2019/06/30 by Shigeki Matsutani
Materials Science · Mathematics · Physics and Astronomy · #Algebraic number #Crystal (programming language) #Crystal structure #Cubic crystal system #Lattice (music) #Mathematical Approximation and Integration #Microstructure and mechanical properties #Quasicrystal Structures and Properties #Riemann zeta function #Simple cubic lattice #cond-mat.mes-hall #cond-mat.stat-mech #math-ph #math.MP #physics.atm-clus
paper · pdf · open access · doi:10.2140/memocs.2021.9.1
published in Mathematics and Mechanics of Complex Systems 9(1), 1-32 (Mathematical Sciences Publishers) · 31 pages
openalex created_date 2019/06/27 · arxiv created 2020/11/18 · arxiv updated 2021/03/17 · openalex publication_date 2021/03/17 · openalex updated_date 2026/08/05
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 \bf10 (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.