Prediction of maximum homogeneous nucleation temperature for crystallization of metallic glasses

A graphical method is used to find out the viscosity at any temperature between the melting temperature and glass transition temperature, which in turn is used to predict the temperature corresponding to the maximum in homogeneous nucleation rate. The present approach does not need any critical experimental data and the model predictions are very close to those experimentally measured in known metallic glasses. This model can be applied for both pure metals and glass forming alloys.     

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.     

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.     

Theoretical prediction of bulk glass forming ability (BGFA) of Ti-Cu based multicomponent alloys

The bulk glass forming ability (BGFA) of Ti-Cu based multicomponent alloys has been evaluated via theoretical modeling and computer simulation studies based on a combination of electronic theory of alloys in the pseudopotential approximation and the statistical thermodynamical theory of liquid alloys. The magnitude of atomic ordering energies, calculated by means of the electronic theory of alloys in the pseudopotential approximation, was subsequently used for calculation of the key thermodynamic parameters such as enthalpy, entropy and Gibbs free energy of mixing, viscosity, and critical cooling rate of the binary Ti-Cu and ternary Ti-Cu-X alloys. The potential alloying elements (X) can be divided in two groups defined by their effect on the variation of the negative heat of mixing and their influence on the critical cooling rate. Most of the predicted candidate alloying elements from either X_I (Al, Si, Ag) or X_II (Co, Ni, Fe, Sn, Be) and/or both groups have already been used successfully for the fabrication of new Ti-Cu based bulk metallic glasses. It was also shown that the critical cooling rate appears to be a more important parameter rather than the change in the negative heat of mixing for the prediction of candidate alloying elements improving BGFA.     

Viscous behaviour of undercooled metallic melts

Viscosity data for non-crystalline Au_0.77Ge_0.136Si_0.094 alloys in the region of the glass transition temperature and above the melting point, are fitted to a single expression of the type proposed by Doolittle. This expression also leads to reasonable values for the activation energy for hole formation in the liquid and for the liquid free volume at the glass transition temperature. A similar procedure was applied to the viscosity data of a Pd_0.775Cu_0.06Si_0.165 non-crystalline alloy. By assuming values for the liquid free volume at both the glass transition temperature and the melting point, the analysis is also extended to Pd_0.82Si_0.18 alloys for which no viscosity data are available. Here, time-temperature-transformation (T-T-T) curves for crystallization are calculated for each of the three alloys, and used to determine the critical cooling rates for the formation of an amorphous solid.     

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.     

The kinetics of formation of A AuGeSi metallic glass

The glass-forming ability of a Au_0.778Ge_0.138Si_0.084 alloy is analyzed theoretically by computing a time-temperature-transformation curve which describes the time required to produce a barely detectable fraction of crystallization, at various temperatures. The calculation is based on an interpolated viscosity-temperature curve, this alloy being exceptional among metallic glass formers in that experimental viscous-flow data are available at both high and low temperatures. Allowing for uncertainties, the critical cooling rate for glass formation lies within the range 10⁶?10⁸ K/sec which is in satisfactory agreement with experimental estimates of cooling rates in splat quenching. This and previous comparisons for Ni and PdSi alloys suggest that the approach may have useful and general applicability to metallic glasses.     

Elastic properties of some bulk metallic glasses

The relationships between the elastic moduli, glass forming ability and response to deformation of bulk metallic glasses are investigated. Five bulk metallic glasses are prepared from high purity elements via suction casting. The results confirm that there exists a correlation between energy absorbed to failure during compression testing and the bulk to shear modulus ratio. This finding is developed such that it corresponds only to the elastic component of energy absorption, and that the bulk modulus dominates this. Plastic deformation appears to be favored by a reduced shear modulus, although it shows greater dependence on structural features that are frozen in during the glass transition, and so may well be dependent on the liquid fragility.     

Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids

Here we compile literature data for dynamic fragility m for six types of glass forming liquids: polymers, small molecule organics, hydrogen bonding organics, inorganics, ionic and metallic glass formers. Our analysis of the data shows that different categories of glass forming liquids exhibit different behaviors in terms of the correlation between m and T_g, a correlation not previously examined. For example, for hydrogen bonding organics, polymeric and metallic glass formers, there is an approximately linear increase in m with increasing T_g. While for inorganic glass formers, m appears almost independent of T_g, remaining nearly constant over a wide range in T_g. At the same time, another important parameter, the apparent activation energy E_g at T_g has been investigated. It was found that E_g increases with T_g to the 2nd power for hydrogen bonding organics, polymeric and metallic glass forming liquids, while E_g of inorganic glasses has a linear dependence on T_g.     

Glass formation and crystallization in highly undercooled Te-Cu alloys

The large undercoolings required for glass formation have been achieved by the slow cooling (10-20°C/min) of liquid Te-Cu alloys in the form of a fine droplet emulsion. Within the region of glass formation, between 19 and 39 at.% Cu, DTA measurements indicate that the glass (T_g) and crystallization (T_c) temperatures during heating exhibit a broad maximum at the eutectic. During slow cooling of Te-rich alloy droplets, the maximum undercooling for nucleation increases from 213°C for pure Te to 264°C for Te-12.5 at.% Cu. An enhanced depression of the nucleation (T_n) temperature compared with the change of the liquidus develops in Te-rich alloys upon approaching the glass forming composition range and can be a useful feature in assessing the glass forming tendency. Thermal cycling experiments indicate that even at an undercooling of 181°C crystallization in an eutectic Te-29 at.% Cu alloy is limited by an inadequate nucleation rate in clean droplet samples. For a eutectic alloy, at undercoolings in excess of 200°C crystal nucleation does develop in the droplet samples, but complete crystallization is hindered by a rapidly rising liquid viscosity with increased undercooling.     

