Engineering of Novel Fe-Based Bulk Metallic Glasses Using a Machine Learning-Based Approach

A broad range of potential chemical compositions makes difficult design of novel bulk metallic glasses (BMGs) without performing expensive experimentations. To overcome this problem, it is very important to establish predictive models based on artificial intelligence. In this work, a machine learning (ML) approach was proposed for predicting glass formation in numerous alloying compositions and designing novel glassy alloys. The results showed that our ML model accurately predicted the glass formation and critical thickness of MGs. As a case study, the ternary Fe–B–Co system was selected and effects of minor additions of Cr, Nb and Y with different atomic percentages were evaluated. It was found that the minor addition of Nb and Y leads to the significant improvement of glass-forming ability (GFA) in the Fe–B–Co system; however, a shift in the optimized alloying composition was occurred. The experimental results on selective alloying compositions also confirmed the capability of our ML model for designing novel Fe-based BMGs.


Introduction
Fe-based metallic glasses (MGs) have drawn a lot of interest for their potential applications in electronic systems, magnetic components and wastewater industry [1][2][3][4][5]. However, design of Fe-based glassy alloys with new chemical compositions, good glass-forming ability (GFA), high casting thickness and significant thermal stability remains a big challenge [6]. In recent years, many works have been done to engineer novel Fe-based bulk metallic glasses (BMGs) with superior physical and mechanical properties [7][8][9][10][11]; however, one knows that obtaining the alloying compositions for desirable properties is accompanied with numerous trial-and-error experimentations. Recently, machine learning-based approaches have been developed in the field of both metallic and amorphous alloys to identify eligible novel materials with no costly and time-consuming experimentations [12][13][14]. For example, Cai et al. [15] proposed a radial based-function artificial intelligence approach for predicting undercooled liquid region of glass-forming alloys and achieved reliable results for design of a group of new Zr-Al-Ni-Cu BMGs. Using statistical learning along with evolutionary intelligence, Tripathi et al. [16,17] estimated the glass-forming possibility of alloying compositions by generic attributes of the constituent elements. Alcobaca et al. [18] indicated that the best machine learning (ML) algorithm for estimating glass transition temperature (T g ) is the Random Forest. Ward et al. [19] developed their ML framework for BMG prediction with a huge database of 8000 alloying compositions and new configurational parameters such as cluster packing efficiency and nearest special cluster. Samavatian et al. [20] proposed a correlation-based neural network approach for estimating critical thickness and GFA and identified new quaternary glassy systems such as ZrCoAlNi, ZrCoAlSi and ZrCoAlW compositions. Using ML iteration and high throughput experimentations, Ren et al. [21] developed ZrCoV ternary systems with considerable glass-forming possibility. They also suggested that the iterative use of ML and experimentations, leading to a synthesis method-sensitive predictor, guides researchers for accelerated discovery of numerous MGs. In another study, it was found that the automated analysis of phase diagrams under an artificial intelligence approach may lead to the prediction of glass-forming alloys [22].
As seen in the published works, the studies mainly focused on the development of ML approaches and there exist few investigations dealing with the identification and prediction of new alloying systems with high glass-forming possibility. Hence, at the first step we decided to develop an ML model with thousands of experimented chemical compositions as the training data source, enabling to accurately predict the glass-forming possibility and the critical casting thickness in a huge space of alloying compositions. At the second step, Fe-based BMGs, which are identified as potential glassy materials for industrial applications, were selected as a case study to develop new chemical compositions with potential glass formation through microalloying process into a known Fe-based alloying system. Figure 1 illustrates the detailed procedure for establishing a ML model. The first step in the ML model is to collect required data from published resources. In this work, we used a database of 7700 MG experiments with 52 different elemental constitutes, which include ribbons, BMGs and crystalline compositions. A great number of ternary alloys were obtained from Landolt-Bornstein Handbook [23]. Other alloying compositions, especially BMG ones, were extracted from Ref. [19,20]. The distribution of elemental constitutes in all the alloying compositions is given in Fig. 2. The casting possibility of alloys, maximum casting thickness (t max ), glass transition temperature (T g ) and liquidus temperature (T l ) are extracted from the resources. All the mentioned data can be found in ref. [24]. After data collection, the input and output items should be carefully described. The alloying composition is considered as the input data, while t max and GFA are the outputs indicating the features of promising alloys. It should be noted that the data are sorted somehow to show the nature of cast alloys, i.e., whether they are amorphous ribbons, BMGs or crystalline alloys. To investigate the GFA, we considered reduced glass transition temperature (T rg ) as the indicator. Although there are many GFA indicators proposed in published works, it is suggested that T rg is a reliable and accurate one for evaluation of glass formation with just knowing the T g and T l values [25]. In general, T rg is the ratio of T g to T l of a glassy alloy. As the T rg Fig. 1 Detailed procedure for establishing the ML model increases for a material, the required cooling rate for glass formation declines and consequently it is possible to produce the thicker glassy alloys with the slower cooling rates. In other words, the increase in the T rg value arises from the need that viscosity must be large at temperatures between T g and T l [26]. After data processing, it is needed to insert a sufficient set of attributes into the ML model for promoting the training performance. In total, there are numerous attributes associated with the inherent characteristics of each elemental constitute. These attributes, which are identified as atomic fundamental properties, are listed in Table 1. Moreover, there are other thermodynamic, kinetic and configurational attributes such as mixing enthalpy, mixing entropy, normalized mismatch entropy, Gibbs free energy of mixing, valence electron distribution, mean atomic volume, mean packing efficiency and viscosity, which are inserted into the model. These attributes are calculated based on linear and reciprocal mixing rules for each alloying composition (see Supp. 1). The details for mentioned attributes and their definitions are explained in ref. [19,20,27] and Supp. 1. In this work, we tried to increase the number of attributes based on previous studies and gather them in our model to significantly improve the predictive performance. It should be noted that the attributes were normalized in a predefined domain, which is called min-max rescaling procedure, to improve the learning process in the model. The normalization was done according to the following equation [28]:

