Article pubs.acs.org/JPCB
Anomalous Crystallization as a Signature of the Fragile-to-Strong Transition in Metallic Glass-Forming Liquids Xiunan Yang,†,‡,⊥ Chao Zhou,† Qijing Sun,† Lina Hu,*,† John C. Mauro,§ Chunzhen Wang,† and Yuanzheng Yue†,∥ †
Key Laboratory of Liquid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China ‡ Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China § Science and Technology Division, Corning Incorporated, Corning, New York 14831, United States ∥ Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark ABSTRACT: We study the fragile-to-strong (F−S) transition of metallic glass-forming liquids (MGFLs) by measuring the thermal response during annealing and dynamic heating of La55Al25Ni5Cu15 glass ribbons fabricated at different cooling rates. We find that the glasses fabricated in the intermediate regime of cooling rates (15−25 m/s) exhibit an anomalous crystallization behavior upon reheating as compared to the glasses formed at other cooling rates. This anomalous crystallization behavior implies the existence of a thermodynamic F−S transition, could be used as an alternative method for detecting the F−S transition in MGFLs, and sheds light on the structure origin of the F−S transition. This work also contributes to obtaining a general thermodynamic picture of the F−S transition in supercooled liquids.
I. INTRODUCTION
Thus far, the experimental studies of the F−S transition in MGFLs are mainly confined to kinetic methods, that is, by measuring temperature dependences of viscosity or specific volume during heating or cooling the liquids.7−10 In addition to these kinetic measurements, it is also of interest to probe the thermodynamic aspect of the F−S transition. This aspect was first proposed by Angell,14 and further related to the abrupt nonmonotonic changes of enthalpy during cooling by Lad based on classical molecular dynamics simulations on Cu−Zr MGFLs.15 However, clear thermodynamic evidence of the F−S transition is still deficient. Recently, by using the hyperquenching−annealing−calorimetric approach, some of the present authors have observed a three-stage sub-Tg enthalpy relaxation pattern in CuZrAl hyperquenched (HQ) glass ribbons (GRs).16,17 Usually, the onset temperature sub-Tg relaxation (Tonset) or the sub-Tg relaxation energy for HQ glass formers (e.g., oxide systems) monotonically depends on the annealing temperature (Ta).18,19 This tendency is expected because the energy trapped in the GRs by hyperquenching will be released upon reheating, and the released amount monotonically increases with increasing Ta for a given duration. However, in contrast to this normal tendency, CuZrAl exhibits an anomalous sub-Tg relaxation pattern, that is, a nonmonotonic Ta dependence of the Tonset or the released energy
The dynamic and thermodynamic evolution of supercooled liquids upon cooling is an essential problem in glass transition physics.1,2 This problem has become even more intriguing and complicated since a new dynamic and thermodynamic phenomenon, the fragile-to-strong (F−S) transition, has been observed. The F−S transition refers to a scenario where, upon cooling, the viscosity of a glass-forming liquid above its liquidus temperature can transform from a highly non-Arrhenius dependence on temperature (fragile) to an Arrhenius-close dependence (strong). For the liquid showing the F−S transition, a high fragility index (m) will be obtained by extrapolating the high temperature viscosity data (e.g., around liquidus temperature) to the glass transition temperature (Tg) by means of a viscosity model. Yet when only the viscosity data around Tg are fitted to a viscosity model, a lower m value will be derived. In contrast, for a fragile liquid or a normal liquid without the F−S transition, an identical m value will be obtained either from high or from low temperature viscosity data. The F−S transition does not occur in fragile liquids, but does in many types of relatively strong glass-forming systems such as water,3 SiO2, BeF2, and Al2O3−Y2O3,4−6 and metallic alloys.7−10 To understand the underlying mechanism of the F− S transition, two different competing local structures, polyamorphism, or other similar effects have been explored.11−13 The F−S transition might be a general phenomenon of metallic glass-forming liquids (MGFLs).9 © 2014 American Chemical Society
Received: May 4, 2014 Revised: July 15, 2014 Published: August 12, 2014 10258
