Structural evolution during fragile-to-strong transition in CuZr(Al) glass-forming liquids Chao Zhou, Lina Hu, Qijing Sun, Haijiao Zheng, Chunzhi Zhang, and Yuanzheng Yue Citation: The Journal of Chemical Physics 142, 064508 (2015); doi: 10.1063/1.4907374 View online: http://dx.doi.org/10.1063/1.4907374 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Anomalous structural evolution in Cu50Zr50 glass-forming liquids Appl. Phys. Lett. 103, 021904 (2013); 10.1063/1.4813389 Signatures of fragile-to-strong transition in a binary metallic glass-forming liquid J. Chem. Phys. 136, 104509 (2012); 10.1063/1.3692610 Abnormal sub- T g enthalpy relaxation in the CuZrAl metallic glasses far from equilibrium Appl. Phys. Lett. 98, 081904 (2011); 10.1063/1.3556659 Fragile-to-strong transition in metallic glass-forming liquids J. Chem. Phys. 133, 014508 (2010); 10.1063/1.3457670 Structural behavior of Zr 52 Ti 5 Cu 18 Ni 15 Al 10 bulk metallic glass at high temperatures Appl. Phys. Lett. 80, 4525 (2002); 10.1063/1.1486480
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THE JOURNAL OF CHEMICAL PHYSICS 142, 064508 (2015)
Structural evolution during fragile-to-strong transition in CuZr(Al) glass-forming liquids Chao Zhou,1 Lina Hu,1,a) Qijing Sun,1 Haijiao Zheng,1 Chunzhi Zhang,2 and Yuanzheng Yue1,3
1
Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China 2 School of Materials Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China 3 Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark
(Received 20 November 2014; accepted 22 January 2015; published online 10 February 2015) In the present work, we show experimental evidence for the dynamic fragile-to-strong (F-S) transition in a series of CuZr(Al) glass-forming liquids (GFLs). A detailed analysis of the dynamics of 98 glass-forming liquids indicates that the F-S transition occurs around Tf -s ≈ 1.36 Tg. Using the hyperquenching-annealing-x-ray scattering approach, we have observed a three-stage evolution pattern of medium-range ordering (MRO) structures during the F-S transition, indicating a dramatic change of the MRO clusters around Tf -s upon cooling. The F-S transition in CuZr(Al) GFLs is attributed to the competition among the MRO clusters composed of different locally ordering configurations. A phenomenological scenario has been proposed to explain the structural evolution from the fragile to the strong phase in the CuZr(Al) GFLs. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907374]
I. INTRODUCTION
To characterize the dynamic properties of liquids in the vicinity of glass transition temperature (Tg), the concept of liquid fragility has been widely applied.1–4 Based on this concept, liquids are normally classified as fragile and strong liquids.5 However, according to recent studies on liquid transport characteristics, such as viscosity, self-diffusion constant, and relaxation time, some glass-forming liquids (GFLs) do not conform to the conventional “strong/fragile” classification scheme but exhibit fragile-to-strong (F-S) transition during cooling.6 The dynamic behavior of these GFLs is characterized by a non-Arrhenian behavior near liquidus temperatures (Tliq). In contrast, it exhibits a quasi-Arrhenian (i.e., slightly deviating from the ideal Arrhenian) temperature dependence of viscosity around Tg. In other words, these GFLs are transformed from a fragile state into a relatively strong state upon cooling toward Tg. The F-S transition was first reported in water7 and further confirmed by experimental studies and theoretical calculations.8–10 Later on, the F-S transition was also discovered in SiO2,11,12 BeF2,13 and metallic glass-forming liquids (MGFLs).14–18 Recently, it is reported that the F-S transition could be a general feature of MGFLs.15,17 A systematic study has been carried out in terms of the correlations of the F-S transition of MGFLs with the sub-Tg relaxation,19 crystallization,20 and relaxation modes.21 In order to clarify the structural origin of the F-S transition in GFLs, possible scenarios have been proposed. Jagla attributed the F-S transition in water to the competition a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064508/8/$30.00
between two different local structures.22 Liu et al. ascribed the pressure dependence of the F-S transition in water to a transition from a high-density liquid to a low-density liquid during cooling.10,23 Both Saika-Voivod and Way et al. related the F-S transition in silica and in a ZrTiCuNiBe liquid to a polyamorphic transition.11,12,14 The extended mode-coupling theory modified by Chong et al. predicted the existence of the F-S dynamic crossover in GFLs during cooling, which was connected with the change from the “cage effect” to the “hopping” process dominated dynamics.24 Although the modeling results have implications for the structural evolution of the F-S transition, experimental studies on such issue are still lacking due to the fact that the crystallization hinders directly probing the structure during the F-S transition, especially for MGFLs. Some physical properties of CuZr(Al) glasses or liquids have been investigated to some extent.25–32 However, to the best of our knowledge, the kinetic F-S transition in CuZr(Al) liquids has not been reported yet. By using the hyperquenching-annealing-calorimetric scanning approach, our previous work has demonstrated a three-stage sub-Tg relaxation pattern in CuZr(Al) liquids.19,29 This anomalous enthalpy change during cooling, which was also observed through molecular dynamics simulation, has been regarded as the thermodynamic evidence of the F-S transition in CuZr(Al) liquids.19,33 The hyperquenching-annealing-x-ray scattering approach could be able to indirectly detect the structural evolution during the F-S transition in MGFLs,34–36 since their structure can be arrested at high temperatures (i.e., the fictive temperature Tf 37) well above Tg and normally below Tliq by hyperquenching, and relax upon subsequent annealing, and
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finally is characterized by x-ray scattering. In the present work, we first measure the kinetic F-S transition in CuZr(Al) GFLs, and then analyze their structural evolution during the F-S transition by means of the hyperquenching-annealing-x-ray scattering approach.
