  Global microphysics models are required for the modelling of
high-energy-density physics (HEDP) experiments, the improvement of which are
critical to the path to inertial fusion energy. This work presents further
developments to the atomic and microphysics code, SpK, part of the numerical
modelling suite of Imperial College London and First Light Fusion. We extend
the capabilities of SpK to allow the calculation of the equation of state
(EoS). The detailed configuration accounting calculations are interpolated into
finite-temperature Thomas-Fermi calculations at high coupling to form the
electronic component of the model. The Cowan model provides the ionic
contribution, modified to approximate the physics of diatomic molecular
dissociation. By utilising bonding corrections and performing a Maxwell
construction, SpK captures the EoS from states ranging from the zero-pressure
solid, through the liquid-vapour coexistence region and into plasma states.
This global approach offers the benefit of capturing electronic shell structure
over large regions of parameter space, building highly-resolved tables in
minutes on a simple desktop. We present shock Hugoniot and off-Hugoniot
calculations for a number of materials, comparing SpK to other models and
experimental data. We also apply EoS and opacity data generated by SpK in
integrated simulations of indirectly-driven capsule implosions, highlighting
physical sensitivities to the choice of EoS models.