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during the sub-Tg relaxation. This behavior is associated with the F−S transition.18,19 These observations suggest that the structures at high and low temperatures in MGFLs are quite different and that the structures in supercooled liquids evolve nonmonotonically during the F−S transition. However, the three-stage sub-Tg relaxation pattern seems indistinct in rareearth-based glass ribbons. For these systems, the evolution of enthalpy and the stability of structures implied by Tonset in GRs display a monotonic dependence on temperature in the supercooled region accompanying the F−S transition.17,18 Now the question arises: for these rare-earth based MGFLs, what are calorimetric signatures of the F−S transition? Answering this question is important for understanding the theoretical framework of the F−S transition in supercooled liquids.1,14 To explore the calorimetric signatures of the F−S transition in the rare-earth-based MGFLs, we mainly investigate the cooling rates dependence of crystallization behavior in La55Al25Ni5Cu15 HQ GRs by performing a series of hyperquenching−annealing−calorimetry experiments. It has been found that the crystallization behavior of La55Al25Ni5Cu15 HQ GRs fabricated around 15−25 m/s is different from that of the GRs made at other cooling rates. The corresponding fictive temperatures Tf of the former GRs fall into the F−S transition temperature range determined by both experimental kinetic methods and atomistic simulations. This anomalous crystallization behavior therefore implies the existence of a thermodynamic F−S transition and could be used as an alternative method for detecting the F−S transition in MGFLs. This work, along with our previous work on the three-stage sub-Tg enthalpy relaxation pattern in CuZrAl HQ GRs,16,17 contributes to obtaining a general thermodynamic picture of the F−S transition in supercooled liquids.
Figure 1. DSC curve of fresh HQ La55Al25Ni5Cu15 GRs. Tg,HQ is the onset temperature of glass transition for HQ GRs. Inset: The enthalpymatching method to calculate the fictive temperature Tf by Cp1 and Cp2. Here, Cp1 and Cp2 represent the typical heat capacity curves of fresh La55Al25Ni5Cu15 HQ GRs and standard glasses measured during the first upscan, respectively.
aforementioned tangents, and an intersection (C) point is given. The tangent of the DSC curve at C intersects with the tangent at B, thereby giving Tg,HQ (D). The fundamental meaning of Tg,HQ will be clarified in section III.2. The fictive temperature (Tf) of the fresh GRs can be increased by raising the ribbon spinning rate (from 10 to 40 m/s). Hereafter, the ribbon spinning rate is used to represent the cooling rate. The Tf of a glass is the temperature at which the structure of equilibrium liquid is frozen in. The structural evolution in high Tf glass ribbons during sub-Tg relaxation reflects the structural changes in supercooled liquids during cooling. The inset of Figure 1 shows how to determine the fictive temperature Tf of GRs by the enthalpy-matching method.24 Here, Cp1 and Cp2 represent the heat capacity curves of fresh La55Al25Ni5Cu15 HQ GRs and standard glasses (i.e., those obtained at the standard cooling rate of 10 K/min) measured during the first upscan, respectively. The detailed procedure for the determination of Tf is described elsewhere.17,24 To determine the activation energy for the glass transition or crystallization in the fresh HQ GRs, the relevant parameters (i.e., E and const) were calculated from the DSC curves of HQ GRs using Kissinger’s equation:25
II. EXPERIMENTAL PROCEDURES In this work, we conduct a series of hyperquenching− annealing−calorimetry experiments.20,21 Hyperquenching (i.e., cooling at 104 to 1010 K/s)22 was used to trap high potential energy microstates of the supercooled liquid into solid glass. The La55Al25Ni5Cu15 alloys were prepared by arc-melting the elemental metals with purities ranging from 99.9% to 99.999%. The samples were melted four times under a high pure argon atmosphere for homogeneity and then spun into HQ GRs under pure argon using a single melt spinner 190 mm in diameter. The noncrystalline nature of all of the fresh HQ samples was confirmed by X-ray diffraction experiments. The HQ states in glass allow us to explore thermodynamics, dynamics, and also structural evolution of supercooled liquids in real time during the subsequent calorimetric protocol. Upon calorimetric upscanning, the thermal responses of the 20 ± 0.5 mg fresh HQ GRs were detected at different heating rates (2− 40 K/min) using a Netzsch DSC 404 calorimeter with highpurity standard Al2O3 crucibles in argon. The heat flow (DSC) signals are then obtained. The largest error range of temperature for our calorimeter is 1 K. To determine the heat capacity (Cp) curve of the GRs, both the baseline and the reference sample (sapphire) were measured. The heat capacity curve is only used for the calculation of Tf. Figure 1 illustrates the determination of the characteristic temperature Tg,HQ for the HQ GRs.23 The tangents at the point of maximum (A) and minimum (B) in the DSC curve are plotted, respectively. A third straight line parallel to the horizontal axis then is plotted equidistant between the two
