Author(s)

Shigeji Fujita¹, James R. McNabb III¹, Hung-Cheuk Ho², Akira Suzuki^3*

¹Department of Physics, University at Buffalo, SUNY, Buffalo, USA.
²Sincere Learning Centre, Kowloon, Hong Kong, China.
³Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan.

Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional; no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.

k-Vectors, Conduction Electron, Reflection Symmetry, Crystal Structure, Lattice Stability

Fujita, S. , McNabb III, J. , Ho, H. and Suzuki, A. (2015) Lattice Stability and Reflection Symmetry. Journal of Modern Physics, 6, 691-697. doi: 10.4236/jmp.2015.65074.