Mathematical analysis and STEM observations of arrangement of structural units in 〈001〉 symmetrical tilt grain boundaries

Kazutoshi Inoue; Mitsuhiro Saito; Chunrin Chien; Motoko Kotani; Yuichi Ikuhara

doi:10.1093/jmicro/dfw034

Mathematical analysis and STEM observations of arrangement of structural units in 〈001〉 symmetrical tilt grain boundaries

Kazutoshi Inoue, Mitsuhiro Saito, Chunrin Chien, Motoko Kotani, Yuichi Ikuhara

Advanced Institute for Materials Research (AIMR)

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

A collaborative work between mathematics and atom-resolved scanning transmission electron microscopy (STEM) has been conducted. The grain boundary in a bicrystal of a simple rock-salt oxide can show a complicated arrangement of structural units, which can be well predicted by an algorithm utilizing the Farey sequence. The estimated arrangements had a nice agreement with those observed by STEM in atomic-scale up to several tens of nanometers.

Original language	English
Pages (from-to)	479-487
Number of pages	9
Journal	Microscopy
Volume	65
Issue number	6
DOIs	https://doi.org/10.1093/jmicro/dfw034
Publication status	Published - 2016 Dec 1

Keywords

Atomic structure
Bicrystal
Farey sequence
Stern-Brocot tree
Structural unit
Symmetrical tilt grain boundary

ASJC Scopus subject areas

Structural Biology
Instrumentation
Radiology Nuclear Medicine and imaging

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10.1093/jmicro/dfw034

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abstract = "A collaborative work between mathematics and atom-resolved scanning transmission electron microscopy (STEM) has been conducted. The grain boundary in a bicrystal of a simple rock-salt oxide can show a complicated arrangement of structural units, which can be well predicted by an algorithm utilizing the Farey sequence. The estimated arrangements had a nice agreement with those observed by STEM in atomic-scale up to several tens of nanometers.",

keywords = "Atomic structure, Bicrystal, Farey sequence, Stern-Brocot tree, Structural unit, Symmetrical tilt grain boundary",

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T1 - Mathematical analysis and STEM observations of arrangement of structural units in 〈001〉 symmetrical tilt grain boundaries

AU - Inoue, Kazutoshi

AU - Saito, Mitsuhiro

AU - Chien, Chunrin

AU - Kotani, Motoko

AU - Ikuhara, Yuichi

N1 - Funding Information: The Elements Strategy Initiative for Structural Materials by the MEXT of Japan and the JSPS Grant-in-Aid for Scientific Research (grant nos 15H02290, 15K06420, 26420662 and 26820288). Publisher Copyright: © The Author 2016.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - A collaborative work between mathematics and atom-resolved scanning transmission electron microscopy (STEM) has been conducted. The grain boundary in a bicrystal of a simple rock-salt oxide can show a complicated arrangement of structural units, which can be well predicted by an algorithm utilizing the Farey sequence. The estimated arrangements had a nice agreement with those observed by STEM in atomic-scale up to several tens of nanometers.

AB - A collaborative work between mathematics and atom-resolved scanning transmission electron microscopy (STEM) has been conducted. The grain boundary in a bicrystal of a simple rock-salt oxide can show a complicated arrangement of structural units, which can be well predicted by an algorithm utilizing the Farey sequence. The estimated arrangements had a nice agreement with those observed by STEM in atomic-scale up to several tens of nanometers.

KW - Atomic structure

KW - Bicrystal

KW - Farey sequence

KW - Stern-Brocot tree

KW - Structural unit

KW - Symmetrical tilt grain boundary

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Mathematical analysis and STEM observations of arrangement of structural units in 〈001〉 symmetrical tilt grain boundaries

Abstract

Keywords

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