II. EXPERIMENTAL PROCEDURES AND DETERMINATION OF LIQUID FRAGILITY A. Experimental procedures
The master alloys of (Cu50Zr50)100−xAlx (x = 0, 2, 4, 8) (in atom %) ingots for viscosity and calorimetric measurements were melted by arc melting under an argon atmosphere with purities ranging from 99.5% to 99.999%. High-temperature viscosity was measured upon cooling from about 400 K above Tliq in vacuum using a torsional oscillating viscometer.38 Samples were placed in a vessel hung by a torsional suspension wire. The vessel was set to oscillate on a perpendicular axis, and therefore, the motion was gradually damped due to frictional energy absorption and dissipation within the melt. Specimens sealed in a vacuum of 10−4 Torr were heated to 400 K above Tliq and held for an hour. Then, the samples were cooled to a given temperature and held for 30 min before the viscosity measurement started. At each temperature, the viscosity was measured for at least four times. Because the relaxation time of metallic melts above Tliq is very short (less than 10−8 s39,40), the measured viscosity can be regarded as the equilibrium viscosity. The hyperquenched (HQ) glass ribbons (GRs) were fabricated by single copper-roller spinning apparatus under argon atmosphere. The GRs were spun at the circumferential velocity of 25 m/s. The master alloys were re-melted by the high-frequency induction technique and rapidly solidified into GRs. Calorimetric measurements were performed using a differential scanning calorimeter (DSC) in a Netzsch DSC 404 with high-purity standard platinum pans under a constant flow of high-purity argon, using pure indium (99.999% mass percent) and zinc (99.999% mass percent) standards and a sample mass of 20 ± 0.5 mg. All the DSC measurements were conducted in a flowing (80 cm3/min) argon gas at a heating rate of 20 K/min.36 The standard glass subjected to a standard cooling rate of 20 K/min was compared to the fresh samples and the annealed samples in order to determine their Tf s and Tg s.36,37 Here, the fresh samples refer to the as-quenched samples prior to annealing, and the standard glass refers to the glass that was cooled at the standard cooling rate of 20 K/min.37 Note that Tf is the temperature at which the structure of glasses is frozen-in during cooling. The x-ray scattering measurements were carried out on a Bruker-AXS D8 ADVANCE x-ray diffractometer equipped with a diffracted beam monochromator set for a Cu Kα radiation. Data were collected in the 2θ range of 10◦∼90◦ with a step size of 0.016 55◦ and a step time of 0.25 s at room temperature. To analyze the structural changes quantitatively, total structure factors (interference functions) S(Q) and pair distribution functions (PDFs), g(r), are extracted from the diffracted intensity patterns, where Q = (4π/λ) sin θ is the scattering vector and λ is the wavelength of the x-ray. PDF is
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therefore obtained as the equation,41 1 g (r) = 1 + 2 2π r ρa
Q max
Q [S (Q) − 1] sin Qr dQ,
(1)
0
where r is the radius from the center of an atom to a certain shell close to the central atom, and ρa = ρN A/ ⟨A⟩ is the average atomic density of sample. Here, ρ is the mass density of sample, N A the Avogadro constant, and ⟨A⟩ the atomic mass of sample. B. Equations for calculating the fragility index (m)
The rapidity of the viscosity (η) changes of glass-forming liquids with temperature near Tg can be characterized by the fragility index m, which can be derived from the Mauro–Yue– Ellison–Gupta–Allan (MYEGA) viscosity model,42 ( ) C B , lg η = lg η ∞ + exp T T
(2)
where η ∞ is the viscosity at the high temperature limit,42,43 and B and C are fitting parameters. Combining Eq. (2) with m = ddTlog/Tη , the fragility m is obtained as42 ( g ) T =Tg m=
( ) ( ) B C C 1+ exp . Tg Tg Tg
(3)
Alternatively, the parameters B and C and, thus, m can be acquired by the dependence of the heating rate ϕ on the fictive temperature Tf in the vicinity of Tg using the DSC.37 With this method, Eq. (2) can be rewritten as lg ϕ = lg ϕ∞ −
( ) B C , exp Tf Tf
(4)
where ϕ∞ is the heating rate at the limit of fictive temperature. The value of m calculated by this method agrees well with that obtained by the kinetic method.44 Here, we explain the reasons and advantages for utilizing the MYEGA viscosity model (Eq. (2)) in the present work, instead of generally accepted Vogel-Fulcher-Tammann (VFT) model (lg η = lg η ∞ + B/(T − T0)). First, the configurational entropy at T0 is zero for the VFT model, which is divergent to the disputable possibility that the configurational entropy is positive at all temperatures.45 In this regard, the MYEGA model offers a more realistic extrapolation of the configurational entropy in the low-temperature limit than the VFT model.42 Second, when the viscosity model is involved to calculate the fragility m, the VFT model shows a poor fit for large-fragility liquids, while the MYEGA model performs well.1,42 Considering the large fragility of wide range of m values in MGFLs, it is much better to choose the MYEGA model to quantify m values. The third advantage is that the distribution of η ∞ values of the MYEGA model is much narrower than that of the VFT model based on best-fit viscosity curves of 568 GFLs.42
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FIG. 1. The Angell plot, i.e., logarithmic viscosity (log η), as a function of the Tg scaled temperature T for (Cu50Zr50)100−xAlx (x = 0, 2, 4, 8) (in at. %) with error bars. Dashed and solid curves are the fits of the MYEGA equation (Eq. (2)) to the high temperature and low temperature viscosity data, respectively. Inset: High temperature region of the Angell plot for Cu48Zr48Al4, where error bars are given.
FIG. 2. The fit of the experimental Angell plot to Eq. (5) for the Cu46Zr46Al8 liquid in the entire temperature range (solid curve). The dashed and dasheddotted curves represent the strong and fragile terms, respectively, and their intersection point is the characteristic temperature Tf -s of the F-S transition.
coefficient.49 The distinct difference of the thermal expansion coefficient between 2Tg and Tg suggests a crossover from a fragile to a strong liquid during cooling in the supercooled regime of CuZr-based alloys. The characteristic temperature Tf -s is an important value, since it defines the temperature of the occurrence of the F-S transition. The Tf -s can be calculated by the extended MYEGA model,15
III. RESULTS AND DISCUSSION A. Characteristics of the F-S transition phenomenon in CuZr(Al) MGFLs
Figure 1 shows the viscosity data of the CuZr(Al) GFLs in both the high temperature (HT) range, i.e., above the Tliq, and the low temperature (LT) range near the Tg.30 As a typical case, the distinct error bars at HT range have been shown in the inset. At the temperatures above Tliq, the viscosity values are around 10−2 Pa s of which the magnitude accords with those alloys around Tliq reported previously.46,47 The viscosity data in HT and LT ranges were fitted to Eq. (2) separately (see the dashed and solid curves in Fig. 1). According to Eq. (3), the HT liquid fragility index mHT and the LT liquid fragility index mLT of four CuZr(Al) liquids have been obtained, as shown in Table I. The mLT value of Cu48Zr48Al4 is quite close to that (mLT = 43 ± 5) obtained from DMA measurements.48 The mLT values of the four MGFLs are in the range of 32∼53, indicating that the CuZr(Al) GFLs at LT are relatively strong. In contrast, the mHT is much larger than mLT. The ratio of mHT to mLT, i.e., f = mHT/mLT, has been used as the strength parameter to describe the extent of the F-S transition.15,21 In Table I, the f values for all the CuZr(Al) GFLs are much larger than 1, implying the existence of the kinetic F-S transition in CuZr(Al) GFLs upon cooling. This finding accords with the phenomenon reported by Bendert et al.49 They observed that, compared with the GFLs with low glass-forming ability in CuZr binary liquids, those with high glass-forming ability have a smaller thermal expansion coefficient near Tg, whereas in the vicinity of Tliq (2Tg to be precise), they exhibit a larger
log η = log η ∞ +
T W1 exp
(
− CT1
1 ) ( ) , + W2 exp − CT2
(5)
where C1 and C2 correspond to two constraint onsets reflecting different dynamic mechanisms at HT and LT, i.e., the fragile and strong terms (weighted by W1 and W2, respectively). Fig. 2 shows the fit of the experimental viscosity data to Eq. (5) for the Cu46Zr46Al8 liquid (solid curve). The dashed-dotted curve refers to the fragile term, whereas the dashed curve represents the strong one. Tf -s is thus calculated as follows: ( ) ( ) C1 C2 W1 exp − = W2 exp − , T f −s T f −s C1 − C2 . (6) T f −s = ln W1 − ln W2 According to Eq. (6), the characteristic temperature Tf -s is the point where the contribution of the fragile term at HT to the whole dynamics is equal to that of the LT strong term. Below Tf -s, the strong term will become dominant. Table II shows the fitting parameters of Eq. (5) for four CuZr(Al) GFLs, and the correlation factors of the fits to Eq. (5) for four liquids are no less than 0.9998. Using these parameters, the Tf -s values
TABLE I. Fragility indices (m HT and m LT) and activation energy differences ∆E of CuZr(Al) GFLs in HT and LT ranges, respectively. f = m HT/m LT, i.e., the strength parameter of the F-S transition in GFLs during cooling.15,21 Composition (at. %) Cu50Zr50 Cu49Zr49Al2 Cu48Zr48Al4 Cu46Zr46Al8
Tg (K)
m HT
m LT
f
∆E HT (kJ/mol)
∆E LT (kJ/mol)
664 674 683 701
127 129 117 130
32 34 44 53
4.0 3.8 2.7 2.5
55.97 61.66 57.88 67.19
10.60 11.33 11.78 21.43
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TABLE II. The glass transition temperature Tg, the F-S transition temperature Tf -s, and fitting parameters of Eq. (5) of four CuZr(Al) GFLs. Composition (at. %) Cu50Zr50 Cu49Zr49Al2 Cu48Zr48Al4 Cu46Zr46Al8
Tg (K)
log η ∞ (Pa s)
W1
C1
W2
C2
Tf -s (K)
664 674 683 701
−2.23 −2.56 −2.32 −2.20
265 1614 373 1809
14 180 16 867 15 282 16 716
0.000 35 0.000 38 0.000 80 0.001 51
795 884 1405 1901
989 1047 1063 1059
of the CuZr(Al) GFLs are calculated to be in the range of 989∼1063 K. The Tf -s values in the present work are comparable to those of some non-MGFLs with F-S transition denoted by the F-S dynamic crossover temperature in literature.6 In Fig. 3, we plot Tf -s against Tg for 98 GFLs including metallic systems, network systems, and organic systems. The characteristic temperatures of MGFLs are derived from Eq. (6) as listed in Table III.15,17,50–54 For the non-MGFLs in Fig. 3, the Tg and Tf -s values are taken from Ref. 6. It is seen that all of the Tg values of metallic glasses fall in the middle of the temperature range. The correlation between Tg and Tf -s is found to be the linear one: Tf -s ≈ (1.36 ± 0.03)Tg with a correlation factor of 0.9599. The viscosities at Tf -s are listed in Table III, where the average lg(η f -s) value for MGFLs is about 0.86 in Pa s, smaller than that of non-MGFLs (around 2 Pa s).6 The relationship Tf -s ≈ 1.36Tg in Fig. 3 can be an important feature of the F-S transition in GFLs. B. Structural evolution during the F-S transition of CuZrAl GFLs
In our previous work, we have verified that, as thermodynamic evidence, the anomalous sub-Tg three-stage relaxation pattern of the CuZrAl HQ GRs has the same structural origin as the dynamic F-S transition in MGFLs.19,29 As shown in Fig. 4(a), for the Cu46Zr46Al8 HQ GRs with the spinning circumferential velocity of 25 m/s, the anomalous relaxation pattern (reflected mainly by the distinct drop of dashed curve E) occurs when annealing temperature (Ta) changes from 583 to 623 K. In accordance with Figs. 4(a) and 4(b) shows the x-ray scattering patterns for the Cu46Zr46Al8
FIG. 3. Tg dependence of the Tf -s for 98 GFLs. The data are from Ref. 6 and Table III. Dashed red line is a linear fit to the data. The shadow area gives a guide to the dispersion of the data.
