Compositions design of Co-Fe-based bulk metallic alloys

Glass forming ability (GFA) is one of the key factors hindering the application of bulk metallic glasses (BMGs). In this paper, a cluster-related method was used to design good glass-formers in the complex Co-Fe-based system. A novel Co-centered Co-Mo binary topologically packed cluster Co-Co8Mo4 with 12-coordination number was found and used. The basic ternary composition in Co-Mo-B system is calculated based on an intersection of cluster lines B-B2Co8 and Co-Co8Mo4. Based on this, a series of novel Co-Fe-based glass-formers with high GFA, were quickly designed using the method of similar element replacement and microalloying. The best glass-former is (Co27.5Fe27.5Mo12.2Cr12.2B16P4.6)98Y2. The source of high GFA of designed glass-formers was also discussed. The results of this paper would offer researchers a novel insight in understanding the source of high GFA of Co/Fe-based system, and lay a solid foundation for exploring Co/Fe-Mo-based glass-formers via newly found Co-Mo binary cluster.


Introduction
In the family of bulk metallic glasses (BMGs), Co-Fe-based amorphous alloys have attracted a lot of attention, owing to their super mechanical properties, unique magnetic properties, remarkable low materials lost and great corrosion resistance [1][2][3][4][5][6][7]. Considering these superb properties, Co-Fe-based BMGs have an excellent application prospect. Meanwhile, limited glass-forming ability (GFA) often acts as the role of limiting the scope of application [8,9]. Due to the sensitivity of GFA to compositions, it is always a big challenge to discover new glass-formers with high GFA.
It is through decades of hard work that some novel Co-Fe-based glass-formers with high GFA have been developed [2,3,5,10]. For example, by the method of drop casting in Cu mould, Fe 41 Co 7 Cr 15 Mo 14 C 15 B 6 Y 2 could be fabricated into a fully amorphous rod with a critical diameter of 16 mm [10]. However, to sum up, most of the found Co-Fe-based glass-formers were developed according to the empirical law. In the field of research on GFA of Co-Fe-based BMGs, there were few research papers, especially from the aspect of microstructure, which would lay a foundation for further understanding glass-formation and enhancing GFA.
In order to understand glass-formation and design good glass-formers with high GFA, a lot of methods have been proposed from different points of view, such as from the aspect of microstructure or thermodynamics [11][12][13][14][15][16]. For example, based on the feature of microstructure, Miracle has proposed an efficient close packing (ECP) model, which has showed a great success in understanding glass formers and glass formation [14,15]. Thermodynamics also plays important role in understanding and designing glass-formers. Researchers have designed a series of novel high-entropy metallic glass-formers only from the aspect of entropy of mixing [17][18][19]. Meanwhile, some methods based on combining microstructure and thermodynamics also work well in Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
developing Zr-based glass-formers [9,11,20]. All of the above methods have achieved certain success in different fields.
From the aspect of microstructure, a novel cluster-related model named cluster-glue-atom model has been proposed by Chuang Dong [21][22][23][24]. This method showed great success in understanding and designing good glass-formers in Fe-based, Ni-based and rare-earth-based and Zr-based systems, etc [13,25,26]. Under the guidance of this cluster-glue-atom model, glass-formers were treated as isolated clusters plus glue atoms. The ratio of isolated clusters to glue atoms in a certain glass-former is always 1:1 or 1:3 [13]. This cluster-glue-atom model is a very efficient method of understanding complex glass-formers and designing good glass-formers with high GFA.
In this work, firstly, Co-Fe-based glass-formers have been understood via similar elements replacement and mixing enthalpy. Secondly, a novel Fe-Mo-based binary cluster was found and used as the basic cluster, which expanded the database of present binary clusters, laying a solid foundation for further developing Co-Mo-based glass-formers. At last, under the guidance of cluster-plus-glue-atom model, a series of novel Co-Fe based glass formers with high GFA have been understood and designed.

