Bulk High-Entropy Hexaborides

For the first time, a group of CaB6-typed cubic rare earth high-entropy hexaborides have been successfully fabricated into dense bulk pellets (>98.5% in relative densities). The specimens are prepared from elemental precursors via in-situ metal-boron reactive spark plasma sintering. The sintered bulk pellets are determined to be single-phase without any detectable oxides or other secondary phases. The homogenous elemental distributions have been confirmed at both microscale and nanoscale. The Vickers microhardness are measured to be 16-18 GPa at a standard indentation load of 9.8 N. The nanoindentation hardness and Young's moduli have been measured to be 19-22 GPa and 190-250 GPa, respectively, by nanoindentation test using a maximum load of 500 mN. The material work functions are determined to be 3.7-4.0 eV by ultraviolet photoelectron spectroscopy characterizations, which are significantly higher than that of LaB6.

For the first time, a group of CaB6-typed cubic rare earth high-entropy hexaborides have been successfully fabricated into dense bulk pellets (>98.5% in relative densities).
The specimens are prepared from elemental precursors via in-situ metal-boron reactive spark plasma sintering. The sintered bulk pellets are determined to be single-phase without any detectable oxides or other secondary phases. The homogenous elemental distributions have been confirmed at both microscale and nanoscale. The Vickers microhardness are measured to be 16-18 GPa at a standard indentation load of 9.8 N. The nanoindentation hardness and Young's moduli have been measured to be [19][20][21][22] respectively, by nanoindentation test using a maximum load of 500 mN. The material work functions are determined to be 3.7-4.0 eV by ultraviolet photoelectron spectroscopy characterizations, which are significantly higher than that of LaB6.

Highlights:
• High-entropy hexaborides were fabricated in the bulk form for the first time.
• A novel boron-metal reactive SPS processing resulted in >98.5 relative densities.
• The novel processing produced high-entropy hexaborides free of oxide inclusion.
• Elemental distributions are homogenous at both microscale and nanoscale.

Introduction
In 2004, Yeh et al. [1] and Cantor et al. [2] published two independent reports on the fabrication of high-entropy alloys (HEAs) or multi-principal element alloys. In the last decade, HEAs have attracted great research interest in the metallurgy community. HEAs usually refer to metallic alloys with five or more elements of equimolar (or near equimolar) compositions, which can be considered as a subclass of complex concentrated (or compositionally complex) alloys (CCAs) [3]. HEAs and CCAs can possess superior, and sometimes unexpected, mechanical and other properties [3][4][5][6].
Among the HECs, high-entropy borides (HEBs) offer abundant design opportunities due to their enormous structural, in addition to the high-entropy compositional, spaces.
Based on a 2017 review by Akopov et al. [31], there are as many as 1253 entries (different crystal structures) for binary boron compounds of various stoichiometry ratios ranging from 4:1 to 1:66 (M4B to MB66, where M represents a metal). In 2016, Gild et al. [12] reported the first class of HEBs, high-entropy metal diborides in the AlB2-typed hexagonal structure. Further studies fabricated monoborides [14,32], M3B4 borides [15], and tetraborides [16] in bulk form by using boro/carbothermal reduction of metal oxides [13,33] or reactive sintering of elemental precursors [14][15][16]32].  [34,35]. The hexaboride structure is schematically illustrated in Fig.   1 (that it is drawn for a high-entropy hexaboride with five metals). In its cubic unit cell, metal cations locate at the body center, while boron octahedra (composed of six boron atoms) situate at eight vertices. A recent review [36] summarized four synthesis routes for rare earth hexaborides: (1) solid-state reactions, (2) melt electrolysis and flux, (3) vapor deposition and metal-gas reactions, and (4) combustion synthesis, while hot-press and spark plasma sintering (SPS) are the most popular densification methods. In general, rare earth hexaborides show great potential for a range of applications, including electron emitters, thermoelectric materials, coatings, and superconductors [35,36]. Specifically, LaB6 is extensively studied and widely used as a thermionic electron emitter due to its low work function and low vapor pressure at high temperatures [37]. The close lattice parameters ranging from 4.069 Å (HoB6) to 4.176 Å (EuB6) [34,35] suggested they are easy to form solid solutions, where their properties can be further tuned.
High-entropy hexaborides (HEHBs; Fig. 1) have been successfully synthesized, but only as powders [33] or highly porous materials [13] (but not yet in the dense bulk form).
Recently, Qin et al. showed a generic in-situ metal-boron reactive SPS method can be used to synthesize and fabricate (in one process) dense bulk pellets of four different classes of HEBs (in the MB, MB2, M3B4, and MB4 stoichiometries) [14][15][16]38]. This motivates us to adopt this direct metal-boron reactive SPS route to fabricate HEHBs in bulk forms and subsequently measure their basic bulk properties.

