Surface and confinement effects in the solidification of three-dimensional helium

Interpretations are given of recent experiments which show that liquid-solid equilibrium of bulk helium is inhibited at the surfaces of containers and within the pores of fine powders, which results in unexpectedly large interfacial coefficients between solid He and copper and glass walls and large overpressures that solidify ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in fine powders. We suggest that the wall effect is due to the grain boundary energy in a polycrystalline layer adjacent to the walls. In fine powders the grain-boundary energy of the solid raises the melting pressure above the equilibrium value. This shift is related to the melting-point depression in small particles of ordinary materials. Estimates of the effect are compared with the measurements and are found to be in semiquantitative agreement.