Extensive atomistic simulations based on the quasiparticle (QA) approach are performed to determine the momentous aspects of the displacive fcc/bcc phase transformation in a binary system. We demonstrate that the QA is able to predict the major structural characteristics of fcc/bcc phase transformations, including the growth of a bcc nuclei in a fcc matrix, and eventually the formation of an internally twinned structure consisting in two variants with Kurdjumov-Sachs orientation relationship. At atomic level, we determine the defect structure of twinning boundaries and fcc/bcc interfaces, and identify the main mechanism for their propagation. In details, it is shown that twin boundaries are propagated by the propagation of screw dislocations in fcc along the <-1-11>_{alpha} direction, while the propagation of fcc screw dislocations along coherent terrace edges is the pivotal vector of the fcc/bcc transformation. The simulation results are compared with our TEM and HRTEM observations of Fe-rich bcc twinned particle embedded in the fcc Cu-rich matrix in the Cu-Fe-Co system.