Structural crossover in a supercooled metallic liquid and the link to a liquid-to-liquid phase transition

The existence of a “crossover region” in glass-forming liquids has long been considered as a general phenomenon that is as important as the glass transition.^1–3 One potential origin for the crossover behavior is a liquid-to-liquid phase transition (LLPT). Although an LLPT is thought to exist in all forms of liquids,⁴ structural evidence for this, particularly in supercooled liquids, is scarce, elusive, and in many cases controversial. Experimental evidence for LLPTs has been found in only a few, primarily covalently bonded, liquids. Among these, the clearest evidence comes from high-pressure experiments. For example, a sharp pressure-induced first-order LLPT was demonstrated in phosphorus by in-situ synchrotron X-ray diffraction. Separately, a neutron diffraction experiment identified two forms of water with distinct densities, and a continuous transformation from the low-density form to the high-density form is suggested under applied pressure.⁵ However, other than when induced by high pressure, evidence for an LLPT in a supercooled liquid is far less clear.⁶ Unlike experiment studies of LLPT at temperature above melting point,⁷ a key challenge to the search for an LLPT in a supercooled liquid is the interference of crystallization during cooling. Crystallization induces major structural changes, which can overwhelm and therefore mask the more subtle changes associated with an LLPT. A recent letter by Tanaka et al.⁸ on triphenyl phosphate (TPP) serves to illustrate this point. Supercooling of TPP leads to a density change, but density data alone cannot reveal whether this is due to an LLPT, or to the formation of nano-crystals, a controversy that has lasted more than a decade. Using light scattering, Tanaka et al. showed that, in fact, both crystallization and LLPT occurred in their experiment, with the LLPT likely catalyzing the crystallization.

Thus, in spite of the extensive studies devoted to this topic, whether or not an LLPT occurs in a supercooled liquid, and if so, the nature of the LLPT remains unsettled issues. The containerless processing of liquids is a powerful experimental method to suppress crystallization, allowing access to the more deeply supercooled liquid region. An electrostatic levitation experiment by Li et al.⁹ suggested the possible occurrence of an LLPT in a metallic glass-forming liquid, based primarily on the observed hysteresis of the specific volume during heating and cooling. Motivated by this observation, we designed a synchrotron X-ray diffraction experiment to search for structural evidence for a possible LLPT. Below, we describe the structural changes observed during cooling to T_g that provide evidence for a structure crossover which suggests an LLPT in the supercooled liquid region. Part of the results has been presented at conferences.¹⁰ 

The selected sample was VIT106 (Zr₅₇Nb₅Al₁₀Cu_15.4Ni_12.6), one of the bulk metallic glass alloys studied by Li et al.⁹ and an excellent glass former. There were two experimental challenges: (1) the ability to levitate a high temperature liquid under high vacuum, while on the synchrotron beam line and (2) an X-ray beam line of sufficiently high intensity to allow quality data to be obtained at an approximately one Hz or faster data rate in order to capture the structure evolution during cooling. We overcame these challenges by using an electrostatic levitation facility constructed at Washington University in St. Louis (WU-BESL) on the 6-ID-D beamline at the Advanced Photon Source, Argonne National Laboratory.¹¹ Molecular dynamics (MD) simulations were conducted to gain physical insights of the structure crossover. The simulations were carried out for a ternary Zr₅₇Al₁₅Cu₂₈, approximating the alloy as a pseudo-ternary system Zr₅₇(Nb₅Al₁₀)(Cu_15.4Ni_12.6) based on atomic size considerations,^12,13 using LAMMPS code¹⁴ with the embedded atom method (EAM) potential developed in Ref. 15. Details of the experiments are described in supplementary material¹⁶ and can also be referred to Refs. 17–19.

Fig. 1(a) shows the temperature of a levitated VIT 106 sample during free cooling in the electrostatic levitator. The absence of a sudden rise in temperature (recalescence) in the temperature-time cooling curve demonstrates that the bulk of the sample was able to supercool through T_g (∼682 K) to form a glass. However, the appearance of small broad diffraction peaks below T ∼ 850 K indicates the formation of a small amount of nano-crystals, which will be discussed further below. Fig. 1(b) shows the specific volume measured during cooling. The scatter of the specific volume data near T_g was due to overcharging. A small discontinuity is indicated by arrows (see the inset) in the slope of the specific volume data; the slope becomes larger at T ∼ 1000 K, but reverts back to its original value at T ∼ 915 K. For comparison, data from Li et al.⁹ are superimposed, which showed a more pronounced effect. We repeated the specific volume measurements several times, and similar discontinuities were detected.