ln(R h /T 2) = −E /(RT ) + const
(1)
where E is the corresponding activation energy at T, Rh is the heating rate, and R is the gas constant. Here, T refers to Tg,HQ or Tp (the main crystallization peak temperature). For each measurement, the fresh GRs were heated from room temperature to the crystallization temperature with Rh of 2− 40 K/min. The values of E were finally determined by the slope of the corresponding fitted line where the variation of ln(Rh/ T2) is plotted against 1000/T. A recent investigation of the kinetics of glass transition of rare-earth based glasses has verified that eq 1 is suitable for describing not only thermally activated processes, but also thermal relaxation (i.e., at Tg,HQ in the present work).23 It has been found that the activation energies calculated from the Moynihan26 and Kissinger equations25 are in good agreement with each other. The 10259
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Figure 2. Influence of the DSC upscan rate on the crystallization peak of the fresh HQ La55Al25Ni5Cu15 GRs fabricated at (a) 10 m/s, (b) 20 m/s, (c) 30 m/s, and (d) 40 m/s.
Figure 3. Influence of the DSC upscan rate on the crystallization peak in the fresh HQ La55Al25Ni5Cu15 GRs fabricated by (a,b) 15 m/s and (c,d) 25 m/s.
temperature and is both enlarged and sharpened. This tendency, which has also been observed in Figure 2b−d, is reasonable but not the emphasis of our current work. Here, we draw the reader’s attention to the difference between Figure 2b and the other plots in Figure 2. In Figure 2b, at 40 K/min only one crystallization peak is observed in the range of 510−550 K. Below 40 K/min, this peak splits into one peak and one shoulder. This phenomenon occurs in the fresh HQ GRs cooled at 20 m/s, but not in the fresh HQ GRs cooled at 10, 30, and 40 m/s. This indicates that the structure in the fresh HQ GRs frozen at 20 m/s differently responds to dynamics heating as compared to the other three GRs.
difference between these two equations is within experimental error, although these two models are derived from different theoretical approaches.23
III. RESULTS AND DISCUSSION 1. Cooling Rate Dependence of Crystallization Pattern. Figure 2 shows the heating rate dependence of the DSC curve during the crystallization process for the fresh HQ La55Al25Ni5Cu15 GRs fabricated at different cooling rates. In Figure 2a, when the heating rate is 5 K/min, there is a small exothermic peak in the range of 510−530 K. With an increase in the heating rate, this exothermic peak shifts to higher 10260
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Furthermore, various heating rates were used for DSC upscans on the fresh HQ GRs formed at 15 and 25 m/s. Figure 3 shows the DSC upscan rate dependence of the crystallization peak of these fresh GRs. For the GRs formed at 15 m/s, there is only one crystallization peak for heating rates in the range of 5−40 K/min, similar to what has been found in the GRs of 10, 30, and 40 m/s in Figure 2. However, Figure 3b shows that when the heating rate decreases to 3 K/min, a splitting of the crystallization peak can be observed. For 25 m/s, shown in Figure 3c and d, the main exothermic peak splits into one peak and one shoulder at the heating rate ≤5 K/min. In contrast, for the HQ GRs at 10, 30, and 40 m/s, the crystallization peaks are not split, even if the heating rate is reduced to 2 K/min (not shown in this Article). In accordance with Figure 2, Figure 3 confirms that the splitting of the crystallization peak is not an artifact of the way in which the experiments are conducted. Figure 4 shows the ribbon spinning rate (i.e., cooling rate) Figure 5. Ribbon spinning rate (i.e., cooling rate) dependence of activation energy of crystallization (Ep) and glass transition (Eg,HQ) for the fresh HQ La55Al25Ni5Cu15 GRs. Dash−dot line: Expected from glasses without a F−S transition.
