Hexagonal Close-Packed $^4\hbox {He}$ as Crystalline Multilayered Polytype: An Alternative for ‘Supersolid’ or ‘Glassy-Like’ Phase

Abstract

We apply the model of a crystalline polytype built of close-packed 2D monoatomic basal planes with triangular lattice to interpret the anomalous thermodynamical and mechanical properties of solid hexagonal close-packed (HCP) $^4\hbox {He}$. The polytype is a 3D stack of the basal planes, and its structure can be built from the simplest periodic packing (HCP, FCC, 4H, 5H, 6R, $\ldots$ etc.) up to random stacking fault system (RSFS) totally aperiodic in only c-direction perpendicular to the basal planes. RSFS is a crystal without microscopic translation symmetry along c-axis, i.e., entirely disordered in only one spatial direction. Despite of packing disorder, c-direction remains the crystallographic axis of third order at arbitrary sequence of the 2D plates in the whole stack. In a long-wave limit the HCP polytype can be treated as 3D anisotropic continuum, as a result its phonon spectrum and Helmholtz free energy have been calculated. The temperature dependence of the phonon pressure is calculated theoretically and compared with experimental data. A quantitative agreement between the theory and the experiment is achieved. Mechanical properties of $^4\hbox {He}$ crystals in the framework of the polytype model are briefly discussed.