Heat capacity of Pd40Ni40P20 in the deeply undercooled liquid state determined by relaxation experiments in the glass transition region

An indirect method is presented which allows for the heat capacity determination of deeply undercooled melts at temperatures in the glass transition region, which are inaccessible to continuous calorimetric measurements. The method is based only on the unique relaxation behavior of glass-forming liquids in the transition region, and thus is generally applicable for vitreous systems. Here it is illustrated by measurements of the specific heat of deeply undercooled Pd₄₀Ni₄₀P₂₀, a metallic bulk-glass former, resulting in a considerable approach of the measurements towards the isentropic limit. Additionally, the consequent application of this method allowed for the determination of the dependence of the glass temperature on the cooling rate during vitrification, yielding a linear relation between the glass temperature and the logarithm of the cooling rate, as observed for several non-metallic glass-forming systems.     

A brief discussion: Thermodynamic and dynamic fragilities,non-divergent dynamics and the Prigogine–Defay ratio

This article brings together some of the work performed by the present author and collaborators that is related to the glass transition event and to some of its entropy aspects. The purpose of the work and discussion was motivated by a view that some of the frameworks in which we currently look at glassy behavior, while potentially useful, may also have limitations that we often do not fully consider. Discussion focuses on isochoric glass formation paths, thermodynamic and dynamic fragilities and how dynamic fragility in many systems (especially polymers, metals, ionic liquids and hydrogen bonding systems) seems to vary primarily with the glass transition temperature itself. This leads to the conclusion that such systems have an apparent activation energy that varies as the square of the glass temperature. The work then discusses evidence for a non-diverging relaxation time or viscosity as the glass temperature is approached and ends with a discussion of the Prigogine–Defay ratio.     

Glassy states: Concentration glasses and temperature glasses compared

The behavior of glass-forming systems in the equilibrium state above the glass temperature is still a heavily investigated field. Surprisingly, the behavior of the glass itself is less widely investigated. Even less investigated is the behavior of glass-forming materials in which composition is changed. Here we look at the behavior of glasses after temperature-jumps and compare that behavior with that of glasses subjected to concentration-jumps. Moisture and carbon dioxide are used as the plasticizing environments. Surprisingly, the glass created by jumping (down) to a given final condition via a change in concentration is more stable than that formed by a change in temperature – this in spite of the external condition of temperature and chemical activity (RH or carbon dioxide pressure) being the same. Furthermore, the concentration glass under such conditions has a higher excess volume than the temperature glass and its response does not ‘merge’ with that of the temperature glass, hence, the concentration glass is not the same as a temperature hyperquenched glass.     

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.     

Discrepancy of structural stability against temperature between metallic liquids and their glasses

The stability of the disordered structure in liquid or glass states could be characterized by the glass-forming ability (GFA) and thermal stability (TS), respectively. The two quantities are often, but not always, positively correlated. Here we show that the discrepancy between GFA and TS originates from the competition between entropy and enthalpy which fairly much relies on local structural characteristics. This inherent interaction and competition determines hierarchy of phase stability against temperature. As a result, the time susceptibility of GFA and temperature susceptibility of TS were derived from the time-temperature-transformation diagram, which are coincided with the above mentioned entropy-enthalpy competition perspective. Thus, the interrelationship among entropy, enthalpy and local cluster feature provides a potential resolution to design and optimize glass formers, and have implications for better understanding the nature of glass transition.     

High mixing entropy bulk metallic glasses

Bulk metallic glasses (BMGs) are usually based on a single principal element such as Zr, Cu, Mg and Fe. In this work, we report the formation of a series of high mixing entropy BMGs based on multiple major elements, which have unique characteristics of excellent glass-forming ability and mechanical properties compared with conventional BMGs. The high mixing entropy BMGs based on multiple major elements might be of significance in scientific studies, potential applications, and providing a novel approach in search for new metallic glass-forming systems.     

