Lattice Stability and Reflection Symmetry


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.

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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.

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[1] Lee, T.D. and Yang, C.N. (1956) Physical Review, 104, 254.
[2] Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics. Saunders, Philadelphia, 216-217, 228-229, 6-7.
[3] Fujita, S., Takato, Y. and Suzuki, A. (2011) Modern Physics Letters B, 25, 223.
[4] Fujita, S. and Suzuki, A. (2010) Journal of Applied Physics, 107, Article ID: 013711.
[5] Zhang, Y., Tan, Y.W., Stormer, H.L. and Kim, P. (2005) Nature, 438, 201.
[6] Kang, N., Lu, L., Kong, W.J., Hu, J.S., Yi, W., Wang, Y.P., Zhang, D.L., Pan, Z.W. and Xie, S.S. (2003) Physical Review B, 67, Article ID: 033404.
[7] Debye, P. (1912) Annalen der Physik, 39, 789.

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