High-pressure high-temperature synthesis and thermal equation of state of high-entropy transition metal boride

High-entropy materials containing a mixture of five or more elemental species represent a paradigm shift in materials science where a variety of oxides, carbides, and borides can be synthesized with superior physical and mechanical properties compared with those accessible from the constituent materials. In an endeavor to create ultrahard and high-temperature materials that retain their physical properties under extreme conditions, high entropy alloys (HEAs) have drawn considerable attention in recent years. Typically, alloys are made up of one base element with an addition of smaller ratios of secondary elements, and rarely are they made using more than two base elements.¹ HEAs, on the other hand, contain a random solid solution of five or more elements combined in equimolar ratios. The introduction of numerous elements that form into a singular metallic phase produces a large entropy of mixing, thereby lowering its Gibbs free energy and resulting in a stable high-entropy material. The entropy of mixing ΔS_mix = R ln(N), where R is the gas constant and N is the number of constituent elements. The large value of ΔS_mix ensures that high-entropy materials are stable at high temperatures and show a superior thermal degradation behavior under oxidizing environments.² Multiple HEAs have been discovered and studied^3–5 with some elastic properties being notably better than those of their conventional alloy counterparts. The incorporation of boron into HEAs forms strong covalent bonds within the single metallic phase that further enhances the material strength in the new high entropy boride (HEB). This motivates the synthesis of HEB that is hard and thermally stable at 2000 K with physical properties similar to those seen in transition metal borides.^6–11 Such a combination would pair a boride’s alluring mechanical strength with an HEA’s thermodynamic stability, producing a resilient material well suited for high temperature applications. In this paper, we report on the synthesis of (Hf_0.2 Ti_0.2 Zr_0.2 Ta_0.2 Mo_0.2)B₂ HEB starting from a powder mixture of HfO₂, TiO₂, ZrO₂, Ta₂O₅, MoO₃, carbon black, and boron carbide. The HEB crystal structure was studied by Energy Dispersive X-ray Diffraction (EDXD) in a Paris–Edinburgh press, under quasi-hydrostatic pressure conditions, utilizing the setup at the Advanced Photon Source, High Pressure Collaborative Access Team (HPCAT) Beamline 16-BM-B, Argonne National Laboratory. We also established the thermal equation of state of the synthesized HEB material to 7.6 GPa and 1873 K and derived its thermoelastic properties.

The precursor materials contained equimolar amounts of five transition metal oxides—HfO₂, TiO₂, ZrO₂, Ta₂O₅, and MoO₃—carbon black, and boron carbide, which were purchased from Alfa Aesar. First, the metal oxides combined with carbon are high energy ball milled (Spex 8000 M) for two hours in a tungsten carbide container and media. At hourly intervals, the ball mill is allowed to cool for 10 min. Boron carbide is then added to the mixture to blend by ball milling, with the milled metal oxides and carbon. To reduce contamination of tungsten carbide, the mixture with B₄C is wet milled in acetone for four hours with zirconia balls. The mixture includes an excess of B₄C (10%–15 wt. %) to account for the boron lost due to the formation of boron oxide and carbon monoxide, B₂O₃ and CO, during high pressure high temperature synthesis.¹² The milled mixture is left to dry in a vacuum oven before being passed through a 200-mesh sieve to ensure uniformity of particle size for subsequent processing.

High pressure–high temperature Energy Dispersive X-ray Diffraction (EDXD) experiments were conducted utilizing the white x-ray source and the Paris–Edinburgh press at the HPCAT beamline 16-BM-B. Data were collected with a diffraction angle 2theta = 5° and over an energy range of 5 KeV–120 KeV. The ball-milled sample mixture was compacted into cylinders of size 1 mm by 2 mm using a die press and placed within a boron nitride capsule, surrounded by a graphite heater, an MgO thermal insulating ring, a boron epoxy gasket, and a Lexan retaining ring. Two caps of ZrO2 are placed on the top and bottom, along with tantalum rods and molybdenum foils, which provide the electrical conduction path from the tungsten carbide press anvils to the graphite heating element, as shown in Fig. 1. The temperature to power relationship was calibrated previously up to 2300 K as a function of applied pressure and measured with a W5%Re–W26%Re thermocouple in place of the sample.¹³ Sample pressure was estimated using the MgO pressure calibrant, which surrounds the sample and is shown in Fig. 1. In situ unit cell volumes of MgO were determined by EDXD, and pressure was calculated using the thermal equation of state formulated by Kono et al.¹⁴ The second order Birch–Murnaghan equation of state (BM EoS) in Eq. (1) was used with the Fei 1995 thermal expansion model^15,16 shown in Eq. (2) to extract the bulk modulus (K₀), dK/dT, and the volumetric thermal expansion coefficient α,

In Eq. (1), x = V₀/V, K₀ is the bulk modulus, and $K0′$ is the first pressure derivative. For Eq. (2), the temperature dependent volumetric thermal expansion α is described by coefficients α₀, α₁, α₂ as α = α₀ + α₁T + α₂T⁻². Some earlier published works^17–19 employ a linear expansion to thermal expansion in Eq. (2) of the form α(T) = α₀ + α₁T. The linear term provides the lowest degree of estimation for temperature effects on expansion while the Fei model introduces a second order term with the added advantage that α(T) describes the volumetric change with temperature $1V0T∂V0T∂T$⁠. The quadratic term is employed in this study for added accuracy in α(T) calculation in the high temperature range up to 1873 K. Temperature and pressure data were taken systematically by holding pressure constant and increasing temperature in 100 K steps up to the maximum temperature of 1973 K. The sample was then allowed to cool to ambient temperature before pressure was increased in ∼0.5 GPa steps. In this manner, data of the thermal equation of state were generated on the high-entropy transition metal boride sample up to 7.6 GPa and 1873 K.

