Compressibility of solid helium

The compressibility of solid helium (3He and 4He) in the hcp and fcc phases has been studied by the path-integral Monte Carlo method. Simulations were carried out in both canonical (NVT) and isothermal-isobaric (NPT) ensembles at temperatures between 10 and 300 K, showing consistent results in both ensembles. For pressures between 4 and 10 GPa, the bulk modulus B is found to decrease by about 10%, when the temperature increases from the low-temperature limit to the melting temperature. The isotopic effect on the bulk modulus of helium crystals has been quantified for a wide range of parameters. At 25 K and pressures on the order of 1 GPa, the relative difference between 3He and 4He amounts to about 2%. The thermal expansion has also been quantified from results obtained in both NPT and NVT simulations