A. Continuous heating

It was already known that HEAs do not always form simple solid solutions with FCC and/or BCC structures. This is entirely dependent on the chemistry of the alloy and the topology/atomic size differences of the alloy constituents. Based on the solid-solution phase formation rules for multicomponent alloys proposed by Zhang et al., ^{Reference Zhang, Zhou, Lin, Chen and Liaw7} Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ alloy is located in the BMG forming zone. Our previous study shows that Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ alloy is a bulk glass former with a critical size of 3 mm. ^{Reference Ding and Yao13} Correspondingly, as shown in Fig. 1, the XRD pattern of as-cast 3 mm-diameter Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ alloy rod consists of only a broad halo and no other sharp peaks corresponding to crystalline phases can be observed, indicating that the alloy rod possesses fully amorphous structure.

FIG. 1.

XRD patterns of as-cast and annealed 3 mm-diameter Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ rod samples.

Figure 2 shows the typical nonisothermal DSC curves of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG obtained at various heating rates of 5, 10, 20, and 40 K/min. All the DSC traces exhibit an endothermic event corresponding to the glass transition followed by three exothermic crystallization peaks. The characteristic temperatures (such as the glass transition temperature T _g, the onset crystallization temperature T _x, and the peak temperatures T _p1, T _p2, and T _p3) and supercooled liquid region (defined as T _x − T _g) are listed in Table I. The crystallization of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is a multiple stage process and rather complex.

FIG. 2.

Continuous DSC traces of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG at different heating rates.

TABLE I.

The thermal properties of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG measured at different heating rates. The measurement errors lie within ±1 K for the temperatures.

To indentify the precipitated phases underlying various crystallization stages, the 3 mm-diameter Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ fully glassy samples were heated in DSC furnace to selected temperatures (T _p1 ^{20 K/min}, T _p2 ^{20 K/min}, and T _p3 ^{20 K/min}) at a heating rate of 20 K/min and cooled to room temperature subsequently without holding time. XRD measurements for samples after annealing treatments at various selected temperatures were carried out. As shown in Fig. 1, the primary crystalline phase was indexed as FCC solid solution appearing at T _p1 ^{20 K/min}. When the annealing temperature increases to T _p2 ^{20 K/min}, two crystalline phases FCC solid solution and Ni₇Zr₂ intermetallic compound were detected. Upon heating to the third exothermic peak, BCC solid solution was observed in addition to the FCC solid solution and Ni₇Zr₂ intermetallic compound. In contrast, there have been a number of reports on Ti and/or Zr containing BMGs showing the formation of icosahedral quasicrystals or Laves type-phases during crystallization. ^{Reference Kim, Park, Lee, Bae, Kim and Kim26–Reference Zhou, Hou, Zhong and Li29} This indicates that the high entropy effect does play an important role on the crystallization behavior of HE-BMGs. With the increase of heating rate, all the characteristic temperatures of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG shift to higher temperature. This phenomenon has also been observed for other BMGs. ^{Reference Cheng, Wang, Ma, Shan and Guo17–Reference Qiao, Pelletier, Wang, Jiao and Wang25}

Based on the DSC data, the apparent activation energy for the glass transition and crystallization can be evaluated by the Kissinger and Ozawa equations, respectively. The Kissinger equation can be written as ^{Reference Kissinger30} :

where $\phi$ is the heating rate, R is the gas constant (8.314 J/mol K), and b ₁ is a constant. T is a specific characteristic temperature, such as T _g, T _x, T _p1, T _p2, and T _p3, while E denotes the corresponding activation energy, such as E _g, E _x, E _p1, E _p2, and E _p3.

The Ozawa equation can be expressed as ^{Reference Ozawa31} :

where b ₂ is another constant.

The Kissinger and Ozawa plots of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG at different heating rates are shown in Fig. 3(a) and 3(b), respectively. By linear fitting, the activation energies such as E _g, E _x, E _p1, E _p2, and E _p3 for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG have been obtained and listed in Table II. The activation energies estimated from Kissinger and Ozawa methods are approximately equal to each other. It can be noticed that E _p1 is smaller than E _x, and this means that the grain growth process is easier to occur than the nucleation process for the first crystallization event. As E _p3 > E _p2 > E _p1, the sequence of the difficulty during the crystallization is the first step, the second step, and the third step.