(activation energy at Tg,HQ) values of the fresh HQ GRs at different cooling rates were calculated using eq 1 and are shown in Figure 5 (●), including the value of Eg for the standard glass.28 In Figure 1, Tg,HQ is different from Tg of the standard glasses due to the existence of a substantial Hrem (the area between the Cp curves of the standard glasses and the HQ GRs as shown in the inset of Figure 1) frozen in the fresh GRs. Both the α and the slow β relaxations contribute to the release of Hrem during reheating of the fresh GRs. The theory of the potential energy landscape,29,30 as well as the experimental results on the sub-Tg relaxation of metallic glasses in refs 17 and 18, have indicated that a faster cooling rate leads to a greater contribution of the slow β relaxation to Hrem. Because the activation energy of the slow β relaxation is much less than that of the α relaxation, it is expected that the values of Eg,HQ of the fresh GRs would increase monotonically with the cooling rate decreasing during glass formation. In other words, there should be a negative relationship between Eg,HQ and the cooling rate. If the cooling rate decreases to 20 K/min (leading to the standard glasses), Hrem will disappear, resulting in Eg,HQ approaching the activation energy of the α relaxation (i.e., Tg,HQ ≈ Tg). In Figure 5, it is found that by reducing the cooling rates from 40 to 30 m/s, Eg,HQ increases from 201 to 246 kJ/mol. This negative relationship agrees well with the trend shown by the dash−dot line in Figure 5. However, with the cooling rate decreasing to 25 m/s, this negative relationship is interrupted as Eg,HQ decreases distinctly beyond the error range of the measurements. At 20 m/s, Eg,HQ is even lower. The expected relationship does not recover until the cooling rate is greater than 25 m/s. Therefore, the abnormal regime where Eg,HQ is significantly lower is 15−25 m/s. Note that the regime is identical to the abnormal regime in Figures 2−4 and that in Figure 5. It is seen that in the cooling rate regime of 15−25 m/s, the number of crystallization peaks (Figures 2 and 3), the main crystallization peak temperature (Figure 4), and the activation energy at the main peak temperature (Figure 5) deviated the trend derived from other cooling rate regime. It is known that a more unstable structure tends to have smaller activation energy and a lower activated temperature for relaxation. Thus, both the anomalous cooling rate dependence of Ep and Eg,HQ in Figure 5
Figure 4. Influence of ribbon spinning rate (i.e., cooling rate) on the main crystallization peak temperature (Tp) of the fresh HQ La55Al25Ni5Cu15 GRs at DSC upscan rates ranging from 5 to 40 K/ min.
dependence of the main crystallization peak temperature (Tp) at each DSC upscanning rate. For each curve in Figure 4, the change of Tp with cooling rate is similar for all heating rates. For instance, at 5 K/min, the value of Tp is nearly equal for the 10, 30, and 40 m/s cooled samples, while there is a distinct decrease of Tp for sample cooled at 15−25 m/s by 15−20 K. This phenomenon is also observed in other heating rates curve in Figure 4. Note the cooling rate regime (15−25 m/s) where the main crystallization peak advances in Figure 4 is the same as the regime where the split of crystallization peak is observed in Figures 2 and 3. The Ep values (activation energy at Tp) calculated from Figures 2 and 3 by eq 1 are plotted in Figure 5 as a function of ribbon spinning rate (⊙). On the basis of the change in Gibbs free energy for the crystallization of MGFLs from an undercooled liquid,27 a slower cooling rate leads to a larger barrier for crystallization. In this context, with a decreasing cooling rate, the magnitude of Ep should increase monotonically, as depicted by the dash−dot line in the figure. In Figure 5, however, the change of Ep with cooling rate is nonmonotonic and displays a three-stage behavior. The Ep values for the glasses cooled at 15−25 m/s (see the shaded area) fall far below the dash−dot line. This distinct drop accords with the decrease of Tp for the same samples in Figure 4. Eg,HQ 10261
