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Can an amorphous crystallize into a high entropy alloy?

On the premise that amorphous-HEA composites could demonstrate high toughness and resistance to embrittlement akin to the phase separating glassy-solid solution composites, we develop a thermodynamics based approach to identify chemical compositions capable of undergoing the amorphous to HEA transformation. We introduce two new parameters called phase selection value (PSV) and molar volume dispersity parameter. Using this thermodynamic approach seven multi-component compositions were proposed and the general guidelines for identifying such compositions was established. The approach also reveals that BMGs may not be as such amenable to undergo an amorphous to HEA transformation.

We believe Amorphous-High entropy alloy (HEA) composites might provide high toughness in line with the metallic glass-solid solution composites developed by Johnson and co-workers [1,2]. Formation of intermetallics and other complex compounds during thermo mechanical processing in the supercooled region is considered as one of the causes of embrittlement of amorphous alloys [3][4][5][6]. Ductile second phases based on HEAs, which are known to bear a remarkable suite of physical properties [7][8][9][10][11], could provide enhanced toughness and hence the important question is, can an amorphous phase transform directly into a HEA leading to development of in situ amorphous-HEA composites.
In this letter, we are proposing a thermodynamics based model for identifying compositions capable of an amorphous to HEA transformation. Herein we would like to mention that phase selection between amorphous, HEAs and intermetallics has already been investigated and reported in literature [12,13]. However, unlike the models discussing phase selection between amorphous, HEAs and intermetallics, our investigation is focused on checking the capability of an amorphous system to crystallize into a HEA as a function of temperature. If HEAs can indeed crystallize from the amorphous phase, then the duration and temperature of phase transformation can be optimized to develop amorphous-HEAs composites with desired volume fraction of the HEA. Notwithstanding the fact that kinetics of the transformation is a key aspect, our model currently approaches this problem only from a thermodynamics standpoint at this point of time. Guided by this thermodynamics model, we identify seven compositions which we believe are amenable to the amorphous-HEA transformation.
In order to determine the possibility of amorphous structure transforming into HEA in preference to intermetallics, it is essential to determine the Gibbs free energy for the three competing phases. For the Gibbs free energy of formation of each of the three phases, it is important to determine the enthalpy of formation and entropy of mixing. The enthalpy of formation for the amorphous phase, solid solution phase and the intermetallic can be determined using the Miedema's model [14,15]. The enthalpy of formation (Δ ) for a binary solid solution according to the Miedema's model is given by The structural term Δ is usually very small and ignored during calculations. The other two terms Δ ℎ and Δ can be determined using the methodology provided in supplementary section.
Where Δ is the enthalpy of formation of HEA, ∆ is the elastic enthalpy due to atomic size mismatch for any two elements A and B and i and j are the ith and the jth element of the multi-component system. The entropy of the multi-component system is primarily due to configurational entropy and is given by the equation below: where xi is the mole fraction of the ith element present in the multi component system. Thus, the Gibbs free energy of high entropy alloy in a multi-component system can be obtained by following equation: Where ∆ is the free energy of formation of HEA and T is the temperature at which the Gibbs free energy is determined. For the amorphous phase, the formation enthalpy (∆ ) in multi-component system is given by [16] (∆ ) where is the enthalpy of amorphization of a pure element and the other terms are as described before. The entropy of the multi-component system in amorphous phase can be obtained by the equation 3. The Gibbs free energy of the amorphous phase can then be determined using equation 3 and equation 5. Between the amorphous and HEA phases, the phase having lower value of Gibbs free energy will be the more stable phase and hence their stability vis-à-vis each other can be understood by where a negative output of equation 6 indicates preference for HEA and a positive output indicates preference for amorphous phase. From equation 2 and equation 5, equation 6 can be re-written as: For the sake of simplicity, let us call the term ∆ − ∆ in equation 7 as the Phase  Table 1, are also reported seven compositions which we propose are capable of undergoing the A-HEA transformation at Tg+20 K.