Machine Learning Method
In which x norm is the normalized attribute; min(x) and max(x) define the minimum and maximum value of the original attribute. "c" and "d" define the general domain with value of 0.2 and 0.8. In total, the domain of 0 and 1 may influence the performance of ML models. As a result, the domain in the range of 0.2 and 0.8 was suggested by  Among the mentioned algorithm, it was found that random forest (RF) algorithm works well for the prediction of glass formation [13,21]. Hence, in this work we focused on RF algorithm for building our model in terms of cross-validation classification and evaluation of glass formation and critical casting thickness. MATLAB 2020b environment was used in order to compose the codes for data preparation, data process and resulting illustrations.

Results and Discussion
The purpose of this work is divided into the two main subjects. As described in Sect. 3.1, we firstly tried to show that our ML model is efficient for classifying the glass-forming possibility and predicting the GFA and the critical casting thickness (t max ) in a wide range of chemical compositions with various elemental constitutes, shown in Fig. 2. As discussed in details in Sect. 3.2, the second subject of this paper is to apply the ML model for predicting new alloying compositions with promising applications. As a case study, Fe-B-Co system was considered and minor additions such as Y, Nb and Cr were alloyed into the system to identify and characterize novel chemical compositions. Some experimental works were also carried out to justify the accuracy of ML model in predicting the features of studied Fe-based MGs.