HQ GRs annealed at different Ta s below Tg for 1 h. In Fig. 4(b), no crystalline peak is observed except for the one annealed at 643 K (not shown), indicating that all the GRs annealed below 643 K are amorphous. Apparently, the annealing temperatures have no detectable influence on both the positions and intensity of the main peaks, whereas the peak intensity at lower angles is significantly affected by the annealing temperature, i.e., it decreases with an increase in Ta. Figure 5 shows the structure factors S(Q) for the annealed Cu46Zr46Al8 GRs. There are two low Q minor peaks and one main peak on each curve, and this is similar to what has been observed in a nickel-based superalloy liquid.56 In literature, the low Q minor peaks prior to the main peak are often called the “prepeaks.”57–59 The position of the main peak (denoted by Pm in Fig. 5) remains unchanged with Ta, indicating that the structural units with short-range order (SRO) are stable upon cooling, and the position of this peak accords well with that obtained from EXAFS measurements.55 This unchanged peak position may be due to the originally glassy state of the annealed samples in the present work rather than a liquid state, because for the latter, the main peak position often has a detectable shift with the decrease of temperature.60 However, the position of the two prepeaks (denoted as P1 and P2) varies with the annealing degree, particularly evident for P1. For P2, the position shifts slightly towards a higher Q value with Ta increasing, and this could be associated with the monotonic decrease of intermediate range ordering units.61 When Ta ≤ 583 K, P1 moves towards a lower Q value with an increase in Ta. When Ta increases from 593 to 613 K, this negative relation is interrupted. Instead, P1 shifts towards a larger Q value with a higher Ta. When Ta ≥ 623 K, P1 shifts to a lower Q with Ta increasing again. In contrast to the non-monotonic change of the P1 position, its intensity decreases especially when Ta increases above 583 K. Since the non-monotonic evolution of the P1 position occurs in the same Ta region as does the three-stage enthalpy relaxation (Fig. 4(a)), a drastic transition of the medium-range ordering (MRO) structure corresponding to the P1 must happen, which is responsible for the F-S transition in CuZrAl GFLs. The structural unit size corresponding to the P1 is calculated using the Ehrenfest’s formula ln Rc = 1.23 ∗ 2π/Q p p ,62 where Qpp is the position of the P1. The statistical errors have been evaluated by the method developed by Egami63 and they get bigger when the prepeak becomes broader. The Ta dependence of Rc is illustrated in the inset of Fig. 5, as well as the error bars of the data. An anomalous decrease of Rc is observed when Ta increase from 593 to 613 K. Since the increase in Ta generally causes a decrease in Tf , this non-monotonic change of Rc implies a discontinuity in the MRO structural evolution during the F-S transition of GFLs. The size of the MRO
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TABLE III. Tg, Tf -s, and log(η f -s) values of 20 MGFLs in an increasing order of Tg. Composition (at. %) La55Al25Ni5Cu15 La55Al25Ni15Cu5 Pr55Ni25Al20 La55Al25Ni20 Sm55Al25Co10Cu10 Ce55Al45 Sm55Al25Co10Ni10 Al87Co8Ce5 Gd55Al25Ni10Co10 Sm50Al30Co20 Gd55Al25Co20 Zr52.5Cu17.9Ni14.6Al10Ti5 Cu50Zr50 Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 Zr57Cu15.4Ni12.6Al10Nb5 Cu49Zr49Al2 Cu47Ti34Zr11Ni8 Cu48Zr48Al4 Cu46Zr46Al8 Ni60Zr30Al10
Tg (K)
Tf -s (K)
log(η f -s) (Pa s)
References
459 474 480 491 534 541 553 558 579 586 589 661 664 668 670 674 676 683 701 738
681 778 739 646 838 670 714 706 729 839 737 1014 989 1047 1059 1047 1057 1063 1059 1121
0.17 −0.29 0.65 1.37 0.71 2.01 2.17 2.14 2.50 1.51 2.54 0.16 1.00 0.28 0.15 0.38 −0.53 −0.11 −0.31 0.76
15 and 50 15 and 50 15 and 51 15 and 50 15 and 50 15 15 and 50 15 and 52 15 and 53 15 and 50 15 and 53 17 This work 17 17 This work 17 This work This work 54
structural units in the supercooled CuZr(Al) GFLs does not increase monotonically upon cooling as predicted by AdamGibbs theory.64 Instead, they are dissociated into smaller clusters during the F-S transition. The dramatic decrease in the structural unit size Rc accords with the anomalous increase in enthalpy of the supercooled CuZr(Al) liquid during cooling around 1.3 ∼ 1.4Tg.19 Fig. 6 shows the g(r) curves for the Cu46Zr46Al8 glasses annealed at different Tas. In Fig. 6, peak positions and widths at the half maximum of the first peak in g(r) on the left-hand side shift slightly to the small values with increasing Ta, as shown by the violet dashed arrow. The shift of the first peak in g(r) is ascribed to the thermal agitation of different types of atoms and thus asymmetric redistribution of neighboring atoms to shorter and longer distances.65 The correlation radius r c′ is often used to describe statistically the averaged size of
MRO clusters in MGFLs. r c′ is the minimum radius where g(r) = 1 ± 0.02, and the error is estimated by the Fourier transition.66 The dependence of r c′ on Ta for the Cu46Zr46Al8 GRs is illustrated in the inset of Fig. 6. Clearly, r c′ exhibits a three-stage dependence on Ta, which is consistent with the change of the structural unit size Rc (Fig. 5). The decrease of r c′ with increasing Ta from 593 to 613 K further indicates the existence of the dissociation of the MRO clusters during cooling. Such non-monotonic evolution of the correlation length in supercooled liquids has also been reported in some theoretical simulation studies.67,68 It is known that the characteristics of clusters are closely related to the dynamics of liquids (e.g., liquid fragility).59 The difference (∆E) between the activation energy for atom aggregation (Ea) and that for cluster dissociation (Ed) can reflect the stability of clusters, and hence, viscous behavior
FIG. 4. (a) The isobaric heat capacity (C p) versus temperature for the HQ Cu46Zr46Al8 GRs annealed at different temperatures (Ta) below Tg for 1 h, exhibiting the effect of different Ta on the enthalpy relaxation pattern. Inset: The relationship between the onset temperature of the exothermic peak (Tonset) and the Ta.19 (b) X-ray scattering patterns after annealed at different Tas.
