Fragility crossover mediated by covalent-like electronic interactions in metallic liquids

Fragility is one of the central concepts in glass and liquid sciences, as it characterizes the extent of deviation of viscosity from Arrhenius behavior and is linked to a range of glass properties. However, the intervention of crystallization often prevents the assessment of fragility in poor glass-formers, such as supercooled metallic liquids. Hence experimental data on their compositional dependence are scarce, let alone fundamentally understood. In this work, we use fast scanning calorimetry to overcome this obstacle and systematically study the fragility in a ternary La–Ni–Al system, over previously inaccessible composition space. We observe fragility dropped in a small range with the Al alloying, indicating an alloying-induced fragility crossover. We use x-ray photoelectron spectroscopy, resistance measurements, electronic structure calculations, and DFT-based deep-learning atomic simulations to investigate the cause of this fragility drop. These results show that the fragility crossover can be fundamentally ascribed to the electronic covalency associated with the unique Al–Al interactions. Our findings provide insight into the origin of fragility in metallic liquids from an electronic structure perspective and pave a new way for the design of metallic glasses.

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Introduction
If a liquid is cooled to temperatures below its melting point, it forms either a crystalline solid or a metastable supercooled.In the latter case, further cooling will eventually result in the formation of a glass.One hallmark feature of this process is the increasingly sluggish dynamics of the liquid on cooling.Several properties, such as viscosity, relaxation time, and diffusion coefficient vary dramatically with cooling.Angell [1] introduced the fragility parameter m = dlog (x) /d (T g /T) | T=Tg (1) to classify liquids as being strong or fragile where x is a dynamic parameter such as viscosity or relaxation time.
Liquids with large m are denoted as fragile, and otherwise strong.Fragility reflects the degree of deviation of the liquid viscosity from the Arrhenius law.A larger deviation from Arrhenius behavior corresponds to a more fragile liquid [1][2][3][4][5][6][7][8].Angell suggested that covalency interaction could reduce fragility and SiO 2 has the lowest fragility [1].Interestingly, although the fragility concept is introduced for describing the properties of liquids [9][10][11][12], it has been reported to correlate with a range of properties of solid glasses.These include the glass-forming ability (GFA) [4,[13][14][15] and mechanical deformability [16,17] of metallic glasses (MGs), elastic properties [18][19][20], heat capacity associated with the glass transition [21,22], the Boson peak that is associated with vibrational properties and low-temperature excess heat capacity [23,24], the surface diffusion coefficient and the formation of ultra-stable glasses [25,26].Fragility is also an important indicator in the casting, annealing, and aging processes of glasses [27][28][29].It represents one of the key concepts across almost all kinds of glassy materials.
Despite its importance, the origin of fragility is not well understood [30][31][32][33].MGs and metallic liquids represent model systems to inquire about the fundamental origin of the fragility, because of their richness in compositions, large variation in m values, and their relatively simple atomic structures without the complex intramolecular effects in molecular or polymer glasses [15].Investigations have shown that fragility could have fundamental relations with the inter-atomic interaction potentials and the structures of the liquids [34][35][36][37][38][39][40][41].Krausser et al [42] developed an analytical expression for temperaturedependent viscosity and thus fragility as its first derivative.Their results suggest that glasses with a steeper repulsive part of the interatomic interaction are more fragile, which is consistent with the previous experimental findings in colloid systems by Mattsson et al [43].On the other hand, Pueblo et al [44], based on fitting the pair distribution function of different metallic liquids, demonstrated that stronger liquids have steeper repulsive potentials.Intriguingly, both proposals found simulation support.Studies also underscored the importance of temperature dependence of medium-range order structural changes for the fragilities of MGs [45].
These debated results indicate that the origin and governing factors of fragility remain to be clarified.We note that for realistic MGs, electron many-body interactions should not be overlooked.Recent studies have shown that MG might contain electron localization, either covalent-like or ionic-like; and this has an important consequence on the GFA and the mechanical properties [46][47][48][49][50][51][52].In chalcogenide glasses, the variation in fragility with compositions is related to their semiconductorto-metallic transition [53].The latter is associated with the enhancement of metallicity and the suppression of the directional covalent bonding [53].However, it is still unclear what roles these factors play in the fragility of MGs.This knowledge would be essential to understanding the origin of fragility and for designing MG materials.
