Abstract
Liquid–liquid transition, a phase transition of one liquid phase to another with the same composition, provides a key opportunity for investigating the relationship between liquid structures and dynamics. Here we report experimental evidences of a liquid–liquid transition in glassforming La_{50}Al_{35}Ni_{15} melt above its liquidus temperature by ^{27}Al nuclear magnetic resonance including the temperature dependence of cage volume fluctuations and atomic diffusion. The observed dependence of the incubation time on the degree of undercooling is consistent with a firstorder phase transition. Simulation results indicate that such transition is accompanied by the change of bondorientational order without noticeable change in density. The temperature dependence of atomic diffusion revealed by simulations is also in agreement with experiments. These observations indicate the need of twoorder parameters in describing phase transitions of liquids.
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Introduction
A liquid of certain complexity could assume different liquid phases of the same composition, a phenomenon called the liquid–liquid transition (LLT)^{1,2,3}. So far, reports of LLT in experiments are quite rare and mostly limited to systems with unique electronic structures. For instance, cerium atom is known to assume either a trivalent 4f^{1}(5d6s)^{3} or a tetravalent 4f^{0}(5d6s)^{4} electronic structure, with the latter having a much smaller ionic size favoured under high pressure^{4}. Polymorphism of pure Ce metal^{4,5} is well known and a LLT with a 14% change in density was observed in liquid Ce metal at 13 GPa^{6}. Theoretical studies of LLT using twoscale spherically symmetrical ramp potential^{7} captures the basic features of such LLT where substantial structural changes of first nearest neighbours take place. The phase transition of liquid to supercritical fluid observed in pure phosphorus above 1 GPa is also related to drastic changes of first nearestneighbour structures and electronic configurations of P atoms, accompanied by an estimated 40% change in density^{8,9,10}. An important question is whether density is always the dominant order parameter associated with LLT. Could LLT be a generic phenomenon that can also take place in liquids containing no elements such as Ce with unique electronic structures? The twoorderparameter description of liquids points out that thermodynamic properties of liquids cannot be described sufficiently by density ρ alone and additional order parameters such as the local bond order parameter S are required^{11,12,13}. It was suggested that LLT associated with the order parameter S is a generic property of liquids although its observation in practice can be difficult when the LLT temperature T_{LL} situates deep in the supercooled liquid region or at negative pressure^{11,12}.
Recently, a LLT was reported in glassforming liquid of Zr_{41.2}Ti_{13.8}Cu_{12.5}Ni_{10}Be_{22.5} (Vit1) where no substantial change of volume related to LLT was detected^{14}. However, since this LLT is in the undercooled regime below the liquidus temperature T_{liq}, it is difficult to obtain unambiguous signatures of firstorder phase transition such as the temperature dependence of the incubation time associated with the phase transition. To unambiguously demonstrate the presence of LLT and rule out the potential influence of crystallization, it is desirable to observe LLT above T_{liq}. Furthermore, to reveal the nature of the LLT in such systems, it is imperative to establish positive confirmation of the LLT by ab initio molecular dynamic (MD) simulations^{15,16}, which allow detailed analysis of structural changes associated with the LLT.
In this work, we observe such LLT with transition temperature T_{LL} above T_{liq} in metallic glassforming liquid La_{50}Al_{35}Ni_{15} that contains no elements such as Ce or P; the detection is made by hightemperature ^{27}Al NMR, which is very sensitive to the changes of atomic structures and dynamics of liquids^{17,18}. The liquid on LLT exhibits a sudden change in the temperature dependence of dynamics as reflected by a sharp change in the temperature dependence of NMR observables. In addition, ab initio MD simulations also reveal an abnormal temperaturedependent behaviour of atomic diffusion in the temperature range of LLT, in good agreement with experimental observations. Such agreement between experiments and ab initio MD simulations provides an opportunity to elucidate the nature of atomic structural changes associated with the LLT. It is found that while the change in density is insignificant, the bondorientational order (BOO) parameter represented by (see Methods) exhibits a substantial drop with decreasing temperature in the temperature range of the experimentally observed T_{LL}. This is consistent with the LLT theory based on the twoorderparameter description of liquids^{11,12}. Such changes of local structures and dynamics with temperature revealed by ab initio MD simulations are also shown to be consistent with changes observed by NMR based on the view of the potential energy landscape (PEL)^{19,20,21}.
