Glass-forming Ability Of Metallic Glasses Research Articles

Machine Learning Aided Prediction of Glass-Forming Ability of Metallic Glass

The prediction of the glass-forming ability (GFA) of metallic glasses (MGs) can accelerate the efficiency of their development. In this paper, a dataset was constructed using experimental data collected from the literature and books, and a machine learning-based predictive model was established to predict the GFA. Firstly, a classification model based on the size of the critical diameter (Dmax) was established to determine whether an alloy system could form a glass state, with an accuracy rating of 0.98. Then, regression models were established to predict the crystallization temperature (Tx), glass transition temperature (Tg), and liquidus temperature (Tl) of MGs. The R2 of the prediction model obtained in the test set was greater than 0.89, which showed that the model had good prediction accuracy. The key features used by the regression models were analyzed using variance, correlation, embedding, recursive, and exhaustive methods to select the most important features. Furthermore, to improve the interpretability of the prediction model, feature importance, partial dependence plot (PDP), and individual conditional expectation (ICE) methods were used for visualization analysis, demonstrating how features affect the target variables. Finally, taking Zr-Cu-Ni-Al system MGs as an example, a prediction model was established using a genetic algorithm to optimize the alloy composition for high GFA in the compositional space, achieving the optimal design of alloy composition.

Data-driven machine learning prediction of glass transition temperature and the glass-forming ability of metallic glasses.

The limited glass-forming ability (GFA) poses a significant challenge for the practical applications of metallic glasses (MGs). The development of high-GFA MGs typically involves trial-and-error processes to screen materials with a large critical diameter (Dmax), which serves as a criterion for determining the GFA. The formation and stability of MGs are influenced by the glass transition temperature (Tg). Over the past decade, the emergence of machine learning (ML) has shown great promise in the exploration of high-GFA materials. However, the contribution of material features to Tg and Dmax predictions, as well as their correlations, remains ambiguous, posing a challenge to achieving high prediction accuracy. Herein, we present a comprehensive dataset consisting of 1764 datapoints for Tg and 1296 datapoints for Dmax. The governing rules for GFA have been established through feature significance analysis. The light gradient boosting (LGB) model exhibits remarkable accuracy in predicting Tg, utilizing sixteen features, achieving a coefficient of determination (R2) score of 0.984 and a root mean square error (RMSE) of 20.196 K. An integrated ML model, based on the weighted voting of three basic models, is developed to enhance the accuracy of Dmax prediction, achieving an R2 score of 0.767 and an RMSE of 2.331 mm. Additionally, a GFA rule is proposed to explore materials with large Dmax values, defined by satisfying the criteria of a thermal conductivity difference ranging from 0.60 to 1.32 and an entropy density exceeding 1.05. Our work provides valuable insights into Tg and Dmax predictions and facilitates the exploration of potential high-GFA MGs through the implementation of a well-established ML model and GFA rules.

Machine learning versus human learning in predicting glass-forming ability of metallic glasses

Complex materials science problems such as glass formation must consider large system sizes that are many orders of magnitude too large to be solved by first-principles calculations. The successful application of machine learning (ML) in various other fields suggests that ML could be useful to address complex problems in materials science. To test its efficacy, we attempt to predict bulk metallic glass formation using ML. Surprisingly, we find that a recently developed ML model based on 201 alloy features constructed using simple combinations of 31 elemental features is indistinguishable from models that are based on unphysical features. The 201ML-model performs better than the unphysical model only when significant separation of training and testing data is achieved. However, it performs significantly worse than a human-learning based three-feature model. The limited performance of the 201ML-model originates from the inability to accurately represent alloy features through elemental features, showing that physical insights about mixing behavior are required to develop predictable ML models.

Effect of Fe addition on the glass-forming ability, stability, and mechanical properties of Zr50Cu34-xFexAl8Ag8 metallic glasses

Zr50Cu34-xFexAl8Ag8 (x = 0, 2, 4, 6, and 8) alloy bars of different diameters were prepared by copper mold suction casting and copper mold casting. The compressive mechanical properties of metallic glass samples with different Fe contents were determined by a universal testing machine. The microstructure and thermodynamics of the alloy samples were analyzed by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and differential scanning calorimetry. According to the experimental results, Fe doping had a significant effect on the glass-forming ability, stability, and mechanical properties of these metallic glasses. The maximum diameter of the Zr50Cu32Fe2Al8Ag8 metallic glass bar was 15 mm, and the cooling rate of the alloy sample was 7.7 K/s. The addition of Fe inhibited the formation of stable crystalline phases inside the alloy sample and improved the glass-forming ability of the metallic glass. With the addition of Fe, the DSC curve of the alloy sample moved to higher temperatures, and the characteristic temperatures and the stability of the metallic glass increased. The fracture strength (σmax) and ultimate strain (εf) of the metallic glass samples reached their maximum values of 1917.6 MPa and 3.97 %, respectively, for Zr50Cu30Fe4Al8Ag8. Compared with the Fe-free Zr50Cu34Al8Ag8 metallic glass, σmax and εf increased by 51.4 MPa and 1.19 %, respectively. With the addition of Fe, the change in the distribution and content of free volume inside the metallic glass sample is the main reason for the improvement of its mechanical properties. This study shows that trace element doping has an important effect on the properties of metallic glasses.