FIG. 3.

(a) Kissinger plots and (b) Ozawa plots of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG.

TABLE II.

The apparent activation energies derived with Kissinger and Ozawa methods for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. The activation energies of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 (Vit 1) BMG obtained by Kissinger method are also listed as a Ref. Reference Song, Gargarella, Pauly, Ma, Kuhn and Eckert19.

To find the difference between HE-BMGs and conventional BMGs, the activation energies of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 (Vit 1) BMG, which is a typical alloy in Zr–Ti–Cu–Ni–Be quinary alloy system with nonequal atomic concentration, are also summarized in Table II. ^{Reference Cheng, Wang, Ma, Shan and Guo17} By comparison, the E _g value of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is smaller than that of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 alloy, indicating that Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG possesses less stable glassy structure. ^{Reference Chen, Li and Yao32} Moreover, the relatively large value of E _x means Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG has a good stability in thermodynamics.

B. Nonisothermal crystallization kinetics

Figure 4 shows the crystallized volume fraction x of the first, second, and third exothermic peak for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG with a dependence of temperature T at different heating rates. All the curves exhibit a sigmoid shape, indicating that the crystallization rate is slower at the beginning and end of the crystallization process.

FIG. 4.

Plots of crystallized volume fraction x versus temperature T of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG at different heating rates for the (a) first, (b) second, and (c) third crystallization events.

As the nucleation and growth always do not remain the same way during the whole crystallization process, the local Avrami exponent n(x) was used to study the crystallization mechanism of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. In case of isothermal process, n(x) can be given as follows based on Johnson-Mehl-Avrami (JMA) equation ^{Reference Málek33} :

where x is the crystallized volume fraction, t is the time corresponding to the crystallized volume fraction, and t ₀ is the incubation time for nucleation.

Blazquez et al. ^{Reference Blázquez, Conde and Conde34} extends the JMA equation to nonisothermal process under the approximation of iso-kinetic behavior, which gives the relation:

where T ₀ is the onset temperature of crystallization for each exothermic peak and E _a is the activation energy.

Figure 5 shows the plots of ln[−ln(1 − x)] versus ln[(T − T ₀)/ $\phi$ ] of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. Based on the JMA curves in Fig. 5 and Eq. (4), the local Avrami exponent n(x) of the first, second, and third crystallization events can be obtained and shown in Figs. 6(a)–6(c), respectively.

FIG. 5.

JMA plots of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG at different heating rates for the (a) first, (b) second, and (c) third crystallization events.

FIG. 6.

Variations of the local Avrami exponent versus the crystallized volume fraction x at different heating rates calculated for the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG: the (a) first, (b) second, and (c) third exothermic peaks.

The Avrami exponent can be expressed as ^{Reference Ranganathan and Von Heimendahl35} :

where a is the nucleation index (a = 0 for zero nucleation rate; 0 < a < 1 for decreasing nucleation rate; a = 1 for constant nucleation rate and a > 1 for increasing nucleation rate), b is the dimensionality of the growth (b = 1, 2, and 3 for one-, two-, and three-dimensional growth, respectively), c is the growth index (c = 0.5 for diffusion-controlled and c = 1 for interface-controlled growth).

It can be seen from Fig. 6 that all the n(x) − x curves exhibit the same tendency that the value of n(x) gradually decreases as the crystallization fraction increases, which means the nucleation rate decreases. For the first and second crystallization processes, the local Avrami exponent begins from 1.5 <n(x) < 2, which indicates that both of the two crystallization processes are initiated by diffusion-controlled one-dimensional growth with a decreasing nucleation rate. As the crystallization proceeds, the local exponent start to decrease and the value of n(x) is below 1.5 in almost the whole crystallization process, indicating that the nucleation is saturated and there are lots of the crystal nuclei growing up directly. For the third crystallization process, the starting value of n(x) is larger than the values of the first and second crystallization processes under the same condition but still smaller than 2.5, and this means that the crystallization mechanism is the growth of primary crystal type and the nucleation rate decreases with time. In the next stage, n(x) also drops below 1.5, indicating that the concentration of pre-existing nuclei has already reached saturation.

