Nazarenko Y. Crowdions as nonlinear excitations of the three-dimensional crystal lattice

Object of study: crowdions as specific defects of crystal structure and as nonlinear solitary waves of the field of displacements in close-packed atomic rows. Aim: the theoretical description of the crowdion excitations in three-dimensional crystal lattice which adequately shows the physical nature of the crowdion and effectively takes into account the most essential fitures of its structure and dynamics in real crystal. Methods: analytical methods of classical mechanics of particles and crystal lattice; known methods of the mathematical physics which is used for description of the space-time evolution of classical fields; methods of precise and approximate solution of nonlinear differential equations; ideas of Lorentz method for derivation of the equation of motion of the electron as a point singularity of the electro-magnetic field and analogous to it Kosevich method for derivation of the equation of motion of the dislocation as a linear singularity of the deformation field in elastic continuum; numerical summation and integration methods with use of personal computer. Results, novelty: The problem of crowdion motion is formulated and analyzed as a dynamical problem of a three-dimensional crystal lattice formed by atoms of several kinds, which interact with each other by means of short-range pair potentials. It is explained that in order for the crowdion excitations of the close-packed atomic rows to be distinguishable against the background of small dynamic deformations of the crystal as a whole, the microscopic parameters of the crystal structure must meet certain stated requirements. The equation of motion of a crowdion in an arbitrary elastic strain field of the crystal is derived in the Lagrangian formalism. Expressions are obtained which relate the effective mass and the rest energy of a crowdion with the geometric and force parameters of the crystal lattice. The numerical values of the crystal field potentials parameters