Multi-Messenger Measurements of the Static Structure of Shock-Compressed Liquid Silicon at 100 GPa

We have used the high-power laser facility OMEGA-EP at the Laboratory for Laser Energetics to measure the liquid structure of the shock-compressed state of warm dense silicon.

Using velocity interferometry and X-ray scattering techniques, concurrent characterization of the compressed sample provided direct measurement of the static structure of silicon in its liquid phase. By combining the predictions of an X-ray scattering model with the analytical technique of Markov-Chain Monte Carlo, convergence of the density and inferred pressure state was found for three unique ion-ion correlation models; effective Coulomb, Debye-Hückel and non-linear Hulthén. Mutual posterior distributions of the silicon state were found by comparing these convergences with the pressure-density state determined by impedance matching techniques. The subsequent parameter distributions on the silicon phase diagrams highlight a consistency between the non-linear Hulthén predictions and the principal Hugoniot. This is a powerful experimental development allowing for exploration of the equation-of-state of high-compression materials which are readily achieved at high-power laser facilities and reducing model selection biases.