Results
Phase transition above the liquidus temperature
La_{50}Al_{35}Ni_{15} glassy rod was used as the sample in this work (see Methods for sample preparation). Hightemperature differential scanning calorimetry (at a heating rate of 10 K min^{−1}) revealed a glass transition temperature (T_{g}) of 528 K and liquidus temperature (T_{liq}) of 970 K for the glassy system (see Supplementary Fig. 1). In situ hightemperature ^{27}Al NMR experiments were carried out above T_{liq} in a magnetic field of 9.4 T using a homemade hightemperature NMR probe^{22,23}. The melted sample cut from the glassy rod is a 10 mg single droplet, ensuring temperature homogeneity and sensitive detection of phase transition events. The ^{27}Al NMR spectrum at each temperature above T_{liq} is a single narrow peak of Lorentzian shape. As discussed later, the peak position of spectrum representing the Knight shift (K_{s}) is sensitive to changes of structures and amplitude of cage volume fluctuations^{17}, while the peak width is sensitive to diffusion^{18} as illustrated in Fig. 1a and b plots the K_{s} versus temperature T. Here the glassy sample (see Methods) was first heated to 1,143 K, held there for 2 h, and then cooled down continuously to 973 K at a constant cooling rate of 1 K min^{−1}. NMR spectra were taken every 1 K interval during such cooling process where each NMR spectrum was acquired in <20 s (see Methods). After cooling down to 973 K the sample was held there for 2 h and was then reheated to 1,143 K at a constant heating rate of 1 K min^{−1}. NMR spectra were taken again at every 1 K interval during the reheating process and the corresponding K_{s} versus T was also shown in Fig. 1b. The cooling curve of K_{s} varies linearly with T from 1,143 K down to 1,013 K with a slope of 0.22 p.p.m. K^{1}, followed by a sharp drop at 1,013 K within a narrow temperature range of 5 K (see the inset in Fig. 1b), and then continues with a linear Tdependence down to 973 K with a slope of 0.33 p.p.m. K^{−1}. The continuous reheating curve of K_{s} reproduces the values of the cooling curve except in the temperature range of 1,008–1,033 K where hysteresis occurs. The error of K_{s} measurement at a given temperature is smaller than 0.2 p.p.m. (see Supplementary Fig. 2). The effect of hysteresis is a few p.p.m., much larger than experimental errors. Therefore, the hysteresis is consistent with the undercooling of a firstorder phase transition. Above results were further evaluated by isothermal measurements. After completing the continuous reheating experiment described above, the sample was kept at 1,143 K for 4 h. NMR spectra were then taken at consecutively decreasing temperatures; at each temperature the system was equilibrated for 4 h before taking the NMR spectrum. Such isothermally measured K_{s} on cooling is plotted versus T in Fig. 1c along with three typical NMR spectra at 1,143, 1,043 and 1,023 K as examples. Subsequently, after reaching the lowest temperature of 973 K, the sample was reheated again and NMR spectra were taken at consecutively increasing temperatures; at each temperature the system was equilibrated for 4 h before taking the NMR spectrum. Such isothermally measured K_{s} on reheating is also plotted versus T in Fig. 1c. Similar to the continuous measurements, the isothermal cooling and reheating curves match perfectly with each other. A kink with slope change from 0.22 p.p.m. K^{−1} in hightemperature regime to 0.33 p.p.m. K^{−1} in lowtemperature regime can be clearly identified at 1,033 K. This temperature can be approximately taken as the transition temperature for the observed phase transition. It is of note that there is no change of NMR peak intensity (the integrated area of the peak) above and below 1,033 K. This suggests that all Al atoms belong to a single macroscopic phase whether it is above or below the phase transition temperature at 1,033 K. It is also noted that the temperature dependence of isothermal K_{s} is completely reversible during cooling and reheating after more than 10 cycles, implying that the changes in stoichiometric composition is negligible during the whole testing process; furthermore, the alloy ingot preserves a metallic shiny surface after 10 cycles of cooling/reheating ruling out oxidation effects.