Glass transition phenomenology and flexibility: An approach using the energy landscape formalism

The thermodynamic phenomenology of the glass transition in chalcogenide glasses is studied by using rigidity theory, which treats covalent bonding as mechanical constraints. Since flexible systems have a certain number of nearly zero frequency modes (called floppy modes), these modes provide channels in the energy landscape of the glass, and as a consequence, the entropy and fragility depend upon the number of constraints, even for the supercooled melt. Using this approach, the variation of the glass transition temperature with the chemical composition can be obtained from the number of floppy modes, since low frequencies enhance in a considerable way the average quadratic displacement of atomic vibrations. The result reproduces the observed experimental variation of the glass transition temperature with chemical composition.     

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.     

Glass formation in the PbBr2–PbCl2–PbF2–PbO–P2O5 system

New glasses in the PbBr₂–PbCl₂–PbF₂–PbO–P₂O₅ system have been prepared and characterized. The glass-forming regions have been explored and the stability of the glasses against crystallization studied. Results show that the PbBr₂–PbCl₂–P₂O₅ ternary system has a broad glass-forming region which extends to 30 mol% P₂O₅. Most of the glasses in this system show strong stability against crystallization and some have glass transition temperatures as low as 146°C. When 5% PbO or 5% PbF₂ is introduced into the PbBr₂–PbCl₂–P₂O₅ system, the glass-forming region becomes smaller and the glass transition temperatures increase. However, the introduction of 2.5% PbF₂ and 2.5% PbO into the ternary system increases the glass transition temperature and broadens the glass-forming region. The introduction of PbF₂ alone improves the glass-forming ability of the system while the introduction of PbO alone lowers the glass-forming ability.     

Defect model for the mixed mobile ion effect

This paper presents a new defect model for the mixed mobile ion effect. The essential physical concept involved is that simultaneous migration of two unlike mobile ions in mixed ionic glass is accompanied by expansion or contraction of the guest-occupied sites with distortion of surrounding glass matrix; in many cases, an intensity of the local stresses in glass matrix surrounding ionic sites occupied by foreign ions is much greater than, or at least comparable to the glass network binding energy. Hence, when the stress exceeds the breaking threshold, relaxation occurs almost immediately via the rupture of the bonds in the nearest glass matrix with generation of pairs of intrinsic structural defects. The specificity of the mechanism of defect generation leads to the clustering of negatively charged defects, so that rearranged sites act as high energy anion traps in glass matrix. This results in the immobilization of almost all minority mobile species and part of majority mobile species, so mixed mobile ion glass behaves as single mobile ion glass of much lower concentration of charge carriers. Generation of defects leads also to the depolymerization of glass network, which in turn results in the reduction of the glass viscosity and T_g as well as in the compaction of glass structure (thermometer effect). In the spectra of mechanical losses of mixed alkali glasses it reflects as a shift of the maximum in mechanical losses corresponding to the glass transition to lower temperatures, and the dramatic increase of the maximum corresponding to the movement of non-bridging oxygens (so-called mixed alkali peak). The magnitude of the mixed mobile ion effect is defined by the size mismatch of unlike mobile ions, their total and relative concentrations, the binding energy of the glass-forming network, and temperature. Although the proposed model is based upon the exploration of alkali silicate glass-forming system, the approach developed here can be easily adopted to other mixed ionic systems such as crystalline and even liquid ionic conductors.     

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.     

Metallic glass formation in the NiBGe system

Metallic glasses may be formed at transition metal/metalloid ratios substantially removed from the usual 80/20 atom fraction for binary systems such as NiB and CoB. The present investigation is of the NiBGe ternary systems in which the Ge is used as a substitutional probe atom for B in a subsequent EXAFS study. Ribbon samples have been fabricated for a wide range of compositions with metalloid content up to 45 at.%, the glass-forming region of which has been determined by bend ductility, XRD, DSC, SEM, and TEM measurements. Samples found to have relatively low thermal stability also tend to crystallize during ion-milling sample preparation for TEM, or during electron irradiation during TEM observation. Some of the ternary ribbon samples are ductile but are partially crystalline on XRD and TEM investigation. Other samples are brittle but show no crystallites, even after careful TEM study. Most ribbon samples made were fully glassy, as determined by XRD and TEM. The dual glass-forming composition range found in the NiB binary system is alternatively interpreted as a single continuous glass-forming regime, interrupted by an Ni₃B intermetallic region which is of such character as to make metallic glass formation very difficult by melt-spinning.     

