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Glass Transition in Binary Eutectic Systems: Best Glass-Forming Composition Li-Min Wang,* Zijing Li, Zeming Chen, Yue Zhao, Riping Liu, and Yongjun Tian State Key Lab of Metastable Materials Science and Technology and College of Materials Science and Engineering, Yanshan UniVersity, Qinhuangdao, Hebei, 066004 China ReceiVed: May 19, 2010; ReVised Manuscript ReceiVed: August 1, 2010
The glass transition and glass-forming ability in a binary eutectic system of methyl o-toluate (MOT) versus methyl p-toluate (MPT) are studied across the whole composition range. The phase diagram is constructed to explore the best glass-forming composition as the characteristic temperatures of the glass transition, crystallization, eutectic, and liquidus are determined. The best vitrification region is found to locate between the eutectic and the midpoint compositions of the eutectic line, indicating a remarkable deviation from the eutectic composition. The compilation of various simple binary eutectic systems covering inorganic, metallic, ionic, and molecular glass-forming liquids reproduces the rule. Kinetics and thermodynamics in binary systems are investigated to associate with the rule. The composition dependence of the structural relaxation time and the kinetic fragility are presented with dielectric measurements. It is found that whereas mixing of binary miscible liquids kinetically favors glass formation, thermodynamic contribution to the deviation of the best glass-forming composition from eutectics is implied. I. Introduction The development of novel glassy materials on the basis of binary or multicomponent systems depends on the determination of the glass-forming region (GFR), where the crystallization can be avoided during liquid quenching with certain cooling rates. The exploration on glass-forming ability (GFA) of materials has been a subject since the preparation of metallic glasses.1,2 The prediction of GFR still remains a challenge, although various attempts from structural, thermodynamic, kinetic, elastic, and other perspectives are explored.3-8 Empirical explanation, such as the negative mixing heat, multicomponent, and large size difference among components,9 has been proposed to guide the initial alloy composition; however, a specific understanding of the best glass-forming composition is less accessible. Common to glass-forming binary or multicomponent systems is the fact that GFRs are in the vicinity of the eutectic composition, and this directly leads to Rawson law that glass formation occurs most probably in eutectic composition.10 Nevertheless, a number of experimental studies show that the glass-forming region generally deviates from eutectic points.11-14 A modified Rawson law is proposed with the introduction of chemical bond strength;15 however, it does not appear to apply to metallic systems. The access to the best glass-forming composition in a phase diagram is a key to develop the understanding of glass formation, and simple principles to restrict composition to a more localized range in phase diagrams would be an improvement. At a specific supercooling, alloys of lower liquid-solid Gibbs free energy difference are believed to favor glass formation thermodynamically because of the low driving force.1,11,16 For multicomponent systems, T0 curves, where the solid phase holds equivalent Gibbs free energy to the liquid phase in a phase diagram, has been highlighted to guide the glass-forming ability across the whole composition range.17,18 Vitrification is argued * To whom correspondence
[email protected].
should
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to occur provided that T0 temperatures can be circumvented at low temperature because T0 curves define the highest temperature for partitionless solidification of liquids. This therefore allows the determination of GFR.19,20 However, the determination of the T0 curves in a binary phase diagram might involve pronounced uncertainty, which leads to the difficulty in locating the best glass-forming composition.21-23 Kinetic consideration for glass formation basically focuses on the depression of atomic diffusion, and high viscosity or structural relaxation time through whole supercooled liquid region is an advantage. Fragility defines the steepness of temperature dependence of viscosity (or relaxation time) at the glass-transition temperature (Tg), where the structural relaxation time approaches 100 s or viscosity approaches 1012 Pa · s,24-26 and low fragility (m index) largely traces high viscosity (or slow dynamics) of liquids in supercooled liquid regions. Although it is argued that liquid fragility relates to the glass-forming ability of materials,27,28 the determination of the best glass-forming composition from the kinetic studies across the entire composition range has not been much reported. For binary or multicomponent systems, glass formation from liquid quenching is mainly studied in metallic alloys and inorganic materials such as oxide and chalcogenide glasses.29-32 The systems hold relatively low GFA, and the best GFR might not be easily determined.33 Molecular systems, in contrast, have higher GFA and favor the studies of glass formation with regards to phase diagram. However, detailed experimental results of glass formation in such systems are less accessible.34 Whereas glass forms more easily in complex systems with more components, the studies of simple binary eutectic systems would facilitate the understanding of the basic knowledge of glass formation characters because they serve as the “primary” units for more complicated systems. In this Article, we chose molecular systems to investigate the glass formation characteristics of binary eutectic systems, and thermodynamic and kinetic analyses are provided to track the composition dependence. New understanding of glass formation in binary eutectic systems is demonstrated.
