Simulating Ramp Compression of Diamond

Abstract:

We model ramp compression, shock-free dynamic loading, intended to generate a well-defined equation of state that achieves higher densities and lower temperatures than the corresponding shock Hugoniot. Ramp loading ideally approaches isentropic compression for a fluid sample, so is useful for simulating the states deep inside convecting planets. Our model explicitly evaluates the deviation of ramp from “quasi-isentropic” compression.

Motivated by recent ramp-compression experiments to 5 TPa (50 Mbar), we calculate the room-temperature isotherm of diamond using first-principles density functional theory and molecular dynamics, from which we derive a principal isentrope and Hugoniot by way of the Mie-Grüneisen formulation and the Hugoniot conservation relations. We simulate ramp compression by imposing a uniaxial strain that then relaxes to an isotropic state, evaluating the change in internal energy and stress components as the sample relaxes toward isotropic strain at constant volume; temperature is well defined for the resulting hydrostatic state. Finally, we evaluate multiple shock- and ramp-loading steps to compare with single-step loading to a given final compression.

Temperatures calculated for single-step ramp compression are less than Hugoniot temperatures only above 500 GPa, the two being close to each other at lower pressures. We obtain temperatures of 5095 K and 6815 K for single-step ramp loading to 600 and 800 GPa, for example, which compares well with values of ~5100 K and ~6300 K estimated from previous experiments [PRL,102, 075503, 2009]. At 800 GPa, diamond is calculated to have a temperature of 500 K along the isentrope; 900 K under multi-shock compression (asymptotic result after 8-10 steps); and 3400 K under 3-step ramp loading (200-400-800 GPa). Asymptotic multi-step shock and ramp loading are indistinguishable from the isentrope, within present uncertainties. Our simulations quantify the manner in which current experiments can simulate the deep interiors of planetary bodies, including super-giant extra-Solar planets.