Fig. 1(c) shows the total structure factor S(Q) at selected temperatures. The diffraction data are characteristic of metallic liquids and glasses, with a first sharp diffraction peak (FSDP), followed by a second peak and a shoulder. The positions of these peaks are denoted as Q₁, Q₂₁, and Q₂₂, respectively. A rather dramatic change is seen in the evolution of the peak height for Q₂₁, which is illustrated in Fig. 1(d). The peak height shows a linear increase with temperature on cooling (due to the Debye-Waller factor) until T* ∼ 1000 K, where a distinct upturn is observed. There is no evidence of crystallization at T*, even in the difference curves for successive S(Q)s, which are sensitive to as low as 10⁻⁶ volume fraction transformed (see Fig. S1 in supplementary material¹⁶). Another upturn is seen at T ∼ 850 K. Close examination of the diffraction data confirms that this is where a small fraction of nano-crystals are first formed (see Fig. S2 in supplementary material¹⁶).

To avoid the subjectivity of an assumed function for the peak shape of the asymmetric FSDP, the first- and second- moments are used to characterize the FSDP's position and width, respectively. As shown in Fig. 2, upon cooling the position of Q₁ shifts linearly with temperature to higher values, corresponding to a decrease in the specific volume and an increase in the density. Again, a significant deviation from the linear relationship begins to develop at T*, and another upturn in Q₁ occurs at ∼850 K, the temperature corresponding to the formation of a small fraction of nano-crystals. To further ensure that T* is not due to crystallization, the integrated intensity was calculated over a Q-range of 3.0347–3.0601 Å⁻¹, a region where prominent diffraction peaks from the crystalline phase are located. As can be seen in Fig. 2, crystallization occurs only below T_x ∼ 850 K. The evolution of peak width and peak height of FSDP (see Fig. S3 in supplementary material¹⁶) showed consistent temperature dependence.

The reduced pair distribution function (PDF) G(r) was obtained by the Fourier transform of Q(S(Q)-1). Fig. 3(a) shows the G(r) at selected temperatures during cooling. The first peak, r₁, in G(r) corresponds to the nearest neighbor shell, and therefore can be used as a crude measure of the short-range order. The integrated intensity in G(r) over a r-range of 2.37–3.31 Å, in which G(r) shows a consistent growth, is plotted as a function of temperature in Fig. 3(b). Like in the S(Q) data, the integrated intensity of G(r) shows an upward deviation from the linear relationship below T*, indicating an enhanced short-range ordering in the low-temperature supercooled liquid.

What is most surprising is that the G(r) shows a growing shoulder on the second peak r₂ (at r ∼ 5.7 Å) during cooling, as marked by the black arrow in Fig. 3(a), indicating the growth of the extended-range order beyond the nearest neighbor shell. Of note, the height of the shoulder starts to grow only when the temperature is below T*. To illustrate this point, the integrated intensity of G(r) over the r-range of 5.69–5.70 Å is superimposed in Fig. 3(b). The integrated intensity is essentially unchanged on cooling until T* is reached, but below T*, there is a sharp increase. This result indicates that the fundamental clusters are becoming increasingly interconnected beyond the nearest neighbors below T*. Integration over the whole range of r, 5.60–5.78 Å, in which the shoulder peak develops, gave essentially the same result.

The results of this study provided unambiguous evidence of a structure crossover in the supercooled liquid region. This crossover is observed at a temperature 150 K above the crystallization temperature Tx. Further examination of the Time-Temperature-Transformation (TTT) diagram for this alloy confirms that the T* cannot possibly be due to crystallization.²⁰ At 950 K, the incubation time is already ∼10⁵ s. This can be compared to the length of our entire experiment, which lasted no more than 300 s. Chemical phase separation is usually a precursor of crystallization,^21–23 and the time scales for phase separation and crystallization are comparable. Thus, no phase separation can be expected either within the time scale of the present experiment.

