Conical Point Crossing in Orthorhombic and Monoclinic Lattices

Abstract

On the basis of simple lattice vibrational models, it is shown that the conical point crossing, known to appear at the K-point in the hexagonal lattice, also appears in the orthorhombic and monoclinic lattices induced from the hexagonal lattice as a result of a ferroelastic phase transition. With decreasing symmetry from the hexagonal lattice, the cone becomes elliptic, and the conical k-point, defined as the point in the reciprocal lattice where the conical point crossing may appear, shifts to a general position inside the Brillouin zone. The existence of the conical point crossing in the orthorhombic and monoclinic lattices may not be determined solely by symmetry consideration, but it can be proved with a simple model, assuming a suitable balance of interatomic interactions for low-symmetry lattices.