Modes of motion of light atoms (hydrogen and helium) in diamond-like lattice

The motion of a foreign atom (e. g. hydrogen or helium isotope) along the interstitials in a diamond-like silicon lattice is considered. The Lagrangian of the system “foreign atom + crystal” accounts for the influence of a foreign atom on the lattice atoms. The symmetries assumed by the Lagrange function allow the multidimensional system of equations describing the behavior of a foreign atom and lattice atoms to be reduced to a one-dimensional nonlinear equation. The solution to the equation is either the Frenkel-Kontorova soliton, which describes the translational behavior of a collective consisting of the foreign atom and the accompanying reversible displacements of the nearest lattice atoms, or the vibrational motion of a foreign atom, as a particle with the mass of an atom.