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FIG. 5. Structure factor S(Q) of the hyperquenched Cu46Zr46Al8 glasses with different annealing temperatures, Tas, for an hour. The bottom curve is extracted from the extended x-ray absorption fine structure (EXAFS) results in literature.55 The short-dashed lines and the dashed line illustrate the shift of the two prepeaks, respectively. Inset: The structural unit size R c of the first prepeak (P1) as a function of Ta.
can be described by the cluster kinetic model,69 ηg lg η = lg η g − lg η∞
(
T /T
) ×
Ωg g − Ωg , 1 − Ωg
(7)
where ln Ωg = (Ed − Ea )/RTg , η g is the viscosity at Tg, and R is the gas constant. Since the activation energy for the aggregation or association process is always less than that for cluster dissociation process during cooling, the ∆E(∆E = Ed − Ea) value should be a positive one.69 The smaller the ∆E value is, i.e., the E values of the two processes are more comparable with each other, the more stable the clusters in liquids are. By fitting Eq. (7) to the HT and LT viscosity data (Fig. 1), respectively, the ∆E values of four MGFLs in both HT and LT ranges (denoted by ∆EHT and ∆ELT, respectively) are obtained as listed in Table I. The ∆ELT values ranging from 10.6 to 21.4 kJ/mol, the magnitude of which is close to that of the Al-based MGFLs in LT range.59 The ∆ELT value is much smaller than the ∆EHT value for each composition. This indicates that the clusters in LT range after the F-S transition are more stable than those in HT range.
FIG. 6. Pair distribution functions, g (r ), of the HQ Cu46Zr46Al8 glasses with different annealing temperature Tas. Inset: Ta dependence of correlation radius (r c′).
The three-stage dependences of both Rc and r c′ on Ta (Figs. 4–6) and the considerable differences between ∆EHT and ∆ELT in Table I verify that the evolution mechanism of MRO clusters is different before and after the F-S transition. During the F-S transition, the MRO structures exhibit a strong tendency to dissociate, rather than to aggregate with other free atoms or clusters. A schematic scenario is proposed in Fig. 7 in order to reveal the structural evolution of the F-S transition in CuZrAl GFLs. As suggested by the two-order-parameter (TOP) model70 and other two models developed for metallic glasses,71,72 we can describe the structure of supercooled Cubased GFLs in terms of both the rearrangements of free atoms and local ordering. Since icosahedra can cause topological frustration and decrease the atomic mobility in liquids and thus improve glass forming ability,73,74 we consider that locally ordered structures in CuZr(Al) GFLs are mainly composed of two types of icosahedra (SRO domain): partially symmetric (distorted) icosahedra and perfect fivefold-symmetric ones. When a liquid is cooled to a certain temperature above Tliq, free atoms will incorporate those in the vicinity to form partially symmetric icosahedra (Fig. 7(b)). The partially symmetric icosahedra continue to correlate with each other to build MRO clusters upon further cooling (Fig. 7(c)). In other words, the structural units in HT are dominantly composed of partially symmetric icosahedra in a relatively low-density state.10 When the liquid is cooled approaching Tf -s, i.e., when the F-S transition starts, both the number and the size of these MRO clusters are expected to increase to a critical value, and then remain almost constant. To minimize the energy of the system, these MRO clusters have to break partly down and, hence, are combined into more stable ones,72 e.g., those composed of perfect fivefold-symmetric icosahedra (Fig. 7(d)).55,75 When MGFLs are cooled further below Tf -s, the new stable MRO clusters aggregate together into larger ones in a high-density state contributing to the strong phase,10 as shown in Fig. 7(e). In terms of the above scenario of structural evolution during the F-S transition in CuZrAl GFLs, the competition among the MRO clusters with different configurations of icosahedra is the characteristic of the F-S transition as illustrated in Fig. 7. Such competition of icosahedra has been confirmed by theoretical modeling on the microstructures in CuZr(Al) glasses or liquids, although the role of MRO size is somewhat neglected.73,76 Topologically speaking, icosahedral clusters with Cu-centered ⟨0 0 12 0⟩, ⟨0 2 8 2⟩, ⟨0 2 8 1⟩, ⟨0 3 6 3⟩, and Al-centered ⟨0 0 12 0⟩ configurations account for the largest fraction of CuZrAl glass structure in terms of the Voronoi tessellation method, whereas the icosahedra with perfect fivefold symmetry (i.e., ⟨0 0 12 0⟩ configuration) are the basic local structural motifs.55,75,77 When the temperature is above Tf -s, all kinds of icosahedra gradually increase and partially symmetric icosahedra have a larger fraction than the icosahedra with ⟨0 0 12 0⟩ configuration. However, below Tf -s, perfect fivefold-symmetric icosahedra with Cu-centered and Al-centered ⟨0 0 12 0⟩ configurations increase rapidly with temperature,33,78 whereas partially symmetric ones decrease smoothly.73 Thus, the evolution of icosahedra leads to a dramatic increase of more stable MRO clusters in CuZr(Al) GFLs at and below Tf -s. The strong competition between the perfect icosahedra and other structural units dictates the
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FIG. 7. Schematic structural evolution scenario of the F-S transition. (a) Replica of Fig. 2; (b)-(e) structural characteristic during the F-S transition of CuZr(Al) GFLs upon cooling. The purple dashed arrows indicate the corresponding structure in liquid state. The structural units are also illustrated by magenta solid arrows in details.
structural evolution, i.e., from the state shown in Figs. 7(b) and 7(c) to that in Figs. 7(d) and 7(e). Here, it should be pointed out that the scenario in Fig. 7 is essentially different from the TOP model, although the latter also considers the role of icosahedra during cooling.79,80 First, the TOP model generally describes the dynamic transformation in liquids from the Arrhenius-type to the VFT-type regime upon cooling.81 This is contrast to the F-S transition phenomenon (i.e., from the highly nonArrhenian to the relatively Arrhenian behaviour), which has been experimentally observed so far.7,10–12,14–17,21 Second, by considering the competition between long-range ordering structure and local tetrahedra in the LT region, the TOP model could be used to explain the F-S transition in covalent-bond tetrahedral liquids, such as water and silicon.82 However, it is known that the microstructure in metallic glasses is densely packed by polyhedral clusters (e.g., icosahedra) and the superclusters of polyhedral.25,83 Thus, compared to the TOP model, the structural scenario in Fig. 7 is suitable for describing the structural evolution in the F-S transition in MGFLs. Concerning the order of a phase transition, the F-S transition in MGFLs could be regarded as a first-order transition since it is accompanied by an abrupt change of enthalpy and density with temperature. From spectroscopic experiments (e.g., using quasi-elastic neutron scattering and Fourier transform infrared spectroscopy) and simulation studies, it has been found that during the F-S transition in water,84–86 the density of supercooled water drops suddenly between Tliq and Tg under ambient pressure. This indicates that the F-S transition in water is a first-order transition as well. Similarly, the F-S transition in the MGFLs under ambient pressure should be of the first-order as evidenced as follows. Based on a simulation study on a CuZr GFL, there is a release of the latent heat in a dynamic regime during the F-S transition upon cooling.33 Also, an abrupt change of density was observed around the Tf -s in a supercooled ZrTiCuNiBe liquid.14,87 In the present work, the three-stage patterns of
both the enthalpy release and the Rc in CuZrAl imply a discontinuity of density. Hence, the F-S transition in MGFLs should be a first-order transition.
IV. CONCLUSION
We have demonstrated direct evidence of the F-S transition in CuZr(Al) GFLs. By accessing the dynamic behavior of a large number of glass-forming liquids, we confirm that the F-S transition in GFLs occurs at Tf -s ≈ 1.36Tg, corresponding to an average viscosity of 100.86 Pa s for MGFLs. Both the three-stage patterns of structural evolution during cooling and the differences of cluster stability in different temperature regions indicate that the F-S transition in CuZrAl GFLs is attributed to the competition among the MRO clusters composed of different configurations of the locally ordered structural units. A schematic scenario is proposed to understand the structural evolution of the F-S transition in CuZr(Al) GFLs.
