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.
Highlights
The valence force-field model (VFM), initially proposed by Born and co-workers more than a century ago,1 is among the most useful approaches to deal analytically with the short-range valence forces in tetrahedrally coordinated crystals
Our computation was implemented on the basis of density functional theory (DFT) and the projector augmented wave (PAW) method15 in the Vienna ab initio Simulation Package (VASP), version 5.4.4.16 The exchange-correlation energy was parameterized by a revised Perdew–Burke–Ernzerhof functional for solids (PBEsol)
We should note that calculation of KVFM by density functional perturbation theory (DFPT) and the VFM is fundamentally different from the method of strain–stress relation, the inputs to which are the responses to external strains, not vibrational properties
Summary
The valence force-field model (VFM), initially proposed by Born and co-workers more than a century ago, is among the most useful approaches to deal analytically with the short-range valence forces in tetrahedrally coordinated crystals. This work evaluates the validity of the VFM in diamond up to the terapascal pressure level, with the aim of establishing a primary pressure scale through an analytical relation between elastic and optical properties, namely, the K–ω relation. Both properties are calculated by first-principles computations, rather than extrapolation. The theoretical K–ω relation obtained here is a preliminary result, but it provides a basis on which opportunities can be explored to establish a practical primary pressure scale through static compression experiments
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