A model of phase transformations in solids is proposed, taking into account the relationship of non-linear processes that occur on various spatio-temporal scales in the non-linear open system of nuclei and electrons. The characteristic times of structural changes are determined by two mechanisms of atoms displacements: thermally activated in thermal fluctuations and athermic during non-adiabatic Landau-Zener transitions of atoms. Cooperative processes on a large spatio-temporal scale are described by two order parameters. The macroscopic kinetics of phase transformation is determined by two coupled nonlinear equations of the parabolic type for order parameters. These equations have two types of solutions describing the characteristic features of morphological changes in a solid with diffusion and martensitic phase transformations. The origin and growth of the new phase during diffusion phase transformations are described by solutions in the form of a switching wave from the metastable phase to a stable one. The formation of the embryo of the new phase is determined by structural changes on the atomic scale. Thermoelastic and reconstructive martensitic transformations are described by solutions in the form of static autosolitons - localized distributions of order parameters. Thermoelastic martensitic transformations develop against the background of a changing short-range order, determined by athermic displacements of atoms. Reconstructive martensitic transformations are determined by athermic displacements in the unstable phase, and the presence of any sources of initial disturbances is not required. Keywords: Phase transformations, non-adiabatic dynamics of atoms, athermic displacements, order parameters, kinetics, diffusion transformations, thermoelastic martensitic transformations, reconstructive martensitic transformations.