ACKNOWLEDGMENTS
We thank Professor K. F. Kelton for useful discussions and Lulu Sun for help in sample preparation. We also appreciate Jie Zhang and Xixia Zhang for experimental support. This research was financially supported by National Natural Science Foundation of China (Grant Nos. 51171090 and 51371107) and Basic Research Project of Qingdao Science and Technology Program (Grant No. 13-1-4-171-jch). 1C.
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THE JOURNAL OF CHEMICAL PHYSICS 142, 064508 (2015)
Structural evolution during fragile-to-strong transition in CuZr(Al) glass-forming liquids Chao Zhou,1 Lina Hu,1,a) Qijing Sun,1 Haijiao Zheng,1 Chunzhi Zhang,2 and Yuanzheng Yue1,3
1
Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China 2 School of Materials Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China 3 Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark
(Received 20 November 2014; accepted 22 January 2015; published online 10 February 2015) In the present work, we show experimental evidence for the dynamic fragile-to-strong (F-S) transition in a series of CuZr(Al) glass-forming liquids (GFLs). A detailed analysis of the dynamics of 98 glass-forming liquids indicates that the F-S transition occurs around Tf -s ≈ 1.36 Tg. Using the hyperquenching-annealing-x-ray scattering approach, we have observed a three-stage evolution pattern of medium-range ordering (MRO) structures during the F-S transition, indicating a dramatic change of the MRO clusters around Tf -s upon cooling. The F-S transition in CuZr(Al) GFLs is attributed to the competition among the MRO clusters composed of different locally ordering configurations. A phenomenological scenario has been proposed to explain the structural evolution from the fragile to the strong phase in the CuZr(Al) GFLs. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907374]
I. INTRODUCTION
To characterize the dynamic properties of liquids in the vicinity of glass transition temperature (Tg), the concept of liquid fragility has been widely applied.1–4 Based on this concept, liquids are normally classified as fragile and strong liquids.5 However, according to recent studies on liquid transport characteristics, such as viscosity, self-diffusion constant, and relaxation time, some glass-forming liquids (GFLs) do not conform to the conventional “strong/fragile” classification scheme but exhibit fragile-to-strong (F-S) transition during cooling.6 The dynamic behavior of these GFLs is characterized by a non-Arrhenian behavior near liquidus temperatures (Tliq). In contrast, it exhibits a quasi-Arrhenian (i.e., slightly deviating from the ideal Arrhenian) temperature dependence of viscosity around Tg. In other words, these GFLs are transformed from a fragile state into a relatively strong state upon cooling toward Tg. The F-S transition was first reported in water7 and further confirmed by experimental studies and theoretical calculations.8–10 Later on, the F-S transition was also discovered in SiO2,11,12 BeF2,13 and metallic glass-forming liquids (MGFLs).14–18 Recently, it is reported that the F-S transition could be a general feature of MGFLs.15,17 A systematic study has been carried out in terms of the correlations of the F-S transition of MGFLs with the sub-Tg relaxation,19 crystallization,20 and relaxation modes.21 In order to clarify the structural origin of the F-S transition in GFLs, possible scenarios have been proposed. Jagla attributed the F-S transition in water to the competition a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064508/8/$30.00
between two different local structures.22 Liu et al. ascribed the pressure dependence of the F-S transition in water to a transition from a high-density liquid to a low-density liquid during cooling.10,23 Both Saika-Voivod and Way et al. related the F-S transition in silica and in a ZrTiCuNiBe liquid to a polyamorphic transition.11,12,14 The extended mode-coupling theory modified by Chong et al. predicted the existence of the F-S dynamic crossover in GFLs during cooling, which was connected with the change from the “cage effect” to the “hopping” process dominated dynamics.24 Although the modeling results have implications for the structural evolution of the F-S transition, experimental studies on such issue are still lacking due to the fact that the crystallization hinders directly probing the structure during the F-S transition, especially for MGFLs. Some physical properties of CuZr(Al) glasses or liquids have been investigated to some extent.25–32 However, to the best of our knowledge, the kinetic F-S transition in CuZr(Al) liquids has not been reported yet. By using the hyperquenching-annealing-calorimetric scanning approach, our previous work has demonstrated a three-stage sub-Tg relaxation pattern in CuZr(Al) liquids.19,29 This anomalous enthalpy change during cooling, which was also observed through molecular dynamics simulation, has been regarded as the thermodynamic evidence of the F-S transition in CuZr(Al) liquids.19,33 The hyperquenching-annealing-x-ray scattering approach could be able to indirectly detect the structural evolution during the F-S transition in MGFLs,34–36 since their structure can be arrested at high temperatures (i.e., the fictive temperature Tf 37) well above Tg and normally below Tliq by hyperquenching, and relax upon subsequent annealing, and
142, 064508-1
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finally is characterized by x-ray scattering. In the present work, we first measure the kinetic F-S transition in CuZr(Al) GFLs, and then analyze their structural evolution during the F-S transition by means of the hyperquenching-annealing-x-ray scattering approach.
II. EXPERIMENTAL PROCEDURES AND DETERMINATION OF LIQUID FRAGILITY A. Experimental procedures
The master alloys of (Cu50Zr50)100−xAlx (x = 0, 2, 4, 8) (in atom %) ingots for viscosity and calorimetric measurements were melted by arc melting under an argon atmosphere with purities ranging from 99.5% to 99.999%. High-temperature viscosity was measured upon cooling from about 400 K above Tliq in vacuum using a torsional oscillating viscometer.38 Samples were placed in a vessel hung by a torsional suspension wire. The vessel was set to oscillate on a perpendicular axis, and therefore, the motion was gradually damped due to frictional energy absorption and dissipation within the melt. Specimens sealed in a vacuum of 10−4 Torr were heated to 400 K above Tliq and held for an hour. Then, the samples were cooled to a given temperature and held for 30 min before the viscosity measurement started. At each temperature, the viscosity was measured for at least four times. Because the relaxation time of metallic melts above Tliq is very short (less than 10−8 s39,40), the measured viscosity can be regarded as the equilibrium viscosity. The hyperquenched (HQ) glass ribbons (GRs) were fabricated by single copper-roller spinning apparatus under argon atmosphere. The GRs were spun at the circumferential velocity of 25 m/s. The master alloys were re-melted by the high-frequency induction technique and rapidly solidified into GRs. Calorimetric measurements were performed using a differential scanning calorimeter (DSC) in a Netzsch DSC 404 with high-purity standard platinum pans under a constant flow of high-purity argon, using pure indium (99.999% mass percent) and zinc (99.999% mass percent) standards and a sample mass of 20 ± 0.5 mg. All the DSC measurements were conducted in a flowing (80 cm3/min) argon gas at a heating rate of 20 K/min.36 The standard glass subjected to a standard cooling rate of 20 K/min was compared to the fresh samples and the annealed samples in order to determine their Tf s and Tg s.36,37 Here, the fresh samples refer to the as-quenched samples prior to annealing, and the standard glass refers to the glass that was cooled at the standard cooling rate of 20 K/min.37 Note that Tf is the temperature at which the structure of glasses is frozen-in during cooling. The x-ray scattering measurements were carried out on a Bruker-AXS D8 ADVANCE x-ray diffractometer equipped with a diffracted beam monochromator set for a Cu Kα radiation. Data were collected in the 2θ range of 10◦∼90◦ with a step size of 0.016 55◦ and a step time of 0.25 s at room temperature. To analyze the structural changes quantitatively, total structure factors (interference functions) S(Q) and pair distribution functions (PDFs), g(r), are extracted from the diffracted intensity patterns, where Q = (4π/λ) sin θ is the scattering vector and λ is the wavelength of the x-ray. PDF is
J. Chem. Phys. 142, 064508 (2015)
therefore obtained as the equation,41 1 g (r) = 1 + 2 2π r ρa
Q max
Q [S (Q) − 1] sin Qr dQ,
(1)
0
