Recent Advances in the Generalized Misorientation Theory

Slip, twinning and solid-state phase transformation all proceed on definite characteristic planes and characteristic directions. Based on this common feature, Researcher Zhao Zibo generalized misorientation into the angular deviation of two grains from a specified geometric feature-matching target, and proposed a generalized misorientation framework whose geometric kernel is the minimum rotation angle, expressed by the unified equation: Dx·G1 = Rxy·Sy·G2 With the minimum rotation angle as its geometric kernel, the framework can accommodate any process for which a feature-matching operator can be defined and whose degree of matching is verifiable.

The generalized misorientation brings interface-structure theories such as the coincidence site lattice (CSL) and the O-lattice into a unified description: the classical misorientation, the three process misorientations and the CSL deviation angle can all be understood as the minimum rotation from an actual orientation state to a particular ideal matching state. These ideal matching states constitute characteristic points in the interface configuration space, and their deviation parameters serve as local coordinates. On this basis an energetic chain is established running from interfacial energy and process barrier to process probability, and through it the framework connects with classical theories such as the Hall–Petch relation, grain boundary nucleation in solid-state phase transformations, and deformation accommodation in polycrystals.

More specifically, the effectiveness of the slip, twinning and phase transformation misorientations in predicting their associated physical behaviour has been confirmed by experimental statistics of slip transfer, twinning transfer and variant selection in several titanium alloy systems. Combined with group-theoretical simplification and quaternion algebra, all three parameters can be extracted from EBSD data efficiently and in batch mode. The generalized misorientation thus advances misorientation from a static geometric description to a quantitative characterization of process tendency, providing a unified crystallographic basis for the analysis of process tendencies at interfaces.

Relevant results have been submitted to Metallurgical and Materials Transactions A and to the Journal of Liaocheng University (Natural Science Edition).

The work spanned six years and was led by Researcher Zhao Zibo, carried out from the Institute of Metal Research, CAS to the Yuhua Institute of Advanced Materials, in collaboration successively with Liu Yuanhong, Li Xiaolong and others. Zhao Zibo proposed the concepts and mathematical framework of the three misorientation types (slip, twinning and phase transformation) and subsequently formulated the generalized misorientation concept together with its framework-level connections to several classical materials science theories. Liu Yuanhong was principally responsible for the theory and experimental validation of the phase transformation misorientation. Li Xiaolong was principally responsible for the derivation of the slip and twinning misorientation formulas, development of the computational programs, implementation of the quaternion algorithm, and the visualization functionality. Yang Jiuxu (Institute of Metal Research), Shao Jun and Zhang Bohua (Yuhua Institute) participated in part of the experimental characterization and data analysis. During the author's time at the Institute of Metal Research, the work was supported by Researcher Wang Qingjiang and Researcher Yang Rui, for which the authors express their gratitude.