Phase transition kinetics
To further elucidate the nature of the phase transition, we performed the isothermal NMR experiments to study the temperature dependence of the incubation time associated with the phase transition. After the sample was held at 1,143 K for 2 h, it was cooled down rapidly (∼20 K min^{−1}) to a chosen undercooled temperature below 1,033 K (herein, 1,033 K is estimated the transition temperature without undercooling on the basis of the results in Fig. 1b,c). At each undercooled temperature, the incubation time τ of the phase transition can be measured by monitoring isothermally the occurrence of phase transition by taking NMR spectrum every 4 s. As shown in Fig. 2a, the K_{s} values measured at 1,023, 1,020, 1,018 and 1,013 K before the transition are on the straight line extended from the values of K_{s} versus T above 1,033 K measured during isothermal cooling and reheating process, indicating the existence of undercooling of the hightemperature liquid (taking into account that 1,033 K is the transition temperature); after certain incubation time τ the transition takes place and K_{s} jumps to the values as expected from the isothermal cooling and reheating measurement below 1,033 K (see the blue line). The phase transition incubation time at four undercooled temperatures was measured systematically. Here incubation time measurements were repeated three times and the average of the three measured τ values for each temperature is plotted versus undercooled degree (ΔT=1,033 K−T) in Fig. 2b. The timescale of the undercooling effect with ΔT>20 K is too short to be captured by the current experimental approach. The incubation time drops quickly from 3,128 to 93 s by increasing ΔT from 10 to 20 K, consistent with a firstorder phase transition. The incubation time of phase transitions in the liquid state can be very long under small degree of undercooling in bulk metallic glass (BMG)forming systems^{24,25}. The change can be described empirically by τ∝T/(ΔT)^{m} with m=5 as shown in the inset of Fig. 2b. Homogeneous nucleation process of crystallization was also found to follow a powerlaw dependence^{26}. The issue of incubation time is very complex. It is still under intensive investigation even for liquid–solid transition in very simple systems such as CuZr alloy^{27}. Since the present case is a liquid–liquid transition rather than liquid to solid transition, the nucleation and growth processes can be quite different from traditional crystallization phenomena and more quantitative understandings of incubation time require more experimental and theoretical studies of LLT in the near future.
Changes of atomic diffusion
To further characterize the observed phase transition, it is important to investigate the change of dynamics associated with the phase transition. Atomic diffusion is an important characteristic of metallic liquid reflecting its structure and dynamics^{28}. For quadrupolar nuclei such as ^{27}Al with spin quantum number I=5/2, atomic diffusion gives rise to efficient spin–lattice relaxation due to diffusioninduced fluctuations of the electricfield gradient (EFG)^{18,29,30}. In the fast motion limit, the quadrupolar spin–lattice relaxation rate R_{Q} can be expressed^{31} as where k is a constant, η is the asymmetry parameter, is the maximum of the EFG tensor at Al site and τ_{c} is the correlation time of the EFG at Al sites, which measures the persistence time of the atomic cage surrounding the Al atom^{18,32,33}. It is of note that diffusion of all atoms neighbouring Al could cause fluctuations of the EFG tensor at Al sites. Smaller diffusion coefficient D leads to less frequent fluctuations of the EFG tensor and thus longer τ_{c}. Here D is proportional to 1/R_{Q} in the melt as being already established previously in other metallic liquids^{34,35}. R_{Q} can be derived from the measured spectral linewidth (see Methods). Figure 1d shows the data of 1/R_{Q} obtained from isothermal cooling and reheating, indicating that 1/R_{Q} decreases with decreasing temperature in the region from 1,143 to 973 K, but a qualitative change occurs at 1,033 K. Here 1/R_{Q} decreases nearly linearly with decreasing T above 1,033 K and shows a much steeper decrease with decreasing T after 1,033 K. The sharp change in the temperature dependence of 1/R_{Q} at 1,033 K indicates that atomic diffusion coefficient D exhibits an increased activation energy below 1,033 K, as reflected by the slope change at 1,033 K in the Arrhenius plots of log(1/R_{Q}) versus 1,000/T (inset of Fig. 1d). Besides the isothermal data of 1/R_{Q}, the inset of Fig. 1d also shows log(1/R_{Q}) versus 1,000/T obtained in the continuous cooling/reheating measurements; it reveals the same trend as that of the isothermal measurement except the hysteresis occurring in the temperature range of 1,008–1,033 K due to the undercooling effect captured by the fast cooling rate. This hysteresis phenomenon is in perfect agreement with the temperature dependence of K_{s} measured in the continuous measurement shown in Fig. 1b.
