Thermal Equation of State of Cubic Boron Nitride: Implications for a High-Temperature Pressure Scale (original) (raw)
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Review of scientific …, 2004
The pressure dependence of Raman peaks of cubic boron nitride (cBN) is determined at 100, 200 and 300°C using pressure scales of ruby and gold. At pressures lower than 6 GPa, the pressure dependences of cBN Raman determined with the ruby pressure scale for transverse-optical ͑TO͒ and longitudinal-optical modes are 3.45Ϯ0.02 and 3.36Ϯ0.02 cm Ϫ1 /GPa at 100°C and 3.43Ϯ0.02 and 3.44Ϯ0.07 cm Ϫ1 /GPa at 300°C, respectively. These values are consistent with those in a previous study conducted at room temperature using the ruby pressure scale. Synchrotron x-ray diffraction experiments using a gold pressure marker also yield 3.45Ϯ0.03 cm Ϫ1 /GPa for TO mode at 200°C in a range of pressure up to 32 GPa. Under the present pressure and temperature conditions, the pressure dependence of Raman peaks of cBN seems to be independent of the temperature conditions. cBN can be used as an optical pressure marker under high temperature conditions.
New Experimental Results on the Phase Diagram of Boron Nitride
Journal of Solid State Chemistry, 2000
In order to clarify the discrepancy of the phase diagram on boron nitride as it is found in the literature we have made numerous in situ di4raction experiments using synchrotron radiation. The conditions were temperatures in the range of 16003C and pressures up to 6.5 GPa. For the experiments diamond anvil squeezers and the MAX80 high-pressure/high-temperature device installed at the DESY synchrotron facility in Hamburg/ Germany were used. We studied the transformation from hBN to cBN at 6.5 GPa/12003C and the backtransformation from cBN to hBN around 0.9 to 2 GPa. The experiments included kinetics measurements. The experiments veri5ed the theoretical results by V. L. Solozhenko (1991, High Pressure Res. 7, 201) and J. Maki et al. (1991, 99Proceedings II: International Conference on New Diamonds Research and Technology::). Further on the calculations for the equilibrium boundary between cBN and hBN were repeated including uncertainties of the thermodynamic data. The cubic phase, cBN, is de5nitely the stable phase, in contrast to metastable diamond.
Equation of state of boron nitride combining computation, modeling, and experiment
Physical Review B, 2019
The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (ACTEX), and all-electron Green's function Korringa-Kohn-Rostoker (MECCA), and compute the pressure and internal energy of BN over a broad range of densities and temperatures. Our experiments were conducted at the Omega laser facility and the Hugoniot response of BN to unprecedented pressures (1200-2650 GPa). The EOSs computed using different methods cross validate one another in the warm-dense matter regime, and the experimental Hugoniot data are in good agreement with our theoretical predictions. By comparing the EOS results from different methods, we assess that the largest discrepancies between theoretical predictions are 4% in pressure and 3% in energy and occur at 10 6 K, slightly below the peak compression that corresponds to the K-shell ionization regime. At these conditions, we find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the high-pressure, high-temperature regime. Moreover, the recently developed SQ and FOE methods produce EOS data that have significantly smaller statistical error bars than PIMC, and so represent significant advances for efficient computation at high temperatures. The shock Hugoniot predicted by PIMC, ACTEX, and MECCA shows a maximum compression ratio of 4.55±0.05 for an initial density of 2.26 g/cm 3 , higher than the Thomas-Fermi predictions by about 5%. In addition, we construct new tabular EOS models that are consistent with the first-principles simulations and the experimental data. Our findings clarify the ionic and electronic structure of BN over a broad range of temperatures and densities and quantify their roles in the EOS and properties of this material. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material. (LLNL-JRNL-767019-DRAFT) I. INTRODUCTION The equation of state (EOS) of materials from the condensed matter to warm dense matter and the plasma regime plays an indispensable role in radiation hydrodynamic simulations 1 , which are required for the design and analysis of inertial confinement fusion (ICF) and high energy density (HED) experiments. In laserdriven capsule experiments, ablator materials are important to implosion dynamics and performance. Currently, the most widely used ablator materials are plastics, such as polystyrene derivatives and glow-discharge polymer, high density carbon (HDC), and beryllium. Materials with higher density and tensile strength, such as boron (B) and its compounds, offer the potential for improvements in performance and additional nuclear diagnostics in exploding pusher platforms. 