A two-step fused machine learning approach for the prediction of glass-forming ability of metallic glasses

Metallic glasses (MGs) are often perceived as quintessential structural materials. However, the widespread application of MGs is hindered primarily by their limited glass-forming ability (GFA) for the manufacture of large-scale MGs. In this work, a two-step fused machine learning (ML) approach is proposed, aiming to provide an efficient tactic for the precise prediction of MGs with robust GFA. In our ML framework, alloy compositions are the only required inputs. Moreover, the dataset comprises alloys that can and cannot be cast into MGs. This departs from the conventional ML approach utilizing only a correct set of training data (i.e. alloys that can cast into MGs). The fusion algorithm is also employed to further improve the performance of ML approach. The critical casting sizes predicted by our ML model are in good agreement with those reported in experiments. This work has extensive implications for the design of bulk MGs with superior GFA.

Free volume evolution dominated by glass forming ability determining mechanical performance in Zr Ti65-Be27.5Cu7.5 metallic glasses

The shear deformation and fracture behaviors of Zr x Ti 65- x Be 27.5 Cu 7.5 metallic glasses (MGs) were systematically investigated in the range x = 20, 25, 30, 35, 40, 45, 50 at% under multi-axial loading mode by small punch test (SPT). Results show that enhanced plasticity can be obtained in MGs with composition ranging from 30 to 45 Zr at%, which is attributed to the large free volume dependent on their better glass forming ability (GFA). It is reasonably concluded that the total free volume consists of two parts: intrinsic free volume ( V 0 ) and excess free volume ( V G ). Intrinsic free volume, involved in an ideal amorphous structure, is defined as the free volume of MGs undergoing fully structural relaxation, which depends on the atomic size of each element. On the basis of atomic dense packing model, intrinsic free volume of the studied MGs is basically same due to a little difference in the atomic size between Zr and Ti. Excess free volume is crucially dominated by the GFA of MGs. In the case of little difference in atomic size of Zr and Ti, the MGs with large GFA possess a much looser atomic stacking structure, leading to the larger content of excess free volume. The large content of free volume not only favor the better atomic mobility, but also facilitate the nucleation of multiple shear bands, which can dramatically improve the plasticity of MGs. Thus, the studied MGs with Zr content ranging from 30 to 45 at% possess the larger content of total free volume than that with 20, 25 and 50 Zr at% due to their better GFA, depicting the enhanced plasticity induced by the initiation and interaction of multiple shear bands. In addition, the MGs with large content of free volume exhibits the lower driving force of shear bands nucleation, showing a soft state.

Ultrastability of metallic supercooled liquid induced by vibration

The range of supercooled liquid region (ΔT) is the key parameter for evaluating the thermal stability and glass-forming ability of metallic glasses. The enhancement of ΔT is of significance not only for the glass formation and stability, but also for their thermoplastic forming ability. Traditional approaches to increase ΔT are composition regulation or dynamical modulation, which are either time-consuming or difficult to be controlled. Here, through a high-frequency ultrasonic vibration treatment, we show that the ΔT of a La-based metallic glass can be significantly widened from 64 K to 83 K, around 30% increment. This behavior is physically originated from the denser atomic packing and a lower stable basin in the energy landscape induced by the ultrasonic vibration energy. This work might provide a ready route to stabilize the supercooled liquid and glass, and give an insight into the understanding of the glass-forming of amorphous materials.