From the experiment perspective, the fragility of MGs can be obtained by measuring the viscosity of the liquid as a function of temperature, i.e. the kinetic fragility m vis .A combination of techniques is usually required to cover the full viscosity range [15,[54][55][56].Alternatively, differential scanning calorimetry (DSC) has been widely used as a convenient tool to estimate the fragility of liquid from a glassy state [57][58][59][60][61][62], where the calorimetric fragility m DSC is obtained.Zheng et al [62] indicated that the relationship between the kinetic fragility measured by viscosity and the calorimetric fragility obtained by calorimetry is m vis = 1.25 m DSC .What's more, Evenson et al [63] investigated the effect of cooling rate on the liquid fragility of zirconium-based MGs by DSC.They found that the fragility obtained by DSC is closest to the liquid fragility obtained by viscosity fitting when the heating rate is identical to the cooling rate.However, there are at least three factors that impede the determination of fragility by DSC over wide composition spaces.
(i) The interference of crystallization.For example, in some Al-based and La-based MGs, the glass transitions were seldomly probed due to the early crystallization as indicated by DSC or viscosity measurements [22,[64][65][66][67].This crystallization is also a major concern in studies of many other properties of metallic liquids.(ii) The limited heating rate of traditional DSC.DSC measurements are narrow and slow, typically ranging from about 0.1-2 K s −1 (or 10-100 K min −1 ).This slow heating rate may not be able to capture fast kinetic events or transient phenomena that occur on shorter timescales than the experiment duration.The narrow window of the heating rate is also a limit for the fragility determination.(iii) Thermal history.As pointed out by Evenson et al [63], glasses with different thermal histories or measured using different protocols may exhibit different apparent fragility values.They reported that the real fragility value can be measured only when a protocol is used in which the heating rate is identical to the cooling rate, and that m DSC is closest to m vis .This requires the glasses to have stable supercooled regions and can sustain a 'heating-coolingreheating' thermal circle without early crystallization in the liquid state.
For these major challenges, fragility data is only available for a small number of MGs or metallic liquids [4,22].Usually, fragility is extracted only for one composition from a large alloy family, because only that specific composition exhibits good thermal stability against crystallization.There is a shortage of experimental data on the dependence of fragility on composition, which limits a fundamental understanding of the nature of fragility [4,68].
These challenges can be overcome by fast heating.For example, the crystallization of MGs can be effectively postponed or even fully suppressed by fast heating [69]; enabling the glass transition and supercooled liquid states to be revealed.With the so-obtained wide supercooled liquid region, one could apply the DSC protocol that yields reliable fragility data.For example, the glass transition and fragility of some Al-based MGs [22] and a Ni 80 P 20 MG [70] have been recently probed with heating rates higher than 100 K s −1 .
In this work, we use a chip-based fast scanning calorimetry (FSC) [71][72][73][74][75][76][77][78][79][80][81][82][83] to investigate the dynamics of the glass transition in a wide composition space, in a ternary La-Ni-Al system.We show that the FSC can probe the glass transition and fragility of MGs which are otherwise unfeasible by conventional DSC.We observe fragility dropped with the Al alloying in a small composition range, indicating a fragility crossover.We combine x-ray photoelectron spectroscopy (XPS), resistance measurements, DFT calculations, and deep learning-based interatomic forcefield to reveal that such a fragility variation is associated with covalency, which is due to the development of covalent-like bonding between the Al-Al interactions.The results consist of the view that fragility is determined by the rigidity of amorphous structures.Our findings suggest a fundamental origin of fragility in MG from the electronic structure perspective and guide to materials design.

Sample preparation
We selected the MG of the La-Ni-Al system for the experiments.High-purity La, Ni, and Al elements (purity ⩾ 99.99at.%)were used to melt the alloy ingots.Ingots were remelted five times in an arc-melting furnace under a Tigettered argon atmosphere to ensure composition homogeneity.Then, each ingot was remelted by RF induction, and the melts were injected onto the surface of the copper rolls to form amorphous ribbons under high-speed cooling.The amorphous properties of these ribbons were subsequently characterized by x-ray diffraction (XRD, Bruke D2 phaser) and DSC (Mettler Toledo DSC 3).