Structure and dynamics from ab initio MD simulations
To reveal the structural origin for the observed phase transition above T_{liq}, we pursued the atomic structure and dynamics of the liquid via ab initio MD simulations. In ab initio MD simulation, the atomic forces are determined with the firstprinciple calculations without using any experimental input or empirical potentials (see Methods). So far, plenty of studies have demonstrated that the independent ab initio MD simulations successfully obtain very reasonable and reliable atomic structures for liquid and amorphous materials^{36,37,38,39}. Ab initio calculations are also capable of monitoring the evolutions of structure and dynamics in the liquid during the cooling process, so that direct comparison to experimental results of liquid dynamics can be made and a link between dynamics and atomic structures of liquids can be established. Figure 3a shows a typical simulated atomic configuration. To obtain dynamic information of liquids, we analysed the selfdiffusion coefficient (D) of each element in the liquid at various temperatures based on the calculation of the meansquare displacement (MSD; see Methods). As shown in Fig. 3b, a clear slope change of the average D is observed around 1,040 K. Among the three elements in the alloy, Ni and La (especially Ni) exhibit more pronounced slope change, while Al displays only a slight change; this suggests that Ni makes a major contribution to the abnormal dynamics of the liquid around 1,040 K. Owing to the thermal fluctuations in hightemperature MD simulations, it is difficult to reveal small discontinuous change by ab initio MD. However, continuous change of D but discontinuous change of its temperature dependence are typical for LLT according to previous theoretical studies^{40,41}. As discussed above on the change of 1/R_{Q} versus T, diffusion of all atoms neighbouring Al will cause fluctuations of the EFG tensor at Al sites such as that of Ni. Thus, the slower temperature dependence of the selfdiffusion coefficient of Ni in the hightemperature region is fully consistent with the slower temperature dependence of 1/R_{Q} above T_{LL}. Furthermore, the transition temperature in dynamics from the ab initio MD simulations is very close to the temperature of 1,033 K in the phase transition observed by NMR. Such high consistency between experiments and ab initio MD simulations further validates the LLT observed in the liquid. It also provides an opportunity to link the LLT with the atomic structural evolution.
To investigate the atomic structural evolution, the total pair distribution functions and the coordination number of each element at various temperatures were calculated and are shown in Fig. 3c. It can be seen that total pair distribution functions and coordination numbers do not show any noticeable change with temperature, indicating that the change of the density in the liquid within the investigated temperature range is very small. Therefore, it can be concluded that the observed LLT in the present Labased alloy system is not a densitydriven phase transition and is very different from what was observed in Ce^{6} and P^{8}. Some other order parameters related to local atomic structures have to be identified for understanding the mechanism of LLT revealed in above analysis^{12}.
To find out the underlying local structure change, we did the analysis of the BOO based on spherical harmonics, which is a quantitative description of the different bondorientational symmetry around a central atom^{42} and is a sensitive measure to the change of local structures (see Methods). Specifically, is sensitive to the appearance of fivefold symmetry. values of facecentred cubic, hexagonal closepacked and icosahedron clusters are −0.01316, −0.01244 and −0.16975, respectively. Figure 3d shows the temperature dependence of the averaged and the individual contributions from La, Ni, Alcentred atomic clusters with error bars in La_{50}Al_{35}Ni_{15} melt. It is shown that below 1,050 K the system enters a temperature region where the individual s change significantly until below 1,000 K. The values of the average change slightly between −0.018 and −0.019 in the temperature range above 1,050 K, but drops to −0.021 below 1,000 K, indicating that La_{50}Al_{35}Ni_{15} melt changes its state from one with lower fraction of fivefold symmetry above the transition region to one with higher fraction of fivefold symmetry below the transition region. The overall trend of increased fivefold symmetry from above to below the transition does not imply that the fivefold symmetry around all atoms have to increase at the same time. The preference of icosahedral order for one element could be at the cost of other elements because of correlations due to short and possibly mediumrange orders. The temperatureinduced variations of of individual elements are coupled, and influence each other. In addition, Voronoi Tessellation analysis^{43} was performed to detect the changes in shortrange order in La_{50}Al_{35}Ni_{15} melt (see Methods). The results also indicate that some major Voronoi clusters change subtly around the transition temperature region (see Supplementary Fig. 3).