Figure 2 displays the EDXD data during heating to 1773 K at an average pressure of 0.9 GPa. The initial ambient temperature spectrum shows a mixture of HfO₂, TiO₂, ZrO₂, Ta₂O₅, and MoO₃ precursor phases mixed with graphite and boron-carbide, with particularly strong peaks between 2.5 Å and 3 Å for several overlapping phases. Synthesis of a new HEB is indicated by a gradual transformation beginning at 1373 K and progressing to completion to a hexagonal structure indicated by the appearance of three strong (101), (100), and (001) diffraction peaks of the AlB₂ hexagonal phase up to a maximum temperature of 1773 K. The indexed peaks of the hexagonal phase are shown in more detail in Fig. 3. The indexed nine diffraction peaks shown in Fig. 3 are used in the least square fit calculation of the interplanar d-spacing to calculate the lattice parameters, with values of a = 3.14 Å and c = 3.43 Å at 1973 K and 0.5 GPa. The residual graphite phase, boron carbide phase, and x-ray fluorescence lines from metal elements are also indicated. The (002) diffraction peak intensity from the residual graphite shown in Figs. 2 and 3 is unusually high and is attributed to preferred orientation effects as other reflections from graphite were not detected in the diffraction pattern. Our claim of equimolar composition of the synthesized HEB (Hf_0.2 Ti_0.2 Zr_0.2 Ta_0.2 Mo_0.2)B₂ is supported by the initial equimolar composition of precursor metal oxides and the fact that we did not detect any residual metal oxides in x-ray diffraction after the high-temperature high pressure treatment, as shown in Fig. 3.

After synthesis, the new phase was shown to be stable when pressure and temperature were relaxed to ambient conditions. Further heating and compression cycles showed the stability of the synthesized AlB₂ phase to 7.6 GPa and 1973 K. Thermodynamic stability is one of the hallmarks of this class of HEB as the high entropy provides phase stability at high temperatures and a possible retention of high hardness at high temperatures.² Figure 4 shows our P-V-T data on the HEB sample up to 7.6 GPa and 1873 K. The data of measured thermal equation of state were fitted to Eqs. (1) and (2), and the elastic and thermal properties were derived from the measured data.

The fits to P-V-T data shown in Fig. 4 yield information on the thermoelastic properties of the synthesized HEB sample. The fits resulted in an ambient pressure volume V₀ = 27.93 ± 0.03 ų and the bulk modulus K₀ = 344 ± 39 GPa at ambient temperature with a fixed value of $K0′$ = 4. The fitted value of the temperature derivative of the bulk modulus is dK/dT = −0.108 ± 0.027 GPa/K. Thermal expansion coefficients were calculated using the Fei 1995 temperature modification and shown to be α₀ = −1.10 × 10⁻⁵ K⁻¹, α₁ = 3.40 × 10⁻⁸ K⁻², and α₂ = 2.97 K with the volumetric thermal expansion expressed as α = α₀ + α₁T + α₂ T⁻² in the temperature range between 300 K and 2000 K.

We have successfully synthesized a high-entropy transition metal boride sample (Hf_0.2 Ti_0.2 Zr_0.2 Ta_0.2 Mo_0.2)B₂ from the precursor oxide materials HfO₂, TiO₂, ZrO₂, Ta₂O₅, and MoO₃ mixed with carbon black and boron carbide under high-pressures and high-temperatures. The synthesis was carried out at a pressure of 0.9 GPa and temperatures above 1373 K, and the sample was shown to be a hexagonal AlB₂ structure with ambient conditions volume V₀ = 27.93 ± 0.03 ų. A bulk modulus of K₀ = 344 ± 39 GPa was derived from the measured equation of state at ambient temperature along with dK/dT = −0.108 ± 0.027 GPa/K. The thermal volume expansion coefficient in the temperature range between 300 K and 2000 K is described by α = α₀ + α₁T + α₂ T⁻², with α₀ = −1.10 × 10⁻⁵ K⁻¹, α₁ = 3.40 × 10⁻⁸ K⁻², and α₂ = 2.97 K. Our studies indicate that the hexagonal AlB₂ phase of the synthesized (Hf_0.2 Ti_0.2 Zr_0.2 Ta_0.2 Mo_0.2)B₂ material is stable up to 7.6 GPa and 1873 K, thereby establishing high-entropy transition metal boride as a promising ultrahard high temperature ceramic material.

This material was based on work supported by the Department of Energy-National Nuclear Security Administration, under Award No. DE-NA0003916. S.I. would like to acknowledge the Graduate Fellowship support under the NASA/Alabama Space Grant Consortium, Grant No. NNH19ZHA001C. Portions of this work were performed at the HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT operations are supported by DOE-NNSA’s Office of Experimental Sciences. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory, under Contract No. DE-AC02-06CH11357. The work of N.V. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.