Experimental Procedure
Commercial powders of Y, La, Pr, Nd, Sm, Gd, Tb, Dy, and Yb (99.9% purity, ~40 mesh, purchased from Alfa Aesar, MA, USA) and boron (99% purity, 1-2 μm, purchased from US Research Nanomaterials, TX, USA) were utilized as elemental precursors for synthesizing bulk specimens of six compositions HEHB1 to HEHB6 listed in Table 1. For each composition, elemental powders were weighted out following the nominal stoichiometric ratios in batches of 5 g. Then, the powders were first mixed by a vortex mixer, and successively high energy ball milled (HEBM) in a SPEX 8000D mill (SPEX CertiPrep, NJ, USA). Tungsten carbide lined stainless steel jars and 11.2 mm tungsten carbide milling media (at a ball-to-powder ratio of 4.5:1) were utilized during the HEBM process of 50 min, and 1 wt. % (0.05 g) of stearic acid was added as lubricant. After HEBM, the powder mixtures were loaded into 10 mm SPS graphite dies lined with graphite foils in batches of 2.5 g, and consecutively sintered into bulk pellets with a Thermal Technologies 3000 series SPS (Thermal Technology LLC, CA, USA) in vacuum (10 -2 Torr). To prevent oxidation, the HEBM and loading/handing of as-milled powder mixtures were both conducted in an argon atmosphere with O2 < 10 ppm. The SPS sintering procedure is similar to that used in our previous work for fabricating rare earth high-entropy tetraborides (HETBs) [16] with isothermal holding at 1700 ℃ and 50 MPa for 10 min during the final densification.
After cooling down in the SPS machine, the sintered specimen pellets were ground (to remove surface carbon contamination) and successively mirror polished before Berkovich indenter was used, and the maximum load was set to 500 mN. For each specimen, a six-by-six array with a distance of 30 μm between the two nearest indents was employed.
Ultraviolet photoelectron spectroscopy (UPS) measurements were conducted on freshly polished surface of each specimen (to avoid any surface oxidation) using a Kratos AXIS Supra spectrometer equipped with a He I (hv = 21.22 eV) source under 10 -8 Torr chamber pressure. The work functions were subsequently calculated based on the incident photon energy (hv) and the high-binding-energy cut-offs (Ecut-off) of each specimen via WF = hv -Ecut-off.  Table   S1) are also tabulated in Table 1. In all six cases, there are negligible differences (~0.1%) between the XRD measured lattice parameters and RoM averages. The calculated XRD patterns based on the nominal compositions and measured lattice parameters are also displayed in Supplementary Fig. S1 for comparison. By the combination of XRD patterns and lattice parameters, it can be clearly observed that single-phase CaB6-typed structures have been successfully obtained in all six compositions studied.