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.     

Evaluation of glass-forming ability criterion from phase-transformation kinetics

Applying kinetic analysis upon crystallization of metallic glass, a quantitative relation between the critical cooling rate and the onset temperature of crystallization was obtained for glass-forming alloys. Effects of the onset temperature of crystallization, the liquidus temperature and the glass transition temperature on the critical cooling rate were analytically described. Three rules guiding the development of more reliable glass-forming ability criteria are suggested.     

Effects of solute–solute avoidance on metallic glass formation

An ideal cluster-distribution configuration is proposed for transition metal–metalloid metallic glasses with high glass-forming ability, in which full solute–solute avoidance and multispecies clusters increase the stability of alloy systems. The liquid structure of four typical Fe-based glass former alloys were investigated by ab initio molecular dynamics simulations, and the simulation results and experimental phenomena confirmed the validity of the proposed configuration.     

Structure formation in liquid and amorphous metallic alloys

Bulk metallic glasses developed in last 15 years represent a new class of amorphous metallic alloys. These multi-component metallic alloys can be obtained at relatively low cooling rates, which allow the production of large-scale materials by conventional casting processes. Furthermore, bulk metallic glasses show a glass transition well below the crystallization temperature enabling hot deformation, but also to investigate the glass transition phenomenon in a metallic system. The thermal behavior of Zr- and Pd-based bulk metallic glasses was studied by in situ X-ray diffraction at elevated temperatures. The temperature dependence of the X-ray structure factor of the glassy state can be well described by the Debye theory. At the caloric glass transition the temperature dependence of the structure alters, pointing to a continuous development of structural changes in the liquid state. The short-range order of the glass, of the super-cooled liquid, and of the equilibrium melt is found to be very similar. The existence of complex chemically ordered clusters in the melt is supposed to be related to the high glass-forming ability of the alloys. The microstructure of metallic glasses consisting of elements with negative enthalpy of mixing is homogeneous at dimensions above 1 nm. Phase separation in the liquid state appears in metallic systems with large positive enthalpy of mixing of the elements like Nb–Y. Thermodynamic calculations of the Ni–Nb–Y phase diagram show that the miscibility gap of the monotectic binary Nb–Y system extends into the ternary up to large Ni content. Experimental evidence of the phase separation in ternary Ni–Nb–Y melts is obtained by in situ X-ray diffraction at elevated temperatures and differential scanning calorimetry. The phase separated melt can be frozen into a two-phase amorphous metallic alloy by rapid quenching from the liquid. The microstructure depends on the chemical composition and consists of two amorphous regions, one Nb-enriched and the other Y-enriched, with a size distribution from several nanometers up to micrometer dimension. The experimental results confirm the close relationship between the structure of metallic glasses and the corresponding under-cooled liquids.     

Glass-forming Mg-Cu-RE (RE = Gd, Pr, Nd, Tb, Y, and Dy) alloys with strong oxygen resistance in manufacturability

One of the unsolved problems for the manufacturability and the applications of bulk metallic glasses is that their glass-forming ability is very sensitive to the preparation vacuum and impurity of components because oxygen in the environments would markedly deteriorate the glass-forming ability. Here we report that the addition of rare earth elements can significantly improve the glass-forming ability and manufacturability of Mg-based alloys. The Mg-based glass-forming alloys can withstand very low vacuum in preparation process. The beneficial effects of the Gd addition on the glass-forming ability and oxygen resistance during the Mg-based glass formation are explored.