Mathematical Model for Diamond-Type Crystals with Impurities or Defects

Abstract

This work develops the geometry and dynamics of diamond-type crystals with impurities or defects and symmetry from the perspective of Langrangian mechanics. We begin by formulating continuous–discret Lagnge-d`Alembert principle, Noer's theorem and momentum equation for diamond-type crystals with impurities are given. Several detailed examples are given illustrate the theory.