Understanding the beneficial microalloying elements in Fe-based bulk metallic glasses via clusters

Glass forming ability (GFA) is one of the key factors hindering the application of bulk metallic glasses (BMGs). Microalloying has shown beneficial effects on GFA. However, the mechanism is still unclear. A new guidance via clusters was applied to understand and quickly choose beneficial microalloying elements for enhancing GFA which might help build a foundation for further quantitative analysis of minor alloying via clusters. Under the guidance, a series of beneficial microalloying elements could be quickly discovered, verified and understood. The results show that the beneficial microalloying elements for enhancing GFA should be chosen under the condition of bringing in new types of topologically efficiently packed clusters.


Introduction
Bulk metallic glasses (BMGs) have attracted specific attention due to their unique combination of excellent magnetic properties, mechanical properties and corrosion resistance, showing good practical application prospect [1]. However, glass-forming ability (GFA) is one of the key factors hindering the practical application. It is of great theoretic and actual significance to design good glass formers with high GFA.
It has been reported that minor alloying techniques have obviously shown beneficial effects on enhancing GFA [2,3]. A lot of research has been done and understood from the aspect of thermodynamics [4,5]. However, a common conclusion has been reached that the microalloying element should have the tendency of compound formation, namely, the microalloying element should have negative enthalpy of mixing between the major element [2,3,6]. Unfortunately, the mechanism of the minor alloying is still unclear. For example, non-metallic elements C, B and Si enjoying a large negative enthalpy of mixing between Fe or Zr element, both of which completely accords with the experience law [6]. However, the results show that these non-metallic elements could obviously enhance the GFA of Fe-based BMGs and deduce the GFA of Zr-based BMGs [7][8][9]. It is obvious that the negative heats of mixing between the major element is not the determining factor influencing GFA. It is still requiring a large number of experiments which might take a lot of time and money to choose minor alloying element.
How to understand the origin of GFA is always a hot topic in research of amorphous alloys. As cluster is the basic microstructural unit, based on this, some cluster-based methods have been proposed and used to understand and design good glass-formers [10][11][12][13][14]. The results prove that these cluster-based methods show the advantages of understanding and quickly designing glass-formers with high glass-forming ability. Recently, a method combining clusters and mixing entropy was applied by authors and used to understand and design good glass formers [14][15][16][17]. Based on it, in this paper, a new guidance via clusters was applied to understand and choose the beneficial microalloying elements. Furthermore, a series of beneficial microalloying elements in Fe-based system were quickly discovered, verified and understood. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Experiment
Among the Fe-based glass-formers, Fe 76 Si 9.6 B 8.4 P 6 has a high saturation magnetization (Js) and good GFA at the same time, which shows a good application prospect [18]. Thereby, Fe 76 Si 9.6 B 8.4 P 6 was chosen as the basic composition. As mentioned above, the microalloying elements which enjoy negative enthalpy of mixing between the major element might not work in well in some places. The enthalpies of mixing of the atomic pairs Fe-C, Fe-Ta and Fe-V at equi-atomic compositions are respectively −50 KJ mol −1 , −15 KJ mol −1 and −7 KJ mol −1 [6]. In order to better solve this problem, the above Fe-based glass-former Fe 76 Si 9.6 B 8.4 P 6 was chosen as the basic composition, a series of elements C, Ta and V, all of which enjoy negative enthalpy of mixing between the major element Fe, were chosen as the microalloying elements. By comparing their different effects on the enhancement of the glass-forming ability of the base components, the cluster-based method was used to understand the origin.
(Fe 0.76 Si 0.096 B 0.084 P 0.06 ) 98 C 2 alloy was prepared by the method of arc melting under a Ti-gettered high purity argon atmosphere. Except this C micro-alloyed alloy, other alloys in this paper were prepared by the method of induction melting under a high purity argon atmosphere. The purities of the constituent elements are respectively: Fe (99.9 mass%), B (99.9 mass%), Si (99.99 mass%), C (99.9 mass%), V (99.5 mass%) and Ta (99.9 mass%). P was added by premelted Fe-P (99.9 mass%) intermediate alloy. Rods with diameter of 2.5 mm and 3 mm were fabricated by copper mold casting. The structure was examined by x-ray diffraction (XRD).