10.1021/jp104562c 2010 American Chemical Society Published on Web 08/23/2010
Glass Transition in Binary Eutectic Systems
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II. Experimental Section The binary system of methyl-o-toluate (MOT 99%) versus methyl p-toluate (MPT 99%) is selected in the study. The two chemicals were purchased from Alfa. The isomeric systems are expected to have a small difference in intermolecular interaction force across the whole composition range. This will assist us in examining the Sun-Rawson criterion of glass-forming regions in molecular systems,10,15,35 which emphasizes the ratio of intermolecular bond energies to melting temperatures. It is inferred that if the criterion works out in molecular systems, then the best glass-forming composition would coincide with eutectic composition. The temperatures for both phase transition and glass transition were recorded in a Perkin-Elmer differential scanning calorimetry (Diamond DSC) from the heating, preceded by the cooling at a fixed rate of 20 K/min. Calibration of DSC is done with indium and cyclohexane for high and low temperatures, as described in a previous publication.36,37 For the MPT-rich solutions, the crystallization easily occurs during the heating, preceded by the glass transition, and the characteristic temperatures for glass transition (Tg), crystallization (Tc), eutectic (Te), and liquidus (Tl) are marked. For the MOT-rich solutions, the crystallization requires long-time annealing in the supercooled liquid regions, and we chose a temperature of Tg + 40 K for the isothermal annealing. For some composition (such as MOT 77%), crystallization did not occur, even after more than 6 hours of annealing. The best glass-forming composition is defined at the compositions where crystallization proceeds least easily. The dielectric relaxation was measured in a Novacontrol broad-band dielectric spectrometer (Concept 80) with the frequency-dependent impedance measurements.36,38 We made the dielectric measurements by holding liquid between two brass electrodes, which were separated by thin Teflon strips of thickness 25 µm. The temperature was controlled by a Novacontrol Quatro controller with temperature accuracy within 0.1 K. The dielectric data were analyzed to obtain the dynamic parameters in terms of the Havriliak-Negami equation,39 ε*(ω) ) ε∞ + ∆ε/[1 +(iωτ)R]γ + σdc/iωε0, where ε∞ is the highfrequency dielectric constant, ∆ε is the dielectric strength, τ is the dielectric relaxation time, R and γ are profile shape factors, and σdc is the dc conductivity. III. Results The glass transition and the melting behaviors in the MOT-MPT solutions are plotted in Figure 1 across the whole composition range, and the characteristic temperatures are obtained. With the characteristic temperatures, the phase diagram is constructed, as shown in Figure 2, displaying a typical eutectic character with the eutectic temperature to be 216 K. The thermodynamics of neat MOT and MPT have been previously reported.40 The melting point of MOT measured in this work, Tm ) 231 K, is comparable to the reported result; however, the melting behavior of MPT is not accessible in our measurements. The heat of fusion in MOT is measured to be 28.3 J/g, which gives the entropy of fusion ∆Sm to be 18.5 J/mol · K, remarkably differing from the reported value, 54.5 J/mol · K.40 Our measurement detects two solid-solid phase transitions prior to the melting, and the cumulative entropy is 51.7 J/mol · K, which is comparable to the value of 54.5. The composition dependence of Tg and Tc is also shown in Figure 2. The linear composition dependence of Tg implies near ideal mixing behavior with negligible excess mixing enthalpy, reminiscent of the glasstransition behaviors in solutions with other isomeric molecular liquids.41,42 The width of undercooling (∆T ) Tc - Tg) is
Figure 1. DSC heating measurements for the glassy and crystallized samples in the mixtures of methyl o-toluate (MOT) and methyl p-toluate (MPT), showing the glass transition and the melting. Tg denotes the glass-transition temperature and is determined at a heating rate of 20 K/min, Te is the eutectic temperature, and Tl is the liquidus temperature. The ratio of the two chemicals is in mole fraction.
