5000 years of metallurgy has tremendously expanded the size and diversity of the materials universe. It started with the strengthening of one base element by minor addition of others, such as the addition of Tin to Copper to produce Bronze, or Carbon to Iron to produce Steel. The development of new alloys was mostly motivated by a desire to produce stronger materials, but presently the use cases are far beyond just the strength of the material. Alloys are now used for their magnetic properties, chemical activity, as well as high-temperature stability, amongst many other bespoke applications. The growth in use cases has also driven the development of more complex alloy systems that aren’t simply composed of just 2 elements, but sometimes up to 3-5 base elements combined with other minor alloying elements. For a set of desirable properties, it has become increasingly difficult to find the right combination of elements that produce them. There are 67 (n) stable metallic elements, and using the formula of unique combinations below, they could produce 47,905 ternary (r = 3) alloys, 766,480, quaternary (r = 4) alloys, and a total of over 110 million new alloys with (r = ) 3, 4, 5 or 6 principal elements. Therefore, it becomes imperative to explore new means other than traditional trial-and-error to explore such vast design spaces.
Bulk Metallic Glasses (BMGs) are one such sub-category of complex alloy systems that generally have over 3-5 elements (sometimes up to 8) and have a unique amorphous (non-crystalline) structure that makes them mechanically superior to their counterpart crystalline alloys. In addition to being stronger, they sometimes also possess unique soft-magnetic properties as well as chemical properties that makes them desirable in many industries. However, as described above, finding the right combination of elements that make for a good BMG with a desirable set of properties is not a trivial process. It requires a deep understanding of the chemistry of such alloys as well as elemental properties.
In this study, Machine Learning (ML) was explored as a potential tool to model the properties of large design space with a data-driven approach. ML is a statistical process that learns from data, recognizes certain patterns, and makes predictions based on the insights learned from training. ML has two main components – data and model. The quality of data is as important as the complexity and effectiveness of the models. For the model to learn patterns in data, certain descriptors (or features) need to be engineered into data that help build a correlation between the label and the target. This process is known as feature engineering. For the purpose of predicting material properties from alloy compositions, a compilation of experimental measurements can be used as training data with certain features that helps the ML model relate the changes in alloy composition to the changes in material properties. During this study, a few models were trained to predict the viability of an alloy composition to form BMGs and then validated against a test set of BMGs that have previously been experimentally tested.
Just as anything in nature, an attractive material like BMG also has its cons. In order to not crystallize and stay amorphous, BMGs generally require a high cooling rate to kinetically arrest the atomic structure of the alloy in a disordered state, limiting the dimensions of any articles produced using it. Researchers have made efforts over time to quantify the Glass Forming Ability (GFA) by measuring several characteristic thermodynamic and physical properties. Some have characterized the Critical Casting Thickness (DMAX) of the BMG, the maximum thickness at which the casted alloy stays amorphous, while others have chosen a more thermodynamic approach by measuring characteristic temperatures like Glass Transition Temperature (TG), Liquidus Temperature (TL), and Crystallization Temperature (TX). Another set of thermodynamic metrics are Reduced Glass Transition Temperature (TRG = TG / TL) and ΔT (= TG – TX), where higher values for both the metrics indicate a better GFA.
DATA & MODELS
In this study, three different ways to predict the GFA were chosen –
Categorizing the alloy compositions in Bulk Metallic Glass, Low DMAX (< 0.2 mm) Ribbon-form Metallic Glass, and Crystalline Alloys. This allowed the model to classify a given composition into three categories and produce a likelihood of forming BMG for any alloy composition.
Critical Casting Thickness (DMAX) (1)
ΔT = TG – TX (1)
BMG Classification: A Random Forest Machine Learning model was employed to classify a given alloy into the three aforementioned categories. The underlying base model for Random Forest was chosen to be Decision Trees and the corresponding optimized hyper-parameterS were obtained through a grid search method as implemented in Scikit-Learn Library (2). To train this model, Data were obtained from various experimental research papers and patents and consisted of a total of 8410 alloy compositions. The dataset was then split into a training and testing set with an 80:20 ratio. The elemental distribution plot shows a histogram of 10 most-occurring principal elements in the training set, where Fe-based alloys were the most common. The features for the Random Forest model included various elemental properties of the alloy constituents. These include atomic radii, atomic numbers, space group, valence electrons, melting point, mixing enthalpy, and other chemical descriptors that describe the elements in the alloy as well as their combination. The feature set was further extended by considering various functions such as mean, max, standard deviation, etc. for these constituent properties set. This resulted in a dataset with 199 features to describe each composition.
Critical Casting Thickness (DMAX): A dataset of 7456 compositions was compiled to train and validate the ML model. The data was uniformly split into training and testing set with an 80:20 ratio. A similar feature set was used as the BMG classification model to assist with DMAX prediction, resulting in a total of 208 features. The hyperparameters of the model were obtained through the feature set5-fold cross-validation method. The evaluation criteria were based on the Gini index.
ΔT (= TG – TX): A dataset of 621 compositions was utilized to train the ML model. The training set and testing set are composed of 496 and 125 compositions respectively. A similar feature set was used as the BMG classification model to assist with DMAX prediction, resulting in a total of 204 features. The hyperparameters of the model were obtained through the 5-fold cross-validation method. The evaluation criteria were based on the Gini index.
One of the ways to validate classification models is to plot a ROC (receiver operating characteristic) curve, which is a plot of True Positive Rate vs False Positive Rate. Visually, the closer the curve is to the top left corner the better the model performance is (3). Numerically, the performance can be quantified by calculating the area under the ROC curve. Figure 2 shows the ROC curve of the BMG classification model. As can be observed from the graph, the model is correctly able to identify most BMG compositions with higher accuracy than other classes.