In our previous work, we have systematically explored the effects of Mo-microalloying to the basic composition Fe 76 Si 9.6 B 8.4 P 6 under the same laboratory environment [19]. As the enthalpy of mixing of the Fe-Mo atomic pair at equi-atomic compositions is −2 KJ mol −1 [6], which also meets the requirement of previous micro-alloying elements selection empirical rules. To better illustrate the different effects of various micro-alloying elements, the results of Mo-microalloying were also cited in the table 1.

Results and discussion
According to our previous study, the critical diameter of the basic composition Fe 76 Si 9.6 B 8.4 P 6 is 2.5 mm under the same laboratory environment. As can be seen in figures 1, 2 at.%C and Ta enhances GFA from 2.5 mm to at least 3 mm, however, 2 at.% V doesn't work well in the aspect of enhancing GFA for the basic Fe-based glassformer. To test this hypothesis more precisely, more varying amounts of microalloying element V, namely, 1, 2, 3, 4 at.% V were also fabricated and tested. As can be seen in figure 1, all of 1 at. % V − 4 at. % V reduced the glass-forming ability of the original composition, which proved that V-microalloying in Fe-based system couldn't enhance the basic Fe-based glass-former's GFA.
As shown in table 1 and figure 1, it can be seen that GFA is sensitive to the microalloying elements. Even for elements with the same characteristics, all of which enjoy large enthalpy of mixing between the element and the major element, it was found that there exists huge discrepancy among the microalloying elements in the field of enhancing GFA.
Understanding the origin of GFA of basic composition is the basis, and should always come before understanding the origin of enhancing GFA by microalloying elements. The enthalpies of mixing of the atomic pairs Fe-Si, Fe-B, Fe-P, Si-B, Si-P and B-P at equiatomic compositions are respectively −35 KJ mol −1 , −26 KJ mol −1 , −39.5 KJ mol −1 , −14 KJ mol −1 , −25.5 KJ mol −1 and 0.5 KJ mol −1 [6]. It can be easily concluded that, among the six atomic pairs, Fe-Si, Fe-B and Fe-P clusters are more apt to accumulate as they enjoy more negative enthalpies of mixing than others. Under the guidance of clusters-and mixing entropy-related method, the glass former could be understood as a mixture of efficiently topologically packed clusters [14][15][16].
The glass former ( C am ) in this system should be written as: Here, α, β and γ are coefficients. It has been reported that there exit efficiently topological packed clusters in Fe-Si and Fe-B binary system, such as cluster B-B 2 Fe 8 , Si-Fe 9 and P-Fe 9 , etc [20,21]. Composition with good GFA in Fe-Si-B-P system could be regarded as a mixture of Fe-Si, Fe-B and Fe-P binary clusters. The topological efficiently packed clusters could hinder the precipitation of crystalline phases which leads to the high GFA in this system. Based on the analysis above and equation (1), the high GFA in Fe-Si-B-P system comes from the topological packed clusters.
Clusters are the key factors of influencing GFA and further understanding the mechanism of enhancing GFA by microalloying elements. The large enthalpy of mixing between elements is the origin of clusters. As mentioned above, all of the chosen microalloying elements have negative heats of mixing between the major element Fe which is consistent with previous empirical rules [2,3,6]. However, the microalloying element V which also enjoys negative heat of mixing between Fe doesn't work in the field of enhancing GFA. It can be concluded that, the microalloying element enjoying negative heats of mixing between the major element is not the determining factor enhancing GFA such as the microalloying element V in this paper. There exist deeper causes that affect the glass-forming ability via microalloying.
Gaskell and Miracle have pointed that, the local structure of amorphous alloys is similar to the microstructure of the competing phases [13,22]. This cluster selection rule has been successfully used in designing and understanding good glass-formers [14,16,20]. Clusters come from the large enthalpy of mixing between components. All of micro-alloying elements C, Mo, Ta and V enjoy large enthalpy of mixing between the element and the major component Fe. However, among the Fe-M (M=C, Mo and Ta) binary system, after carefully analyzing the microstructure of Fe-based binary competing phases, only binary clusters C-Fe 9 (derived from phase CFe 3 ), Fe-Fe 4 M 8 (M=0.25Fe + 0.75Mo) (derived from phase FeMo) and Fe-Fe 6 Ta 6 (derived from phase Fe 2 Ta) could be obtained in each corresponding binary system.