Figure 2. Phase diagram in the binary systems of methyl o-toluate (MOT) and methyl p-toluate (MPT), featuring a typical eutectic case. Composition dependence of the glass-transition temperature, Tg, is accessible as well. Crystallization temperatures, Tc, in a few MPT-rich mixtures are detected. The eutectic temperature, Te, is 216 K. The shadow area defined the best glass-forming region with the highest glass-forming ability, locating at near- but off-eutectic composition. The thick solid curves are calculated based on the entropies of fusion of MPT and MOT.
observed to increase with MOT toward the eutectic point. The crystallization in 60, 70, and 95 mol % MOT solutions is accessible with annealing, whereas the 77 and 90% MOT solutions are extremely difficult to crystallize; even the longtime annealing does not induce any crystallization. The composition of maximum GFA appears to locate between 70 and 90 mol % MOT, defining the best glass-forming composition in the binary systems. The dielectric relaxation results of the MOT-MPT systems are given in Figure 3. The dielectric loss spectra of tan δ ) ε′′/ε′ for different compositions (inset (a)) and imaginary part ε′′ for the MOT 51%-MPT (inset (b)) are shown. For clarity, we did not present all dielectric measurements of the solutions. A primary dielectric relaxation peak is obvious in Figure 3 (inset) for each measurement, and the fit of the HN equation to
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Figure 3. Dielectric measurements of the binary systems of methyl o-toluate (MOT) and methyl p-toluate (MPT) with four concentrations, showing the temperature dependence of relaxation time, τ. The lines are obtained on the basis of the fit of VFT equation to the data. The dielectric loss of tan δ ()ε′′/ε′) at a fixed frequency is plotted in inset (a), the frequency dependence of imaginary part ε′′ of MOT51%-MPT is given in inset (b), and the temperatures are set from 169 to 193 K with 3 K interval.
the frequency-dependent dielectric constants allows the determination of relaxation times. The temperature dependence of the relaxation time is explained with the Vogel-FulcherTammann (VFT) equation,43 τ ) τ0 exp[B/(T - T0)], where τ0, B, and T0 are constants. The relaxation time curves of the solutions remain basically parallel. Liquid fragility (m index) defined by m ) (d(log τ)/d(Tg/T))|T)Tg is calculated, and the composition dependence of m is obtained. To improve the stability of the calculated fragility index, τ0 is fixed at a constant of 10-22 s for all of the fitting, as applied in previous studies.36,44 IV. Discussion Assuming that solid solubility and solid-liquid heat capacity difference at melting point are negligible, the depression of the freezing point Tm of the solvent with the addition of a solute can be approximately expressed as ln γx ) (∆Sm/R)(1 - (Tm/T)), where R is the gas constant and γ is activity coefficient.45 With the values of ∆Sm for MOT (18.5 J/mol · K from our measurement) and MPT (67.8 J/mol · K from ref 40), the liquidus line is calculated with the assumption of γ ≈ 1, as plotted in Figure 2 with thick lines. The calculated curves show excellent agreement with the experimental data at the MOT- and MPT-rich regions, implying an ideal mixing behavior.46 A key quantity, ∆Sm, therefore controls the profile (slope) of the liquidus line at the region of x f 1 (high activity of γ ≈ 1) in the plot of T/Tm versus x, and small ∆Sm of two components basically leads to deep eutectic temperatures in binary phase diagrams. Figure 2 shows that the best glass-forming composition is not centered around the eutectic composition, displaying a notable deviation from the eutectic. The off-eutectic behavior agrees with the experimental reports in metallic alloys.11,14,47,48 To clarify the basic rule regarding the position of the best glassforming composition, simple glass-forming binary eutectic systems are collected and compiled from refs 49-51. Figure 4 exhibits four typical systems covering ionic (LiAlO4-LiClO4),52 molecular (H2O-ethylamonium nitrate (EAN)),53 metallic (Al-Ge),54 and chalcogenide (GeSe-Sb2Se3)55 glasses. The experimentally accessible glass-forming region in LiAlO4LiClO4 systems is seen off-eutectic. Similar behavior is also
Wang et al.
