Reducing the size of the lamellar structures and increasing the number of twin structures are both effective strategies for enhancing the ductility and fracture toughness of gamma-TiAl alloys. Hot isostatic pressing combined with heat treatment is an promising method to optimize the microstructure of TiAl alloys and improve their mechanical properties. However, systematic investigations into the microstructural evolution under high temperature pressure/external stress are limited. In this study, by integrating phase field simulations and CALPHAD thermodynamic database, a unique microstructural response to external stress during aging process is revealed. With the increase of external stress, the size of the lamellar structure initially decreases but then increases, while the number of twin structures initially rises but then decreases, showing nonlinear relationships. An increase in external stress shifts the free energy curves, altering the position of c0 (the intersection position between free energies of alpha 2 and gamma), which leads to a change in the nucleation mechanism from classical nucleation to pseudo-spinodal decomposition and influences the final microstructure of gamma precipitates. Further simulations indicate a linear correlation between optimal external stress and varying Al content. A deeper analysis indicates that the observed variations in the size and twin structures can be attributed to the interplay among the growth rate of existing variants, the competitive nucleation rates of twinned variants and the redistribution of composition under different external stresses. Our findings provide new insights into optimizing microstructures by pressure/external stress in precipitation processes. (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)gamma-TiAl(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)TiAl(sic)(sic)(sic)(sic)(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)/(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)CALPHAD(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)c0(alpha 2(sic)gamma(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic))(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)gamma(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)Al(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)/(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).