where r is the radius from the center of an atom to a certain shell close to the central atom, and ρa = ρN A/ ⟨A⟩ is the average atomic density of sample. Here, ρ is the mass density of sample, N A the Avogadro constant, and ⟨A⟩ the atomic mass of sample. B. Equations for calculating the fragility index (m)
The rapidity of the viscosity (η) changes of glass-forming liquids with temperature near Tg can be characterized by the fragility index m, which can be derived from the Mauro–Yue– Ellison–Gupta–Allan (MYEGA) viscosity model,42 ( ) C B , lg η = lg η ∞ + exp T T
(2)
where η ∞ is the viscosity at the high temperature limit,42,43 and B and C are fitting parameters. Combining Eq. (2) with m = ddTlog/Tη , the fragility m is obtained as42 ( g ) T =Tg m=
( ) ( ) B C C 1+ exp . Tg Tg Tg
(3)
Alternatively, the parameters B and C and, thus, m can be acquired by the dependence of the heating rate ϕ on the fictive temperature Tf in the vicinity of Tg using the DSC.37 With this method, Eq. (2) can be rewritten as lg ϕ = lg ϕ∞ −
( ) B C , exp Tf Tf
(4)
where ϕ∞ is the heating rate at the limit of fictive temperature. The value of m calculated by this method agrees well with that obtained by the kinetic method.44 Here, we explain the reasons and advantages for utilizing the MYEGA viscosity model (Eq. (2)) in the present work, instead of generally accepted Vogel-Fulcher-Tammann (VFT) model (lg η = lg η ∞ + B/(T − T0)). First, the configurational entropy at T0 is zero for the VFT model, which is divergent to the disputable possibility that the configurational entropy is positive at all temperatures.45 In this regard, the MYEGA model offers a more realistic extrapolation of the configurational entropy in the low-temperature limit than the VFT model.42 Second, when the viscosity model is involved to calculate the fragility m, the VFT model shows a poor fit for large-fragility liquids, while the MYEGA model performs well.1,42 Considering the large fragility of wide range of m values in MGFLs, it is much better to choose the MYEGA model to quantify m values. The third advantage is that the distribution of η ∞ values of the MYEGA model is much narrower than that of the VFT model based on best-fit viscosity curves of 568 GFLs.42
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FIG. 1. The Angell plot, i.e., logarithmic viscosity (log η), as a function of the Tg scaled temperature T for (Cu50Zr50)100−xAlx (x = 0, 2, 4, 8) (in at. %) with error bars. Dashed and solid curves are the fits of the MYEGA equation (Eq. (2)) to the high temperature and low temperature viscosity data, respectively. Inset: High temperature region of the Angell plot for Cu48Zr48Al4, where error bars are given.
FIG. 2. The fit of the experimental Angell plot to Eq. (5) for the Cu46Zr46Al8 liquid in the entire temperature range (solid curve). The dashed and dasheddotted curves represent the strong and fragile terms, respectively, and their intersection point is the characteristic temperature Tf -s of the F-S transition.
coefficient.49 The distinct difference of the thermal expansion coefficient between 2Tg and Tg suggests a crossover from a fragile to a strong liquid during cooling in the supercooled regime of CuZr-based alloys. The characteristic temperature Tf -s is an important value, since it defines the temperature of the occurrence of the F-S transition. The Tf -s can be calculated by the extended MYEGA model,15
III. RESULTS AND DISCUSSION A. Characteristics of the F-S transition phenomenon in CuZr(Al) MGFLs
Figure 1 shows the viscosity data of the CuZr(Al) GFLs in both the high temperature (HT) range, i.e., above the Tliq, and the low temperature (LT) range near the Tg.30 As a typical case, the distinct error bars at HT range have been shown in the inset. At the temperatures above Tliq, the viscosity values are around 10−2 Pa s of which the magnitude accords with those alloys around Tliq reported previously.46,47 The viscosity data in HT and LT ranges were fitted to Eq. (2) separately (see the dashed and solid curves in Fig. 1). According to Eq. (3), the HT liquid fragility index mHT and the LT liquid fragility index mLT of four CuZr(Al) liquids have been obtained, as shown in Table I. The mLT value of Cu48Zr48Al4 is quite close to that (mLT = 43 ± 5) obtained from DMA measurements.48 The mLT values of the four MGFLs are in the range of 32∼53, indicating that the CuZr(Al) GFLs at LT are relatively strong. In contrast, the mHT is much larger than mLT. The ratio of mHT to mLT, i.e., f = mHT/mLT, has been used as the strength parameter to describe the extent of the F-S transition.15,21 In Table I, the f values for all the CuZr(Al) GFLs are much larger than 1, implying the existence of the kinetic F-S transition in CuZr(Al) GFLs upon cooling. This finding accords with the phenomenon reported by Bendert et al.49 They observed that, compared with the GFLs with low glass-forming ability in CuZr binary liquids, those with high glass-forming ability have a smaller thermal expansion coefficient near Tg, whereas in the vicinity of Tliq (2Tg to be precise), they exhibit a larger
log η = log η ∞ +
T W1 exp
(
− CT1
1 ) ( ) , + W2 exp − CT2
(5)
where C1 and C2 correspond to two constraint onsets reflecting different dynamic mechanisms at HT and LT, i.e., the fragile and strong terms (weighted by W1 and W2, respectively). Fig. 2 shows the fit of the experimental viscosity data to Eq. (5) for the Cu46Zr46Al8 liquid (solid curve). The dashed-dotted curve refers to the fragile term, whereas the dashed curve represents the strong one. Tf -s is thus calculated as follows: ( ) ( ) C1 C2 W1 exp − = W2 exp − , T f −s T f −s C1 − C2 . (6) T f −s = ln W1 − ln W2 According to Eq. (6), the characteristic temperature Tf -s is the point where the contribution of the fragile term at HT to the whole dynamics is equal to that of the LT strong term. Below Tf -s, the strong term will become dominant. Table II shows the fitting parameters of Eq. (5) for four CuZr(Al) GFLs, and the correlation factors of the fits to Eq. (5) for four liquids are no less than 0.9998. Using these parameters, the Tf -s values
TABLE I. Fragility indices (m HT and m LT) and activation energy differences ∆E of CuZr(Al) GFLs in HT and LT ranges, respectively. f = m HT/m LT, i.e., the strength parameter of the F-S transition in GFLs during cooling.15,21 Composition (at. %) Cu50Zr50 Cu49Zr49Al2 Cu48Zr48Al4 Cu46Zr46Al8
Tg (K)
m HT
m LT
f
∆E HT (kJ/mol)
∆E LT (kJ/mol)
664 674 683 701
127 129 117 130
32 34 44 53
4.0 3.8 2.7 2.5
55.97 61.66 57.88 67.19
10.60 11.33 11.78 21.43
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TABLE II. The glass transition temperature Tg, the F-S transition temperature Tf -s, and fitting parameters of Eq. (5) of four CuZr(Al) GFLs. Composition (at. %) Cu50Zr50 Cu49Zr49Al2 Cu48Zr48Al4 Cu46Zr46Al8
Tg (K)
log η ∞ (Pa s)
W1
C1
W2
C2
Tf -s (K)
664 674 683 701
−2.23 −2.56 −2.32 −2.20
265 1614 373 1809
14 180 16 867 15 282 16 716
0.000 35 0.000 38 0.000 80 0.001 51
795 884 1405 1901
989 1047 1063 1059
of the CuZr(Al) GFLs are calculated to be in the range of 989∼1063 K. The Tf -s values in the present work are comparable to those of some non-MGFLs with F-S transition denoted by the F-S dynamic crossover temperature in literature.6 In Fig. 3, we plot Tf -s against Tg for 98 GFLs including metallic systems, network systems, and organic systems. The characteristic temperatures of MGFLs are derived from Eq. (6) as listed in Table III.15,17,50–54 For the non-MGFLs in Fig. 3, the Tg and Tf -s values are taken from Ref. 6. It is seen that all of the Tg values of metallic glasses fall in the middle of the temperature range. The correlation between Tg and Tf -s is found to be the linear one: Tf -s ≈ (1.36 ± 0.03)Tg with a correlation factor of 0.9599. The viscosities at Tf -s are listed in Table III, where the average lg(η f -s) value for MGFLs is about 0.86 in Pa s, smaller than that of non-MGFLs (around 2 Pa s).6 The relationship Tf -s ≈ 1.36Tg in Fig. 3 can be an important feature of the F-S transition in GFLs. B. Structural evolution during the F-S transition of CuZrAl GFLs
In our previous work, we have verified that, as thermodynamic evidence, the anomalous sub-Tg three-stage relaxation pattern of the CuZrAl HQ GRs has the same structural origin as the dynamic F-S transition in MGFLs.19,29 As shown in Fig. 4(a), for the Cu46Zr46Al8 HQ GRs with the spinning circumferential velocity of 25 m/s, the anomalous relaxation pattern (reflected mainly by the distinct drop of dashed curve E) occurs when annealing temperature (Ta) changes from 583 to 623 K. In accordance with Figs. 4(a) and 4(b) shows the x-ray scattering patterns for the Cu46Zr46Al8
FIG. 3. Tg dependence of the Tf -s for 98 GFLs. The data are from Ref. 6 and Table III. Dashed red line is a linear fit to the data. The shadow area gives a guide to the dispersion of the data.
