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

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 KT0 of 23.7 GPa at 0 GPa and 300 K, we obtained the first and the second pressure derivatives of KT0, 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-Grüneisen 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 Grüneisen 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 KT 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 KT, 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.