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Formation of the Ni₄Ti₃ precipitate has a strong effect on the shape memory properties of NiTi alloys. In this work, growth of this precipitate is studied using phase-field modelling and density functional theory (DFT) calculations. Using first-principles calculations, the composition-dependent stability and elastic properties of the B2 phase are obtained. Composition-dependent elastic constants are incorporated into our phase-field model to investigate the interplay between stress and concentration fields around the precipitate. The model introduces a source of diffusion due to mechanical relaxation which is accompanied by local softening/hardening of the B2 phase. The results are discussed in light of previous experimental and simulation studies.