Liquid dynamics and glass formation of Gd55Co20Al25 metallic glass with minor Si addition

Liquid dynamics plays an essential role in glass formation. Here we observed a distinct change of liquid dynamics in Gd55Co20Al25 metallic glass induced by microalloying Si element. In the equilibrium melt, minor Si (0.5 at.%) addition leads to a more fragile liquid behavior and a smaller strength of liquid-liquid transition with the transition strength (ΔF) decreasing from 0.76 to 0.35. However, in the supercooled liquid, Si-doped liquid exhibits a remarkable enhanced fragile-to-strong transition (FST), and the value of FST factor f increases sharply from 1.63 to 3.84, resulting in a stronger liquid behavior and more sluggish crystallization kinetics for Gd55Co20Al24.5Si0.5 metallic glass. Moreover, minor Si addition promotes the formation of a crystal-like structure with a size of 1−2 nm. The interactions between the crystal-like structures and other local favored clusters frustrate the further growth of crystal-like phases, thus stabilizes the amorphous structure. As a result, the glass-forming ability (GFA) was largely improved. The critical diameter of Gd55Co20Al25 metallic glass increased from 2 to 7 mm with 0.5 at.% Si addition without deterioration of the magnetocaloric effect. This study provides valuable insight for understanding the distinct effect of microalloying on GFA of metallic glasses from the aspect of the evolution of the liquid.

Machine learning-based glass formation prediction in multicomponent alloys

Metallic glasses (MGs) have attracted considerable academic attention owing to their unique properties and great application prospects. Unlike other glassy materials, such as oxide glasses, MGs have limited glass forming-ability (GFA) that often leads to failure during new MG development. Although intensive studies have proposed various parameters and criteria enabling the evaluation of the GFA of MG samples, achieving accurate predictions of glass formation before the actual MG sample synthesis remains a great challenge and an open topic. In this study, we investigated the glass formation through the data-driven machine learning technique and trained a backpropagation neural network model based on a dataset assembled from thousands of ternary alloys. Applying the well-trained model, we accurately identified the MG and non-MG classes. More importantly, our model can effectively predict glass-formation likelihood of multicomponent alloys and locate the probable MG compositions without any prior experiment, thereby directing the MG design. From the model's predictions, we discovered several new MGs in the ribbon form. Glass-formation likelihood reveals the correlation with the thermodynamic and topological parameters, which provides insights into the GFA of MGs.

A new mathematical expression for the relation between characteristic temperature and glass-forming ability of metallic glasses

Based on the classical theory of nucleation, a new criterion ϖ, defined as (Tx−Tg)⋅Tg⋅Tx/(Tl−Tx)3 (where Tg, Tx and Tl are the glass transition temperature, the onset crystallization temperature and the liquidus temperature) and correlated to the critical casting diameter (Dmax), which has been proposed to evaluate the glass-forming ability (GFA) of bulk metallic glasses (BMGs). According to the linear fitting results of 667 reported BMGs, the relationship between Dmax and ϖ is expressed as Dmax=(1.08±0.26)+(10.22±0.45)ϖ. The interrelationship between the new criterion ϖ and Dmax exhibits better ability for evaluating GFA of the alloys than nine criteria reported in literature, and the values of Dmax of Fe-BMGs could be calculated by this ϖ parameter in an appreciable range. Therefore, the proposed ϖ parameter has certain significance for the development of new metallic glasses and the determination of their Dmax.

Estimation of the glass-forming ability of metallic glasses with monolayer two-dimensional model

In present work, the glass-forming ability of Cu-Zr and Cu-Al systems has been estimated by utilizing a monolayer two-dimensional model. The structure of 2D Cu-Zr MGs can be simply characterized by three kinds of Voronoi polygons, i.e. pentagon, hexagon and heptagon, and the structural translational symmetry is broken down by the strong coupling effect between pentagon and heptagon, promoting the formation of MGs. Moreover, the larger bond lengths of Cu-Zr and Zr-Zr pairs are found responsible for the outstanding GFA of Cu-Zr system. The 2D model provides a promising avenue for accurately predicting the GFA of alloys of interest, which is important both in theoretical research and engineering.

Tuning the glass-forming ability of metallic glasses through energetic frustration

The design of multi-functional BMGs is limited by the lack of a quantitative understanding of the variables that control the glass-forming ability (GFA) of alloys. Both geometric frustration (e.g. differences in atomic radii) and energetic frustration (e.g. differences in the cohesive energies of the atomic species) contribute to the GFA. We perform molecular dynamics simulations of binary Lennard-Jones mixtures with only energetic frustration. We show that there is little correlation between the heat of mixing and critical cooling rate $R_c$, below which the system crystallizes, except that $\Delta H_{\rm mix} < 0$. By removing the effects of geometric frustration, we show strong correlations between $R_c$ and the variables $\epsilon_- = (\epsilon_{BB}-\epsilon_{AA})/(\epsilon_{AA}+\epsilon_{BB})$ and ${\overline \epsilon}_{AB} = 2\epsilon_{AB}/(\epsilon_{AA}+\epsilon_{BB})$, where $\epsilon_{AA}$ and $\epsilon_{BB}$ are the cohesive energies of atoms $A$ and $B$ and $\epsilon_{AB}$ is the pair interaction between $A$ and $B$ atoms. We identify a particular $f_B$-dependent combination of $\epsilon_-$ and ${\overline \epsilon}_{AB}$ that collapses the data for $R_c$ over nearly $4$ orders of magnitude in cooling rate.