Discussion
The significance of the current experiment is that the observed phase transition around 1,033 K is significantly above T_{liq}=970 K. This allows detailed isothermal measurements to obtain the evidence of firstorder phase transition, such as the temperature dependence of the incubation time associated with the phase transition, and to elucidate the changes of dynamics associated with the phase transition without the influence of potential crystallization. The effect of crystallization can be easily detected by NMR when the sample is cooled below T_{liq}. Once the sample was cooled down to 960 K (<T_{liq}), as shown in Fig. 4a, the K_{s} value shows deviations when it was reheated above T_{liq}. The deviation of K_{s} near T_{liq} is large and still remains after equilibrating for 4 h near T_{liq}. This effect associated with crystallization is common in metallic alloys^{44}. Crystallization produces phaseseparated ingot, and thorough mixing to form homogeneous liquid near T_{liq} might be difficult due to many factors such as viscosity and gravity. This effect can be even more pronounced in BMGforming alloys due to enhanced viscosity. However, thorough mixing can be achieved quickly at elevated temperatures^{44} such as 1,100 K in our case. To rule out possible nanocrystallization and macroscopic phase separation associated with the phase transition, a glass ribbon sample was made by melt spinning at high quenching rate of 10^{5}–10^{6} K s^{−1} (see Methods) from 1,003 K (after cooling down from 1,143 K), which is below the phase transition temperature 1,033 K. Such rapidly quenched glass could capture the structure in the melt at 1,003 K such as the potential presence of nanocrystallization and macroscopic phase separation if they would have occurred. Figure 4b,c show transmission electron micrographs (TEMs) and highresolution TEM of the prepared glass ribbon. The results show that the quenched sample is completely amorphous without any trace of nanocrystallization and macroscopic phase separation. In addition, there is also no evidence of phase separation by NMR. A single sharp Lorentzian peak of ^{27}Al NMR was observed both before and after the transition without the change of peak intensity. Furthermore, K_{s} can be traced reversibly on cooling and reheating crossing the transition temperature 1,033 K over a relatively short time. Thus, liquid–liquid phase separation on macroscopic scale is very unlikely. Ostwald ripening and coalescence would make reversible mixing over a short time very difficult.
In metallic systems, the dominant contribution to K_{s} comes from the direct Fermi contact shift due to sconduction electrons. The orbital effect for Al is very small compared with the Fermi contact contribution except in cases of very narrow gap semiconductors^{45}. Even in such a case, the temperature dependence of the shift with T is very weak^{45}, unlike in the present case where the shift changes over 100 p.p.m. Therefore, the observed temperature dependence is dominated by the Fermi contact interaction, which is also confirmed in other metallic glassforming liquid^{17}. In such a case, K_{s} can be expressed as where χ_{P} is the Pauli paramagnetic susceptibility and P_{F} is the probability density of an electron wave function at the nucleus averaged over states at the Fermi level E_{F}^{46,47}. χ_{P} can be chosen as the volume susceptibility and electron wave function is then normalized over the unit volume. It is of note that direct numerical calculation of K_{s} requires knowing the precise value of the electron wave function at the nucleus and the calculation of the precise value of the Knight shift in metallic alloys by densityfunctional theory remains very challenging^{48,49}. However, the importance in the current study is not the absolute value of K_{s} but its temperature dependence. The K_{s}(T,V) is a function of the density (or the volume V with a constant number of atoms) and T. Since V is a function of T and pressure P, we have K_{s}(T,V(T,P)) Therefore, the following thermodynamic relation holds^{50}
The first term on the righthand side of equation (1) represents the change in K_{s} due to volumetric thermal expansion, and the second term represents the change in K_{s} due to temperatureinduced dynamic variation. In this study, the measured value of (∂lnK_{s}/∂T)_{P} is 2.8 × 10^{−4} and 4.1 × 10^{−4} K^{−1} above and below 1,033 K, respectively. (∂lnK_{s}/∂V)_{T} is usually negative with a value of −1.0 for Al as determined from its pressure dependence^{51}. The volumetric thermal expansion coefficient (∂lnV/∂T)_{P} is estimated to be ∼10^{−4} K^{−1} for La_{50}Al_{35}Ni_{15} liquid based on previously reported data^{52,53}. Therefore, the first term in equation (1) would contribute about −10^{−4} K^{−1} to (∂lnK_{s}/∂T)_{P} and the observed change of (∂lnK_{s}/∂T)_{P} from 2.8 × 10^{−4} to 4.1 × 10^{−4} K^{−1} might come predominantly from the explicit temperaturedependent term (∂lnK_{s}/∂T)_{V} in equation (1). The term (∂lnK_{s}/∂T)_{V} is related to thermal fluctuations of atomic volume (or the fluctuations of nearestneighbour atomic distance)^{17} and can be formally expressed as^{50}