S. Cheng et al. ^{Reference Cheng, Wang, Ma, Shan and Guo17} have investigated the nonisothermal kinetics of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG. For the first crystallization event, the local Avrami exponent curves at relatively high heating rates (20 and 40 K/min) increase slowly from ∼2.0 (x = 0.1) to ∼2.5 (x = 0.9), while the n(x) − x curves at lower heating rates (5 and 10 K/min) decrease first from ∼2.0 (x = 0.1) to the minimum and then increase to ∼2.5. The crystallization mechanism of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG is quite different from that of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG.

As the activation energy during the crystallization process is not a constant, Kissinger–Akahira–Sunose (KAS) ^{Reference Patel and Pratap36} method is used to calculate the local values of activation energy:

where E _a(x) and T(x) stand for activation energy and temperature corresponding to the given crystallized volume fraction x; d ₁ is a constant.

Figure 7 shows the KAS plots of the first, second, and third crystallization peaks for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. By linear fitting, the evolution of E _a(x) as a function of crystallized volume fraction x (ranging from 0.1 to 0.9) was determined (as shown in Fig. 8). As can be seen, for all the crystallization peaks, the value of E _a(x) is almost stable and can be taken as a constant. The average E _a(x) values for the first, second, and third crystallization peaks are 279.5 ± 14.3, 336.7 ± 12.3, and 351.1 ± 15.3 kJ/mol, respectively. In contrast, for Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG, ^{Reference Cheng, Wang, Ma, Shan and Guo17} the value of E _a(x) for the first crystallization peak increases dramatically from ∼170 kJ/mol (x = 0.1) to ∼230 kJ/mol (x = 0.9), which indicates that the crystallization process of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG is more complex.

FIG. 7.

KAS plots for different crystallization volume fractions x (ranging from 0.1 to 0.9) for the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG: the (a) first, (b) second, and (c) third exothermic peaks.

FIG. 8.

Dependence of local activation energy E _a(x) on the degree of crystallization volume fraction x.

C. Kinetic fragility

Kinetic fragility (m) presents the degree of deviations from the Arrhenius law above T _g and is widely used to estimate the thermal stability or glass-forming ability of metallic glass. ^{Reference Qiao, Pelletier, Wang, Jiao and Wang25} Angell introduced the kinetic fragility parameter m as a metric for the viscosity behavior of the undercooled liquid around the glass transition temperature. ^{Reference Angell37}

where D* is the strength parameter, T _g ⁰ is the asymptotic value of T _g, which is usually approximated as the onset of the glass transition temperature at the limit of infinitely slow cooling, and T _g is the glass transition temperature at a heating rate of 20 K/min. The variation of T _g with the heating rate $\phi$ can be fitted by using Vogel–Fulcher–Tammann (VFT) equation ^{Reference Brüning and Samwer38} :

where C is a constant. The values of D* and T _g ⁰ can be obtained by fitting the VFT equation from the heating rate dependence of the glass transition temperature, then the fragility index m can be calculated using Eq. (8).

Figure 9 shows the variation of ln $\phi$ with T _g fitted by VFT equation for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. The m value of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is calculated to be 23, which is much smaller than those of other BMGs in the same alloy system, such as Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 (m = 44) and Zr_46.75Ti_8.25Cu_7.5Ni₁₀Be_27.5 (m = 44.2). ^{Reference Cheng, Wang, Ma, Shan and Guo17} Glass forming liquids can be classified into three general categories based on the concept of fragility: strong glass formers (m < 30), intermediate glass formers (30 ≤ m < 100), and fragile glass formers (m ≥ 100). ^{Reference Angell37} In this sense, the studied Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG can be classified to the strong glass former. However, it has been perceived that a low m value is not necessarily associated with a superior GFA. ^{Reference Senkov39–Reference Chattopadhyay, Sangal and Mondal41}

FIG. 9.

VFT fit of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG.

