A Novel Discrete Theory of a Screw Dislocation in the BCC Crystal Lattice
Abstract
In this paper, we proposed a novel method using the elementary number theory to investigate the discrete nature of the screw dislocations in crystal lattices, simple cubic (SC) lattice and body centered cubic (BCC) lattice, by developing the algebraic description of the dislocations in the previous report (Hamada, Matsutani, Nakagawa, Saeki, Uesaka, Pacific J. Math.~for Industry {\bf{10}} (2018), 3). Using the method, we showed that the stress energy of the screw dislocations in the BCC lattice and the SC lattice are naturally described; the energy of the BCC lattice was expressed by the truncated EpsteinHurwitz zeta function of the Eisenstein integers, whereas that of SC lattice is associated with the truncated EpsteinHurwitz zeta function of the Gauss integers.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.04332
 Bibcode:
 2019arXiv190604332M
 Keywords:

 Mathematical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Physics  Atomic and Molecular Clusters
 EPrint:
 31 pages