where V_{0} is the thermal equilibrium volume. The timeaveraged mean squared fluctuation in volume can be expressed as using Taylor expansion, where α is the value of at T=T_{LL}, and β is a coefficient reflecting the fluctuation amplitude of atomic volume in the system^{17,50,54}, which is related to and will be discussed later on. Similar vibrationinduced linear temperature dependence was also observed previous in the chemical shift of hightemperature liquids^{55}. Since the fluctuation amplitude of atomic volume always decreases with decreasing temperature in metallic liquids, that is, β is always positive, the observed K_{s} will decrease with decreasing T both in hightemperature and lowtemperature liquids, irrespective of the presence of local fivefold symmetry represented by . In the liquid state, the relevant fluctuation to the NMR observation is Al atomic volume fluctuation before cage collapsing and is thus of high frequency^{17}. is on the order of 1 (ref. 50). Therefore, the observed change of (∂ ln K_{s}/∂T)_{P} determined by the change of (∂ ln K_{s}/∂T)_{V} is predominantly the result of the change of the coefficient β. The larger slope of K_{s} versus T below 1,033 K indicates that the magnitude of Al atomic volume fluctuations decreases faster with decreasing T below T_{LL} compared with that above T_{LL}. Therefore, the steeper slope of K_{s} versus T below T_{LL} is predominantly related to a change of cage volume fluctuation around Al. In addition to K_{s}, 1/R_{Q} is sensitive to the collapse of atomic cage and thus to diffusion^{18,32,33} (see Fig. 1a). Since diffusion of all atoms neighbouring Al could cause fluctuations of the EFG tensor at Al sites, the atomic diffusion D is proportional to 1/R_{Q}. It is clear that the diffusion of atoms always decreases with decreasing temperature in metallic liquids, leading to a decrease of 1/R_{Q} with decreasing T. Since decreasing cage volume fluctuations would lead to lower success rate of cage escape and slower atomic diffusion, the steeper decrease of the amplitude of cage volume fluctuations versus T below T_{LL} (as measured by the steeper decrease of K_{s}) would also lead to steeper decrease of diffusion (as measured by 1/R_{Q} shown in the inset of Fig. 1d). The temperature dependences of both K_{s} and 1/R_{Q} measure the dynamic properties with the former measuring cage volume fluctuation and the latter measuring the rate of cage collapsing (of atomic cages around Al atoms).
As discussed earlier, the change in density associated with the observed LLT is small, consistent with an earlier study of a metallic glassforming alloy^{14}. Therefore, the nature of LLT observed in La_{50}Al_{35}Ni_{15} melt is different from that observed in Ce (ref. 6) and P (ref. 8) where density exhibits drastic change. This indicates that density is not the dominant order parameter for describing the observed LLT in La_{50}Al_{35}Ni_{15} melt. The nature of LLT in La_{50}Al_{35}Ni_{15} melt is consistent with the twoorderparameter description of liquids proposed by Tanaka^{11,12}. In this twoorderparameter theory, two order parameters are invoked in describing LLT, namely, density ρ and local bond order parameter S characterized by BOO. It is proposed that there exist distinct locally favoured structures that are energetically more favourable and its population is defined as the order parameter S. These locally favoured structures interact with the surrounding environment represented by a term JS(1−S) (J is the cooperativity strength) in the free energy, which could lead to cooperativity, and a thermodynamic phase transition in liquid could occur between two free energy valleys, which are determined by two distinct values of the S parameter. Therefore, a LLT could correspond to a sudden change of S associated with a change of BOO (see Supplementary Fig. 4)^{11,12}. As demonstrated in the analysis of BOO versus T (see Fig. 3d), a significant decrease of the average indeed occurs before and after the LLT in La_{50}Al_{35}Ni_{15} melt, consistent with a substantial increase of locally favoured structures (that is, clusters with enhanced fivefold symmetry) below T_{LL}.
In the PEL picture^{19,20,21}, the liquid properties are associated with the manner in which a liquid system samples its inherent structures as a function of temperature. At high temperatures, the atoms with high kinetic energy are only weakly restricted and the liquid system is in the socalled free diffusion regime^{20}. Here the liquid system samples a broad region of the PEL and the sampled average inherent structure energy is shown to depend only weakly on temperature^{19,20}. Therefore, both cage volume fluctuations and diffusion rate decrease slowly with decreasing temperature as observed in simple metallic liquids^{56}. However, as LLT occurs with decreasing temperature, the liquid possesses more locally energetically favoured structures with increased fivefold symmetry shortrange order clusters (that is, more negative ); atomic diffusions are now more restricted with more stable cage structures and the system enters into the PELinfluenced regime^{18,19,20}. In such PELinfluenced regime, effects of energy barriers become important and the average energy of inherent structures is shown to decrease rapidly with decreasing temperature^{19,20}. Similarly, as the inset of Fig. 1d shows, diffusion exhibits increased activation energies with decreasing T similar to previous NMR and diffusion studies of liquids^{57,58}. Rapid decreases of cage volume fluctuations and diffusion rate are also expected in the regime where energy barriers play an important role as compared with the free diffusion regime. Therefore, steeper temperature dependences of K_{s} and 1/R_{Q} below T_{LL} are fully consistent with substantially increased locally favoured structures below T_{LL} as revealed by the change of in MD simulations.
