Researchers construct an EOS delivery paradigm for beryllium

Beryllium is a lightweight, low-density material used in a wide range of applications that require stability at high temperatures and pressures. Because of beryllium’s favorable traits, it has been considered as a potential capsule material for inertial confinement fusion (ICF) applications. Hydrodynamic simulations of ICF are frequently used to model the capsule behavior under the intense compression initiated by laser pulses, and an equation of state (EOS) that accurately describes material response is essential to these models. However, models for beryllium are limited by EOS uncertainties and a phase diagram that is not yet well established.

To address these uncertainties, Lawrence Livermore researchers have constructed a family of beryllium multiphase EOS models that consist of a baseline (“optimal”) EOS and variations on the baseline to account for physics-based uncertainties. To create these EOS models, the team considered three phases: the known hexagonal closed-packed (hcp) phase, the high-temperature liquid phase, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the liquid and bcc phases lack any experimental data, the team carried out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. They also examined the effect of different exchange–correlation functionals on bcc compression and the hcp–bcc transition boundary.

The results yielded a phase diagram that is consistent with observed stability fields of the three phases. The baseline EOS predicts the first density maximum to be 4.4-fold in compression, while the hcp–bcc–liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, the team generated eight variations that address different types of uncertainties arising from the choice of free-energy model, lack of constraints, systemic biases, or errors in experimental measurements or theoretical calculations. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the beryllium EOS, providing a paradigm for future hydrodynamic simulations of ICF and other high-pressure applications.

[C.J. Wu, P.C. Myint, J.E. Pask, C.J. Prisbrey, A.A. Correa, P. Suryanarayana, and J.B. Varley, Development of a Multiphase Beryllium Equation of State and Physics-based Variations, J. Phys. Chem. A 125, 1610 (2021), doi: 10.1021/acs.jpca.0c09809.]