A model to predict the preferred orientation relationships of in situ synthesized TiB in titanium matrix composites

A geometrical model is proposed to predict the preferred orientation relationship (OR) between two crystals. While the rotating crystal is rotated with respect to the fixed crystal, a crystallographic OR emerges as long as some intersected reciprocal lattice points (RLPs) lie in a plane and form a periodic pattern. The preferred ORs can be determined when the coplanar RLPs of both crystals reach maximum on the plane determined by the intersected RLPs. Calculations were carried out on TiB/alpha-Ti, TiB/beta-Ti and alpha-Ti/beta-Ti systems, and the predicted preferential ORs are consistent with most experimental observations in publication, showing the validity of the model on the prediction of preferred OR between BCC, orthorhombic and HCP crystals. Moreover, a full OR space with a right cylinder shape is introduced to characterize an OR between two crystals. The basal plane of the cylinder reflects the symmetry of the fixed crystal and the vertical height of the cylinder represents the symmetry of an indicator axis of the rotating crystal. According to the symmetry of both crystals, the full OR space can be divided into several equivalent subspaces. This unique geometrical OR presentation effectively eliminates the ambiguities in conventional Miller indices OR presentation and enable a visual and convenient comparison of ORs from different research sources.