Abstract
The room-temperature bulk modulus of rhenium (Re) was measured in the pressure range 0 to 115 GPa using a laser-annealing diamond anvil cell and the synchrotron X-ray diffraction method. Thermal properties of Re were investigated up to 4000 K based on first-principles molecular dynamics calculations, and the equation of state for Re was determined using experimental and calculated data. A Vinet equation of state fitted to the 300 K data yielded a bulk modulus of KT0 = 384 GPa and a pressure derivative of K T 0 ′ = 3.26. The contribution of thermal pressure was determined to have the form ΔPth = [αKT(Va) + (∂KT/∂T)Vln(Va/V)]ΔT. When αKT(Va) was assumed to be constant, the fit to the data yielded αKT(Va) = 0.0056 GPa/K. In contrast, the volume dependence of the thermal pressure was very small, and fitting yielded a value of (∂KT/∂T)V = −0.00042.
Highlights
Rhenium (Re) is a group VII transition metal that crystallizes in a hexagonal close-packed structure and has an axial c/a ratio of 1.615, slightly less than the ideal hcp value of 1.633. e space group is P63/mmc, and two Re atoms occupy the 2c Wyckoff sites (1/3, 2/3, 1/2) and (2/3, 1/3, 3/4).e high-pressure behaviors of Re have been studied widely as Re has a high bulk modulus value (∼350 GPa) compared with other metals
First-principles calculations were performed using the Vienna Ab Initio Simulation Package (VASP) [12]. e PBEsol functional for the exchange-correlation potential was used in the generalized gradient approximation (GGA) calculations [13]. e electronic wave functions were expanded using a plane-wave basis set with a cutoff energy of 600 eV, and the electron-ion interactions were described using the projector augmented wave (PAW) method. e PAW potential for Re had an outermost cutoff radius for the valence orbital of 1.434 A, with a valence configuration of 5d56s2
Powdered sample was sandwiched between pellets of NaCl powder, which was used as the pressure-transmitting medium and the pressure reference. e sample was loaded into a hole 50–100 μm in diameter drilled into a Re gasket, which was pre-indented to a thickness of 30–50 μm. e starting material was compressed at room temperature using a symmetrical or motordriven diamond anvil cell (DAC) [15, 16]
Summary
Rhenium (Re) is a group VII transition metal that crystallizes in a hexagonal close-packed (hcp) structure and has an axial c/a ratio of 1.615, slightly less than the ideal hcp value of 1.633. e space group is P63/mmc, and two Re atoms occupy the 2c Wyckoff sites (1/3, 2/3, 1/2) and (2/3, 1/3, 3/4). The double-stage and the toroidal diamond anvil cells have extended the pressure range over 600 GPa [3, 9,10,11] In such experiments, the equation of state (EOS) for Re has often been used as a pressure marker at extremely high pressures. Advances in Condensed Matter Physics theoretical studies using first-principles calculations have investigated the physical properties of materials at high pressures and temperatures. We used density functional theory to investigate the thermal properties of Re and performed high-pressure experiments to determine the room temperature EOS for Re. is combination of first-principles molecular dynamics calculations and high-pressure experiments allowed us to determine reliable values for the thermoelastic properties over a wide range of pressures and temperatures
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