Lattice Stability and Reflection Symmetry

The basic stability condition for a general crystal lattice is the availability of parallel material planes. If this condition is met, then phonons (quanta of lattice vibrations) can be generated and can stabilize the lattice. A triclinic (TCL) lattice has three sets of material planes containing atoms subjected to restoring stresses represented by Young and rigidity moduli. Longitudinal and transverse lattice vibrations obeying one-dimensional (1D) wave equations stabilized the lattice. The phonon distribution is highly directional. There can be no spherical distribution. Earlier we show [1] that the TCL lattice has no ${\mathbf k}$-vectors for electrons and it is is an intrinsic insulator. Consider next an orthorhombic lattice. This lattice has 3D phonons obeying a 3D wave equation with a Laplacian space-derivative. The phonon distribution is over a 3D anisotropic ${\mathbf k}$-space. PACS numbers: 61.50.Ah, 72.15.Eb, 72.20.-i\\[4pt] [1] S.~Fujita, A.~Jovaini, S.~Godoy, and A.~Suzuki, {\it Phys. Lett. A}, {\bf 376}, 2808 (2012).