In summary, the evidence of a LLT is identified by hightemperature ^{27}Al NMR in glassforming La_{50}Al_{35}Ni_{15} melt above its T_{liq}. Since the LLT occurs above T_{liq}, detailed experiments such as the dependence of the incubation time τ on the degree of undercooling ΔT can be carried out. The obtained experimental evidence is consistent with a firstorder phase transition. In addition, NMR also reveals significant changes of atomic diffusion behaviour on LLT. Evidence supporting LLT was also obtained by ab initio MD simulations; changes of atomic diffusion behaviour was revealed over the same temperature region in agreement with NMR results. Such agreement between experiments and ab initio MD simulations provides a unique opportunity to reveal the structural origin associated with the LLT. Ab initio MD simulations show that the observed LLT is associated with changes in BOO and such changes do not produce significant change in density. The present result indicates the order parameter S closely related to the BOO characterized by the average could be the dominant order parameter associated with the observed LLT (instead of density) in this alloy system containing no special elements such as Ce and P. The observed LLT is consistent with the theory of LLT based on the twoorderparameter description of liquids.
Methods
Sample preparation
The La_{50}Al_{35}Ni_{15} BMG rods with diameter of 3 mm were obtained by watercooled copper mould casting with highpurity ingredients of La, Al and Ni (purity>99.9 wt%) under argon atmosphere. Their amorphous nature was identified by Xray diffraction and no crystallization peak was found. A single piece of such BMG sample weighted about 10 mg was cut from the ascast BMG rod and used for the hightemperature NMR experiments. Experiments using different batches of samples give identical results. The samples were vacuum sealed in a quartz tube under high vacuum (better than 10^{−5} Pa) by a turbo pump after six times flushing with 99.9999% highpurity argon gas to prevent the sample from oxidation. The sample was supported on a magnesiastabilized zirconia substrate that prevents the melt from touching the wall of quartz container. The sample remains in spherical shape and its surface remains shiny after more than 10 times cooling and heating cycles at high temperatures.
To obtain the glass ribbon of La_{50}Al_{35}Ni_{15} fast frozen from its liquid state below 1,033 K for TEM, a BMG sample was heated up to 1,143 K, held there for 2 min and then cooled down to 1,003 K. After holding the liquid at 1,003 K for 2 min, the melt was rapidly quenched by melt spinning with a copper wheel at a speed of 50 m s^{−1}.
Hightemperature NMR experiments
The temperature was carefully calibrated and the gradient at the sample’s position varied <0.3 K over the whole temperature range by pinpointing the melting point of pure copper and pure aluminum using their temperature dependence of K_{s}. The accuracy of the temperature is ±2 K.
The hightemperature NMR experiments were carried out using a Bruker Avance III 400WB spectrometer with a magnetic field of 9.4 T. This gives a resonance frequency of 104.28 MHz for ^{27}Al with spin quantum number I=5/2. A standard one pulse with the 90° pulse width of 10 μs was used for the experiments above T_{liq}. Recycle delay of 20 ms was used for signal averaging. A total of 128 scans (about 20 s) were accumulated for each measurement during continuous cooling and reheating process at 1 K min^{−1}. A total of 5,120 scans (about 640 s) were accumulated in the measurement at every temperature during isothermal experiments to get a better signal to noise ratio. For the measurement of incubation time with different degree of undercooling, a total of 32 scans (about 4 s) were accumulated to detect the start of the transition behaviour promptly. All ^{27}Al NMR spectra were referenced to 1 mol l^{−1} Al(NO_{3})_{3} aqueous solution.
Calculation of the quadrupolar relaxation rate
R_{K,} which is the contribution of the magnetic interaction associated with K_{s}, was subtracted from the total spin–lattice relaxation rate (R) to obtain R_{Q}. R_{K} can be estimated from the Korringa relation^{47}
where γ_{A1}and γ_{e} are the gyromagnetic ratios of the aluminum nucleus and the electron spin, respectively; f is the enhancement factor due to electron–electron interactions. In this study, f was estimated to be 2.3 according to the equation (3) based on the data of K_{s} at 323, 373, 423 and 473 K. In the fast motion limit, spin–lattice relaxation rate and spin–spin relaxation rate are the same, which can be extracted from the full width at half maximum (Δv_{1/2}) of the Lorentzianshaped spectrum by Δv_{1/2}=π^{−1}R (refs 18, 47).
