Non-Isothermal Crystallization Kinetics of a Rapidly Solidified as-Cast TiZrHfNiCu High Entropy Bulk Metallic Glass

This paper aims to investigate the thermal behavior and crystallization kinetics of TiZrHfNiCu high entropy bulk metallic glass (HE-BMG) alloy using the standard procedure of Differential Scanning Calorimetric (DSC) annealing technique. The alloy was produced using an arc melting machine with a critical diameter of 1.5 mm. The crystallization kinetics and phase transformation mechanism of TiZrHfNiCu HE-BMG was investigated under the isochronal condition at a single heating run based on the Johnson-MehlAvrami (JMA) theory. In isochronal heating, the apparent activation energy for glass transition and crystallization events was analyzed by Kissinger and Ozawa methods. The average activation energy value for crystallization of TiZrHfNiCu amorphous alloys in isochronal modes was 226.41 kJ/mol for the first crystallization and 297.72 kJ/mol for second crystallization stages. The crystallization mechanism of the first step was dominated by twoand three-dimensional growth with increasing nucleation rate, while the crystallization mechanism in the second stage was dominated by two-dimensional crystallization growth with a constant nucleation rate. The diffusion mechanism result proved the theory of sluggish atomic diffusion of HEA at elevated temperature.


Introduction
High Entropy Alloys (HEAs) and Bulk Metallic Glasses (BMGs) are two types of novel materials that exhibit unique physical and mechanical properties [1] [2]. that the overall nucleation process occurs during the initial crystallization process and becomes neglected afterward [12]. This method is also widely used for non-isothermal crystallization kinetics studies in various amorphous alloys [13] [14] [15] [16] [17]. Different models have been proposed to measure the E a for non-isothermal conditions includes the Ozawa-Flynn-Wall method [18], Kissinger method [19], and Augis-Bennett method [20]. All of them are derived from Johnson Mehl Avrami (JMA) method having an Arrhenian temperature dependence.
However, there are issues reported which discussed regarding the applicability of the Kissinger model [21], particularly to determine the glass transition activation energy. It was found that the Kissinger method was influenced by the thermal history of the sample that differed from the value obtained from the simulations [22]. It was suggested that the Moynihan model utilized the concept of "fictive temperature" [23], which can be used to represent relevant cases of structural relaxation behavior. In contrast, the Kissinger model is not capable of determining the activation energy for glass transition correctly since it only considers the simple thermal activated process. Therefore, the Moynihan model was claimed to be more accurate than the Kissinger model since it considers the main features of structural relaxation behavior [24]. However, [25] was compared the apparent activation energies of some novel near-equiatomic high-entropy bulk metallic glasses samples using Kissinger, Moynihan, Ozawa, and Boswell methods and found that the calculated value of apparent activation energy, E g and E x for Kissinger and Moynihan are almost the same.
In this work, the crystallization kinetics of TiZrHfNiCu HE-BMG was investigated by isochronal condition using the standard procedure of Differential Scanning Calorimetric (DSC) annealing technique. The mechanism of nucleation and growth of this alloy obtained from the calculated kinetics parameters can be used to determine the thermal behavior of this alloy at elevated temperature. This will also prove the sluggish diffusion behavior of HE-BMGs at elevated temperatures.

Experimental
TiZrHfNiCu HE-BMG in equal atomic proportion (at.%) was prepared by arc melting under Ti-gettered argon atmosphere using highly pure elements, which were above 99.5 wt%. The alloys were melted for at least five times to ensure homogeneity. The alloy ingots were suction cast into a water-cooled copper mold with dimensions of 1.5 mm, 2 mm, and 3 mm diameters and 30 mm length. Meanwhile, rapidly quenched ribbons form was prepared by re-melting the alloy ingots in quartz crucible by induction melting while ejecting with a pressure of 40 kPa through a nozzle onto a Cu wheel rotating with a surface velocity at 40 m/s.

