How far away are accurate equations of state determinations? Some issues on pressure scales and non-hydrostaticity in diamond anvil cells

The equations of state (EOSs) of materials are the cornerstone of condensed matter physics, material science, and geophysics. However, acquiring an accurate EOS in diamond anvil cell (DAC) experiments continues to prove problematic because the current lack of an accurate pressure scale with clarified sources of uncertainty makes it difficult to determine a precise pressure value at high pressure, and non-hydrostaticity affects both the volume and pressure determination. This study will discuss the advantages and drawbacks of various pressure scales, and propose an absolute pressure scale and correction methods for the effects of non-hydrostaticity. At the end of this paper, we analyze the accuracy of the determined EOS in the DAC experiments we can achieve to date.