Calorimetry measurement
Calorimetric measurements for this experiment were performed using flash DSC (Mettler Toledo Flash DSC 2+).Samples were micro-cut under an optical microscope and the experimental sample size should be as uniform as possible to ensure the reliability of the experimental data.Samples were then transferred to the sample end of the sensor with the electrostatic manipulator hair.Measurements were completed under an argon gas flow of 80 ml min −1 .Finally, baseline measurements were performed, followed by the heat flow curves.MultiSTAR UFS1 sensor was used in this experiment, which was preconditioned and calibrated according to the manufacturer's recommendations before the experiment.

Resistivity measurement
Resistivity measurement was carried out in Physical Property Measurement Systems (PPMS).

XPS measurement
XPS was conducted on a Thermo Scientific ™ K-Alpha ™+ spectrometer equipped with a monochromatic Al Kα x-ray source (1486.6 eV) operating at 100 W. Samples were analyzed under vacuum (P < 10 −8 mbar) with a pass energy of 150 eV (survey scans) or 25 eV (high-resolution scans).All peaks were calibrated with C 1s peak binding energy at 284.8 eV for adventitious carbon.

Ab initio molecular dynamics (MD) and density functional theory (DFT) calculations
We used DFT calculations within the framework of the Vienna Ab Initio Simulation Package (VASP) [84,85].The projector augmented-wave potentials are used to describe the corevalence interaction, with the valence electrons described by periodic plane waves with a cut-off energy of 450 eV.
The supercells with 128 atoms were initially constructed with a periodic boundary condition for La 50 Al x Ni 50-x (x = 15, 20, 25, 30, 35) alloys, respectively.They were firstly melted and equilibrated at 2000 K (the temperature of the system was stabilized using a Nosé-Hoover thermostat) for 10 ps with time steps of 5 fs.Supercell volumes were adjusted to correspond to the zero pressure.Then the density of states (DOS), electron localization function (ELF), and charge density distribution were calculated after the system reached equilibrium.
Regarding ELF, it is defined as in which, D r is a measure of Pauli repulsion and scales with the probability density of finding another same-spin electron near the reference electron, related to the expressions, and D hr is the D r value in a homogeneous electron gas having the same local spin density.They are defined as And where τ σ is the positive-definite kinetic energy density and ρ σ (r) represents the probability density of a σ-electron appearing at r.

DNN potential and MD
A DNN potential of the La 50 Ni 50−x Al x system was obtained using the DeePMD-kit (DP) package [86,87].Data sets of 25 different compositions obtained by AIMD were fitted to yield high-precision interatomic interaction potentials.The details of the data sets are displayed in table S1.During training, the DP describes the energy of an atom as a function of the environment in which that atom is located, and the force as the first-order derivative of the energy.After 4 million iterations, the root-mean-square errors for energy and force can reach 6.69 meV atom −1 and 0.512 eV Å −1 (figure S11), respectively.This is a reliable accuracy for systems where the training set is a large span of temperature and pressure.For La 50 Ni 50−x Al x series models, MD simulations were carried out based on DNN potential, using the open-source LAMMPS code [88].All the models contain 8788 atoms, and they were prepared by quenching a liquid from 900 K to 200 K at a rate of 10 10 K s −1 with a time step of 2 fs.NPT ensembles, periodic boundary conditions, and a Nose-Hoover thermostat were applied for all MD simulations.The Voronoi analysis uses the open-source Voro++ code [89], and atomic radii were applied.