Crystallization Kinetics Experiments
The experiments were conducted using a Perkin Elmer DSC-diamond, with a N. H. Nordin et al. computerized data acquisition system. The sample with 10 -20 mg in weight was put in the aluminum pan and heated from 200˚C -500˚C with a different heating rate at 20 K/min to 80 K/min. Purified argon gas was used throughout the experiment. The onset crystallization temperature was defined as the slope of the tangent intersection in the DSC curve.

Characterizations
Structures of the as-cast and melt-spun ribbons were examined by X-ray diffraction (XRD) using (Phillips D5000) Cu-Kα radiation. It was then marked as S1, S2, S3, and S4 for ribbon, 1.5 mm, 2 mm, and 3 mm, respectively. Thermal analysis of the samples was carried out using (DSC, Perkin-Elmer Instruments, diamond) from 200˚C -500˚C at 20 K/min to determine glass transition temperature (T g ) and crystallization temperature (T x ).

Alloys Design
The multicomponent high entropy alloys, TiZrHfNiCu HE-BMG alloys was reproduced from [26] based on the idea of forming glassy high entropy alloys from the equal concentration of constituent elements which did not contain any host element. The selection of the elements well in accordance with the three empirical rules is described by Inoue [27]. In order to determine the formability of solid solution in this alloy, thermodynamic and electronic parameters of the alloys include the enthalpy of mixing (ΔH mix ), the entropy of mixing (ΔS mix ), atomic size difference (δ), electronegativity difference (Δ χ ), and valence electron concentration (VEC) were calculated as shown in Table 1, where the relationship of enthalpy of mixing in each element pair is shown in Figure 1. This calculation has been used extensively for phase formation in predicting HEAs and BMGs [28] [29].  The relationship of the heat of mixing among the constituent elements in Figure 1 shows that Ni and Cu possessed negative heats of mixing against Ti, Zr and Hf. Ni provided larger absolute values compared to Cu with Ti, Zr, and Hf, which resulted in the strong attraction of interatomic forces between those elements that contributed to the formation of the glassy phase in the alloys as calculated according to Miedema's model [30]. On the other hand, Ni and Cu were located next to each other in the periodic table which results in positive enthalpy of mixing. The thermodynamic analysis revealed that the glass-forming behaviour of Zr and Hf was similar, whereas it was different from that of Ti. The preferred formation of amorphous phases in the system was attributed to high negative mixing enthalpy between the constituent elements.
The atomic size ratios in the present system were the second factor for the formation of the bulk glassy alloy. Table 2 has summarized the atomic size ratios among the elements in the present system. The atomic size ratios among Ti, Zr and Hf were less than 10%. While, the atomic size ratios for Ni and Cu with Ti, Zr or Hf were more significant than 12%. Therefore, the more massive negative heats of mixing for Ni with Ti, Zr and Hf might be suggested as the main reason for the formation of the bulk glassy while the atomic size ratio of Ni and Cu with Ti, Zr and Hf could be considered as an additional factor that contributed to the glass formation in Ti 20 Zr 20 Hf 20 Cu 20 Ni 20 alloy. Figure 2 shows the XRD patterns of the equiatomic TiZrHfNiCu samples with cooling rate variations while Table 3 summarised the findings from the patterns. According to the diffractogram, it was clearly shown a broadened peak of 1.5 mm as-cast rod and 40 m/s melt-spun ribbon at 2θ = 30˚ -45˚, indicating that the alloy possessed fully amorphous structure. The partially amorphous structure could be observed in a 2 mm rod due to the existence of halo humps with some crystalline peaks at a lower angle (2θ = 30˚ -45˚). Since the sample composes of a mixture of amorphous and crystalline structures, the peaks are less intense and not clear at a lower angle (20˚ to 30˚). It may because of the small sample size, which needs a smaller step size and slower scan rate to get ideally sharp profile data, particularly at a lower angle.