Compositions design
In this work, Co-Fe-Mo-Cr-P-B-(Y) was chosen as the basic system to study the glass-formation in Co-Fe-based alloys. Co, Fe, Mo, Cr, P, B and Y are chosen as the basic elemental compositions in Co-Fe-based alloys due to the reasons below: (1) The atomic radiuses, atomic size difference and heat of mixing between each elements meet the requirement of Inoue's empirical law, which means potential high GFA [27]. (2) The best glass-formers in Fe-based and Co-based glassy alloys locate at Fe 41 Co 7 Cr 15 Mo 14 C 15 B 6 Y 2 and Co 48 Cr 15 Mo 14 C 15 B 6 Er 2 , respectively [10,28,29]. It can be seen that, Mo, Cr, C, B and rare-earth element are the main elements in the above best Fe-best and Co-best glass-formers. According to the literature, P was also one of the common constitute elements in Fe/Co based glassy alloys, such as in (Fe-Co-Ni)-P-C-B, etc [1]. The results show that P element was also beneficial to GFA in Co-Fe based alloys. Based on this, C was replaced by P and Y was chosen as the candidate of rare-earth elements. On the other hand, the study on glass-formation of (Co-Fe)-(Mo, Cr)-(P, B)-Y study is limited., Under the guidance of Dong's cluster-related method, in the field of research on the GFA of (Co-Fe)-(Mo, Cr)-(P, B)-Y system, a series of novel Co-Fe-based glass-formers with high GFA would be found, which might lay a foundation of understanding the source of high GFA of Fe 41 Co 7 Cr 15 Mo 14 C 15 B 6 Y 2 and Co 48 Cr 15 Mo 14 C 15 B 6 Er 2 , and further guide researchers to enhance GFA of Co-Fe-based amorphous alloys.
To study the GFA of the complex system of Co-Fe-Mo-Cr-P-B-Y, the first step is simplifying the system. Firstly, rare earth Y always plays the role as micro-alloying element, which could further enhance the GFA of basic system, such as in Fe-based, Cu-based and Zr-based amorphous system, etc [30]. So, Y was also regarded as the micro-alloying element in this Co-Fe-based system. Secondly, Miracle once pointed that, similar elements might replace each other's location in cluster's shell [14,15]. In this system, the radius of Co and Fe are 0.125 nm and 0.128 nm, respectively. They share similar location in the periodic table and enjoy similar chemical properties. So, Co and Fe could be regarded as similar elements. Similarly, Mo/Cr and P/B could be also regarded as similar elements. Based on the above analysis, this complex system Co-Fe-Mo-Cr-P-B-Y could be simplified as Co/Fe-Mo/Cr-P/B-microalloying element Y. Further ignoring the microalloying element and considering similar element, the pseudo-ternary Co-Mo-B system could be regarded as the basic system of Co-Fe-Mo-Cr-P-B-Y.
In the pseudo-ternary Co-Mo-B system, considering the content of Co is much higher than Mo and B, Co has more opportunities to form clusters. The enthalpies of mixing of binary pairs Co-Mo and Co-B at equiatomic composition are respectively −5 kJ mol −1 and −24 kJ mol −1 [31]. The negative enthalpy means Co tends to form clusters between B and Mo during the rapid cooling process.
According to the above analysis, Co-B and Co-Mo are more favored to form together. In Co-B binary pair, Zhu has analyzed Co-B crystalline phases, and chosen a series of Co-B binary clusters [32]. Among the clusters, the B-centered archimedean octahedral anti-prism cluster B-B 2 Co 8 was the most topologically packed. Its coordination number (CN) is 10. This cluster has been proven to be successful in designing Co-based system [32]. Therefore, B-B 2 Co 8 was chosen as the representative cluster in Co-B binary system.
It has been demonstrated that, the local structure of amorphous alloys is similar to the microstructure of competing phases [14]. In Co-Mo binary system, there exists four crystalline phases, namely, Co 2 Mo 3 (CrFe type), Co 3 Mo (Ni 3 Sn type), Co 7 Mo 6 (Fe 7 W 6 type) and CoMo (Mg type). After analyzing, a novel CN12 cluster Co-centered Co-Co 8 Mo 8 cluster was derived from phase Co 3 Mo. The image of cluster Co-Co 8 Mo 4 is shown in figure 1. However, the cluster should meet the requirement of topological packing. In terms of certain number of CN, Miracle has calculated the best radius ratio (the radius of atom in the center of cluster to the average radius of atoms in the shell of cluster) [15]. As for the cluster Co-Co 8 Mo 4 , the center atom is Co. There exist twelve atoms in this cluster's shell, namely eight Co atoms and four Mo atoms. The Goldschmidt radiuses of Co and Mo are 0.125 nm and 0.140 nm. The average radius of atoms in Co-Co 8 Mo 4 cluster's shell is 0.962. As for the CN 12 cluster, the best ideal radius ratio is 0.902 [15]. Based on this, the deviation between the actual and ideal radius ratio is 6.65%. Co-Co 8 Mo 4 could be regarded as a topologically packed cluster, due to the reason that its deviation is less than 10% [15]. Therefore, Co-Co 8 Mo 4 was chosen as the representative cluster in Co-Mo binary system.
In the ternary Co-Mo-B system, two binary clusters B-B 2 Co 8 and Co-Co 8 Mo 4 were shown in figure 2. Based on the cluster-glue-atom model, the cluster line method was always used to design compositions. The best glassformer always locates at the intersection point of two binary clusters.
As can be in figure 2, the glass-former Co 55 Mo 24.4 B 20.6 is calculated based on an intersection of cluster lines B-B 2 Co 8 and Co-Co 8 Mo 4 . It has been proven that similar element replacement could greatly enhance GFA of the basic system. According to the above analysis, Co/Fe, Mo/Cr and B/P could be regarded as similar elements. Hence, half content of Co and Mo were replaced by Fe and Cr, separately. Through this step, a pseudo-ternary Co/Fe-Mo/Cr-B glass-former Co 27