Fragility crossover
We selected the ternary La-Ni-Al MGs as model materials, due to their wide glass formation range (see figure S1 for the samples and XRD). Figure 1(a) shows conventional DSC (Q = 20 K min −1 or 0.333 K s −1 ) and FSC (Q = 200 K s −1 ) heat flow curves for a La 50 Ni 35 Al 15 MG as a typical example.The DSC heat flow curve indicates that the MG undergoes a sub-T g exothermic enthalpy relaxation, followed by crystallization after the glass transition.The temperature difference between the crystallization onset temperature (T x ) and the glass transition temperature (T g ) is defined as the supercooled liquid region.It is as narrow as 30 K and seems to be truncated by the crystallization before the T g is fully revealed.Therefore, it may not be possible to directly apply the 'heating-coolingreheating' DSC protocol to probe fragility in this MG.On the other hand, the FSC curve with a heating rate of Q = 200 K s −1 exhibits a clear glass transition and a wide supercooled liquid region (T x − T g = 70 K).This provides us an opportunity to measure the fragility of MGs by fast heating.
To determine fragility, we used FSC to heat-treat and scan the as-cast MG.As illustrated in figure 1(b), the as-cast sample was heated at a selected heating rate to reach a temperature T q , which is in the supercooled liquid region.We ensure T q is above T g but below T x .The sample was then cooled back to the glassy state using a cooling rate of Q c .This heatingcooling cycle was used to eliminate the thermal history and yield a glass with a consistent fictive temperature.
Then, a re-heating is conducted at a heating rate of Q h (Q h = Q c = Q) to a final temperature well above T x .The heat flow curve obtained for this heating shows a clear glass transition, whereas the other accompanying processes such as the shadow glass transition and enthalpy relaxation in front of T g disappear.In this way, one can obtain the T g value accurately at this heating rate.
After cooling down to room temperature, we obtained a fully crystallized sample and then scanned it upward at the same heating rate Q h to obtain a baseline.We then subtracted the baseline from the heat flow curve obtained by re-heating to obtain the final heat flow curve.By this protocol, the measured T g during the second heat flow curve is equal to the fictive temperature T f [63,[90][91][92][93], T f = T g .We repeat this procedure for a range of other Q, and record the T g as a function of Q.As previously reported by Evenson et al [63], this protocol is the most reliable method to probe the fragility of MGs from the glass state.
Figure 1(c) shows some typical FSC curves over the range of Q = 50-400 K s −1 heating rates.T g increases with the up-scan rate, which is consistent with the general rule of the thermally activated process.For systems like La-based MG, we fitted the fragility with an equation as suggested by Wang et al [94] Here The fitting to T f data yields fragility m = 42 as represented by the solid line in figure 1(d).The slope of the fitted solid line is the fragility [94].
When evaluating the fragility, one has to obtain a standard T g value.Typically, it is defined by a standard heating rate Q s = 20 K min −1 (0.3 K s −1 ).As shown in figure 1(a), such a low cooling rate could not reveal the T g .Here, we choose one of the FSC heating rates as the standard value.In figure 1(d), we can see that the difference between the fitted fragility values for Q s = 50 K s −1 and Q s = 300 K s −1 is small enough to be considered negligible.The two fitted lines are almost in the same straight line, indicating that the fitted fragility values are insensitive to the selection of the standard values.In the following, we select Q s = 50 K s −1 as the standard rate, T s f is the standard fictive temperature corresponding to T f measured at the standard rate Figure 2 shows the DSC and FSC heat flow curves for the La 50 Ni 50−x Al x series MGs.The upright and inverted triangles indicate T g and T x , respectively.Figure 2    We used the 'heating-cooling-reheating' thermal circle method based on FSC to measure the fragility of 20 different La-Ni-Al MGs (figures S2-S6).Figure 3 shows the data obtained from this process (the specific fragility values are listed in table 1).In figures 3(a) and (b), the fictive temperature T f and corresponding heating (cooling) rate Q of the La 50 Ni 50−x Al x series MGs obtained are plotted in the form of equation (5), where data for the same composition are represented using the same color.To better display the data and the fitted solid lines, we have horizontally shifted the data in figure 3(a).In figure 3(b), only the fitted solid lines are shown, for clarity.It can be seen that as the content of Al increases, the slopes of these fitted lines become smaller, which means that their fragility is decreasing.
We then investigated the composition dependence of the fragility of these La-Ni-Al MGs.As shown in figure 3(c), each black dot in the figure represents one composition.It can be seen that the variation of fragility with composition is neither homogenous nor linear.Instead, there are regions with lower and higher fragility, respectively.Figure 3(d Additionally, we measured the fragility of the (Cu 50 Zr 50 ) 100−x Al x (x = 0-8) series MGs using the same method as described above.With the increase of Al content, the fragility of Cu-Zr-Al is decreasing continuously.The specific fragility values are listed in table 1.Here, the fragility of the Cu-Zr-Al series MGs was determined by DSC.This is because the supercooled liquid region of the Cu-Zr-Al series MGs can be fully revealed on DSC, and their glass transition temperatures are too high to be measured by FSC.