HQ GRs annealed at different Ta s below Tg for 1 h. In Fig. 4(b), no crystalline peak is observed except for the one annealed at 643 K (not shown), indicating that all the GRs annealed below 643 K are amorphous. Apparently, the annealing temperatures have no detectable influence on both the positions and intensity of the main peaks, whereas the peak intensity at lower angles is significantly affected by the annealing temperature, i.e., it decreases with an increase in Ta. Figure 5 shows the structure factors S(Q) for the annealed Cu46Zr46Al8 GRs. There are two low Q minor peaks and one main peak on each curve, and this is similar to what has been observed in a nickel-based superalloy liquid.56 In literature, the low Q minor peaks prior to the main peak are often called the “prepeaks.”57–59 The position of the main peak (denoted by Pm in Fig. 5) remains unchanged with Ta, indicating that the structural units with short-range order (SRO) are stable upon cooling, and the position of this peak accords well with that obtained from EXAFS measurements.55 This unchanged peak position may be due to the originally glassy state of the annealed samples in the present work rather than a liquid state, because for the latter, the main peak position often has a detectable shift with the decrease of temperature.60 However, the position of the two prepeaks (denoted as P1 and P2) varies with the annealing degree, particularly evident for P1. For P2, the position shifts slightly towards a higher Q value with Ta increasing, and this could be associated with the monotonic decrease of intermediate range ordering units.61 When Ta ≤ 583 K, P1 moves towards a lower Q value with an increase in Ta. When Ta increases from 593 to 613 K, this negative relation is interrupted. Instead, P1 shifts towards a larger Q value with a higher Ta. When Ta ≥ 623 K, P1 shifts to a lower Q with Ta increasing again. In contrast to the non-monotonic change of the P1 position, its intensity decreases especially when Ta increases above 583 K. Since the non-monotonic evolution of the P1 position occurs in the same Ta region as does the three-stage enthalpy relaxation (Fig. 4(a)), a drastic transition of the medium-range ordering (MRO) structure corresponding to the P1 must happen, which is responsible for the F-S transition in CuZrAl GFLs. The structural unit size corresponding to the P1 is calculated using the Ehrenfest’s formula ln Rc = 1.23 ∗ 2π/Q p p ,62 where Qpp is the position of the P1. The statistical errors have been evaluated by the method developed by Egami63 and they get bigger when the prepeak becomes broader. The Ta dependence of Rc is illustrated in the inset of Fig. 5, as well as the error bars of the data. An anomalous decrease of Rc is observed when Ta increase from 593 to 613 K. Since the increase in Ta generally causes a decrease in Tf , this non-monotonic change of Rc implies a discontinuity in the MRO structural evolution during the F-S transition of GFLs. The size of the MRO
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TABLE III. Tg, Tf -s, and log(η f -s) values of 20 MGFLs in an increasing order of Tg. Composition (at. %) La55Al25Ni5Cu15 La55Al25Ni15Cu5 Pr55Ni25Al20 La55Al25Ni20 Sm55Al25Co10Cu10 Ce55Al45 Sm55Al25Co10Ni10 Al87Co8Ce5 Gd55Al25Ni10Co10 Sm50Al30Co20 Gd55Al25Co20 Zr52.5Cu17.9Ni14.6Al10Ti5 Cu50Zr50 Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 Zr57Cu15.4Ni12.6Al10Nb5 Cu49Zr49Al2 Cu47Ti34Zr11Ni8 Cu48Zr48Al4 Cu46Zr46Al8 Ni60Zr30Al10
Tg (K)
Tf -s (K)
log(η f -s) (Pa s)
References
459 474 480 491 534 541 553 558 579 586 589 661 664 668 670 674 676 683 701 738
681 778 739 646 838 670 714 706 729 839 737 1014 989 1047 1059 1047 1057 1063 1059 1121
0.17 −0.29 0.65 1.37 0.71 2.01 2.17 2.14 2.50 1.51 2.54 0.16 1.00 0.28 0.15 0.38 −0.53 −0.11 −0.31 0.76
15 and 50 15 and 50 15 and 51 15 and 50 15 and 50 15 15 and 50 15 and 52 15 and 53 15 and 50 15 and 53 17 This work 17 17 This work 17 This work This work 54
structural units in the supercooled CuZr(Al) GFLs does not increase monotonically upon cooling as predicted by AdamGibbs theory.64 Instead, they are dissociated into smaller clusters during the F-S transition. The dramatic decrease in the structural unit size Rc accords with the anomalous increase in enthalpy of the supercooled CuZr(Al) liquid during cooling around 1.3 ∼ 1.4Tg.19 Fig. 6 shows the g(r) curves for the Cu46Zr46Al8 glasses annealed at different Tas. In Fig. 6, peak positions and widths at the half maximum of the first peak in g(r) on the left-hand side shift slightly to the small values with increasing Ta, as shown by the violet dashed arrow. The shift of the first peak in g(r) is ascribed to the thermal agitation of different types of atoms and thus asymmetric redistribution of neighboring atoms to shorter and longer distances.65 The correlation radius r c′ is often used to describe statistically the averaged size of
MRO clusters in MGFLs. r c′ is the minimum radius where g(r) = 1 ± 0.02, and the error is estimated by the Fourier transition.66 The dependence of r c′ on Ta for the Cu46Zr46Al8 GRs is illustrated in the inset of Fig. 6. Clearly, r c′ exhibits a three-stage dependence on Ta, which is consistent with the change of the structural unit size Rc (Fig. 5). The decrease of r c′ with increasing Ta from 593 to 613 K further indicates the existence of the dissociation of the MRO clusters during cooling. Such non-monotonic evolution of the correlation length in supercooled liquids has also been reported in some theoretical simulation studies.67,68 It is known that the characteristics of clusters are closely related to the dynamics of liquids (e.g., liquid fragility).59 The difference (∆E) between the activation energy for atom aggregation (Ea) and that for cluster dissociation (Ed) can reflect the stability of clusters, and hence, viscous behavior
FIG. 4. (a) The isobaric heat capacity (C p) versus temperature for the HQ Cu46Zr46Al8 GRs annealed at different temperatures (Ta) below Tg for 1 h, exhibiting the effect of different Ta on the enthalpy relaxation pattern. Inset: The relationship between the onset temperature of the exothermic peak (Tonset) and the Ta.19 (b) X-ray scattering patterns after annealed at different Tas.