Results and Discussion
The formation of single high-entropy phase can be understood because of (1) high thermal stability of binary hexaborides [39,40] and (2) extended homogeneity range at boron-rich end of hexaboride structures [40]. For the binary hexaborides involved in this study, they will either melt congruently (LaB6, PrB6, NdB6, SmB6, and YbB6) or dissociate into tetraboride and boron-rich liquid phase (YB6, GdB6, TbB6, and DyB6) at high temperatures [34]. Except for TbB6, DyB6, and YbB6 that melt/dissociate within a temperature range of 2200~2400 ℃, all constitutive binary hexaborides can maintain thermodynamic stability until the temperature is higher than 2500 ℃ based on the phase diagrams in Ref. [40]. At the same time, hexaborides are known to possess extended homogeneity range at the boron-rich boundary by formation of metal vacancies [40].
Studies have demonstrated the stability of the hexaboride structure (mainly the boron sublattice) to a metal content as low as Sm0.68B6 and Pr0.69B6 [41,42]. On the other hand, the existence of native oxides in metal precursors can alter the metal-to-boron ratios, resulting in excessive boron (or insufficient metal) in the system [16]. The tolerance of metal vacancies in the hexaboride structure may prevent the formation of boron-rich secondary phases. The existence of metal vacancies (due to native oxides in precursors) is difficult to quantify in the sintered HEHB systems. However, based on the results of HETB systems [16] where the same precursors and fabrication route were utilized, the amount of metal vacancies in HEHBs (or equivalently, excessive boron resulted in boron-rich phase in HETBs) should not be significant. Moreover, all sintered specimens exhibit dark steel blue hue with iridescent tarnish after polishing, an appearance observed for stoichiometric binary hexaborides (with an exception of red-violet LaB6) [35]. This color also implies insignificant metal vacancies, as severely metal-deficient binary hexaboride samples are shown to be blue-gray to gray [35].  Fig. S2) with barely 1-2% black spots of porosity and/or unreacted boron also confirm the high relative densities for different specimens.
The homogenous elemental distributions of metal cations in specimen HEHB1 and HEHB3 are confirmed by both microscale SEM-EDS elemental maps and nanoscale STEM-EDS elemental maps (Fig. 3), whereas the elemental homogeneities of other specimens at microscale can be verified by the SEM-EDS elemental maps in Supplementary Fig. S4. AC-STEM high-angle annular dark-field (HAADF) imaging at high magnifications also illustrates the CaB6-typed hexaboride solid solution (for both HEHB1 and HEHB3) at atomic level in Fig. 3(a1) and (b1). In Fig. 3(a1), STEM HAADF image on [001] zone axis demonstrates the cubic structure of the specimen with lattice parameter a ≈ 0.41 nm, and in Fig. 3(b1), the [211] zone axis and two perpendicular atomic planes (011 ̅ ) and (11 ̅ 1 ̅ ) are marked accordingly. Supplementary Fig. S3 provides the corresponding fast Fourier transform (FFT) diffraction patterns of these two specimens.
SEM-EDS quantitative analyses are utilized to determine the cation compositions of sintered specimens at microscale, and the results are listed in Table 1. Comparing with the nominal equimolar compositions, the measured compositions are different by 1-3%, which are within the typical EDS measurement errors. Hence, the equimolar compositions are confirmed for the sintered specimens and are adopted for the discussion in this study.
Combining all the results above from XRD, SEM, AC-STEM, and EDS, it is clearly demonstrated that a group of CaB6-typed cubic rare earth HEHB solid solutions have been successfully synthesized to fully dense (relative density >98.5%) in bulk pellets via in-situ metal-boron reactive SPS. Since the previously reported rare earth HEHBs (prepared by thermal reduction of rare earth metal oxides) are synthesized in forms of powders [33] or highly porous materials [13], the successful fabrication of HEHBs in this study epitomizes the first group of dense HEHBs in the bulk form. Moreover, previous studies only involve Y, Ce, Nd, Sm, Eu, Er and Yb (for powders) [33] as well as Y, Nd, Sm, Eu, and Yb (for porous materials) [13], this study further successfully incorporates La, Pr, Gd, Tb, and Dy into HEHB systems for the first time.
Performed on polished specimen surfaces normal to the direction of pressure and current during SPS, EBSD analyses are utilized to measure the grain size and examine the texture of all sintered specimens. Normal direction inverse pole figure orientation maps for all HEHB specimens are illustrated in Fig. 4 with insets of corresponding grain size distributions. The average grain sizes (± one standard deviations) of specimen HEHB1 to HEHB6 are measured to be 4.72 ± 32.87 μm, 4.12 ± 2.48 μm, 4.22 ± 2.10 μm, 4.62 ± 2.50 μm, 5.05 ± 2.83 μm, and 3.48 ± 2.56 μm, respectively. All these sintered HEHB specimens exhibit similar averaged grain sizes of ~3.5-5.0 μm due to the same synthesizing route of HEMB succeeded by SPS at 1700 ℃ applied. Noticeably, specimen HEHB6 contains a small number of large grains and some clusters of tiny grains, which is commonly observed in borides prepared by in-situ metal-boron reactive SPS [16,38,43,44]. All sintered HEHB specimens show no noticeable texture in the grain orientation maps, which can also be verified by the consistency in relative peak intensities between the measured and calculated XRD patterns (Fig. 2 vs. Fig. S1).
In addition, nanoindentation tests conducted at 500 mN measured the nanoindentation hardness values between 19-22 GPa ( Table 1). The nanohardness values are 10-30% higher than those of Vickers microhardness measured at 9.8 N, which is reasonable due to the indentation size effect [52] at different indentation loads as well as the different Oliver and Pharr method [53] adopted for nanoindentation hardness analysis (that utilizes projected contact area at peak load, instead of the residual projected area, and assumes purely elastic contact). For example, nanoindentation hardness has been reported to be ~20% higher than the microhardness (at the same indentation load) for Si and fused silica [54]. The measured hardness values via both routes for all six specimens are also illustrated in Fig. 5(a).
The microhardness of binary hexaborides have been widely investigated (via different methods and loading conditions) and summarized in a handbook [35], as well as a recent review [31]. Among them, Binder [55] systematically investigated the hardness of most rare earth hexaborides on polycrystalline samples via Knoop microhardness test at 0.98 N; and their measured hardness are all within the range of ~18-21 GPa. Considering that Knoop microhardness test generally gives a similar (but slightly lower) measured value than Vickers microhardness at the same indentation loads on ceramic materials [56], the hardness of the HEHBs are roughly comparable to the RoM average of constituent binary hexaborides. It should also be noted that the hardness of some binary hexaborides have also been reported to be 23-27 GPa by Vickers microhardness test at 0.98 N or lower in early reports [31,35]. On the other hand, limited reports on nanohardness of binary hexaborides have been found. LaB6 has been reported to possess a nanoindentation hardness of ~23 GPa at 50 mN [57], whereas a higher indentation hardness of ~35 GPa has been found at a lower load of 10 mN [58]. These results are not surprising given the difference in nanoindentation loads.
Young's moduli are also determined to be 190-250 GPa by nanoindentation tests for all six specimens (illustrated in Fig. 5(b) and listed in Table 1). Higher values of 376 GPa [57] and 393 GPa [58] have been reported for LaB6 at lower nanoindentation loads of 50 mN and 10 mN, respectively. Besides the difference in nanoindentation loads, this big discrepancy of Young's moduli between the HEHB and LaB6 specimens might also related to the melting process during the fabrication of LaB6 specimens. While some early studies also reported the Young's moduli for binary hexaborides to be 350-400 GPa [35], a recent study in 2018 reported the Young's modulus of hot-pressed SmB6 to be 271 GPa by fracture strength test and 244 GPa by ultrasonic test [59], which are more comparable with our HEHBs.
UPS measurements were performed on freshly polished specimen surfaces, with the resultant spectra shown in Fig. 6. Work functions have been determined based on the incident photon energy of He I emission (21.22 eV) and the respective high-binding-energy cut-off (marked by the black vertical line in Fig. 6) of each specimen. All HEHB specimens demonstrate comparable measured work functions within 3.7-4.0 eV (listed in Table 1), which are noticeably higher than the constituent LaB6 (that commonly used as hot cathode material) work function of ~2.6-2.8 eV on (100) [37,60]. Various early studies also demonstrated the work functions of other constituent binary hexaborides to be ~2.9-3.5 eV with results summarized in Ref. [35] (except for YB6 that experiences severe vaporization at elevated temperature [61]). It should be pointed out that most of the reported work functions are obtained by thermionic emission and Richardson's law. Nevertheless, the method of photoelectric yield should generate consistent results, as similar work function results have been obtained from both methods for LaB6 [62] (also found in Ref. [35]). In this scenario, it can be deduced that the work functions of HEHBs are higher than the RoM average of their constituent binary hexaborides, which implies that they might not be desirable for hot cathode application.

