Three-body interactions and the elastic constants of hcp solid ⁴He

The effect of three-body interactions on the elastic properties of hexagonal close packed solid ⁴He is investigated using variational path integral (VPI) Monte Carlo simulations. The solid's nonzero elastic constants are calculated, at T = 0 K and for a range of molar volumes from 7.88 cm³/mol to 20.78 cm³/mol, from the bulk modulus and the three pure shear constants C₀, C₆₆, and C₄₄. Three-body interactions are accounted for using our recently reported perturbative treatment based on the nonadditive three-body potential of Cencek et al. Previous studies have attempted to account for the effect of three-body interactions on the elastic properties of solid ⁴He; however, these calculations have treated zero point motions using either the Einstein or Debye approximations, which are insufficient in the molar volume range where solid ⁴He is characterized as a quantum solid. Our VPI calculations allow for a more accurate treatment of the zero point motions which include atomic correlation. From these calculations, we find that agreement with the experimental bulk modulus is significantly improved when three-body interactions are considered. In addition, three-body interactions result in non-negligible differences in the calculated pure shear constants and nonzero elastic constants, particularly at higher densities, where differences of up to 26.5% are observed when three-body interactions are included. We compare to the available experimental data and find that our results are generally in as good or better agreement with experiment as previous theoretical investigations.