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and the drop of Tp in Figure 4 imply that the structure of the La55Al25Ni5Cu15GRs becomes unstable within a certain cooling rate regime (15−25 m/s). Note that the main crystallization peak splits into one peak and a shoulder (Figures 2 and 3) in the cooling rate range where Eg,HQ and Ep deviate from the linear trend. The split also suggests that during cooling there are more types of local structures with different tendencies to crystallize in the cooling rate regime (15−25 m/s). Therefore, in the Tf range corresponding to 15−25 m/s, the supercooled liquids tend to become more heterogeneous. By using the enthalpy-matching method (Figure 1), the Tf values of the fresh HQ GRs quenched at 25 and 15 m/s are calculated to be 585 K (1.31Tg) and 562 K (1.26Tg), respectively. The former could be regarded as the onset temperature and the latter as the ending temperature of an unusual structural evolution in the supercooled liquid region of La55Al25Ni5Cu15 during cooling. 2. Correlations between the Abnormal Crystallization and F−S Transition. The nonmonotonic effect of temperature (Tf in the present work) on the crystallization behavior accords with what has been observed by changing pressure on La62Al15.7(Cu0.5Ni0.5)22.3 bulk metallic glasses.31 When the applied pressure ranges from 3.5 to 4 GPa, both the positions and the number of crystallization peaks exhibit unexpected changes that are quite different from those present at higher or lower pressure. In the literature, this pressure-induced phase transition has often been regarded as evidence for polyamorphism in glasses.32−34 The correlation between the pressure-induced polyamorphism and the temperature-induced F−S transition phenomenon has been depicted by the P−T diagram based on Jagla’s model.11 It has also been reported that increasing pressure or decreasing temperature could result in the same F−S transition.35 As experimental evidence, the nonmonotonic effects of pressure on the crystallization process or the microstructural characteristics have been reported in the Zr-, rare earth-based, and Mg-BMGs,33,34,36,37 for which the F− S transition was observed in the corresponding supercooled liquids.9 Therefore, the abnormal crystallization behavior exhibited by the GRs fabricated at 15−25 m/s, that is, the Tf-induced nonmonotonic crystallization behavior in the present work, is closely related to the F−S transition in La55Al25Ni5Cu15 MGFLs. Different from the kinetic F−S transition phenomenon observed by the viscosity measurements in MGFLs,7−9 this anomaly in crystallization behavior observed by DSC measurements concerns the thermodynamic aspect of the F−S transition in the supercooled liquids. Figure 6 shows a comparison of the temperature range of the thermodynamic F−S transition Tf,c with that of the kinetic F−S transition Tf‑s for La55Al25Ni5Cu15 MGFLs. The Tf‑s value was determined on the basis of viscosity measurements of the La55Al25Ni5Cu15 MGFL both in the high-temperature (fragile) regime using an oscillating viscometer and in the lowtemperature (strong) regime based on DSC data. These data are fit to the extended Mauro−Yue−Ellison−Gupta−Allan (MYEGA) model for viscosity given in ref 9 (see the solid black curve). Because direct viscosity measurements are not feasible in the F−S region itself for this composition, the range of the F−S transition is determined by interpolation with the extended MYEGA model. Figure 6 shows that the Tf,c value determined in the present work lies in a much narrower temperature range than the kinetic Tf‑s value and is centered at the low temperature end of the kinetic F−S transition region. This difference between Tf,c and Tf‑s accords well with the thermodynamic evidence of the F−S transition observed in the
Figure 6. Comparison of the thermodynamic F−S transitions with the kinetic F−S transitions in La55Al25Ni5Cu15 MGFLs. The viscosity data in the whole temperature range are plotted on the basis of the model parameters given in ref 9, as depicted by the solid curve. The two dashed curves represent the fits to measurements in the fragile and strong temperature regimes, respectively.