DSC Analysis
Non-Isothermal Annealing Figure 3 shows typical DSC curves for the amorphous TiZrHfNiCu HE-BMG alloy at five different heating rates (10, 20, 40, 60, and 80 K•min −1 ). All DSC curves in the temperature range of 650 -850 K showed an endothermic event corresponding to the glass transition followed by two exothermic crystallization peaks, which indicated the multi-stage crystallization process of the alloy. Therefore, the crystallization process of this alloy was somewhat complicated, in contrast to most of the conventional metallic glasses. It was suggested that the multiple exothermic peaks were attributed to the decomposition of the metallic bonding N. H. Nordin et al. World Journal of Engineering and Technology that leads to the crystallization process [31]. The onset of the glass transition temperature, T g and crystallization temperature, T x along with peak temperature for each crystallization events, and supercooled liquid region (ΔT x ) were listed in Table 4. Apparently, the temperatures of all peaks shifted to a higher temperature, and the heat flow became more significant with the increasing heating rate, which showed that the alloy possessed an apparent thermodynamic effect. This scenario also represented different thermal activation of each step in the crystallization process. Interestingly, it was found that the second crystallization peak at 40 K/min is slightly intense than at 60 K/min. Theoretically, a sharp peak represents a faster rate of transformation with more considerable enthalpy change that usually occurs at a higher heating rate [32]. Nevertheless, a slightly intense peak does not necessarily mean a higher rate of transformation since it probably happens due to a higher volume of materials tested or element additions in the chemical composition of the sample during the testing.
where β is the heating rate, T denotes the characteristics temperatures at certain heating rate β, R is the ideal gas constant, E corresponds the average apparent activation energy for each crystallization events. Activation energy can be defined as the energy required for an atom before it becomes a part of the activated cluster. The value of apparent activation energy for E g , E x1 , E p1 , E x2 , and E p2 can be obtained by the linear fitting method in Kissinger and Ozawa plot in Figure 4, and the values were listed in Table 5. From the table, it is evidently obvious that the apparent activation energy of glass transition and crystallization estimated from the Kissinger equation and Ozawa equation are reinforcing each other. It was noticed that, for the first crystallization event, the E p1 was smaller than E x1 in the Ozawa method, which explained that more energy was required for the nucleation than the grain growth process. However, Kissinger's value provided different results, where the value of E p1 was larger than E x1 . This phenomenon might result in considerable R 2 value (0.878) of E p1 linear fitting in the Kissinger plot. Besides, E x2 > E x1 shown in all analytical methods explained that high energy barrier in second crystallization compared to the first, implying that the first crystallization stage was much easier for nucleation to occur. Therefore, the estimated data above implied that nucleation and growth apparent energy for the first crystallization stage gave almost similar value. İn contrast, the difficulties of the growth process were much more significant in the second crystallization stage. The above statements were in agreement with the other crystallization kinetics studies in metallic glass alloys [5] [7] [38] [39].
The relatively high activation crystallization energy values in the second crystallization stage shows that a significant number of atoms participated from the glassy alloys in the structural reorganization during the second stage of the crystallization process. Besides, this phenomenon might be attributed to a sluggish diffusion in high entropy alloys, which resulted in difficulty for atomic diffusion [40]. It might also due to greater fluctuation of lattice potential energy that results in significant atomic traps and blocks, which can lead to high activation energy. Consequently, the nucleation and growth mechanism become slower due to the reduction of the nucleation rate that resulted from the sluggish diffusion. However, as compared to other reported HE-BMGs such as TiZrCuNiBe [5] and Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5 [37], the value of the apparent activation energy for TiZrHfNiCu was relatively small, indicated lower thermal stability of this alloy compared to the former alloys.   