Figure 4. Glass transition and phase diagram in four systems: (a) ionic LiAlO4sLiClO4, (b) molecular H2Osethylammonium nitride (EAN), (c) metallic Al-Ge, and (d) chalcogenide GeSe-Sb2Te3. The shadow area defines the best glass-forming composition regions. The data are from previously published refs 52-55.
seen in the Al-Ge system with lower GFA. Our recent studies found that EAN-H2O systems have high GFA in wide EANrich regions,53 but the best glass-forming composition is also found to deviate from the eutectic. GeSe-Sb2Te3 systems are somehow different with high solid solubilities, in particular, on the Sb2Te3 side. Strikingly, the best glass-forming composition is still off eutectic. Similar behavior can also be observed in more complex binary systems.56 It is inferred that the deviation of the best glass-forming composition from eutectic composition might be a common behavior in the binary eutectic systems, independent of the kinetics- or thermodynamics-dominant glass formation. Further analyses find that the best glass-forming composition basically locates between the eutectic composition xE and a medium point x1/2, which is defined as the algebraic average of the two maximum solid solubilities (x1 and x2) in the two components, x1/2 ) (x1 + x2)/2. A schematic plot is drawn in Figure 7, showing the possible position of the best glass-forming composition in a eutectic phase diagram. Glass formation has been widely explored, and some parameters such as reduced glass transition (Tg/Tl), degree of supercooling (∆Tx ) Tx - Tg), and similar variables are used to characterize GFA.57-59 Figure 5 gives the composition dependence of Tg/Tl and ∆Tx ) Tx - Tg in the MOT-MPT solutions. The position of the maximum of Tg/Tl does not agree with the best glass-forming composition, and Tg/Tl therefore fails to predict the desirable GFR in eutectic systems. In the region of near eutectic, the crystallization is not easily detected, and the parameter ∆Tx does not, therefore, provide much information. The intermolecular interaction in the binary MOT-MPT system does not vary much with composition, and according to the Sun-Rawson criterion by using the ratio of bond energy to liquidus temperature,13,15 the maximum of the ratio should appear at the eutectic points. The criterion does not appear to be supported by the experimental observation in this work. The studies of the best glass-forming composition in metallic alloys associate the off-eutectic behavior with a skewed eutectic coupled zone.14 Yet, the universal deviation from eutectics (if xE * 0.5) observed in this work can hardly be derived from the microstructure-based explanation. The present results encourage the further exploration with kinetic and thermodynamic consideration. The glass formation kinetics often emphasizes
Glass Transition in Binary Eutectic Systems
Figure 5. Composition dependence of the ratio of glass-transition to liquidus temperature. The composition of the highest Tg/Tl does not coincide with the best glass-forming composition. The composition dependence of the supercooling degree (∆T ) Tx - Tg) is plotted as well.
Figure 6. Composition dependence of relaxation times and liquid fragility in the systems of methyl o-toluate (MOT) and methyl p-toluate (MPT). The relaxation time at the characteristic temperatures is determined by the extrapolation of the low-temperature data (in Figure 3).
J. Phys. Chem. B, Vol. 114, No. 37, 2010 12083 of the relaxation time for the three fixed temperatures. In contrast, along the liquidus temperatures, the longest relaxation time is reached at the eutectic composition, corresponding to the highest viscosity. The high viscosity together with the high Tg/Tm (or narrow supercooling region) proves the eutectic composition to be kinetically the most desirable for glass formation. Figure 6 also gave the composition dependence of fragility, and a minimum value at x ≈ 80% is visible. The decrease in fragility (or a negative deviation) upon mixing agrees with the recently identified universal behavior in binary miscible liquids.60 It is argued that liquids of lower fragility (m index) hold higher GFA.27,28 Apparently, the composition of the minimum m value coincides with the best glass-forming composition. However, a dominant effect of fragility on the best glass-forming composition is not expected from the somehow small (