Conclusions
A group of CaB6-typed cubic rare earth high-entropy hexaborides or HEHBs have been successfully synthesized into bulk forms via HEBM followed by direct metal-boron reactive SPS. The sintered bulk HEHB specimens are >98.5% in relative densities without detectable oxides or other secondary boride phases. The homogenous distributions of metal cations have been verified by both SEM-EDS at microscale and STEM-EDS at nanoscale.
The averaged grain sizes have been determined to be between 3.5-5.0 μm. Vickers microhardness has been measured to be 16-18 GPa at a standard load of 9.8 N. The nanoindentation hardness and Young's moduli have been determined to be [19][20][21][22] GPa, respectively, by nanoindentation tests using a maximum load of 500 mN.
Noticeably, work functions of these sintered HEHB specimens have been determined to be 3.7-4.0 eV by UPS characterizations, which are significantly higher the work function of LaB6.
In contrast to the previously reported rare earth HEHB in powders [33] or highly porous materials [13], HEHBs have been fabricated in bulk form for the first time in this study.
This added a new class to bulk HECs and enabled us to measure some basic bulk properties of HEHBs.       . 6. UPS spectra of specimens HEHB1 to HEHB6: (a) high-binding-energy cut-off region and (b) lowbinding energy region. The work function is calculated utilizing the high-binding-energy cut-off, marked by the black vertical line, for each specimen. Table 1. Summary of the six specimens (HEHB1 to HEHB6) synthesized in this study. All specimens were fabricated via the same routine of in-situ metalboron reactive SPS. The measured compositions for each specimen were directly attained from SEM-EDS analyses. The lattice parameters were measured by XRD spectra. Averaged lattice parameters were calculated via the rule of mixture (RoM) on weighted means of binary hexaborides (individual metal hexaborides). Theoretical densities were calculated from the measured lattice parameters and the nominal compositions for each specimen. The densities were measured experimentally via Archimedes method. Grain size information was obtained from EBSD analyses. Vickers microhardness were measured at indentation load of 9.8 N (1 kgf), whereas the nanoindentation hardness were measured at 500 mN. Young's moduli were also obtained by nanoindentation. Work functions were calculated by the incident photon energy of He I emission (hv = 21.22 eV) and the high-binding-energy cut-offs (Ecut-off) of each specimen via WF = hv -Ecut-off.