Born's valence force-field model for diamond at terapascals: Validity and implications for the primary pressure scale

Abstract

Born's valence force-field model (VFM) established a theoretical scheme for calculating the elasticity, zero-point optical mode, and lattice dynamics of diamond and diamond-structured solids. In particular, the model enabled the derivation of a numerical relation between the elastic moduli and the Raman-active F2g mode for diamond. Here, we establish a relation between the diamond Raman frequency ω and the bulk modulus K through first-principles calculation, rather than extrapolation. The calculated K exhibits a combined uncertainty of less than 5.4% compared with the results obtained from the analytical equation of the VFM. The results not only validate Born's classic model but also provide a robust K-ω functional relation extending to megabar pressures, which we use to construct a primary pressure scale through Raman spectroscopy and the crystal structure of diamond. Our computations also suggest that currently used pressure gauges may seriously overestimate pressures in the multi-megabar regime. A revised primary scale is urgently needed for such ultrahigh pressure experiments, with possible implications for hot superconductors, ultra-dense hydrogen, and the structure of the Earth's core.