Ab initio MD simulations
The ab initio MD simulations were performed to achieve the atomic configurations of the liquid, using the projector augmentedwave method within the densityfunctional theory as implemented in the Vienna ab initio simulation package^{59}. Canonical NVT (constant number, volume, temperature) ensembles containing 500 atoms in a cubic box with periodic boundary conditions were well equilibrated in the liquid state at 1,193 K for 2,000 time steps (each time step is 3 fs). The temperature was controlled with a Nose–Hoover thermostat^{60}. Then the systems were cooled down to 893 K at a constant cooling rate of 0.05 K per step. In our simulations, the density of the system is determined as follows. At each temperature, the conjugated gradient method was used to obtain the inherent structure^{61} of the liquid. The density was adjusted to have a zero pressure of the inherent structure of the liquid. The inherent structure of the liquid at each temperature was further relaxed isothermally for 5,000 time steps for the analysis of the structure and dynamical properties. The ab initio MD simulations were carried out only at the Г point. Projected augmented plane waves^{62,63} with the generalized gradient approximation of Perdew and Wang (PW91) exchangecorrelation potentials^{64} have been adopted.
Calculation of selfdiffusion coefficient D
The selfdiffusion coefficient D in liquids was obtained by fitting the long time MSD at different temperatures after 15 ps isothermally annealing. MSD is defined as . Here r_{i}(t) is the atomic position of atom i at time t and denotes ensemble average. The diffusion coefficient D can be calculated by .
Bondorientational order parameter
To quantitatively describe the bondorientational symmetry around centre atom, Steinhardt et al. developed BOO by employing spherical harmonics^{42}. The BOO of atom i can be represented by the lfold symmetry as a 2l+1 vector defined as
where Y_{lm} are spherical harmonics and N_{i} is the number of bonds around atom i. The rotational invariants can be defined as:
and
Here the term in bracket in equation (6) is the Wigner 3j symbol. It has been found that q_{l} and W_{l} are the key to a type of cluster shape spectroscopy in liquids and glasses. The normalized parameter is a sensitive measure of the different orientational symmetries and often used to evaluate the BOO and differentiate the various local environments^{65}. Different atomic clusters may correspond to different values of . For example, values of facecentred cubic, hexagonal closepacked and icosahedron clusters are −0.01316, −0.01244 and −0.16975, respectively. Uncertainties in were estimated from the s.d. of in two independent MD simulations.
Voronoi tessellation
Voronoi tessellation divides space into closepacked polyhedral around atoms by constructing bisecting planes along the lines joining the central atom and all its neighbours^{66}. The Voronoi index <n_{3},n_{4},n_{5},n_{6}> is used to characterize the geometry feature of atomic clusters, where n_{i} (i=3,4,5,6) denotes the number of iedged faces of the Voronoi polyhedron. In our analysis, a cutoff distance of 5 Å was chosen so that the Voronoi index distribution was converged^{67}.
Additional information
How to cite this article: Xu, W. et al. Evidence of liquid–liquid transition in glassforming La50Al35Ni15 melt above liquidus temperature. Nat. Commun. 6:7696 doi: 10.1038/ncomms8696 (2015).
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51271082, 51271081, 51271195 and 51271197). M.T.S. and Y.W. acknowledge the support of the U. S. Army Research Office under Contract No. W911NF0910343. We thank Limei Xu for fruitful discussions.
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W.X. and Y.Y. conducted NMR experiments at School of Materials Science and Engineering and Wuhan National High Magnetic Field Center at HUST and M.T.S. conducted NMR experiments at UNCChapel Hill; W.X. and M.T.S. analysed the data; H.B.K. and W.H.W. made the samples and conducted differential scanning calorimetry experiments; H.P.Z. and M.Z.L. conducted MD simulations; L.L. supervised the experiments at HUST and Y.W. conceived and directed the project; W.X., Y.W., M.Z.L. and L.L. wrote the paper with major input from M.T.S., Y.Y. and W.H.W.
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Xu, W., Sandor, M., Yu, Y. et al. Evidence of liquid–liquid transition in glassforming La_{50}Al_{35}Ni_{15} melt above liquidus temperature. Nat Commun 6, 7696 (2015). https://doi.org/10.1038/ncomms8696
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DOI: https://doi.org/10.1038/ncomms8696
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