2,3 30 At ambient conditions, BN exists in two stable, nearly 31 degenerate phases: hexagonal BN (h-BN) and cubic BN 32 (c-BN), similar to the graphite and diamond phases of 33 its isoelectronic material, carbon (C). Because of this 34 similarity, BN is widely investigated for the synthesis of 35 superhard materials and fabrication of thin films or het-36 erostructures for various applications. 4 Nanostructured 37 c-BN, whose hardness is almost twice that of bulk c-BN 38 and close to that of diamond, has been synthesized at 39 high-pressure and temperature conditions 5. Other appli-40 cations for low-dimensional BN include nanoelectronic 41 devices 4 and expanded h-BN for hydrogen storage 6. It 42 has also been demonstrated that the density and me-43 chanical properties of BN can be tuned by constructing 44 a mixture of its cubic and hexagonal phases. 7 126 can be found in the cited references. 127 A. Path Integral Monte Carlo 128 PIMC is a quantum many-body method for materials 129 simulations that is based on sampling the finite temper-130 ature density matrix derived from the full many-body 131 Hamiltonian, H. In PIMC, particles are treated as quan-132 157 matrix, T , by implementing the fixed-node approxima-158 tion 49. The condition T = 0 in 3N-dimensional space 159 defines the nodal surface, where N is the number of par-160 ticles. In high temperature simulations, T is chosen to 161 be a Slater determinant of free-particle density matrices 162 [1] (r i , r j ; β) = k exp(−βE k)Ψ * k (r i)Ψ k (r j), (2) where Ψ * k (r) denotes a plane wave with energy E k. 163 The corresponding nodal surface is called free-particle 164 nodes. The assumption of free-particle nodes is appro-165 priate at high temperature. The PIMC method with 166 free-particle nodes has been successfully developed and 167 applied to hydrogen 50-58 , helium 59,60 , and calculations 168 of the EOS for a range of first-row elements 3,61-64 and 169 compounds 61,65-67. Recent developments 68-70 have ex-170 tended the applicability of PIMC to second-row elements 171 at lower temperatures by appending localized orbitals to 172 [1] , opening a possible route toward accurate quantum 173 many-body simulations of heavier elements. 174 In this study, we apply PIMC for the simulations of 175 BN with free-particle nodes using the CUPID code 71. 176 All electrons and nuclei are treated explicitly as quan-177 tum paths. The Coulomb interactions are described via 178 pair density matrices 47,72 , which are evaluated in steps 179 of τ = 1 512 Hartree −1 (Ha −1). The nodal restriction is 180 enforced in much smaller steps of 1 8192 Ha −1. The cal-181 culations are performed over a wide range of densities 182 0.23-45.16 g/cm 3 , or 0.1-to 20-times the ambient density 183 ρ 0 ∼ 2.26 g/cm 3 based on that of h-BN 73 , and temper-184 atures 10 6-5×10 8 K. Each simulation cell consists of 24 185 atoms, which is comparable to our previous simulations 186 for pure B 3 , nitrogen (N) 63 , and hydrocarbons 66,67. The 187 cell size effects on the EOS are negligible at such high 188 temperature conditions 74. 189 B. DFT-MD with plane-wave basis and projector 190 augmented wave potentials 191 DFT-MD is a widely used method for accurately simu-192 lating condensed matter systems at finite temperatures. 193 In DFT-MD, the ions are classical particles, which move 194 according to Newton's classical equations of motion. The 195 forces are computed by solving the Kohn-Sham DFT 196 equations for the electrons at each time step. The appli-197 cability and accuracy of DFT-MD for EOS calculations 198 has been previously demonstrated for condensed phase 199 materials in multiple studies (see Ref. 75 as an exam-200 ple). One difficulty lies in using this method for high 201 temperatures, which is originated from significant ther-202 mal excitation of electrons and intractable computational 203 cost. 204 Our DFT-MD simulations for BN are performed in two 205 different ways. One way is by using the projector aug-206 mented wave (PAW) pseudopotentials 76 and plane-wave 207 basis (PAWpw), as implemented in the Vienna Ab initio 208 Simulation Package (VASP) 77 and used in our previous 209 studies (e.g, Refs. 3, 66, 67, 69, and 78). Similar to our 210 recent work on pure B 3 , we choose the hardest PAW po-211 tentials available in VASP, which freeze the 1s electrons 212 in the core and have a core radius of 1.1 Bohr for both B 213 and N. We choose the Perdew-Burke-Ernzerhof (PBE) 79 214 functional for describing electronic exchange and correla-215 tion interactions, a large cutoff energy of 2000 eV for the 216 plane-wave basis, and the Γ point to sample the Brillouin 217 zone. The simulations are carried out using a Nosé ther-218 mostat 80 to generate MD trajectories in the canonical 219 ensemble. The MD time step is chosen to ensure total 220 energy conservation and takes on values of 0.05-0.55 fs 221 in these calculations, with smaller values corresponding 222 to higher temperatures. We typically run for 5000 steps 223 at each density-temperature (ρ − T) condition, which is 224 found to be sufficient for convergence of the computed 225 energies and pressures. 