On the glass transition in metallic melts

doi:10.1016/j.jnoncrysol.2007.05.121

Journal of Non-Crystalline Solids

Volume 353, Issues 32–40, 15 October 2007, Pages 3318-3326

https://doi.org/10.1016/j.jnoncrysol.2007.05.121 Get rights and content

Abstract

Experimental determinations of the glass transition and related properties in alloys are reviewed. Several recent measurements of viscosity, specific volume and heat capacity in the undercooling regime have become possible after the discovery of bulk glass forming alloys. The data allow verification of models on the kinetics and thermodynamics of such melts. The notion of melt fragility, borrowed from the description of inorganic and molecular glasses, has become popular also for metallic alloys: the kinetic fragility is described by the viscous behavior of the liquid and the thermodynamic fragility by the entropy loss on undercooling. The experimental viscosity data for metallic glass formers presently available can be reasonably framed within the strong–fragile classification. On the other hand, there are major discrepancies for the thermodynamic fragility of metallic glass formers with respect to conventional ones. The reason for such disagreement is twofold: on the experimental ground there are difficulties in obtaining fully reliable thermodynamic data in sufficiently wide temperature ranges; on the conceptual side the definition of the configurational entropy of the liquid with a suitable reference state is controversial. Among fragility indexes, the reduced width of the transition range proves most useful. The trend of the glass transition as a function of composition is also discussed in relation to the progressive ordering of the liquid on undercooling.

Introduction

The glass transition is the distinctive feature of amorphous solids synthesized via the freezing of the liquid phase. Glasses can be obtained in all materials classes provided that the liquid is cooled at a rate suited to bypass the nucleation and growth of crystals. When a glass forming melt freezes into the glassy state its viscosity is high and the mobility of the constituent species is low [1]. This can occur in different temperature ranges. The best glass formers have high viscosity already at elevated temperatures, say above the melting point, but there are numerous examples of glasses obtained with substances of relatively low viscosity at high temperatures. For these the kinetics of crystal formation is depressed in the undercooling regime, e.g., when the crystal packing cannot be easily achieved because of low molecular symmetry or when crystals are structurally complex [2]. Therefore, although glass formation is correlated with high liquid viscosity at high temperature, this appears as a necessary but not exhaustive condition.

Metals conform to the above general behavior. Numerous alloys can be vitrified at elevated cooling rates of the melt in the form of thin long ribbons in order to prevent the occurrence of either stable or metastable crystal phases [3]. It is now about a decade that glassy alloys have been obtained in various systems at cooling rates comparable to those employed for conventional glasses [4]. It has been shown that the viscosity of such liquids is much higher than that of other metallic melts already at their melting point, T_m. The viscosity then increases continuously for several orders of magnitude on undercooling causing the glass transition to be reached at temperatures in excess of 0.6 T_m. However, glassy alloys are obtained in bulk form also with alloys having lower viscosity for which the glass transition is reached at temperatures of the order of 0.5 T_m [5], [6]. The reasons for the diverse behavior of metallic melts are not fully understood.

Glass forming liquids have been classified according to their strength or, alternatively, fragility. The fragility is measured by the rate with which some liquid properties change on undercooling. Typically, the viscosity of a strong liquid increases regularly with decreasing temperature as shown by linear trends in an Arrhenius plot, whereas the viscosity of a fragile liquid increases faster when approaching the glass transition [7]. For conventional glass formers this indicates that there is a single microscopic mechanism determining the viscosity, e.g., the breaking and forming of Si–O bonds in silica. For fragile liquids (e.g., molecular liquids) viscosity is determined by the motion of a few molecules at high temperature and by collective rearrangements of several molecules at low temperature. In terms of energy, the liquid has been described by means of a potential energy landscape made of various basins (i.e., local minima) which it can sample by means of activated processes. A strong liquid can be represented with a homogeneous energy landscape where a principal deep basin predominates with respect to less prominent potential wells whereas in a fragile liquid the energy landscape is complex with several basins of comparable depth. Relaxation times for atoms or molecules sampling the alternative energy landscapes, should be markedly different, especially at low temperature, because of the probability of being trapped in basins of different depth. The liquid viscosity reflects such variation of relaxation times [1].

The thermodynamic counterpart of this picture of transport properties, is that the extensive thermodynamic quantities should display changes on undercooling. The indication of the sampling of various landscape configurations is that fragile liquids should loose entropy faster than strong ones when approaching the glass transition [8].

Experimental evidence of the glass transition in metallic systems is usually provided by analyses with differential scanning calorimetry (DSC) performed on heating the sample. After suitable calibration of the instrument the calorimetric trace gives the apparent specific heat of the material, C_p, and displays a jump in a temperature interval corresponding to the transition from the glassy structure to the undercooled liquid, provided that this is not obscured by the impending crystallization. The glass transition temperature, T_g, is often taken as the onset of the jump [9]. With the advent of bulk metallic glasses viscosity and specific volume data of the liquid phase have become available in temperature ranges sufficiently wide to provide further evidence of the transition. The strong–fragile distinction has been applied to these data, but extensive probing of the correlation between kinetic fragility as expressed by viscosity behavior and thermodynamic fragility as given by the entropy loss on undercooling, is still lacking [10].