It is worth noting that, Miracle once further pointed that, the degree of efficient packing in clusters, which was linked to the radius ratio, plays important role in glass formation [23]. In terms of coordination number (CN) for the certain cluster, the ideal radius ratio R * has been calculated [23]. The CN of cluster C-Fe 9 , Fe-Fe 4 M 8 (M=0.25Fe + 0.75Mo) and Fe-Fe 6 Ta 6 is respectively 9, 12, 12 and 12. The ideal radius ratio R * of CN9 and  CN12 is 0.710 and 0.902 [23]. The Goldschmidt radius of Fe, C, Mo and Ta is respectively 0.128 nm, 0.77 nm, 0.140 nm and 0.147 nm. The actual radius ratio R is decided by atomic radius of center atom of the cluster and the average atomic radius of atoms in the cluster's shell. For example, as for the cluster Fe-Fe 4 M 8 (M=0.25Fe + 0.75Mo), the atomic radius of center atom of this cluster is 0.128 nm, and the average atomic radius of atoms in the cluster's shell is 0.134 nm. Thereby, the actual radius R in cluster Fe-Fe 4 M 8 (M=0.25Fe + 0.75Mo) equals 0.128 nm divided by 0.134nm, namely 0.955. Similarly, the actual radius ratio R in cluster C-Fe 9 , Fe-Fe 4 M 8 (M=0.25Fe + 0.75Mo) and Fe-Fe 6 Ta 6 is respectively 0.602, 0.955 and 0.931. The percent difference Δ between R and R * is respectively −15.2%, 5.9% and 3.2%. These clusters are quite close to the requirement of efficiently topologically packed which means beneficial microalloying elements equals introducing new topological clusters. From a thermodynamic point of view, topological clusters would enhance the viscosity of alloy melt increasing the difficulty of rearrangement of atoms. From an energy point of view, the efficiently topologically packed clusters would decrease the thermodynamics free volume of system, which would also simultaneously increase the stability of microstructure. To sum up, beneficial microalloying elements should be chosen under the condition of bringing in new type of topologically efficiently packed clusters rather than enjoy negative heats of mixing between the major element.
The schematic diagram of understanding and choosing the beneficial microalloying elements in Fe-based bulk metallic glasses via clusters is shown in figure 3.
The microalloying elements should have negative heat of mixing between the major element Fe. However, from the aspect of clusters, this type could be further subdivided. For some of the microalloying elements, such as V, which also has negative heat of mixing between the major element Fe, however, there doesn't exist specific clusters in Fe-V binary system. Under the guidance of method related clusters and mixing entropy reported in Refs, the GFA is quite related to microstructure. And cluster is the basic structure unit of BMGs. Microalloying with V would not bring in new type of clusters. Those microalloying elements, having negative heat of mixing between the major element, failing to bring in specific cluster, are categorized as Type 1, such as V etc. element in Fe-based system. Conversely, those microalloying elements, having negative heat of mixing between the major element, bringing in specific cluster, are be categorized as Type 2, such as C, Mo and Ta etc. elements in Fe-based system. The newly introduced type of efficiently topologically packed clusters would increase the number of clusters, leading to a higher entropy of mixing, adding the difficulty of precipitation of crystalline phases, and enhance the original system's GFA.

Conclusion
To sum up, to further enhance GFA, new type of topologically efficiently packed cluster is welcome. That's to say, beneficial microalloying elements for enhancing GFA should be chosen under the condition of bringing in new type of topologically efficiently packed clusters rather than simply enjoy negative heats of mixing between the major element.
In this paper, a new guidance via clusters was applied to understand and choose the beneficial microalloying elements. Under this guidance, a series of beneficial microalloying elements could be quickly discovered. This method will help quickly choose beneficial microalloying elements for enhancing GFA and build a foundation for further quantitative analysis of minor alloying.