226 To ensure consistency with the all-electron PIMC en-227 ergies, our PAWpw energies from VASP reported in this 228 study are shifted by-79.017 Ha/BN. This is determined 229 with all-electron calculations for isolated B and N atoms 230 with OPIUM 81 using the PBE functional. 231 Our PAWpw calculations are performed at temper-232 atures between 6.7×10 3 K and 5.05×10 5 K (∼0.6-233 43.5 eV). Due to limitations in applying the plane-wave 234 expansion for orbitals at low densities and limitations in 235 the applicability of the pseudopotentials that freeze the 236 1s 2 electrons in the core at high densities, we consider 237 4 a smaller range of densities (ρ 0 up to 10×ρ 0) than that was examined via PIMC simulations. These conditions 239 are relevant to shock-compression experiments and span 240 the range in which Kohn-Sham DFT-MD simulations are 241 feasible by conventional wavefunction based approaches.
In this paper, we have calculated the molar heat capacity for cubic zinc blende (cZB) BN and GaN binary semiconductors at high pressure-temperature (PT). For the calculation of heat capacity, we firstly obtained the Debye temperature (ϴ D ) variation with temperature and at higher temperature it becomes constant with temperature in quasi-harmonic approximation limits. We have also calculated the static Debye temperature (ϴ D ) from elastic constant for the both BN and GaN binary semiconductors. The elastic constants are calculated from the energy-strain relation using plane wave method in DFT approach. All the calculated results are well consistence with experimental and reported data.
Dynamical Charge and Force Constant Calculations in cBN under Pressure
Physica Status Solidi B-basic Solid State Physics, 1996
A combination of an adjusted pseudopotential method and the bond-orbital model of Harrison was used to derive the polarity and the force constants of cubic boron nitride (c-BN) under pressure up to 900 kbar. The results show that the hybrid covalent energy dominates at high pressure and the transverse effective charge changes by less than 3.3% between normal condition and 900 kbar. The idea of taking the free-atom term values and the 1/d2 formulae for the covalent energy is not a good approximation to estimate the variation of the transverse effective charge under pressure. In fact, this approximation overestimates the relative variation to 10.2% in the same range of pressure.
Applied Surface Science, 2018
After rapid cooling, cubic boron nitride (c-BN) single crystals synthesized under high pressure and high temperature (HPHT) are wrapped in the white film powders which are defined as growth interface. In order to make clear that the transition mechanism of c-BN single crystals, the variation of B and N atomic hybrid states in the growth interface is analyzed with the help of auger electron spectroscopy in the Libased system. It is found that the sp 2 fractions of B and N atoms decreases, and their sp 3 fractions increases from the outer to the inner in the growth interface. In addition, Lithium nitride (Li 3 N) are not found in the growth interface by X-ray diffraction (XRD) experiment. It is suggested that lithium boron nitride (Li 3 BN 2) is produced by the reaction of hexagonal boron nitride (h-BN) and Li 3 N at the first step, and then B and N atoms transform from sp 2 into sp 3 state with the catalysis of Li 3 BN 2 in c-BN single crystals synthesis process.
Materials science of ternary metal boron nitrides
International Journal of Inorganic Materials, 2001
The present article intends to cover a brief review on the state of art of the materials science of ternary metal boron nitrides, comprising the stability of binary boron nitride BN, the formation of ternary compounds, their crystal structure(s) and the phase relations in ternary systems M-B-N. Furthermore the role of metal boron nitride compounds in the high-pressure conversion of hBN to cBN will be considered and physical properties of ternary metal borides will be briefly discussed from the viewpoint of band structure calculations.