CuZrAl MGFLs by hyperquenching strategy17 and in the CuZr alloys by molecular dynamic simulation studies.15 In these simulations, the enthalpy of supercooled liquids changes abnormally at 1.2−1.3Tg, also at the low temperature end of the kinetic Tf‑s range. Here, we give two possible explanations for the shift in the F−S transition region detected by thermodynamic methods relative to the kinetic F−S transition. First, the fitting parameters of the MYEGA model could be exaggerating the width of the kinetic F−S transition in MGFLs due to the lack of sufficient viscosity data for fitting within the F−S transition range itself.9 Because there are no direct viscosity measurements within the F−S transition range itself, the positioning of the kinetic F−S transition is determined by fitting of the model parameters to data on either side of the transition region. While the fit is optimized by minimizing the mean squared error between the model and measured results, the fit itself is not necessarily unique and will be more accurate if additional viscosity data are available in the F−S transition regime. Second, the F−S transition determined by thermodynamic aspect is based on a mapping of the complicated thermal history of the glass to a single effective Tf. Tf is an approximated average value reflecting the average enthalpy in the entire sample. The shift between the thermodynamic and kinetic F−S transitions could be explained by the fast kinetics that occur in the higher-temperature part of the kinetic F−S transition; that is, the relaxation rate of the fragile phase increases in a superArrhenius fashion, making it difficult to trap any regions of the glass in the fragile phase. At this point, further experimental studies are necessary to get a more precise explanation. For La55Al25Ni5Cu15 MGFLs, the thermodynamic aspect of the F−S transition is manifested as an anomaly in crystallization behavior of HQ GRs. During sub-Tg relaxation below Tg,HQ, we did not observe the abnormal three-stage sub-Tg relaxation pattern even for the GRs fabricated at 20 m/s, as shown in Figure 7a. In other words, the remnant excess enthalpy Hrem of the fresh GRs is released gradually with the increase in the annealing temperature Ta. A similar phenomenon has also been found for pressure-induced effects in La62Al15.7(Cu0.5Ni0.5)22.3 10262
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Figure 7. Sub-Tg relaxation pattern of the HQ GRs (a) La55Al25Ni5Cu15 with the cooling rate 20 m/s, and (b) Cu45Zr45Al10. Reprinted with permission from ref 16. Copyright 2011 American Institute of Physics. All of the Cp curves were obtained at a heating rate of 20 K/min.
BMG.31 There the pressure at ambient temperature has little influence on the glass transition, although there are distinct pressure-induced changes in crystallization peaks. This trend follows the energy release of normal glass formers.18,19 In contrast, for Cu-based MGFLs, the thermodynamic aspect of the F−S transition has been depicted by the nonmonotonic Ta dependence of Hrem before crystallization of the GRs (see Figure 7b).16,17 In Figure 7b, the three-stage sub-Tg relaxation pattern of Hrem can be discerned, which manifests itself as the nonmonotonic Ta dependence of the onset release of the trapped excess energy in the glasses, Tonset. From curve A to D, Tonset increases with Ta monotonically (Ta ≤ 593 K). From curve E to H, Tonset decreases with Ta (613 K ≤ Ta ≤ 693 K). Starting with curve I, the Tonset rises again. To explain the difference between the above-mentioned nonmonotonic thermodynamic trend of the F−S transition, we recall the generalized view of glass-former thermodynamics proposed by Angell.14 This generalized view illustrates the correlation among liquid fragility, ΔCp at Tg, and the Cp jump of the F− S transition (i.e., the Lambda peak) (see Figure 12 in ref 14). According to this picture, the position of the F−S transition peak could be between Tg and Tm (melting point) or above Tm, depending on the nature of glass formers and their fragility at Tg. It is known that fragile glass formers at Tg generally have larger ΔCp at Tg as compared to strong glass formers.38−41 This generalized view suggests that a larger ΔCp at Tg is associated with a lower thermodynamic F−S transition temperature relative to Tm. We note that the ΔCp of the Cu45Zr45Al10 glass is around 0.2 J g−1 K−1 at Tg, much higher than that of La55Al25Ni5Cu15 (0.08 J g−1 K−1). Thus, if the above-mentioned difference follows the general picture, thermodynamic F−S transition in Cu45Zr45Al10 metallic glasses (i.e., the Lambda peak shown in ref 1) should occur at lower temperatures than that in La55Al25Ni5Cu15 during heating. The predication consists with our observations, and therefore both our previous16,17 and this work contribute to obtaining a general thermodynamic picture of the F−S transition in supercooled liquids. The thermal history (i.e., the cooling rate of fabrication in the present work) dependence of crystallization is reminiscent of dynamic arrest originating from the environment-dependent energetics of local clusters.42 In other words, different thermal histories can lead to various types of local clusters with different concentrations and packing distributions in HQ glass.43 It has been demonstrated that some clusters such as icosahedron44 and face-centered cubic lattice45 are important locally ordered
