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The structural characterization of the various phases that occur in Ti-Ta-based high-temperature shape memory alloys is complicated by the presence of many competing phases as a function of composition. In this work, we resolve apparent inconsistencies between experimental data and theoretical calculations by suggesting that phase separation and segregation of undesired phases are not negligible in these alloys, and that finite temperature effects should be taken into account in the modelling of these materials. Specifically, we propose that the formation of the ω phase at low Ta content and of the σ phase at high Ta content implies a difference between the nominal alloy composition and the actual composition of the martensitic and austenitic phases. Additionally, we show that temperature affects strongly the calculated values of the order parameters of the martensitic transformation occurring in Ti-Ta.