  Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy
of a crystal composed of atomic nuclei and uniform incompressible electron
background in the temperature and density range, covering fully ionized layers
of compact stellar objects, white dwarfs and neutron stars, including the
high-density regime, where ion quantization is important. We have approximated
the results by convenient analytic formulae, which allowed us to integrate and
differentiate the energy with respect to temperature and density to obtain
various thermodynamic functions such as Helmholtz free energy, specific heat,
pressure, entropy etc. In particular, we have demonstrated, that the total
crystal specific heat can exceed the well-known harmonic lattice contribution
by a factor of 1.5 due to anharmonic effects. By combining our results with the
PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work,
we were able to determine density dependences of such melting parameters as the
Coulomb coupling strength at melting, latent heat, and a specific heat jump.
Our results are necessary for realistic modelling of thermal evolution of
compact degenerate stars.