Results and discussion
The XRD patterns of designed compositions are shown in figure 3. As can be seen, there exist unknown phases peaks in XRD pattern of Co 55 Mo 24.4 B 20.6 . It couldn't form a full amorphous ribbon. The GFA of original designed ternary composition Co 55 Mo 24.4 B 20.6 is quite low. In contrast, there doesn't exist any shark crystalline peaks in the XRD patterns of Co 27 As analyzed above, the designed compositions could be understood by cluster-plus-glue-atom model, namely, [cluster] 1 (glue atom) x , x=1 or 3 [12]. Based on this model, the primary ternary composition Co 55 Mo 24.4 B 20.6 could be expressed as the cluster formula [B 3 Co 8 ]-Mo 3.5 . The glue number is 3.5, which has a small deviation from the theoretical value of 3. The deviation might be the reason of the poor GFA of Co 55 Mo 24 ) 98 Y 2 is 2 mm, 3 mm and 4 mm, respectively. It can be seen that, both similar elements replacement and microalloying could greatly enhance GFA. Among our designed compositions, the best glass-former is (Co 27.5 Fe 27.5 Mo 12.2 Cr 12.2 B 16 P 4.6 ) 98 Y 2 . The critical diameter of typical Co/Fe-Mo/Cr-C/B-Er could reach to the centimeter level. The GFA of (Co 27.5 Fe 27.5 Mo 12.2 Cr 12.2 B 16 P 4.6 ) 98 Y 2 is lower than typical Co-Fe-based glass-formers containing with element C. However, its GFA is higher than other Co-Fe-based glass-formers reported in literature, e.g., Fe 40 Co 20 Ni 15 P 10 C 10 B 5 (Dc=2.5 mm) [1], Fe 70 Co 10 P 13 C 7 (Dc= 2.5 mm) [33], Fe 63 Co 7 Nb 4 B 23 Y 3 (Dc=3 mm) [2]and Fe 53 Co 27 Mo 9 P 14 B 6 (Dc=3 mm) [3].
As for the enhancement of GFA by similar element replacement, the reasons can be explained by the increase in mixing entropy. It has been reported that, on the precondition of meeting the requirement of topologically packed in clusters, the more mixing entropy the system possesses, being less likely to crystallize, the higher GFA would reach [11]. Elements would replace its similar element's position in the cluster formula. Based on this, Co 27 Y-microalloying could also enhance the GFA of Co-Fe-based alloys, it might be caused by rare-earth element doping could decrease the oxygen impurity concentration [30]. In addition, due to the fact that the enthalpy of mixing of binary pairs Fe-Y at equiatomic composition is −1 kJ mol −1 [31]. There exist amounts of topological clusters, e.g., a Fe-centered CN12 Fe-Fe 11 Y cluster [34]. With Y-doping, the newly introduced topological cluster would greatly increase the difficulty in crystallization, which is beneficial for glass-formation.
A series of crystallization behaviors of as-cast Co 27 are close to eutectic point. With the micro-alloying Y doped, the crystallization behavior has changed, and the new Y-doped composition possesses the largest undercooled liquid region among our designed compositions in Co-Fe-based metallic alloys. This wide undercooled liquid region and its high GFA would lay a foundation for further fabrication and application.

Conclusion
A novel Co-Mo binary topologically packed cluster Co-Co 8 Mo 4 was found and used. Based on cluster line method, a series of novel Co-Fe-based glass-formers with high GFA were quickly designed, combining with similar element replacement and microalloying. Among the designed glass-formers, (Co 27.5 Fe 27.5 Mo 12.2 Cr 12.2 B 16 P 4.6 ) 98 Y 2 owes the largest and undercooled liquid region. This glass-former is designed based on an intersection of cluster lines B-B 2 Co 8 and Co-Co 8 Mo 4 . The critical diameter of (Co 27.5 Fe 27.5 Mo 12.2 Cr 12.2 B 16 P 4.6 ) 98 Y 2 is 4 mm. The results in this paper offer the researchers a novel insight in understanding the source of high GFA of Co/Fe-based system, and lay a solid foundation for exploring Co/Fe-Mo-based glass-formers via newly found Co-Mo binary cluster.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).