D. Thermodynamics

The Gibbs free energy difference (ΔG) between the supercooled liquid and crystalline states is the driving force of crystallization and plays an important role in predicting the glass-forming ability of multicomponent metallic alloys. The Gibbs energy difference ΔG can be calculated as follows ^{Reference Busch, Kim and Johnson42} :

where

and

where T _m is the melting temperature, ΔS _m is the entropy of fusion, and ΔH _m is the enthalpy of fusion. They are related to each other by the following equation:

Using Eqs. (10)–(12) in Eq. (9), we obtain the following expression for ΔG:

where $\Delta C_{\rm{p}}^{{\rm{l}} - {\rm{s}}}$ is the heat capacity difference between solid and liquid.

For Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG, ΔH _m and T _m can be easily obtained by DSC (as shown in Fig. 10). However, it is difficult to measure the heat capacity of the supercooled liquid $\left( {C_{\rm{p}}^{\rm{l}}} \right)$ accurately. Based on the approximation of $\Delta C_{\rm{p}}^{{\rm{l}} - {\rm{s}}}$ , Lad et al. ^{Reference Lad, Raval and Pratap43} got the following equation to calculate ΔG for metallic alloys which have wide supercooled liquid region:

where ΔT = T _m − T.

FIG. 10.

DSC curve of the Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG around the melting temperature at a heating rate of 20 K/min.

Figure 11 shows the Gibbs free energy difference as a function of temperature normalized to T _m for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG. For comparison, the Gibbs energy difference curve of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG is also provided. ^{Reference Cheng, Wang, Ma, Shan and Guo17} It is found that the value of the Gibbs energy difference of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is slightly higher than that of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG. As Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG is a well-known alloy with high glass-forming ability, the Gibbs free energy difference of this alloy is lower than that of most other BMGs. ^{Reference Busch, Kim and Johnson42} Correspondingly, Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG shows relatively low Gibbs free energy difference.

FIG. 11.

Gibbs free energy difference curves for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG and Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG.

E. Glass-forming ability

In general, the alloys which possess high crystallization activation energy, small fragility index, and low Gibbs energy difference are probably good glass former. Based on the above results, Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is expected to have good glass-forming ability by comparison with Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG. However, Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG also exhibits a wider supercooled liquid region (82 K, heating rate 20 K/min), ^{Reference Cheng, Wang, Ma, Shan and Guo17} implying a higher thermal stability. Moreover, the critical size of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG is only 3 mm, which is much smaller than that of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG (over 20 mm). ^{Reference Peker and Johnson14}

This result can be explained from several aspects. First, by treating Ti–Zr–Cu–Ni–Be alloy system as a pseudo ternary system, it has been found that the good glass forming alloys in this quinary system always locates at the (Ti + Zr)-rich corner (60–65 at.%), while poor in (Cu + Ni), which is less than 25 at.%. ^{Reference Ding and Yao13} Thus, Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ alloy deviates from the good glass-forming area. As strong evidence of the above analysis, the liquidus temperature T _l (also the melting temperature T _m) of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG (993 K) ^{Reference Ding and Yao13} is obviously lower than that of Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG (1176.6 K), resulting in a higher value of T _rg (defined as T _g/T _l, heating rate: 20 K/min, 0.584 for Ti₂₀Zr₂₀Cu₂₀Ni₂₀Be₂₀ HE-BMG and 0.629 for Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 BMG). It should be noted that a higher melting point always corresponds to the presence of a higher volume fraction of high melting point phases, which would also well explain why the E _p1, E _p2, and E _p3 values are considerably higher than those reported for Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 alloy. Second, from the topological perspective, Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 alloy satisfies ideal efficient atomic-packing conditions, which is beneficial to the glass formation. Third, based on Eq. (9), the high entropy of mixing is beneficial to decrease the Gibbs free energy difference. But meanwhile, according to Adam–Gibbs equation, ^{Reference Adam and Gibbs44} the high entropy of mixing also leads to low viscosity and a high mobility of the atoms in the liquid. ^{Reference Zhang, Zhou, Lin, Chen and Liaw7} So high entropy effect has both advantageous and disadvantageous to the glass-forming ability and the negative effect might play a greater role.