Arrangements of three to six cubes with maximum disorientation angles

ABSTRACT

The well-known problem of determining the maximum possible disorientation angle of two cubes is extended to groups of three to six cubes. This problem is considered here to allow identification of specific arrangements of grains with a cubic structure at triple-line or quadruple junctions in polycrystals. The minimum disorientation angle between cubes in the group is defined as the characteristic disorientation angle ${\theta }_{\mathrm{c}\mathrm{d}}$ of the group. The maximum values of ${\theta }_{\mathrm{c}\mathrm{d}}$ and the arrangements of cubes giving the maximum ${\theta }_{\mathrm{c}\mathrm{d}}$ are determined for groups of three to six cubes.

KEYWORDS:

• Grain arrangement
• triple-line junction
• quadruple junction
• orientation relationship
• polycrystal

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Susumu Onaka http://orcid.org/0000-0002-9617-8908

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI [grant number 19K04985].