Figure 5(a) and Figure 5(b) show the crystallized volume fraction, x for the first and second exothermic peaks was for TiZrHfNiCu HE-BMG with a dependence of temperature T at different heating rates. In contrast, Table 6 shows the stages. In general, it was clearly shown that crystallization occurred at a slower rate at the beginning (x < 0.2), propagated at the middle (0.2 < x < 0.9), and subsequently was slowed at the end of the process (x < 0.9). Therefore, it was suggested that the transformation was divided into three stages; 1) the nuclei started to precipitate from the amorphous matrix slowly where the bulk crystallization played an important role; 2) subsequently increased the surface contact between nuclei and the amorphous matrix that caused the crystallized volume fraction to increase intensely and 3) finally the surface between the crystalline phase and amorphous matrix decreased due to grain coalescence [12].  [42]. Noticeably, the average value of local activation energy of E x1 was smaller than E x2 , which was in a consistency with the result of apparent activation energy.  Local Avrami exponent, n(x), has been widely used to relatively measures the average value of crystallization transformation at specific conditions. The definition of "local" indicates the nucleation and growth behavior of the alloy at the specific crystallization volume fraction, x [43]. In order to utilize the JMA equation for the non-isothermal crystallization process, several conditions need to be satisfied [12]. It was suggested that the crystallization peak temperature, T p of the alloy must occur at 0.60 to 0.63 range of crystallization volume fraction, x [12]. For the present studies, the value of x p at T p was found in the range of 0.60 to 0.63.
By plotting ln[−ln(1 − x)] versus ln[(T − T 0 )/β], the n values might be obtained from the slope of the graphs, as displayed in Figure 6. The values of the slope were listed in Table 7. The plot was found to be linear over most of the temperature range but slightly deviated at higher temperatures for all heating rates. The deviation could be due to the saturation of nucleation at the final stages of the crystallization process. Besides, this situation also resulted in crystal growth constraint for the small particles that restricted the nucleation process [44].
From the calculated JMA exponent, n, the value (which was the nucleation mode of the alloy) was proportionally increased as a function of heating rate in the first crystallization stage where it was initially more significant than 3 and subsequently increased to 4. The n value was not an integer, and it was equal to n = m + 1. Therefore, the value of m (which was an indicator of crystallization behavior) was equal to 2 but then increased to 3 at 60 K/min. The finding suggested that the growth mechanism changed from the interface-controlled two-dimensional growth to the diffusion-controlled three-dimensional growth with the increasing heating rate for the first crystallization process. In contrast, for the second stage, the n values were constant (n = 3) with an increased heating rate, which signified that the growth of crystallization two-dimensional growth with increasing nucleation rate at all heating rates. In this case, the activation energy is increased since the mechanism changed from the interfacecontrolled two-dimensional growth to the diffusion-controlled three-dimensional growth. On the other hand, the activation energy is much lower if the reaction is slower; thus, Avrami exponent is smaller [45]. It is known that the sluggish effect of HEA concerning the activation energy and pre-exponential factor determined by the Arrhenius equation. The high activation energy proved that a low grain growth rate occurs in the alloy, which reflects the pre-exponential factor value [40]. It is also found that the n values increased in the first stage, but then became constant in the second stage as a function of heating rate. This is because the sluggish atomic diffusion of this alloy due to densely random packed atomic configuration of the structure of multicomponent alloy, particularly at higher temperatures (second stage), result in lower mobility of atomic diffusion, leading to lower nucleation rate compared to first crystallization stage for all heating rates.   Table 7. The value of n and m of Avrami exponent to determine nucleation modes and crystallization mechanism in the alloy respectively.

Conclusion
Kinetics of crystallization in TiZrHfNiCu HE-BMG was investigated by DSC method in non-isothermal condition. The information regarding activation energy and crystallization mechanism reflects the resistance of crystallization during heating. Two stages of the crystallization process were found under non-isothermal conditions. It was shown that TiZrHfNiCu has higher apparent activation energy (E x1 and E p1 ) compared to conventional Zr-based alloys but lower than TiZrCuNiBe HE-BMG. It is suggested that high mixing entropy in TiZrHfNiCu alloy successfully retard lattice diffusion at higher temperatures in non-isothermal conditions, lead to a slow crystallization process.
N. H. Nordin et al.