed for the glassy states of nematic and cholesteric liquid crystals. The present results give a fair evidence that the unusual glass transition phenomenon previously found for the S_G state of 6O?4 (a homologous compound) is not exceptional at all but common to the smectic glasses; at least common to the glassy S_G states. Two possible origins responsible for the double glass transitions have been discussed.     

An electrospray technique for hyperquenched glass calorimetry studies: Propylene glycol and di-n-butyl phthalate

We describe an electrospray technique for in situ preparation, for differential scanning calorimetry study, of samples of molecular liquids quenched into the glassy state on extremely short time scales (hyperquenched). We study the cases of a hydrogen-bonded liquid, propylene glycol, PG and a Van der Waals liquid, di-n-butyl phthalate DBP. Using a fictive temperature method of obtaining the temperature dependence of enthalpy relaxation, we show that the electrospray method yields quenching rates of ∼10⁵ K/s, while the more common method, dropping a sealed pan of sample into liquid nitrogen, yields only 120 K/s. These hyperquenched samples start to relax, exothermically, far below the glass temperature, at a temperature (0.75T_g) where the thermal energy permits escape from the shallow traps in which the system becomes localized during hyperquenching. This permits estimation of the trap depths, which are then compared with the activation energy estimated from the fictive temperature of the glass and the relaxation time at the fictive temperature. The trap depth in molar energy units is compared with the ‘height of the landscape’ for PG, the quasi-lattice energy of the liquid based on the enthalpy of vaporization, and the single molecule activation energy for diffusion in crystals. The findings are consistent with the mechanism of relaxation invoked in a current model of relaxation in glassforming liquids. In the case of di-n-butyl phthalate we investigate the additional question of sub-T_g annealing effects. We find the ‘shadow’ glass transition, (an annealing prepeak) seen previously only in multicomponent mineral and metallic glasses. The phenomenon is important for understanding microheterogeneities in viscous liquid structures.     

Relation between configurational entropy and relaxation dynamics of glass-forming systems under volume and temperature reduction

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 reciprocal of 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.     

Sound velocity in liquid and glassy selenium

The speed of longitudinal sound waves at 7 and 22 MHz has been measured in liquid, supercooled, and amorphous selenium, including the region around the glass transition temperature, T_g, near 35 °C. In amorphous selenium the speed of shear waves at 7 MHz was also measured. The experiments were performed with high purity Se (99.9999%) hermetically sealed in an evacuated silica ampoule. Four temperature regions with strongly different relaxation times can be distinguished between room temperature and the melting point: (1) a glassy state below T_g, which is stable on the time scale of the experiments, (2) a glassy state above T_g, which is metastable on the time scale of the experiments, (3) a region where homogeneous crystal nucleation occurs, and (4) a supercooled liquid, which is stable on the time scale of the experiments. Each region is marked by a change in the slope of the temperature dependence of the sound velocity. Near the glass transition temperature the velocities of longitudinal and transverse sound exhibit hysteresis with a step-like drop on heating and a more continuous rise on cooling. The step-like anomaly in sound velocity may be a general property of the glass transition.     

The effect of cooling rate on the glass transition of an amorphous polymer

Cooling down from the equilibrium state at different rates reveals the dynamic behavior of glass forming materials. In particular, the dependence of the glass transition region on the cooling rate, q is commonly agreed to contain information regarding the activation energy of the relaxation time, τ. In this work experimental and theoretical aspects of such a relationship have been highlighted. Experimentally, the glass transition zone of amorphous polystyrene films has been investigated over two decades of cooling rate (0.5–50 K/min) by using refractive index measurements. The shift of the glass transition temperature and the broadening of the transition zone at increased cooling rate have been characterized. Theoretically, the cooling experiments have been simulated within the integral formulation of the Kovacs–Aklonis–Hutchinson–Ramos (KAHR) model using the Vogel temperature dependence for the relaxation time. The Frenkel–Kobeko–Reiner equation, τq = constant, provided the needed relationship between the experiments and the theory, enabling the evaluation of the relevant parameter of the kinetic model, i.e. the Vogel activation energy and the zero configurational entropy temperature, from the shift of the glass transition temperature with cooling rate.     

Structural aspects of volume nucleation in silicate glasses

An interrelationship between parameters of short and intermediate range order in silicate glasses and the tendency to nucleate homogeneously in the volume is tested. Changes in the average coordination number and metal-oxygen distance of network modifying cations as well as changes in the concentration of constitutive silica tetrahedra accompanied with the crystallization of 18 stoichiometric glass compositions into their crystalline analogs are determined. The intermediate range structure of the glasses is investigated by configurational entropy and flow birefringence. The changes in structural parameters are analyzed in terms of the reduced glass transition temperature T_rg, which is negatively correlated with the maximal rate of volume nucleation. The results indicate that the short-range structure in stoichiometric glasses is, in general, very similar to the corresponding crystal structure but independent of the T_rg-scale and for this reason independent of nucleation properties. In contrast to the short range of the glass structure, birefringence induced by a forced flow above the glass transition temperature and configurational entropy are positively correlated with increasing T_rg. The results indicate increased structural order in the intermediate range for melts with a high supercool limit (T_rg < 0.58). It is concluded that this order phenomena may promote nucleation events and may help to explain the tendency to volume nucleation of silicate glasses with T_rg < 0.58.     

Communal entropy and glass transition

Using the partition function formulated by Kirkwood, the glass transition temperature is shown to be the temperature at which the communal entropy vanishes in a liquid system. The non-existence of T₂ is inferred from the theory in accordance with the experimental fact that all the glasses made so far have some residual entropy compared with the crystal state.     

