[en] Highlights: • The double-island phenomenon is studied at atomic scale by binary phase field crystal. • The morphological evolution of epitaxial layer depends on signs of misfit strains. • Misfit strains with different signs have important influences on concentration field and density field. • Free energy of systems under different misfit strains has similar variational trend. Influences of misfit strains with different signs on liquid phase heteroepitaxial growth are studied by binary phase field crystal model. It is amazing to find that double islands are formed because of lateral and vertical separation. The morphological evolution of epitaxial layer depends on signs of misfit strains. The maximum atomic layer thickness of double islands under negative misfit strain is larger than that of under positive misfit strain at the same evolutional time, and size differences between light and dark islands is much smaller under negative misfit strain than that of under positive misfit strain. In addition, concentration field and density field approximately have similar variational law along x direction under the same misfit strain but show opposite variational trend under misfit strains with different signs. Generally, free energy of epitaxial growth systems keeps similar variational trend under misfit strains with different signs.