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FIG. 5. Structure factor S(Q) of the hyperquenched Cu46Zr46Al8 glasses with different annealing temperatures, Tas, for an hour. The bottom curve is extracted from the extended x-ray absorption fine structure (EXAFS) results in literature.55 The short-dashed lines and the dashed line illustrate the shift of the two prepeaks, respectively. Inset: The structural unit size R c of the first prepeak (P1) as a function of Ta.
can be described by the cluster kinetic model,69 ηg lg η = lg η g − lg η∞
(
T /T
) ×
Ωg g − Ωg , 1 − Ωg
(7)
where ln Ωg = (Ed − Ea )/RTg , η g is the viscosity at Tg, and R is the gas constant. Since the activation energy for the aggregation or association process is always less than that for cluster dissociation process during cooling, the ∆E(∆E = Ed − Ea) value should be a positive one.69 The smaller the ∆E value is, i.e., the E values of the two processes are more comparable with each other, the more stable the clusters in liquids are. By fitting Eq. (7) to the HT and LT viscosity data (Fig. 1), respectively, the ∆E values of four MGFLs in both HT and LT ranges (denoted by ∆EHT and ∆ELT, respectively) are obtained as listed in Table I. The ∆ELT values ranging from 10.6 to 21.4 kJ/mol, the magnitude of which is close to that of the Al-based MGFLs in LT range.59 The ∆ELT value is much smaller than the ∆EHT value for each composition. This indicates that the clusters in LT range after the F-S transition are more stable than those in HT range.
FIG. 6. Pair distribution functions, g (r ), of the HQ Cu46Zr46Al8 glasses with different annealing temperature Tas. Inset: Ta dependence of correlation radius (r c′).
The three-stage dependences of both Rc and r c′ on Ta (Figs. 4–6) and the considerable differences between ∆EHT and ∆ELT in Table I verify that the evolution mechanism of MRO clusters is different before and after the F-S transition. During the F-S transition, the MRO structures exhibit a strong tendency to dissociate, rather than to aggregate with other free atoms or clusters. A schematic scenario is proposed in Fig. 7 in order to reveal the structural evolution of the F-S transition in CuZrAl GFLs. As suggested by the two-order-parameter (TOP) model70 and other two models developed for metallic glasses,71,72 we can describe the structure of supercooled Cubased GFLs in terms of both the rearrangements of free atoms and local ordering. Since icosahedra can cause topological frustration and decrease the atomic mobility in liquids and thus improve glass forming ability,73,74 we consider that locally ordered structures in CuZr(Al) GFLs are mainly composed of two types of icosahedra (SRO domain): partially symmetric (distorted) icosahedra and perfect fivefold-symmetric ones. When a liquid is cooled to a certain temperature above Tliq, free atoms will incorporate those in the vicinity to form partially symmetric icosahedra (Fig. 7(b)). The partially symmetric icosahedra continue to correlate with each other to build MRO clusters upon further cooling (Fig. 7(c)). In other words, the structural units in HT are dominantly composed of partially symmetric icosahedra in a relatively low-density state.10 When the liquid is cooled approaching Tf -s, i.e., when the F-S transition starts, both the number and the size of these MRO clusters are expected to increase to a critical value, and then remain almost constant. To minimize the energy of the system, these MRO clusters have to break partly down and, hence, are combined into more stable ones,72 e.g., those composed of perfect fivefold-symmetric icosahedra (Fig. 7(d)).55,75 When MGFLs are cooled further below Tf -s, the new stable MRO clusters aggregate together into larger ones in a high-density state contributing to the strong phase,10 as shown in Fig. 7(e). In terms of the above scenario of structural evolution during the F-S transition in CuZrAl GFLs, the competition among the MRO clusters with different configurations of icosahedra is the characteristic of the F-S transition as illustrated in Fig. 7. Such competition of icosahedra has been confirmed by theoretical modeling on the microstructures in CuZr(Al) glasses or liquids, although the role of MRO size is somewhat neglected.73,76 Topologically speaking, icosahedral clusters with Cu-centered ⟨0 0 12 0⟩, ⟨0 2 8 2⟩, ⟨0 2 8 1⟩, ⟨0 3 6 3⟩, and Al-centered ⟨0 0 12 0⟩ configurations account for the largest fraction of CuZrAl glass structure in terms of the Voronoi tessellation method, whereas the icosahedra with perfect fivefold symmetry (i.e., ⟨0 0 12 0⟩ configuration) are the basic local structural motifs.55,75,77 When the temperature is above Tf -s, all kinds of icosahedra gradually increase and partially symmetric icosahedra have a larger fraction than the icosahedra with ⟨0 0 12 0⟩ configuration. However, below Tf -s, perfect fivefold-symmetric icosahedra with Cu-centered and Al-centered ⟨0 0 12 0⟩ configurations increase rapidly with temperature,33,78 whereas partially symmetric ones decrease smoothly.73 Thus, the evolution of icosahedra leads to a dramatic increase of more stable MRO clusters in CuZr(Al) GFLs at and below Tf -s. The strong competition between the perfect icosahedra and other structural units dictates the
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FIG. 7. Schematic structural evolution scenario of the F-S transition. (a) Replica of Fig. 2; (b)-(e) structural characteristic during the F-S transition of CuZr(Al) GFLs upon cooling. The purple dashed arrows indicate the corresponding structure in liquid state. The structural units are also illustrated by magenta solid arrows in details.
structural evolution, i.e., from the state shown in Figs. 7(b) and 7(c) to that in Figs. 7(d) and 7(e). Here, it should be pointed out that the scenario in Fig. 7 is essentially different from the TOP model, although the latter also considers the role of icosahedra during cooling.79,80 First, the TOP model generally describes the dynamic transformation in liquids from the Arrhenius-type to the VFT-type regime upon cooling.81 This is contrast to the F-S transition phenomenon (i.e., from the highly nonArrhenian to the relatively Arrhenian behaviour), which has been experimentally observed so far.7,10–12,14–17,21 Second, by considering the competition between long-range ordering structure and local tetrahedra in the LT region, the TOP model could be used to explain the F-S transition in covalent-bond tetrahedral liquids, such as water and silicon.82 However, it is known that the microstructure in metallic glasses is densely packed by polyhedral clusters (e.g., icosahedra) and the superclusters of polyhedral.25,83 Thus, compared to the TOP model, the structural scenario in Fig. 7 is suitable for describing the structural evolution in the F-S transition in MGFLs. Concerning the order of a phase transition, the F-S transition in MGFLs could be regarded as a first-order transition since it is accompanied by an abrupt change of enthalpy and density with temperature. From spectroscopic experiments (e.g., using quasi-elastic neutron scattering and Fourier transform infrared spectroscopy) and simulation studies, it has been found that during the F-S transition in water,84–86 the density of supercooled water drops suddenly between Tliq and Tg under ambient pressure. This indicates that the F-S transition in water is a first-order transition as well. Similarly, the F-S transition in the MGFLs under ambient pressure should be of the first-order as evidenced as follows. Based on a simulation study on a CuZr GFL, there is a release of the latent heat in a dynamic regime during the F-S transition upon cooling.33 Also, an abrupt change of density was observed around the Tf -s in a supercooled ZrTiCuNiBe liquid.14,87 In the present work, the three-stage patterns of
both the enthalpy release and the Rc in CuZrAl imply a discontinuity of density. Hence, the F-S transition in MGFLs should be a first-order transition.
IV. CONCLUSION
We have demonstrated direct evidence of the F-S transition in CuZr(Al) GFLs. By accessing the dynamic behavior of a large number of glass-forming liquids, we confirm that the F-S transition in GFLs occurs at Tf -s ≈ 1.36Tg, corresponding to an average viscosity of 100.86 Pa s for MGFLs. Both the three-stage patterns of structural evolution during cooling and the differences of cluster stability in different temperature regions indicate that the F-S transition in CuZrAl GFLs is attributed to the competition among the MRO clusters composed of different configurations of the locally ordered structural units. A schematic scenario is proposed to understand the structural evolution of the F-S transition in CuZr(Al) GFLs.
ACKNOWLEDGMENTS
We thank Professor K. F. Kelton for useful discussions and Lulu Sun for help in sample preparation. We also appreciate Jie Zhang and Xixia Zhang for experimental support. This research was financially supported by National Natural Science Foundation of China (Grant Nos. 51171090 and 51371107) and Basic Research Project of Qingdao Science and Technology Program (Grant No. 13-1-4-171-jch). 1C.
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