For the DMAX and ΔT models, typical accuracy metrics were calculated, such as a) Mean absolute error (MAE), b) Mean squared error (MSE), c) Root mean squared error (RMSE), and d) R2 between predicted and true value. Table 1 shows these values for Cu-based and Zr-based compositions, two of the most well-studied BMG systems.
The model seems to perform better for Cu-based alloys than Zr-based alloys. One thing to consider here is that the data was expected to be highly noisy. Due to the lack of any standardization in collecting these measurements, the values could differ significantly from source to source. Both DMAX and ΔT are highly sensitive to the processing conditions and measurement techniques and as both of these properties can be measured through a variety of experimental methods, the data contained a high level of variability for similar compositions.
Studying the effect of Nb addition to Cu-Zr-Al ternary system: The Cu-Zr-Al ternary system is known to be a good glass-forming alloy system, which has further been improved by minor addition of Nb in the mix (4) (5) (6). One such commercially available alloy system is ZR01 offered by Heraeus AMLOY with the composition Zr70Cu24Al4Nb2 (wt. %) (7). The effect of Nb addition on the Cu-Zr-Al ternary was further studied by using the BMG classification model described in this study. Figure 3 shows 7 ternary plots with incremental addition of Nb to the mix. The colors – green, red, and purple, correspond with classes BMG, Ribbon, and Crystalline, respectively. The diameter of each point corresponds to the associated probability of prediction. The ternary plot with 0% Nb shows that most of the Cu-Zr-Al BMGs are concentrated in regions with a higher percentage of Cu-Zr with minor Al addition. This is expected as most of the Cu-Zr-Al BMG systems reported in the literature have Al in the range of 1%-20% (at. %). With the incremental addition of Nb, the glass-forming region in the ternary map was found to expand in size. This indicates that Nb could improve the GFA of the Cu-Zr-Al ternary system by introducing variability in its composition, i.e., researchers could choose a range of compositions in the green region and optimize for other properties without having to worry about the GFA of the alloy. A similar approach can be used to create a map of other alloy systems and identify the regions that show high potential for being strong candidates to form BMG. While this approach was only tested on a well-studied Cu-Zr-Al-Nb system, it can be extended to identify new and unique compositions.
Machine Learning serves as a very useful tool in effectively exploring a vast design space for Materials Discovery. Where manual trial-and-error becomes unfeasible, ML is able to efficiently screen a large number of material compositions for some target properties. In this study, the use of ML was explored for the development of Bulk Metallic Glasses (BMGs), a high-performance class of alloys. In order to predict the Glass Forming Ability (GFA) of the alloys, three models were developed to classify alloy compositions into BMG and non-BMG classes and to predict their Critical Casting Thickness (DMAX) and ΔT. High accuracy in the classification of alloys into BMGs was observed. However, with DMAX and ΔT, the accuracy of the model was lower. This could be attributed to the noise in data and the lack of standardization in the experimental measurement of these two quantities. The classification model was then used to study the effect of Nb-addition to the Cu-Zr-Al system, and it was found that with the minor addition of Nb, the BMG forming region expands in the ternary map.
To conclude, ML serves as a powerful tool in expediting material development timelines. It can be used in conjunction with other computational tools to model material properties at a much faster pace than experimentation.
Phaseshift Technologies is a materials development company that develops novel high-performance alloys using Machine Learning and Computational Chemistry. As demonstrated in this study, ML serves as one of several tools Phaseshift uses to develop the chemistry of alloys and guide the experimental efforts. Constantly iterating and developing new and unique computational workflows, Phaseshift aims to reduce the time requirement and cost of materials research and development. The company currently comprises a team of Materials Scientists, Machine Learning Engineers, and Physicists, with a highly specialized set of domain expertise in high-performance alloys.
1. A machine learning approach for engineering bulk metallic glass alloys. L. Ward, S. C. O'Keeffe, J. Stevick, G. R. Jelbert, M. Aykol, and C. Wolverton. s.l. : Acta Materialia, 2018, Vol. 159, pp. 102-111.
2. Random Forest Classifier. scikit-learn. [Online] https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html.
3. Classification: ROC Curve and AUC. Google Developers. [Online] https://developers.google.com/machine-learning/crash-course/classification/roc-and-auc.
4. Effects of Al addition on atomic structure of Cu-Zr metallic glass. F. Li, H. Zhang, X. Liu, Y. Dong, C. Yu, and Z. Lu. 5, s.l. : Journal of Applied Physics, 2018, Vol. 123.
5. Formation of Cu–Zr–Al bulk metallic glass composites with improved tensile properties. Y. Wu, H. Wang, H.H. Wu, Z.Y. Zhang, X.D. Hui, G.L. Chen, D. Ma, X.L. Wang, and Z.P. Lu. 8, s.l. : Acta Materialia, 2011, Vol. 59, pp. 2928-2936.
6. Relationship Between the Liquidus Surface and Structures of Zr–Cu–Al Bulk Amorphous Alloys. Y. Yokoyama, H. Inoue, K. Fuaura, and A. Inoue. 3, s.l. : Materials Transaction, 2002, Vol. 43, pp. 575-579.
7. Amorphous metals: Properties and special features. Heraeus Group. [Online] [Cited: 08 16, 2021.] https://www.heraeus.com/en/group/products_and_solutions_group/amorphous_metals/about_amorphous_metals/about_amorphous_metals.html.
8. Amorphous metals: Properties and special features. Heraeus Group. [Online] [Cited: 08 16, 2021.] https://www.heraeus.com/en/group/products_and_solutions_group/amorphous_metals/about_amorphous_metals/about_amorphous_metals.html.