**1. Introduction**

In the past few decades, bulk metallic glasses (BMGs) [1–9] and high entropy alloys (HEAs) [10–18] have attracted much attention, owing to their unique structure and properties, such as high strength/hardness, good corrosion/wear resistance, etc. Previously, BMGs and HEAs were developed separately in most cases, following different composition design and fabrication routes. While recent studies show that intersections exist between these two domains, namely some HEAs with meticulously designed composition could be made into BMGs, and hence the high entropy bulk metallic glasses (HE-BMGs) were developed [19–41]. An investigation into HE-BMGs is beneficial for understanding the phase formation rules of HEAs and fundamental issues of BMGs, so it is very important to develop more HE-BMGs.

In our previous work, a Ti20Zr20Cu20Ni20Be20 HE-BMG with a critical diameter of 3 mm was successfully obtained by copper mold casting method [24]. By introducing Hf as the sixth constituent element, Ti16.7Zr16.7Hf16.7Cu16.7Ni16.7Be16.7 with a critical diameter of 15 mm [25] and a series of Ti20Zr20Hf20(Cu20−xNix)Be20 HE-BMGs with critical diameters of larger than 12 mm was developed [26,27]. These results indicate that similar element substitution/addition is an effective way for developing new HE-BMGs, just the same as traditional BMGs. Since Hf is an element chemically similar to Zr while Nb and Zr are also very close in the periodic table of elements, it is reasonable to suppose that by substituting Zr with Hf, or by adding Nb in the Ti20Zr20Cu20Ni20Be20 quinary HEA system, new HE-BMG with good properties can be obtained. Accordingly, two new HEAs, namely Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7, were designed to verify this assumption, and their glass-forming ability, atomic size distribution characteristics, lattice distortion, and phase selection rules of HEAs are discussed in detail.

**Citation:** Ding, H.; Luan, H.; Bu, H.; Xu, H.; Yao, K. Designing High Entropy Bulk Metallic Glass (HE-BMG) by Similar Element Substitution/Addition. *Materials* **2022**, *15*, 1669. https://doi.org/ 10.3390/ma15051669

Academic Editor: Filippo Berto

Received: 31 December 2021 Accepted: 15 February 2022 Published: 23 February 2022

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#### **2. Experimental**

The master alloy ingots with nominal compositions of Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 in equal atomic ratio were prepared by arc melting the mixtures of high purity Ti, Hf, Cu, Ni, Zr, Nb plates, and Be granules (purity higher than 99.99 wt.%) within a pure argon gas environment. Cylindrical rods with different diameters were prepared by copper mold injection or suction casting method. Arc melting and casting was conducted on multi-functional high vacuum arc-melting and melt-spinning system, which was produced by SKY Technology Development Corporation, Shenyang, China. The glassy nature of these as-prepared samples was examined by X-ray diffraction (XRD) technique using a Rigaku D/max-RB XRD spectrometry (Rigaku Corporation, Tokyo, Japan) with Cu Kα radiation (λ = 0.15406 nm). Thermal properties of the glassy alloys were examined by a Shimadzu DSC-60 differential scanning calorimeter (Shimadzu Corporation, Kyoto, Japan) instrument under the protection of N2 gas (flow rate: 50 mL/min). The applied heating rate was set as 20 K/min. The DSC instrument was calibrated with In and Zn standard specimens. The errors are within ±1 K. Compression tests with specimens of Ø2 × 4 mm and Ø1.5 × 3 mm in size were carried out on WDW-100 testing machine (Shanghai Precision Instrument Co., Ltd, Shanghai, China) under a stain rate of <sup>4</sup> × <sup>10</sup>−<sup>4</sup> <sup>s</sup><sup>−</sup>1.

#### **3. Results**

Figure 1 shows the XRD spectra of the as-cast Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7 Nb16.7Cu16.7Ni16.7Be16.7 rods with different diameters. No sharp diffraction peak corresponding to the crystalline phase was observed in the Ø2 mm Ti20Hf20Cu20Ni20Be20 and Ø1.5 mm Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 samples, indicating that they both possess a fully amorphous structure.

**Figure 1.** XRD spectra of the Ø2 mm Ti20Hf20Cu20Ni20Be20 rod sample and Ø1.5 mm Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 rod sample.

