I'm making XRD analysis for annealed pure titanium and titanium managanese alloy and I could determine whether if the material is in anatase or rutile phase, but how can I determine if it's alpha or beta?
If I got your question, you were able to identify the anatase and rutile phases developed during the annealing of titanium and titanium managanese alloy, and you are asking about alpha and beta phases of TiO2.
Actually, the (α-TiO2) is nothing but rutile, and the (β-TiO2) is nothing but anatase, while (γ-TiO2) is nothing but brookite.
When you consider the metallic pure Titanium and its alloys, you may find a mixture of the two main crystalline phases : the alpha phase which is HCP (Hexagonal Closed Packed) and, at the higher temperatures, the beta phase which is BCC (Body Centered Cubic).
Different crystal structures have the Titanium oxides : anatase, rutile and brookite.