TITLE:
Lattice Stability and Reflection Symmetry
AUTHORS:
Shigeji Fujita, James R. McNabb III, Hung-Cheuk Ho, Akira Suzuki
KEYWORDS:
k-Vectors, Conduction Electron, Reflection Symmetry, Crystal Structure, Lattice Stability
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.5,
April
29,
2015
ABSTRACT: 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.