In metallic glasses, the fundamental building blocks are solute-centered clusters, with solute or minor atom at the center surrounded by solvent or majority atoms.^12,13,24,25 Near the melting temperature, chemical and topological orderings begin to develop cooperatively and eventually percolate at the glass transition temperature, T_g, below which the amorphous material is kinetically frozen. This is demonstrated by MD simulations for Zr-Cu^26–28 and for Zr-Cu-Al metallic glasses,²⁶ with atomic clusters of icosahedral symmetry. Our data, summarized in Fig. 3(b), showed that the crossover is accompanied by enhanced short-range ordering. Furthermore, Fig. 3(b) indicates that below T*, there is increased ordering on a longer scale. Between T* and T_x, the integrated intensity of G(r) over the r-range of 5.69–5.70 Å increased by almost a factor of two. The increased correlation length is also reflected in the temperature dependence of Q₁, where a distinct decrease is observed in the 2nd moment of the peak, see Fig. S3 in supplementary material.¹⁶ 

MD simulations indicate that the dramatically increased extended-range order corresponds to the enhanced correlation between solute atoms of the fundamental clusters. Fig. 4 shows the evolution at r ∼ 5.7 Å of the partial pair distribution functions g(r) obtained by MD simulation upon cooling. While all atomic pairs contribute to the g(r) at r ∼ 5.7 Å, the temperature dependence of individual pairs is different, see Fig. S4 in supplementary material.¹⁶ The population of solute-solute pairs such as Cu-Al, Cu-Cu, and Al-Al increases below the temperature of T* ∼ 1000 K. However, the population of the solvent-solvent pair, i.e., Zr-Zr, shows a decrease below T*. The contrasting behaviors suggest that the increased correlation between solute atoms is responsible for the growing connectivity between clusters.

The observed structure crossover is suggestive of an LLPT in the supercooled liquid region as the experimental observations support the depiction of LLPT by current theories. Consider, for example, Tanaka's theory^29,30 for an LLPT which is predicated on two order parameters: density and bond ordering. The density order parameter maximizes the density (or packing) to lower the attractive interaction energy, which ultimately leads to long-range ordering or crystallization. The bond order parameter, on the other hand, describes the packing of “locally favored structures”¹ which captures both short- and medium-range order. A liquid is in an excited state at high temperatures. Upon cooling, the liquid transforms into an energetically more favorable state with higher density. Density changes were observed in the experiment by Li et al.,⁹ and to a lesser extent in this study, see Fig. 1(b). Fig. 3(b) shows growing orders upon cooling, in both short and, more importantly, longer length scales.

Recent MD simulations by Egami et al.³¹ for metallic liquids suggest that elementary excitations in high temperature metallic liquids are local configurational changes in the atomic connectivity network. These excitations, involving changes in the local coordination number, are the elementary steps to change the atomic connectivity network and directly control the macroscopic viscosity. A further MD simulation of Cu₆₄Zr₃₆²⁸ expanded this study and has identified a temperature T_D, located at approximately 1.4 Tg, where the diffusion coefficients for both Cu and Zr decrease abruptly and the lifetime of the interconnected clusters becomes longer than the Maxwell time for viscous flow. In essence, the ordered regions begin to “solidify” below this temperature. An estimate for VIT106 yields a T_D ∼ 954 K, remarkably close to the T* found in our experiment, below which the atomic clusters are shown to become increasingly connected. Taking into account the population of different atomic pairs, shown in Fig. 4, it is quite likely that the increased correlation between solute atoms characterizes the order parameter of the LLPT.

It may be tempting to associate the observed structure changes with the crossover predicted by the Mode-Coupling Theory (MCT).^9,32 In MCT, the crossover temperature T_c is determined by scaling the diffusion data as a function of temperature, $D∼[(T−Tc)/Tc]γ$⁠.³³ For Zr-based metallic liquids T_c ∼ 870 K,³⁴ which is more than 100 K lower than T* observed in the present experiment and in Li's work.⁹ Given this large difference, it is unlikely that the observed structure changes are related to the MCT crossover.

In summary, fast in-situ synchrotron measurements coupled with electrostatic levitation have enabled the direct observation of a structural crossover in a supercooled metallic liquid. Below the crossover temperature, the atomic clusters develop strong chemical and topological ordering, and the clusters also become increasingly connected. These results, when viewed in light of current theories and MD simulations, suggest that an LLPT has occurred in the supercooled liquids. The findings of our study will make an important contribution to fundamental understanding of the nature of structure crossover and the underlying LLPT in supercooled liquids and, in practical sense, the development of metallic glasses with superior glass forming abilities.

X.L.W. thanks W. L. Johnson for discussions alluding to his work in Ref. 9. S.L. and X.L.W. acknowledge Shenzhen Science and Technology Innovation Committee Grant No. R-IND8701 for financial support. The research at Washington University was partially supported by the National Aeronautics and Space Administration (NNX10AU19G) and the National Science Foundation (DMR 12-06707). The use of the Advanced Photon Source, an Office of Science User Facility operated by the U.S. Department of Energy (DOE) by Argonne National Laboratory, was supported under DOE Contract No. DE-AC02-06CH11357. The assistance of D. Robinson with the X-ray measurements is gratefully acknowledged.