Electronic structure
To understand how composition influences fragility, we carried out electronic structure studies of these MGs.We use the DFT model to study electron distribution.Particularly, the ELF is an effective method to determine the bond between atoms [95][96][97][98][99].It is defined to take values between 0 and 1.A value of ELF = 0.5 suggests that the spatial distribution of electrons resembles that of a homogeneous electron gas.As ELF approaches 0, D r tends towards infinity, indicating that the electrons are significantly more diffuse compared to the electron gas; in other words, there are almost no electrons present in that region.Conversely, a higher ELF value indicates that the electrons are more localized.Figure 4(a) shows the slice of the ELF distribution for the La 50 Ni 50−x Al x series models.We find that the percentage of the green-yellow region (0.3 ⩽ ELF ⩽ 0.8) between atoms on the plane expands with Al content above 20%.To further explore the variation of ELF, a statistical analysis of all ELF values was performed, and the results are shown in figure 4(b).The percentage of EFL > 0.5 varies more when the Al content is 20% to 25%.Interestingly, the trend of ELF > 0.5 (figure 4(b)) is the mirror of the variation of fragility with composition.In addition, we also study the electronic structure of the (Cu 50 Zr 50 ) 100−x Al x system, see figure S7, similar to that of the La 50 Ni 50−x Al x system.Both m and ELF > 0.5 change gradually with composition in the (Cu 50 Zr 50 ) 100−x Al x system.
The aggregation and distribution of electrons in figures 4(a) and (b) for these models are reminiscent of the covalent bonds, which share and localization of valence electrons between the bonding atoms.Figure 4(c) shows the threedimensional isosurface of partial charge density distribution.It can be observed that the distinct electron density aggregations between Al atoms in the La 50 Ni 15 Al 35 model.Furthermore, the Al atoms in this model share valence electrons, forming a covalent-like bonding structure.In contrast, the Al atoms in the La 50 Ni 35 Al 15 model are far away from each other and do not correlate.Therefore, it can be concluded that a higher Al content leads to more covalent-like bonds, and this effect is mainly reflected in the Al-Al interactions.

Atomic structure
To study the structure and dynamics of these systems, we use the DNN Potential method employing a deep learning technique, which is based on DFT to fit ab initio molecular dynamics (AIMD) data.What is more, its yielding interatomic interaction potentials have approximated empirical potentials' computational efficiency, and DFT accuracy at a large scale.
As shown in figure 5(a), based on a wide range of compositions for the training data set, we used the DeepPMDkit package [86,87] to train the DNN interatomic potential (more training details are contained in supplemental information).Based on this potential, we obtain La 50 Ni 50−x Al x series glass models at a cooling rate of 10 10 K s −1 (T g = 610 K, 615 K, 640 K, 680 K, and 690 K respectively, as indicated by the arrows).The alpha-relaxation time can be obtained when the ISF decayed to 1/e.Subsequently, figures 5(c) and (d) shows the evolution of the alpha-relaxation time with temperatures and content of Al.As can be seen, the alpha-relaxation time increases with increasing Al content and abruptly changes at above 20%.These results are consistent with that Al alloying would decrease the fragility of the liquids, agreeing with our experiment results.Figure 7(e) shows the variation of the total DOS with Al content.At the Fermi surface, there is a rise in DOS corresponding to the change of Al content from 20 to 25.The electrical resistivity (ρ) is related to DOS at the Fermi surface, and generally the higher the DOS, the higher the ρ.This is because when current is conducted in a metal, electrons scatter with phonons in the lattice.This scattering affects the motion of electrons and thus influences the transmission of current.When the DOS near the Fermi surface is high, it means that more electrons are moving near the Fermi surface and are therefore more likely to scatter with phonons, leading to an increase in ρ.This is consistent with the increasing trend of ρ with increasing Al content in figure 7(f).On the other hand, the increase in ρ results from the decrease in free electrons due to the enhancement of covalent-like character in the structure.These results are in agreement with XPS and DFT calculations.

Discussion
We collect fragility data for different MG systems with Al as the doping element.Figure 8 shows the data presented in a plot of m-Al content.
It has been widely suggested that a high GFA correlates with a strong liquid behavior [13-15, 36, 106-109].This is because strong liquids exhibit higher viscosity across the vitrification temperature range and are thought to be more densely packed, which reduces the kinetic factor of nucleation and growth of crystals, and promotes vitrification [15].For example, Johnson et al [4] analyzed the possible factors that influence the GFA and arrived at a simple empirical expression for GFA that depends exponentially on m and T g /T l .Stronger glass formation is favored by larger values of T g /T l and smaller values of m.Our studies indicate that deploying the electron interaction would be an effective method for fragility control.Enhancing or suppressing the covalency could be embodied by alloying or composition design.Besides the Al element in figure 8, other metalloid elements (B, P, S, etc) might be also effective.
Finally, we note that our results might be aligned with the Krausser-Samwer-Zaccone model [42], which states that the fragility is mainly controlled by the repulsive part of the interaction, steep repulsive interaction would result in high fragility, and the gentle repulsive one for low fragility.Our results indicate that the fragility drop as induced by Al-alloying is associated with covalency.Covalency would provide more attraction between two neighboring atoms in addition to the metallic interaction, which weakens the repulsive interactions.