Through our calculations we found that systems capable of A-HEA transformation should have PSV value in the range of 0-0.5 kJ/mol at room temperature. Since the PSV value is strongly influenced by the elastic enthalpy which in turn is dependent on the difference in molar volume of the constituent elements the distribution of the molar volume of the constituent elements is crucial. We introduce a parameter Γ called the molar volume dispersity parameter to describe the molar volume distribution. This parameter is similar to that of the polydispersity parameter δ proposed by Guo et al. [12]. The parameter Γ can be determined using  Table 1. However, the is a good as a screening parameter only and has to be used in conjunction with the PSV for identifying systems capable of A-HEA transformation. It is interesting to note that most of the BMGs reported in Table 1  To validate this correlation and with an objective of determining the Tg of the systems # 6 to # 12, we calculated the Tm for a number of amorphous systems (whose experimentally determined Tg is reported in literature and shown in supplementary Table S1) and plotted it against the Tg calculated using the Lu and Li scheme. Figure 1 shows a plot of calculated and  Table S1 [19,20,[25][26][27][28][29][30][31][32][33][34][35][36].
experimental Tg of a variety of amorphous systems against the system Tm. This plot shows that there is a good agreement between actual and calculated Tg and by and large the Tg of an amorphous system is found to fall in the range of 0.35 -0.4 Tm. Using this knowledge, we estimated the Tg for the predicted systems and determined their PSV at Tg+20 K. These systems supported the A-HEA transformation Tg+20 K.
Since these compositions support A-HEA transformation, we were keen to understand their location in the plot of ΔHmix and δ proposed by Guo et al. [12]. In addition to alloy systems mentioned in Table 1, few popular HEAs (compositions shown in supplementary Table S2) were also placed in Guo et al. plot to highlight contrast in their location compared to BMGs.
As per Guo et al. [12], top left quadrant is assigned to HEA forming compositions and the bottom right quadrant is assigned to BMG forming compositions. Indeed, all BMGs (serial # 1 to 5), except one, reported in Table 1 are located in the bottom right quadrant. As shown in  Table 1 are shown in supplementary Figure S1. As Figure 3 reveals, the strong glass formers such as BMGs bear a high positive value of PSV at RT and undergo a small decrease of PSV at Tg +20 K implying that they will remain the stable phase vis-à-vis HEA. On the other hand, the predicted systems have a small positive value of PSV at RT which changes to a negative value at Tg+20 K implying the capability of the A-HEA transformation.  Table  1.
It is apparent that systems capable of A-HEA transformation should have a small positive value of PSV at RT ensuring that the A-HEA transformation is not very difficult.
As a further validation of the PSV approach, we plot PSV value of a particular High Entropy Bulk Metallic Glasses (HE-BMG) bearing a composition Fe25Co25Ni25B15Si10 at RT and Tg+20 K in Figure 3 [37]. This composition according to Guo et al. plot [12] (shown in Figure 2) should exist as an amorphous phase and it is indeed so when it is cast at high cooling rates. However, the same composition prefers forming a HEA phase (largely a mixture of fcc phase with an unknown compound) instead of an amorphous phase when cooling rates are lower [37].
This seems to be in good agreement with the predictions of the PSV approach which suggests formation of a HEA based on the negative value of PSV at RT. This implies that this composition is supposed to exist as a HEA at room temperature under equilibrium conditions as correctly captured by PSV approach. As a further validation, we calculated the value of PSV for Al0.5TiZrPdCuNi system suggested by Takeuchi et al. [38] and found it to be -1 kJ/mol at RT. It is interesting to note that ∆ and for Al0.5TiZrPdCuNi is -46.7 kJ/mol and 8.8 % respectively and this combination of values makes it fall within the amorphous domain suggested by Guo et al. [12]. However, this particular system formed an amorphous phase only when processed by melt spinning but formed a bcc solid-solution when processed through copper-die casting. This is in contrast to the predictions of Guo et al. [12] who suggested that ∆ should not be more negative than -25 kJ/mol for solid-solution formation [12]. However, PSV approach captures correctly that the Al0.5TiZrPdCuNi system [38] will prefer HEA over amorphous phase under low cooling rates. This, indicates that the PSV in addition to identifying A-HEA compositions can help predicting the preferred phase.