Nanocrystalline nanowires: 2. Phonons.
Nanocrystalline nanowires (NCNW) are fragments of bulk crystals that are infinite in only one direction. A construction is given for calculating eigenstates belonging to the symmetry labels (k,m) (wavevector and rotational quantum number). Vibrational harmonic eigenstates are worked out explicitly for a simple model, illustrating the general results: the LA mode has m=0, while with sufficient rotational symmetry, the TA branch is doubly degenerate, has m=+/-1, and has quadratic dispersion with k for k less than the reciprocal diameter of the NCNW. The twiston branch (a fourth Goldstone boson) is an acoustic m=0 branch, additional to the LA and two TA branches.
Allen
Philip B
PB
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA. philip.allen@stonybrook.edu
D003460:Crystallization; D053770:Nanowires; D011789:Quantum Theory