Conclusion
In summary, we utilized FSC to investigate the composition dependence of fragility in MGs, which minimizes inferences such as early crystallization and thermal history under nonequilibrium conditions.Our experiments reveal that the addition of Al in the ternary La-Ni-Al MGs caused a decrease in fragility, i.e. a fragility crossover.By combining XPS, resistance measurements, and DFT-based calculations, we discovered that the decrease in fragility could be attributed to the development of covalent-like bonding between Al-Al interactions induced by the addition of Al.These results highlight the critical role of electronic structure in the origin of fragility in MG.

Future perspective
Fragility plays a significant role in the properties of solid glasses and is a crucial concept for various glass materials.However, there is a lack of fragility data for metallic liquids due to the challenges of viscosity testing.The origin of fragility remains poorly understood, but this study aims to address this issue using ultrafast calorimetric analysis to obtain fragility data for an alloy family.DFT calculations and deep learning potentials are also used to suggest the fundamental origin of fragility in MGs from an electronic structure perspective, which can guide material design.In the future, ultrafast calorimetric analysis is expected to provide a more comprehensive fragility database, and the correlation between fragility and electronic structure may lead to new opportunities for designing amorphous materials.For instance, the discovery implies the potential for hybrid amorphous materials that combine MGs with electronegative elements (O, N, S, P).
(a) shows the conventional DSC curves, with a heating rate of 20 K min −1 .Most of these curves have a narrow region of supercooled liquid as a common characteristic.Some of the MGs, such as La 50 Ni 37.5 Al 12.5 and La 50 Ni 35 Al 15 , immediately crystallized before the glass transition was fully revealed.As the Al content increases, the supercooled liquid region becomes wider.The widest supercooled liquid region is 62 K, concurring at La 50 Ni 15 Al 35 MG.The FSC heat flow curves of 200 K s −1 are shown in figure 2(b).At this heating rate, both the glass transition and the supercooled liquid state are fully exposed.For the

Figure 1 .
Figure 1.Thermal analysis and fragility.(a) Heat flow curves for La 50 Ni 35 Al 15 MG at low and high heating rates.The FSC chip sensor is shown in the upper right inset, with the sample positioned in the sensitive area (top of the FSC chip sensor) and the reference area located below.The crucible for DSC is displayed in the lower left inset, with the sample crucible on the left and the reference crucible on the right, both placed in the same DSC heating furnace for heating and cooling.(b) Schematic diagram of the scanning steps of FSC.(c) Heat flow curves of different heating rates measured by FSC.(d) Fictive temperature (T f ) dependence of logarithm heating (or cooling) rate Q.The solid line is fitted using equation (5).

Figure 2 .
Figure 2. DSC (20 K min −1 ) and FSC (200 K s −1 ) heat flow curves for La 50 Ni 50−x Alx series MGs.Tg is indicated by upright triangles, and Tx is indicated by inverted triangles.To facilitate comparison of the DSC and FSC curves in the temperature range of 300-700 K, a vertical line was drawn at 700 K, as shown in (a).

Figure 3 .
Figure 3. Composition and fragility variation in La-Ni-Al MG system.(a), (b) The relationship between the fictive temperature (T f ) and the logarithmic heating (or cooling) rate Q of La 50 Ni 50−x Alx (x = 12.5, 15, 17.5, 20, 25, 30, and 35) series MGs.The data is the same in both figures, but in (a), a horizontal shift has been applied for clarity, whereas in (b), only the fitted solid line is displayed.(c), (d) Statistics of the variation of fragility with composition in the La-Ni-Al MG system.
) shows the variation of fragility with composition in a few pseudobinary systems.For the La 40 Ni 60−x Al x , La 45 Ni 55−x Al x , and La 50 Ni 50−x Al x series MGs, the value of m decreases from 43 to 32 with increasing Al content.Notably, the fragility decreases more when the Al content increases from 20% to 25%.The compositional variation is dm/ dc = 2/at.%,which means that a one percent increase in Al content will reduce the value of m by 2.