General Performance of ML Model
The first step for predicting of materials classification, GFA and t max is to validate the performance of ML model. Figure 3a represents the receiver operating characteristic (ROC) plot, which determines the efficiency of classification model for predicting of casting possibility of amorphous alloys. According to the results, one can see that the ML model shows a prominent proficiency to distinguish BMGs from other categories. As an excellent classifier, it is also observed that the MGs (amorphous ribbons) and crystalline compositions are also distinguished with true positive rates of 96.5% and 97%, respectively. This accuracy is in the level of other works classifying the glassy alloys by ML approaches [20]. The values of predicted and experimental T rg and t max for glassy alloys are plotted in Fig. 3b, c, respectively. According to the data distribution, it is observed that the T rg values show an isotropic trend, which imply on the efficiency of our model for quantitatively predicting the glass formation in glassy alloys. Moreover, one can see that the t max values have a converge trend with correlation coefficient (R) of 0.92966 and root-mean-square error of 0.95869. There are just few alloying compositions separated from the main trend. As marked in Fig. 3c , which were also reported as inconsistent data in previous works [19]. Hence, it is concluded that the possible error in the experimental works or lacking adequate data for similar materials compositions may lead to this inconsistency. One of the main reasons for achieving a proficient ML model is to select numerous and related attributes affecting the glass formation. In addition to fundamental elemental features, we tried to gather other attributes proposed by other researchers [20,29]. For example, the configurational attribute, i.e., mean packing efficiency, and kinetic parameter are added into the thermodynamic attributes, which lead to the strengthening of ML model. In general, gathering different attributes in the ML model promotes the efficiency of prediction, compared to the conventional physical approaches with their restricted parameters. To give some examples, Śniadecki [30] indicated that an Fig. 3 a Receiver operating characteristic curve as indicator of classification model, and efficiency of regression model, experimented-predicted results for b T rg , c T max accurate prediction of the glass formation in Fe-Ni amorphous alloys would be resulted by considering the formation enthalpy and the normalized mismatch entropy. On the other side, Jiang et al. [31] suggested that the critical cooling for glass formation strongly depends on concentration of valence electrons. In another work, Zhou et al. [32] proposed thermodynamic description of the Al-Cu-Zr system for glass formation using a substitutional solution model. Ganorkar et al. [33] claimed that the glass formation is dominantly governed by thermodynamics rather than kinetics in Cu-Zr systems. Hu and Tanka [34] applied molecular dynamic (MD) simulation to characterize glass formation in the alloying systems. They found that the driving force of crystallization is similar in metallic systems; however, the level of liquid-crystal interface tension leads to the difference in the glass formation possibility. In another study, Ojovan [35] showed that the topological rearrangements of the bonding system lead to the different properties of glasses and melt and affect the glass transition temperature. Investigating on different MGs, Mukherjee et al. [36] indicated that the viscosity at the melting temperature is associated with the change in volume upon crystallization, which is consistent with Cohen-Grest free-volume theory. Some investigations also demonstrated that the short and medium range orders play a fundamental role in stabilizing the liquid phase and in enhancing the glass-forming possibility of the multicomponent alloys [37,38]. As a result, it seems very important to build a ML model with multiple attributes, covering topological and thermodynamic features, to comprehend a huge space of alloying compositions.

