High-Entropy Metal Diborides: A New Class of High-Entropy Materials and a New Type of Ultrahigh Temperature Ceramics

Abstract

Seven equimolar, five-component, metal diborides were fabricated via high-energy ball milling and spark plasma sintering. Six of them, including (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, (Hf_0.2Zr_0.2Ta_0.2Mo_0.2Ti_0.2)B₂, (Hf_0.2Zr_0.2Mo_0.2Nb_0.2Ti_0.2)B₂, (Hf_0.2Mo_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, (Mo_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, and (Hf_0.2Zr_0.2Ta_0.2Cr_0.2Ti_0.2)B₂, possess virtually one solid-solution boride phase of the hexagonal AlB₂ structure. Revised Hume-Rothery size-difference factors are used to rationalize the formation of high-entropy solid solutions in these metal diborides. Greater than 92% of the theoretical densities have been generally achieved with largely uniform compositions from nanoscale to microscale. Aberration-corrected scanning transmission electron microscopy (AC STEM), with high-angle annular dark-field and annular bright-field (HAADF and ABF) imaging and nanoscale compositional mapping, has been conducted to confirm the formation of 2-D high-entropy metal layers, separated by rigid 2-D boron nets, without any detectable layered segregation along the c-axis. These materials represent a new type of ultra-high temperature ceramics (UHTCs) as well as a new class of high-entropy materials, which not only exemplify the first high-entropy non-oxide ceramics (borides) fabricated but also possess a unique non-cubic (hexagonal) and layered (quasi-2D) high-entropy crystal structure that markedly differs from all those reported in prior studies. Initial property assessments show that both the hardness and the oxidation resistance of these high-entropy metal diborides are generally higher/better than the average performances of five individual metal diborides made by identical fabrication processing.

Figure 1. Schematic illustration of the atomic structure of the high-entropy metal diborides.

Here, M₁, M₂, M₃, M₄, and M₅ represent five different transition metals (selected from Zr, Hf, Ti, Ta, Nb, W, and Mo). This new class of high-entropy materials and new type of UHTCs have a unique layered hexagonal crystal structure with alternating rigid 2D boron nets and high-entropy 2D layers of metal cations (as essentially a class of quasi-2D high-entropy materials), with mixed ionic and covalent (M-B) bonds between the metals and boron.

Figure 2

XRD patterns showing the phase evolution during the HEBM and SPS fabrication processes in (a) HEB #2 as an examplar in an expanded scale and (b) six other specimens. Only the first three peaks of the high-entropy hexagonal AlB₂ phases are shown here for figure clarity; full-range XRD patterns (of 2θ = 20°–100°, showing eleven XRD peaks of the high-entropy hexagonal phases) are documented in the Supplementary Figs S1–S7.

Figure 3. XRD patterns of all seven specimens after SPS at 2000 °C, where the peaks of the primary hexagonal phase are indexed.

Six of seven specimens (except for HEB #6) exhibit largely a single hexagonal phase of the AlB₂ structure, albeit the presence of minor secondary (Zr, Hf)O₂ (native oxides), which are represented by the low-intensity peaks that are not indexed here the figure clarity (but indicated by the solid dots in Supplementary Figs S1–S7). As the only special case, a secondary boride phase was observed in HEB #6, with XRD peaks matching those of the (Ti_1.6W_2.4)B₄ compound, while the major XRD peaks still represent a hexagonal metal diboride solid-solution phase.

Figure 4

Cross-sectional SEM image and the corresponding EDX compositional maps of three selected specimens after SPS, showing the formation of largely homogeneous high-entropy solid-solution phases except for the HEB #6 shown in (c). The compositions are largely uniform albeit the presence of minor (Zr, Hf)O₂ based native oxides, e.g., in (a), and some Nb clustering in four Nb-containing specimens, e.g., in (b). The formation of a secondary boride phase was observed only in HEB # 6, as shown in (c). Additional EDX compositional maps (in expanded views) of all seven specimens are documented in the Supplementary Figs S1–S7.

Figure 5. Atomic-resolution STEM ABF and HAADF images of HEB #2 (Hf_0.2Zr_0.2Ta_0.2Mo_0.2Ti_0.2)B₂.

(a) and (b): ABF and HAADF images at a low magnification, showing the homogeneity of the solid-solution phase. (c) and (d): ABF and HAADF images at a higher magnification, showing atomic configuration. The electron beam is parallel to the zone axis of hexagonal structure. (0001) and planes are indexed in (c). The red circles highlight the columns of transition metal atoms (Hf, Zr, Ta, Mo and Ti). The green dots indicate the B atoms. Additional STEM images from different regions and a different specimen are documented in the Supplementary Figs S8–S10; a further digital analysis of HAADF and ABF images in Supplementary Fig. S11 shows that the standard variations in the (0001) lattice spacings are only ~0.6% or ~0.02 Å, indicating homogenous mixing of five metal atoms (Hf, Zr, Ta, Mo and Ti) within the 2-D metal layers in (0001) planes.

Figure 6. STEM-HAADF image and the corresponding EDS compositional maps for HEB #2 (Hf_0.2Zr_0.2Ta_0.2Mo_0.2Ti_0.2)B₂, showing the homogeneous chemical distribution at nanoscale.

These compositional maps were taken when the electron beam is parallel to the zone axis, showing no significant layer-to-layer variations of metal composition in different basal (0001) planes. Additional EDX compositional maps obtained from a different region are documented in the Supplementary Fig. S12.

Figure 7. Measured hardness of six single-phase high-entropy metal diborides, which are generally greater than the “rule-of-mixtures” averages of the hardness values measured from individual metal diborides that were fabricated via the same HEBM and SPS route.

Since MoB₂ is not an equilibrium bulk phase below 1500 °C, the averages for HEB#2-HEB#5 were calculated without MoB₂. However, MoB₂ has a lower melting temperature and theoretical hardness than all other five other metal diborides in question; thus, the actual rule-of-mixtures averages should be even lower. It is also important to note that the hardness can be affected by porosity and oxide inclusions so that fully-dense and oxide-free metal diborides should have greater hardness than these measured values. We choose to compare the measured hardness values of high-entropy and conventional metal diborides fabricated by the same method to allow a fair assessment of relative values.

Figure 8. A snapshot of the relative oxidation performance of various high-entropy and individual metal diborides fabricated and tested with the same conditions.

This figure displays percentage weight gain vs. oxidation temperature curves during annealing in flowing dry air at 1000 °C, 1100 °C, and 1200 °C (for one hour each) sequentially for six single-phase high-entropy metal diborides [HEB #1 = (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, HEB #2 = (Hf_0.2Zr_0.2Ta_0.2Mo_0.2Ti_0.2)B₂, HEB #3 = (Hf_0.2Zr_0.2Mo_0.2Nb_0.2Ti_0.2)B₂, HEB #4 = (Hf_0.2Mo_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, HEB #5 = (Mo_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, and HEB #7 = (Hf_0.2Zr_0.2Ta_0.2Cr_0.2Ti_0.2)B₂], along with six individual metal diborides fabricated via the same HEBM and SPS route. See the “Methods” section for the experimental procedure and Supplementary Figs S13–S15 for additional results, including weight gain per surface area plots, weight percentage gains at higher temperatures, and images of all specimens after oxidation at different temperatures. In this figure (and Supplementary Fig. S13), solid lines represent the high-entropy metal diborides and dashed lines represent the individual (conventional) metal diborides made by the same fabrication route.