Unified equation of state of tungsten up to 527 GPa using modified toroidal diamond anvil cells

The equation of state (EoS) of a system is vital in multiple fields, including physics, geophysics, and astrophysics. However, the available EoSs of simple metals under pressures of more than 400 GPa are far from adequate for the research under extreme conditions. In this work, we have extended the isothermal EoS of metal tungsten (W) to the most extreme pressures up to \ensuremath{\sim}527 GPa by employing the modified toroidal diamond anvil cells (mt-DACs), based on the known EoS of gold (Au) according to the synchrotron x-ray-diffractions experiments. Upon compression to the highest pressure of 527 GPa, the structure of W remains unchanged and consistently retains its body-centered-cubic structure. By optimizing the force patterns of the mt-DAC with a modified toroidal process method, the present experiment is capable of producing pressures over 500 GPa, overcoming the 400-GPa limit of the conventional DAC. A minor maximum equivalent stress and maximum principal strain of the mt-DAC in the Boehler-Almax type revealed by the finite-element analysis are crucial for the pressure limit. This result would provide an extensive reference for the pressure calibration in experiments under extreme conditions.