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.     

The correlation between the pressure sensitivity and the fragility/glass transition temperature in bulk metallic glasses

The correlations between the pressure sensitivity and the fragility/glass transition temperature have been addressed in various bulk metallic glasses in the present work. The results demonstrate that the pressure sensitivity of bulk metallic glasses is closely related to both the fragility index (m) and the glass transition temperature (T_g). The physical origin of the correlations has been discussed from their disordered structure, which is determined by the glass transition behavior and the glass transition temperature.     

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.     

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.     

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.     

Rheological and thermodynamic behaviors of different calcium aluminosilicate melts with the same non-bridging oxygen content

The relationships between the chemical composition and the derivative rheological and thermodynamic values have been determined for two melt series in the anorthite-wollastonite-gehlenite (An-Wo-Geh) compatibility triangle. The melt series have 0.5 and 1 non-bridging oxygens per tetrahedrally coordinated cation (NBO/T), respectively. The influences of the ratio Si/(Si + AlCa_1/2) and NBO/T on the fragility and the configurational entropy at T_g are evaluated. Linear dependencies of the viscosity, the glass transition temperature and the fragility on the ratio Si/(Si + AlCa_1/2) are found for the two melt series. A crossover in the viscosity-temperature relationship is observed for both series, i.e. an inverse compositional dependence of viscosity in the high and low viscous range. The crossover presumably reflects different responses of the adjustment of melt structure to the substitution of Al³⁺ + 1/2Ca²⁺ for Si⁴⁺ in the low versus the high viscous ranges. The crossover shifts to higher temperature with increasing NBO/T.     

Thermodynamic characteristics of Ti-based glass-forming alloys

Based on thermodynamic characteristics of the stable metallic liquid at melting temperature and the supercooled liquid, the present work calculated the mixing enthalpy ΔH^mix, the mixing entropy ΔS^mix and the Gibbs free energy difference between the supercooled liquid and the resulting crystalline phases ΔG of typical Ti-based amorphous alloys. The results show that for the case of larger ΔS^mix, moderate ΔH^mix for the stable liquid and smaller ΔG for the supercooled liquid, Ti-based alloys tend to achieve high glass-forming ability (GFA). A new parameter, β, defined as (T_g ? T_k)/(T_l ? T_g), has been introduced to evaluate the GFA of Ti-based bulk amorphous alloys (wherein T_g, T_l, and T_k represent the glass transition temperature, the liquidus temperature, and the Kauzmann temperature, respectively). Experimental data imply that the larger the β, the better the GFA for Ti-based amorphous alloys.     

The mechanism of crystal growth in glass forming systems

A critical survey on experimental results on the mode of growth in simple glass forming melts is given, attention being mainly concentrated to data obtained at small undercoolings. Dissolution rates, change of interfacial conditions at constant undercooling as well as detailed structural determinations are considered as experimental evidences, complementary to a thorough analysis of growth-temperature dependences. For network glass formers (SiO₂, GeO₂, P₂O₅, Na₂B₄O₇) with melt structures, similar to those of the corresponding crystals, the normal mode of growth is typical. For a number of simple glass forming substances in which the crystallization is connected with a process of molecular reconstruction (NaPO₃, LiPO₃), spiral growth could be proved. Dislocation-free crystals of high entropy of melting glass forming substances (Na₂S₂O₃ · 5 H₂O, thymol) are obtained after prolonged annealing and growth in thin bored capillaries. Two-dimensional growth is verified for the resulting perfect crystals.     

On the glass transition in vitreous silica by differential thermal analysis measurements

Scanning calorimetry measurements of the glass transition in vitreous SiO₂ (about 120 wt ppm. OH groups) are reported. Data were obtained upon heating after controlled cooling through the glass transition, and after annealing at temperatures between 990 and 1292 K. The onset of the glass transition is at 1247 K, and the supercooled liquid state is reached at 1475 K. The step in the specific heat is (2.9 ± 0.7) J mol⁻¹ K⁻¹. This value, lower than the results of drop calorimetry experiments, agrees with the calculated value from viscosity data. The glass transition is nearly twice as wide as expected from the temperature dependence of the viscosity. Annealing reduces the enthalpy of glasses as usually expected, and the corresponding entropy decrease is in agreement with results for other network glasses. In vitreous silica, depending on the annealing temperature, both exothermic and endothermic processes take place. Based on Davis’ and Tomozawa’s results, endothermic processes upon annealing are attributed to the diffusion of the OH groups.     

On the dependence of the properties of glasses on cooling and heating rates: I. Entropy, entropy production, and glass transition temperature

The glass transition is theoretically described in terms of a generic non-equilibrium thermodynamics approach employing De Donder's structural order parameter method, appropriate expressions for the relaxation behavior of glass-forming systems and a simplified but qualitative correct model of glass-forming melts with one order parameter related to the free volume of the system. Employing this approach the behavior of a variety of thermodynamic quantities describing glass-forming systems in vitrification and devitrification processes is interpreted theoretically. The present paper is devoted to the computation of the entropy, the entropy production and the glass transition temperature in dependence on the cooling and heating rates, varying latter parameter in a broad interval. A comparison with experimental results is given and some further consequences and possible extensions are discussed briefly.