The DSC curves of the Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 samples are shown in Figure 2. The highest test temperature reached 1273 K (1000 ◦C). However, since the endothermic peak is very high in the high temperature part, glass transition would be very ambiguous in the curve. In order to demonstrate the glass transition phenomenon (which is very important for glasses) clearly, we just cut out temperature less than 1000 K in Figure 2. The glass transition temperature *T*<sup>g</sup> and initial

crystallization temperature *T*<sup>x</sup> were marked with arrows. *T*g, *T*x, *T*<sup>m</sup> (melting temperature) and *T*<sup>l</sup> (liquidus temperature) were measured as 717 K, 760 K, 1095 K, and 1220 K for the Ti20Hf20Cu20Ni20Be20 HE-BMG, and 684 K, 739 K, 1066 K, and 1218 K for the Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 HE-BMG, respectively. These data were listed in Table 1.

**Figure 2.** DSC curves of the Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 HE-BMGs.



The stress strain curves of Ø2 × 4 mm Ti20Hf20Cu20Ni20 Be20 and Ø1.5 × 3 mm Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 HE-BMG samples in uniaxial compression test were shown in Figure 3. The fracture strength *σ*<sup>b</sup> was 2425 MPa for Ti20Hf20Cu20Ni20Be20 HE-BMG, the yield strength σ0.2, fracture strength *σ*<sup>b</sup> and plasticity *ε*<sup>p</sup> were 2330 MPa, 2450 MPa and 0.5% for Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 HE-BMG, respectively, which were also listed in Table 1. The specimens fractured in a shear mode. It is interesting to note that both Ti20Hf20Cu20Ni20Be20 and Ti20Zr20Cu20Ni20Be20 quinary HE-BMGs fractured without any plasticity [24], while Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 and Ti16.7Zr16.7Hf16.7Cu16.7Ni16.7Be16.7 senary HE-BMGs exhibited a compressive plasticity of about 0.5%, as well as serration behavior [25]. The reason of this difference remains unclear.

**Figure 3.** Stress strain curves of the Ti20Hf20Cu20Ni20Be20 and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 HE-BMGs.

#### **4. Discussion**

#### *4.1. Glass Forming Ability (GFA) of High Entropy Alloys by Element Addition/Substitution*

The parameters of supercooled liquid region Δ*T* (= *T*<sup>x</sup> − *T*g), reduced glass transition temperature *T*rg (= *T*g/*T*l), and γ parameter (= *T*x/(*T*<sup>g</sup> + *T*l)) are calculated as 43 K, 0.588, and 0.392 for Ti20Hf20Cu20Ni20Be20, while 55 K, 0.562, and 0.388 for Ti16.7Zr16.7Nb16.7 Cu16.7Ni16.7Be16.7, respectively. Compared with Ti20Zr20Cu20Ni20Be20 alloy (3 mm), the critical diameter of Ti20Hf20Cu20Ni20Be20, alloy (2 mm) and Ti16.7Zr16.7Nb16.7Cu16.7Ni16.7Be16.7 (1.5 mm) both decreased. It is noticed that by substitution Zr with Hf, although *T*rg remains the same, Δ*T* and γ decreased; by addition of Nb as the sixth element, both *T*rg and γ decreased, although Δ*T* increased [24]. It implies that the parameter γ is better than *T*rg and Δ*T* in judging the GFA in these high-entropy glassy alloys; meanwhile high entropy is not always beneficial to the GFA of the HEAs. The substitution of element Hf and the addition of Nb brings the liquidus temperature *T*<sup>l</sup> higher than that of Ti20Zr20Cu20Ni20Be20 alloy [24]. As a result, the GFA of the HEA was slightly deteriorated. On the other hand, by the addition of Hf as the sixth element, liquidus temperature *T*<sup>l</sup> was lowered down. Therefore, the GFA of the Ti16.7Zr16.7Hf16.7Cu16.7Ni16.7Be16.7 was greatly improved as compared with Ti20Zr20Cu20Ni20Be20 alloy [25]. These results indicate that lowering down liquidus temperature would be helpful for enhancing the GFA.

## *4.2. Atomic Radius Characteristics of HE-BMG*

The atomic size distribution characteristics of existing HE-BMGs were shown in Table 2. Based on the atomic radius of constituent elements, they were divided into five categories, namely super large atom (*r* > 0.165 nm), large atom (*r* ≈ 0.16 nm), medium atom (*r* ≈ 0.14 nm), small atom (*r* ≈ 0.12 nm), and ultra-small atom (*r* < 0.12 nm). It is noticed that most HE-BMGs were comprised of 3 to 4 categories, except for those containing nonmetal element such as Si, P, B, C, etc [29,33,36]. In high entropy alloys, larger atomic radius difference leads to larger lattice distortion. In case that lattice distortion exceeds some degree, the lattice collapse and amorphous structure formed accordingly. This is in agreement with Zhang's work [13].


**Table 2.** Atomic size distribution characteristics of existing HE-BMGs.
