Predictions of the solid helium phase diagram

Abstract

The hcp‐fcc phase transition of helium is predicted on the basis of a quantum mechanical, anharmonic, anisotropic cell model calculation. The small heat of transition agrees with experiment within the uncertainty in the knowledge of the pair potential. The phase line is extended beyond present experimental range by introducing lattice dynamics corrections, which are increasingly important at high densities. The phase line is predicted to curve over and intersect the pressure axis at 0 °K at about 20 000 atm. This behavior of the phase line is independent of the quantitative results of the models used here, since the harmonic approximation, which becomes exact in the high‐density limit, requires that fcc be stable relative to hcp. Anharmonic lattice dynamic correlations are shown to be essential to the prediction of the bcc‐hcp transition. They are introduced here via a correlated cell model. For the highly accurate cell model calculations several numerical methods of solution are compared.