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During β-processing of α/β and β titanium alloys, variant selection (VS) of grain boundary α (GBα) is one of the key factors in determining the final transformation texture and mechanical properties. It has been observed frequently that GBα prefers its< 0 0 0 1> α pole to be parallel to a common< 1 1 0> β pole of the two adjacent β grains and results in a micro-textured region across the grain boundary (GB) and, as a consequence, slip transmission may take place more easily across that GB. In order to investigate how such a special prior β GB contributes to VS of GBα, we develop a crystallographic model based on the Burgers orientation relationship (BOR) between GBα and one of the two β grains. The model predicts all possible special β grain boundaries at which GBα is able to maintain BOR with both β grains. A new measure for VS of GBα,(β Δ J β BOR), ie, a measure of the deviation of the actual OR between the …