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The rhombohedral twinning in hematite has an important role in the accommodation of the deformation of hematite single crystals and hematite aggregates. It is a contact twinning and occurs as lamellae parallel to the 
planes of hematite as a result of twin gliding on such planes. On account of the recent applications of electron backscatter diffraction (EBSD) techniques in a wide range of microstructural studies, the determination of symmetry operations that relate crystals in a deformed crystalline aggregate is crucial for the full textural characterization. This study presents an EBSD-based crystallographic analysis of the rhombohedral twinning on hematite crystals of a naturally deformed banded iron formation. Manipulations of theoretical pole figures depicting the symmetry relation of the rhombohedral twinning and misorientation and crystallographic data obtained by EBSD are used to establish the rotational relationship between twin and parent crystals. A method for determining pairs of axes and angles of rotation was developed which can be extended to any other twin laws or misorientation patterns in any other crystal system. It was found that the hematite rhombohedral twins are related to the parent crystal by an approximately 85° rotation about the <
> directions. Hence it could be determined that this consists of a macroscopic twinning element which is an alternative to the conventional ones used to describe the symmetry of the twin. It also matches microscopic twinning elements for the rhomb twinning law. Additionally, this method allows the determination of the crystallographic orientation of the twin lamellae and which particular <> axis satisfies the 85°<> pair of rotation. The use of an unambiguous angle-axis pair of rotation allows the identification of twin boundaries in complex and finely grained aggregates and the distinction of twinning laws in a particular crystal.
planes of hematite as a result of twin gliding on such planes. On account of the recent applications of electron backscatter diffraction (EBSD) techniques in a wide range of microstructural studies, the determination of symmetry operations that relate crystals in a deformed crystalline aggregate is crucial for the full textural characterization. This study presents an EBSD-based crystallographic analysis of the rhombohedral twinning on hematite crystals of a naturally deformed banded iron formation. Manipulations of theoretical pole figures depicting the symmetry relation of the rhombohedral twinning and misorientation and crystallographic data obtained by EBSD are used to establish the rotational relationship between twin and parent crystals. A method for determining pairs of axes and angles of rotation was developed which can be extended to any other twin laws or misorientation patterns in any other crystal system. It was found that the hematite rhombohedral twins are related to the parent crystal by an approximately 85° rotation about the <
> directions. Hence it could be determined that this consists of a macroscopic twinning element which is an alternative to the conventional ones used to describe the symmetry of the twin. It also matches microscopic twinning elements for the rhomb twinning law. Additionally, this method allows the determination of the crystallographic orientation of the twin lamellae and which particular <> axis satisfies the 85°<> pair of rotation. The use of an unambiguous angle-axis pair of rotation allows the identification of twin boundaries in complex and finely grained aggregates and the distinction of twinning laws in a particular crystal.
