Melting of atomic materials under high pressures using computer simulations

Enormous progress has been made in high-pressure research over the last decades in both, experiments and computer simulations, many challenges still remain. This is evidenced by controversial experimental and numerical data even for the simplest atomic systems exhibiting different types of bonding. Here we discuss the determination of the solid-liquid co-existence (melting) lines reviewing the computational techniques for studying the high-pressure melting of atomic systems based on molecular dynamic or Monte Carlo algorithms. Some emphasis is put on presenting the parallel-tempering Monte Carlo method that gives direct access to heat capacity curves and entropic information as a function of temperature allowing for an easy detection and interpretation of the melting transition. For molecular dynamics simulations there exist a variety of methods to extract melting information - here we include a more thorough discussion of thermodynamic integration as it is frequently used for high-pressure melting. Applications of these techniques and discussion for different atomic systems are presented including an overview of experimental and numerical results of the weakly, van-der-Waals bond noble gases, of diamond as a representative for covalent bonding and of alkali metals and iron. We conclude by summarizing some outstanding problems and challenges for numerical simulations.