A Novel Discrete Theory of a Screw Dislocation in the BCC Crystal Lattice
Abstrak
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 Epstein-Hurwitz zeta function of the Eisenstein integers, whereas that of SC lattice is associated with the truncated Epstein-Hurwitz zeta function of the Gauss integers.
Topik & Kata Kunci
Penulis (1)
Shigeki Matsutani
Akses Cepat
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