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Transition-metal and rare-earth borides are of considerable interest due to their electronic, mechanical, and magnetic properties as well as their structural stability under extreme conditions. Here, we report on a series of high-pressure Raman and x-ray diffraction experiments on the cubic rare-earth hexaboride EuB6 to an ultrahigh pressure of 187 GPa in a diamond anvil cell. In EuB6, divalent europium ions occupy the corners of the cubic structure, which encloses a rigid boron-bonded cage. So far, no structural phase transitions have been reported, while the nanoindentation studies indicate amorphization in nanoscale shear bands during plastic deformation. Our x-ray diffraction studies have revealed that the ambient cubic phase of EuB6 shows broadening and splitting of diffraction peaks starting at 72 GPa and the broadening continuing to 187 GPa. The high-pressure phase is recovered on decompression, and the Raman spectroscopy of the recovered sample from 187 GPa shows a downward frequency shift and broadening of T2g, Eg, and A1g modes of boron octahedron. The density functional theory simulations of EuB6 at 100 GPa have identified five possible lowest energy crystal structures. The experimental x-ray diffraction data at high pressures is compared with the theoretical predictions and the role of structural distortions induced by shear stresses is also discussed.

 

The compression behavior of the hexagonal AlB2 phase of Hafnium Diboride (HfB2) was studied in a diamond anvil cell to a pressure of 208 GPa by axial X-ray diffraction employing platinum as an internal pressure standard. The deformation behavior of HfB2 was studied by radial X-ray diffraction technique to 50 GPa, which allows for measurement of maximum differential stress or compressive yield strength at high pressures. The hydrostatic compression curve deduced from radial X-ray diffraction measurements yielded an ambient-pressure volume V0 = 29.73 Å3/atom and a bulk modulus K0 = 282 GPa. Density functional theory calculations showed ambient-pressure volume V0 = 29.84 Å3/atom and bulk modulus K0 = 262 GPa, which are in good agreement with the hydrostatic experimental values. The measured compressive yield strength approaches 3% of the shear modulus at a pressure of 50 GPa. The theoretical strain-stress calculation shows a maximum shear stress τmax~39 GPa along the (1−10) [110] direction of the hexagonal lattice of HfB2, which thereby can be an incompressible high strength material for extreme-environment applications. 

Abstract The compression behavior of osmium metal was investigated up to 280 GPa (volume compression V/Vo =0.725) under nonhydrostatic conditions at ambient temperature using angle dispersive axial x-ray diffraction (A-XRD) with a diamond anvil cell (DAC). In addition, shear strength of osmium was measured to 170 GPa using radial x-ray diffraction (R-XRD) technique in DAC. Both diffraction techniques in DAC employed platinum as an internal pressure standard. Density functional theory (DFT) calculations were also performed, and the computed lattice parameters and volumes under compression are in good agreement with the experiments. DFT predicts a monotonous increase in axial ratio (c/a) with pressure and the structural anomalies of less than 1 % in (c/a) ratio below 150 GPa were not reproduced in theoretical calculations and hydrostatic measurements. The measured value of shear strength of osmium (τ) approaches a limiting value of 6 GPa above a pressure of 50 GPa in contrast to theoretical predictions of 24 GPa and is likely due to imperfections in polycrystalline samples. DFT calculations also enable the studies of shear and tensile deformations. The theoretical ideal shear stress is found along the (001)[1-10] shear direction with the maximal shear stress ~24 GPa at critical strain ~0.13. 

Thermoelastic behavior of transition metal boride Os2B3 was studied under quasi-hydrostatic and isothermal conditions in a Paris-Edinburgh cell to 5.4 GPa and 1273 K. In-situ Energy Dispersive X-ray diffraction was used to determine interplanar spacings of the hexagonal crystal structure and thus the volume and axial compression. P-V-T data were fitted to a 3rd Order Birch-Murnaghan equation of state with a temperature modification to determine thermal elastic constants. The bulk modulus was shown to be K0 = 402 ± 21 GPa when the first pressure derivative was held to K0’ = 4.0 from the room temperature P-V curve. Under a quadratic fit α=α_0+α_1 T-α_2 T^(-2), the thermal expansion coefficients were determined to be α_0=1.862×10^(-5) K-1, α_1=0.841×10^(-9) K-2, and α_2=-0.525 K. Density functional theory (DFT) with the quasi-harmonic approximation (QHA) were further employed to study Os2B3, including its P-V-T curves, phonon spectra, bulk modulus, specific heat, thermal expansion, and the Grüneisen parameter. A good agreement between the first-principle theory and experimental observations was achieved, highlighting the success of the Armiento-Mattsson 2005 generalized gradient approximation functional employed in this study and QHA for describing thermodynamic properties of Os2B3. 

High pressure study on ultra-hard transition-metal boride Os2B3 was carried out in a diamond anvil cell under isothermal and non-hydrostatic compression with platinum as an X-ray pressure standard. The ambient-pressure hexagonal phase of Os2B3 is found to be stable with a volume compression V/V0 = 0.670 ± 0.009 at the maximum pressure of 358 ± 7 GPa. Anisotropic compression behavior is observed in Os2B3 to the highest pressure, with the c-axis being the least compressible. The measured equation of state using the 3rd-order Birch-Murnaghan fit reveals a bulk modulus K0= 397 GPa and its first pressure derivative K0'= 4.0. The experimental lattice parameters and bulk modulus at ambient conditions also agree well with our density-functional-theory (DFT) calculations within an error margin of ~1%. DFT results indicate that Os2B3 becomes more ductile under compression, with a strong anisotropy in the axial bulk modulus persisting to the highest pressure. DFT further enables the studies of charge distribution and electronic structure at high pressure. The pressure-enhanced electron density and repulsion along the Os and B bonds result in a high incompressibility along the crystal c-axis. Our work helps to elucidate the fundamental properties of Os2B3 under ultrahigh pressure for potential applications in extreme environments. 

An emerging class of superhard materials for extreme environment applications are compounds formed by heavy transition metals with light elements. In this work, ultrahigh pressure experiments on transition metal rhenium diboride (ReB2) were carried out in a diamond anvil cell under isothermal and non-hydrostatic compression. Two independent high-pressure experiments were carried out on ReB2 for the first time up to a pressure of 241 GPa (volume compression V/V0 = 0.731 ± 0.004), with platinum as an internal pressure standard in X-ray diffraction studies. The hexagonal phase of ReB2 was stable under highest pressure, and the anisotropy between the a-axis and c-axis compression increases with pressure to 241 GPa. The measured equation of state (EOS) above the yield stress of ReB2 is well represented by the bulk modulus K0 = 364 GPa and its first pressure derivative K0´ = 3.53. Corresponding density-functional-theory (DFT) simulations of the EOS and elastic constants agreed well with the experimental data. DFT results indicated that ReB2 becomes more ductile with enhanced tendency towards metallic bonding under compression. The DFT results also showed strong crystal anisotropy up to the maximum pressure under study. The pressure-enhanced electron density distribution along the Re and B bond direction renders the material highly incompressible along the c-axis. Our study helps to establish the fundamental basis for anisotropic compression of ReB2 under ultrahigh pressures.