structures contributing to the stability of supercooled liquids against crystallization. It has been argued7 that the extended clusters composed by icosahedral structures in strong liquids can be effectively destroyed by increasing the temperature, leading to a much more fragile liquid. However, this scenario does not consider the F−S transition region itself that usually falls in a certain narrow temperature range as shown in Figure 6. According to both our recent work16,17 and the work about the nonmonotonic temperature dependence of enthalpy during cooling,15 an anomalous evolution of clusters in the F−S region occurs; that is, the clusters dramatically change and become unusually less stable upon cooling. The anomalous crystallization in our intermediate cooling rate range (15−25 m/s) (Figures 2−5) could be associated with an abrupt increase in cluster heterogeneity in the F−S region. The cluster size distribution in the middle of the F−S transition is the broadest, and hence the activation energy for crystallization is smallest (Figure 5). These clusters with this size distribution can be arrested just by an intermediate cooling rate (15−25 m/s). On the basif of Schneiders’ result on Vit 1 that the chemical deconstruction of clusters is a relatively low activation energy process as compared to crystallization,46 the anomalous crystallization in Figures 2−4 may also partly result from deconstruction of short-range-order clusters. It is known that the mode coupling temperature Tc (about 1.2Tg), where slow β relaxation diverges from α relaxation,47 is close to the thermodynamic F−S transition regime (i.e., the anomalous crystallization regime, about 1.2−1.3Tg). It is also known that the F−S transition can be linked to the competitions between α and slow β relaxations in supercooled liquids.48 Therefore, by exploring the cluster change with the slow β relaxation diverging from α relaxation at Tc, we can get insights into the anomalous structural evolution of the F−S transition. A direct imaging of relaxation near the colloidal glass transition gives an explicit picture of the connections between α/β relaxation and clustering.49 At longer time scales (α relaxation) in supercooled liquids or above Tc, clusters are relatively large and could rearrange, whereas at shorter time scales (β relaxation) or below Tc, clusters are much smaller, and some small clusters persist even for glassy samples where particles are constrained by other particles as cages, and can rearrange only within cages. Therefore, under cooling a sudden divergence of β relaxation from α relaxation at Tc is likely to be accompanied by nonmonotonic structural evolutions such as the unusual cluster expansions around 1.2Tg in the PdNiCuP MGFLs50 and the nonlinear rapid cluster growth around 10263
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1.2Tg.51 This nonmonotonic structural evolution may in turn lead to the F−S transition.10 This scenario confirms that 1.2− 1.3Tg is the temperature range, where unconventional evolutions of clusters tend to occur.52−54
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IV. CONCLUSIONS We have studied the cooling rate dependence of the crystallization behavior of hyperquenched La55Al25Ni5Cu15 glass ribbons. An intermediate cooling rate range (15−25 m/ s) for fabricating glass ribbons has been found in which the samples exhibit anomalous crystallization behavior as compared to glass ribbons fabricated at other cooling rates. This indicates that the anomalous crystallization behavior is a thermodynamic signature of the F−S transition. Thus, the determination of the anomalous crystallization behavior could be used as a thermodynamic tool to detect and characterize the F−S transition in some MGFLs. It could be used as a potential approach for estimating the position and width of the F−S transition in the studied systems. The difference in the abnormal nonmonotonic thermodynamic trends of the F−S transition between various MGFLs (such as the anomalous crystallization or the three-stage Tonset relaxation behavior) could be associated with the difference in liquid fragility or heat capacity jump ΔCp at Tg.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ⊥
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant nos. 50801041 and 51171090), Shandong Province Natural Science Foundation (Grant no. ZR2010EQ026), and the Basic Research Project of Qingdao Science and Technology Program (Grant no. 13-1-4-171-jch).
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