Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: Application as a primary pressure standard

Abstract

The elastic compressional (P) and shear (S) wave velocities in NaCl were measured up to 12 GPa at 300 K, and up to 8 GPa at 473 and 673 K, by combining ultrasonic interferometry, in situ synchrotron X-ray diffraction, and X-ray radiographic techniques in a large-volume Kawai-type multi-anvil apparatus. The simultaneously measured sound velocity and density data at 300 K and high pressures up to 12 GPa were corrected to transform the adiabatic values to isothermal values and then used to estimate the 300 K equation of state (EOS) by a least-squares fit to the fourth-order Birch-Murnaghan finite strain equation, without pressure data. For a fixed isothermal bulk modulus K T0 of 23.7 GPa at 0 GPa and 300 K, we obtained the first and the second pressure derivatives of K T0, K ′T0 = 5.14 ± 0.05 and K ″T0 = −0.392 ± 0.021 GPa−1, respectively. A high-temperature and high-pressure EOS of NaCl was then developed using the Mie-Gruneisen relation and the Debye thermal model. To accomplish this, the simultaneously measured sound velocities and densities up to 8 GPa at both 473 and 673 K, as well as previously reported volume thermal expansion data of NaCl at 0 GPa were included in the fit. This resulted in a q parameter of 0.96, while holding the Gruneisen parameter and the Debye temperature, both at 0 GPa and 300 K, fixed at 1.56 and 279 K, respectively. Our EOS model accurately modeled not only the present measured K T data at pressures up to 12 GPa and temperatures between 300 and 673 K, but also the previously reported volume thermal expansion and the temperature dependence of K T, both at 0 GPa. The new temperature-pressure-volume EOS for NaCl, presented here, provides a pressure-independent primary pressure standard at high temperatures and high pressures.