A ameliorative criterion for predicting the glass-forming ability of metallic glasses

Abstract A ameliorative criterion for predicting the glass-forming ability of metallic glasses was presented. The coefficient of determination (R2) of experimental log10(Rc) versus the predicted log 10 { R c l i n e a r ( T r g , D ) } is 0.72. When the predicted log 10 { R c l i n e a r ( T r g , D ) } is replaced with our predicted log 10 { R c l i n e a r ( T r g , 1 D ) } , the coefficient of determination (R2) will increase from 0.72 to 0.94, which is a great improvement for evaluating glass-forming ability (GFA).

Order at the interface

Discrepancies in the glass-forming ability of metallic glasses have been explained in terms of the presence of local structural features in the liquid. Findings from molecular dynamics simulations now show that the structure of the crystal/liquid interface may play a bigger role than previously thought.

The nature of the atomic-level structure in the Cu–Zr binary metallic glasses

Ab initio simulations on the basic clusters in the best glass formers of Cu–Zr metallic glasses (MGs) provide the most straightforward evidence that a gap in the density of states (DOSs) at the Fermi level is observed. We establish a direct connection between the electronic structure of the basic clusters in MGs and the glass-forming ability (GFA) of MGs, providing a new avenue to examine the GFA of MGs. And our findings provide a check for the atomic structural models of MGs, and have implications for understanding the formation and properties of MGs.

Erratum: “Evaluation of glass-forming ability for metallic glasses based on order-disorder competition” [Appl. Phys. Lett. 89, 091917 (2006)

Erratum: “Evaluation of glass-forming ability for metallic glasses based on order-disorder competition” [Appl. Phys. Lett. 89, 091917 (2006)

Investigation on Correlation between the Modified Criterion and the Glass-Forming Ability for Metallic Glasses

A modified criterion γ’ (=Tx/(1.5Tg+Tl) of glass-forming ability (GFA) for metallic glasses is suggested on the basis of present criterion γ (=Tx/(Tg+Tl) that correlates well with some systems including metallic glasses, some glassy oxides and some cryo-protective aqueous solutions. Results show that the modified criterion γ’ shows stronger correlation with the critical cooling rate Rc for metallic glasses than the criterion γ, which is demonstrated by a value increase in the statistical correlation parameter R2 from 0.9022 to 0.9037. Furthermore, a modified equation is given to reflect the relationship between γ’ and Rc.

An electronic structure perspective on glass-forming ability in metallic glasses

Through systematic study of glass-forming ability (GFA) and the electronic specific heat coefficient in typical ternary (Cu50Zr50)100−xAlx bulk metallic glasses, we provide compelling experimental evidence that the density of electronic energy states at the Fermi level indeed is closely correlated with the GFA of metallic glasses, and the best GFA can be obtained when the Fermi surfaces nearly touch the quasi-Brillouin boundaries, as predicted by the nearly free electron model. Our results highlight the significance of electronic structural effects on the formation of metallic glasses.

Glass Formation and Mechanical Properties of Ti–Cu–Ni Alloys with High Ti Content

Abstract A series of Ti–Cu–Ni alloys with Ti content as high as 50–70 at. % expected to possess potential high glass-forming ability (GFA) was designed according to the ε criterion (Xia, M. X., Zhang, S. G., Ma, C. L., and Li, J. G., “Evaluation of Glass-Forming Ability for Metallic Glasses Based on Order-Disorder Competition,” Appl. Phys. Lett. Vol. 89, 2006, pp. 091917-1–091917-3) and were prepared by melt spinning and suck casting methods. The samples were examined by X-ray diffractometry, differential scanning calorimetry, optical microscopy, scanning electronic microscopy, and quasistatic compression test. The GFA of the melt-spun ribbons is enhanced with increasing ε. Ti58Cu32Ni10 alloy with the maximum designed ε value of 0.542 exhibits best GFA with a glass transition temperature of 627 K and a wide supercooled liquid region of 45 K. However, this alloy failed to form a fully glassy rod of 1 mm in diameter. Room temperature compression tests reveal that the 1 mm diameter Ti58Cu32Ni10 glass composite exhibits work-hardening characteristic, with ultimate compressive stress of 2418 MPa, yielding stress σ0.2 of 1448 MPa and about 7.8 % plastic strain. The combination of high strength and ductility was attributed to a dendritic TiCu(Ni) network embedded in the hard glass matrix.

Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass

Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce70-xAl10Cu20Cox upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by 27Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.