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A novel discrete
investigation of screw dislocations in the BCC crystal
lattice
Shigeki Matsutani
Vol. 9 (2021), No. 1, 1–32
DOI: 10.2140/memocs.2021.9.1
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Abstract |
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In this paper, we propose a novel method using elementary number theory to investigate the discrete nature of the screw dislocations in crystal lattices, namely the simple cubic (SC) lattice and body-centered cubic (BCC) lattice, by developing the algebraic description of the dislocations in the previous report of Hamada, Matsutani, Nakagawa, Saeki, and Uesaka (Pac. J. Math. Ind. 10 (2018), art. id. 3). Using this 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 the SC lattice is associated with the truncated Epstein–Hurwitz zeta function of the Gauss integers. |
Keywords
crystal lattice, screw dislocation, truncated
Epstein–Hurwitz zeta function, Eisenstein integer, Gauss
integer, dislocation, algebraic investigation, number
theory, BCC lattice
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Mathematical Subject Classification
Primary: 08A99, 55R05, 20H15, 11R60, 34M35
Secondary: 82D25, 74E15, 82-10, 74-10
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Milestones
Received: 19 June 2020
Revised: 8 October 2020
Accepted: 9 November 2020
Published: 17 March 2021
Communicated by Victor A. Eremeyev
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Authors |
| Shigeki Matsutani | |
| Graduate School of Natural Science
and Technology Kanazawa University, Kakuma Kanazawa Japan |
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