Thermodynamic and thermokinetic characteristics of the glass transition in a GeSe2GeTeSb2Te3 alloy

Glassy alloys of (GeSe₂)₇₀ (GeTe)₁₅ (Sb₂Te₃)₁₅ were prepared by water-quenching and subjected to several thermal treatments through the glass transition region. The thermodynamic and thermokinetic characteristics of the glass were inferred from heat capacity measurements by differential scanning calorimetry. It was demonstrated that the undercooled liquid obtained by heating the glass is in equilibrium, and what is more, that not only each particular cooling process through the glass transition produces a given glass, but also that any trance of the glass may be suppressed by reheating above glass transition. The enthalpy and entropy differences between each glass and the undercooled liquid used to obtain that particular glass were taken as properties sensitive to the relaxation inherent to the formation of the glass. The activation energy spectrum characterizing the relaxation processes on cooling through the glass transition has been obtained. It has a peak energy of 1.43 eV which may be related to the bonds between the constituent atoms of the sample with weaker interaction energy. Therefore, the relaxation may be due to a breaking and rearrangement of these bonds in the glassy structure.     

The boson peak in melt-formed and damage-formed glasses: A defect signature?

We describe the preparation and characterization of a glassy form of the moderately good glassformer PbGeO₃, by mechanical damage, and compare its properties with those of the normal melt-quenched glass and the crystal. The damage-formed glass exhibits a DSC thermogram strikingly similar to that of a hyperquenched glass, implying that it forms high on the energy landscape. The final glass transition endotherm occurs within 4 K (0.006T_g) of that of the melt-quenched glass, but crystallization occurs at a lower temperature, as if pre-nucleated. In particular, we have studied the low frequency vibrational dynamics of the alternatively prepared amorphous states in the boson peak region, and find the damage-formed glass boson peak to be almost identical in shape to, but more intense than, that of the normal melt-formed glass, as previously found for hyperquenched glasses. In view of the quite different preparation procedures, this similarity would seem to eliminate equilibrium liquid clusters as a source of the boson peak vibrations, but leaves plausible a connection to force constant fluctuations or to specific vitreous state defects.     

Thermodynamic investigation on glassy states of pure simple compounds

The present review deals primarily with glass transition phenomena in pure simple compounds and pays special attention to the thermodynamic aspects of the vitrification process. The concept of glassy state is extended to liquid crystalline and even to crystalline materials which have any type of disorder. Thus the familiar supercooled liquid-glass transition is shown to be just one example of a class of ‘glass transitions’ due to loss of equilibrium which must occur quite frequently in condensed matter. Evidence of several glass transition phenomena in one and the same compound is given. The fact that glass should be considered as one of the states of aggregation of matter, irrespective of either the method of formation or the existence of three-dimensional periodicity in molecular arrangements, is stressed.     

On the reality of the residual entropy of glasses and disordered crystals: The entropy of mixing

We have previously shown that the assumption that the configurational entropy of a supercooled liquid vanishes at T_g leads to a non-trivial violation of the second law. Here we consider the example of the entropy of mixing. We use as a model system two similar chemical substances which form an ideal solution in a mixed phase. We apply the reasoning of our earlier paper to show that this vanishing would lead to a dilemma; either it violates the second law of thermodynamics, or else it cannot be demonstrated by any conceivable experiment. We show further that the vanishing of the entropy of mixing on kinetic arrest leads to the counter-intuitive result that the chemical potential of each component in an infinitely dilute kinetically arrested (or glassy) solution can equal or the chemical potential of the pure component. The most parsimonious conclusion from these results is that residual entropies are real.     

On the phase diagram of polymorphic ethanol: Thermodynamic and structural studies

It is well known that ethanol exhibits a very interesting polymorphism presenting different solid phases: a fully-ordered (monoclinic) crystal, a (bcc) plastic crystal, which by quenching becomes an orientationally-disordered crystal with glassy properties (hence sometimes named ‘glassy crystal’), and the ordinary amorphous glass. We have carried out calorimetric, X-ray diffraction, and Brillouin-scattering experiments above liquid-nitrogen temperatures and have found several new features that shed more light on the rich and interesting phase diagram of ethanol. Firstly, we have identified up to four different varieties of the monoclinic crystalline phase depending on the thermal history. We also present new specific-heat data of these glassy and crystalline phases below the glass transition temperature up to the melting temperature. Furthermore, we have unexpectedly found that the amorphous phase can also be obtained by the unusual route of a very slow cooling of the liquid in some particular experimental set-ups, evidencing the heterogeneous character of the crystallization kinetics of these molecular glass-formers.     

Octahedral fluoride glasses: Raman spectra and structure of niobium pentafluoride

Raman spectroscopy is used to characterize the NbF₅ phases in the temperature range 80–500 K. A new clear glass is formed by quenching the melt to liquid nitrogen temperatures having a glass transition at ～206 K and crystallization at ～233 K. For all phases including the melt, the glass, the supercooled liquid, the crystalline solid and the gas, the Raman spectra show a rather common high frequency band at ～760 cm^?1 which is attributed to the Nb–F terminal frequency of partially bridged ‘NbF₆’ octahedra. Based on the systematics of the Raman spectra for all phases and the literature physicochemical data a model is proposed for the glass and the liquid phases where ‘NbF₆’ octahedral bridged in cis and/or trans configurations form a variety of cyclic and/or chain structures which intermix building up the overall structure. At exceptionally low energies (<11 cm^?1) a rather weak in intensity Boson peak is observed in the glass which shifts to even lower energies with increasing temperature. Librational and/or tortional motions of the bridged octahedra participating in the glass structure are possible candidates for the origin of this peak.