Novel Fe-Based BMGs
Our aim in this work is to adjust chemical compositions of a Fe-based amorphous alloy using elemental minor addition to improve the glass formation and critical casting thickness. For this purpose, we selected a well-known composition, namely FeBCo-based type, as the promising glassy alloy and added elements into this alloying system to engineer new BMGs with eligible characteristics. Yttrium (Y), niobium (Nb) and chromium (Cr) are added into the mentioned system with 2, 4 and 6 at.% to change the glass formation. It should be noted that we did not restrict our evaluation to a certain composition and considered all the FeBCo system as a search space for optimization of GFA. The picked-out elements for minor addition, i.e., Y, Nb and Cr, lead to the different heat of mixing in the system (See Table 2). Hence, it is expected to identify alloying compositions with a wide range of GFA in the predicted plots. In order to be possible for studying the GFA in the mentioned system, it is necessary to consider some criteria for the outputs. As mentioned before, the T rg was determined for glass formation analysis in our study. To focus on the identification of promising alloys, we also filtered the chemical compositions with T rg higher than 0.4 and critical thickness of 0.1 mm. Moreover, we considered a criterion defining the Fe-based alloying compositions, which means that the Fe percentage is higher than other constitutes. Figure 4 illustrates the GFA maps of Fe-B-Co system with T rg higher than 0.4. As observed, a considerable part of the ternary maps is white, which indicates the crystalline alloying compositions or glassy compositions with T rg less than 0.4. On the other side, the colored regions include chemical compositions with high glass formation possibility (T rg > 0.4). Hence, one can conclude that there are numerous alloying compositions in Fe-B-Co system for producing metallic glasses. Taking a glance on the ternary map, it is revealed that the T rg region mostly lies in the composition range of Fe 0.4-1.0 B 0.1-0.5 Co 0.0-0.43 , which may be due to the large negative heat of mixing in Fe-B pairs. It is generally suggested that the Fe-B pairs show strong interaction leading to the formation short range order (SRO) clusters in the amorphous structure [39]. When B content goes under 0.1, it seems that the formation of SRO clusters is postponed in the structure and consequently, the glass formation is considerably weakened. Figure 5 represents the GFA maps of Fe-B-Co system with minor addition of Y, Nb and Cr at 2, 4 and 6 at.%. According to the ternary maps, it is detected that the microalloying of Y and Nb extends the composition range of glass formation in Fe-B-Co system and improves the T rg parameter. However, the level of improvement strongly depends on the  added element type. Considering 2-4% Y-added systems, it is identified that the maximum T rg lies in the composition range of Fe 0.68-0.79 B 0.12-0.23 Co 0-0.2 , while the increase in the Y content leads to a tendency to Co-richer regions (as marked in the image). This indicates that the large negative heat of mixing in Co-Y pairs tends to glass formers with higher Co content. Moreover, the increase in Y content leads to the increase in glass-forming compositions, which is due the higher configurational entropy in the system. It is also revealed that a crystalline gap in the ternary composition is growing with the increase of Y, which shows that the composition range of Fe 0.5-0.7 B 0.12-0.15 Co 0.25-0.45 has potential for crystallization under cooling process. Considering Nb-added maps, it is seen that there is no significant crystalline gap in the map. Despite Fe-Y pairs, the Fe-Nb pairs have large negative heat of mixing (− 16 kJ/mol). Therefore, it is reasonable to see the strengthening of glass formation in the Fe-based side of the map. As marked in the figure, the maximum T rg lies in the regions with Fe more than 0.85. Similar to Y-added systems, the increase in Nb content also extends the glass formation regions in the ternary map.
With minor addition of Cr into our ternary system, one can see that a slight shift occurs into the higher B-content regions, which is due to the large negative heat of mixing in B-Cr pairs and small negative heat of mixing in Fe-Cr and Co-Cr pairs. Compared to the earlier discussed systems, this event also affects the total heat of mixing in Fe-B-Co-Cr system and decreases the glass formation region in the ternary maps. Moreover, it was clear that the increase in the Cr content constricts the glass formation region and reduces the T rg intensification. In summary, it is seen that the ML model facilitates the identification of good glass formers without doing any time-consuming and expensive experiments. The results accurately show that how much a minor addition can change the inherent features of a certain alloying system.
Previous studies revealed that an optimal balance exists between critical thickness and GFA in the ZrCoAl and ZrTiCuAl MGs [19,20]. To clarify this hypothesis for Fe-based MGs, we evaluate the relation between critical thickness and T rg in FeBCo system when 4 at.% Y, Nb and Cr are added. The distribution plots of t max -T rg for the mentioned sets of alloying compositions are presented in Fig. 6a-c. As clear, an optimum value of T rg is obtained for the critical thickness. In other words, finding the critical casting thickness in alloying system is accompanied with an optimized GFA. The optimization between thickness and GFA was obtained by Pareto optimality method. As marked in Fig. 6a-c, the results showed that the Nb minor addition leads to the higher optimized T rg and thicker amorphous alloy, while the optimized parameters are weakest for the Cr-added systems. The chemical compositions of alloying systems at the optimized points in Fig. 6 4 , which shows a good consistency with the outcomes presented in Fig. 5.
To validate our ML model in the prediction of good glass formers in Fe-based alloys, we fabricated the optimized BMG compositions mentioned in Fig. 6 with different diameters, and did experimentations such as X-ray diffraction (XRD) and differential scanning calorimetry (DSC) analyses. The XRD was carried out to detect the amorphousness of cast samples, while the DSC at the heating rate of 20 K/min under argon atmosphere was performed to measure the T rg indicator (T g /T l ). The details of materials fabrication and the following experimentations are given in Supp. 1. According to Fig. 7 and Table 3, the experimental t max for Cr-added sample was obtained 1.5 mm, which is slightly lower than our prediction. On the other side, Nb-and Y-added samples show a higher t max in the experimentation. It is also seen that the T rg outcomes in the fabricated samples and the prediction have a meaningful closeness, indicating the efficiency of our ML model for identification of Fe-based BMGs.

Conclusion
In order to design new Fe-based BMGs, a predictive ML model was developed. According to the results, the ML model accurately predicted the glass formation, i.e., T g and T l , and critical thickness of all the BMGs. As a case study, Fe-B-Co ternary system was picked and effects of Y, Nb and Cr minor addition were studied. It was found that Y and Nb minor addition improves the GFA of ternary system; however, Cr microalloying did not significantly affect the glass formation. It was also revealed that the minor addition of elements leads to the shift and broadening of optimal glass-forming compositions. The experimental works, including Fe-based BMG fabrication and