Finally, it has been reported in various instances that decoupling of viscosity and translational diffusion occurs around 1.2 T_g implying that the inverse relationship between viscosity and diffusivity (Stokes–Einstein equation) fails. One of the consequences is that the diffusivity in the metallic glass needed for the description of crystal nucleation and growth cannot be derived from the viscosity [1], [2], [11].

In this paper a few distinctive experimental evidences on the glass transition and on the related properties are discussed at first. The most used expressions for the description of viscosity of the liquid are then introduced, either phenomenological or with reference to the free volume and configurational entropy models, to obtain parameters for the kinetic fragility of metallic melts. Then, thermodynamic data are reviewed to evaluate thermodynamic fragility showing that a parameter derived from calorimetric measurements is most suited for the correlation with the kinetic fragility. The entropy model of the viscosity is finally employed to discuss the temperature dependence of the glass transition in alloys.

Section snippets

Experimental evidences regarding the glass transition in metallic alloys

Most glass transitions in alloys have been revealed by DSC as an endothermic step with sigmoidal shape of the specific heat extending from the onset temperature, T_g, to the end temperature, T_f. Although a better accuracy could be reached by taking the inflection point in the C_p curve, the onset is usually taken as the glass transition temperature because this temperature more closely corresponds to the definition of T_g in terms of viscosity (η(T_g) = 10¹² Pa s) and, for practical purposes, is more

Viscosity models

The viscosity of liquid metallic elements and alloys at high temperature is well represented by an Arrhenius behavior. At the melting point the viscosity can be computed by means of the Andrade formula [20] $η (T_{m}) = A_{C} \frac{\sqrt{{MT}_{m}}}{V_{m}^{2 / 3}},$ with V_m molar volume and M the average atomic weight. The proportionality coefficient A_C has the value 1.8 × 10⁻⁷ ± 0.1 (J K⁻¹ mol^1/3)^1/2 and holds for elements, intermetallic compounds and normal eutectics (normal eutectics occur in systems having ideal behavior in the liquid or

The fragility of metallic melts

The available viscosity data for metallic glass forming melts are collected in Table 1 in the form of a VFT parameters and the VFT curves are plotted in Fig. 5 versus T_g/T (Angell plot). T_g is taken as the calorimetric onset of the transition determined at the rates of either 10 or 20 K/min. As a consequence, the temperature may not correspond strictly to the conventional temperature where viscosity becomes 10¹² Pa s, so log η curves scatter around the 12 value at T_g/T = 1. Care was taken in

Composition dependence of T_g

Metallic glasses can be produced in definite composition ranges. The AG equation suggests a mean to study the composition dependence of the glass transition properties. At any given temperature the entropy of a binary liquid alloy can be written as a function of the molar fraction of components, x_i, as $S_{c} (T) = x_{A} S_{A} (T) + x_{B} S_{B} (T) + Δ S_{mix},$ where S_i are the entropies of pure components and ΔS_mix is the entropy of mixing in the liquid state. The difference in entropy of the liquid between a high and a low

Conclusions

Metallic alloys conform to the general behavior of glass forming melts. There are now data available for liquid specific heat, enthalpy, specific volume, viscosity spanning wide ranges of the undercooling regime with which the applicability of models for glass formers can be confidently checked. Attention has been posed on alloys able to give metallic glasses in bulk form having reduced T_g well above 0.6. A classification for these alloys is provided by the strong/fragile scheme based on

Acknowledgements

Studies on thermophysical properties of alloys are supported by ESA-ESTEC Contract no. 14306/01/NL/SH-MAP Project No. AO-99-022 ‘Thermolab’.

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¹: Present address: Inst. für Metallforschung und Metallurgie, ETH Zentrum, 8092 Zürich, Switzerland.

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On the glass transition in metallic melts

Abstract

Introduction

Section snippets

Experimental evidences regarding the glass transition in metallic alloys

Viscosity models

The fragility of metallic melts

Composition dependence of Tg

Conclusions

Acknowledgements

Mater. Sci. Eng. A

Acta Mater.

J. Phys. Chem. Solids

J. Non-Crystal. Solids

J. Non-Crystal. Solids

J. Non-Crystal. Solids

Mater. Lett.

Acta Mater.

Acta Metall.

J. Non-Crystal. Solids

J. Non-Crystal. Solids

J. Non-Crystal. Solids

Acta Metall.

Acta Metall.

Mater. Sci. Eng.

J. Non-Crystal. Solids

Intermetallics

J. Non-Crystal. Solids

Acta Mater.

Mater. Sci. Eng. A

J. Non-Crystal. Solids

Acta Metall.

Nature

Int. J. Rapid Solidification

Composition dependence of T_g