Figure 5 (
b) shows the intermediate scattering function (ISF) of two representative compositions, it can be seen that the La 50 Ni 15 Al 35 model is much slower than the La 50 Ni 35 Al 15 model in the dynamics.

Figure 6 (
a) shows the composition-dependent N bonded which is the number of Al atoms that form Al-Al bonds (cutoff = 3.5 Å, which corresponds to the first minimum of the Al-Al pair correlation function), N Al is the total number of Al atoms.Their ratio varies with the Al content, reflecting the tendency of the Al atoms toward forming Al-Al bonds.It can be seen that N bonded /N Al increases with Al content, and when the Al content reaches 35%, more than 90% of the Al atoms form Al-Al bonds.The slices of the Al-Al bond configuration clearly illustrate this result, in figures 6(b) and (c).
Figure 6(d)  enumerates the pair correlation function g(r) at T g of La 50 Ni 50−x Al x series glassy models.The most pronounced changes are the first peak and its pre-peak, which correspond to the La-Al bond and the La-Ni bond (figures S8 and S9), respectively.

Figure 4 .
Figure 4. Electron localization function (ELF) and electron density distribution of La 50 Ni 50−x Alx (x = 15, 20, 25, 30, and 35, respectively) series model MGs.The slice (a) of the ELF distribution and the histogram (b) of ELF values are shown for La 50 Ni 50−x Alx series models.The color in (a), indicates that the more green-yellow, or close to red, the higher the value of ELF.The percentage of EFL > 0.5 varies more when the Al content is 20% to 25%.(c) The isosurface of the partial charge density distribution shows that compared to the La 50 Ni 35 Al 15 MG model, more covalent-like (Al-Al) bonds are found in the La 50 Ni 15 Al 35 model.

Figure 5 .
Figure 5. Dynamics analysis based on DNN Potential of La 50 Ni 50−x Alx (x = 15, 20, 25, 30, and 35, respectively) series model MGs.(a) The procedure of the DNN Potential model training and the potential energy as a function of temperature during the continuous cooling of La 50 Ni 50−x Alx series models.(b) The intermediate scattering function of La 50 Ni 35 Al 15 and La 50 Ni 15 Al 35 models.(c), (d) The alpha relaxation time of La 50 Ni 50−x Alx series models at different temperatures.In (d), the red and blue lines are guides for the eyes of Al 15 and Al 35 .

Figure 6 .
Figure 6.Structure analysis based on DNN Potential of La 50 Ni 50−x Alx (x = 15, 20, 25, 30, and 35, respectively) series model MGs at Tg. (a) The proportion of Al atoms that form Al-Al bonds at Tg. 10 Å slices of the Al-Al bond configuration for (b) La 50 Ni 35 Al 15 and (c) La 50 Ni 15 Al 35 models.(d) Pair correlation function g(r).(e) Al-centered and (f) Ni-centered Voronoi analysis.The upper panel shows the percentages are normalized by the atomic number of Al (Ni).The lower panel shows the absolute percentages.

Figure 7 .
Figure 7. Properties related to electronic structures.In La 50 Ni 50−x Alx series MGs, (a) Al 2p x-ray photoelectron spectroscopy (XPS), (b) binding energy of Al, (c) fragility, (d) covalency between the atoms (the percentage of ELF > 0.5), (e) total density of states, (f) electrical resistivity (ρ) versus temperature are shown as a function of Al content.

Figure 8 .
Figure 8. Relationship between Al content and fragility m in MGs of different compositions.La-Ni-Al (positive hexagonal representation, different series filled with different colors) and Cu-Zr-Al series MGs are the work of this paper.The fragility data of U-Co-Al [100], Cu-Hf-Al [101], Hf-Ni-Al [102], Gd-Co-Al [103], and Pr-Ni-Al [104, 105] MGs are obtained from literature, the specific fragility data are listed in table 2.

Table 1 .
The fragility values of the La-Ni-Al and Cu-Zr-Al series samples fitted with different methods are listed below.Tg and Tx were measured at 20 K min −1 .m 1 is fitted by equation (5), Qs = 50 K s −1 .m 2 is fitted by the same equation but Qs = 20 K min −1 .m 3 is fitted by equation lnη = lnη 0 + E/RT, the standard Tg is extrapolated from the FSC data.The fragility data for La-Ni-Al MGs used in the text are m 1 .

Table 2 .
Relationship between Al content and fragility m in MGs of different compositions.