Sn and Sn-based compounds have been attracting great interest as promising alternative materials for commercial anodes in lithium ion batteries.In this study,the phase evolution of the Li-Sn system during charge-discharge cycles and the effects of the elastic-strain energies caused by volume changes to the phase transition were investigated based on density functional theory.The formation energies of the LiaSnb alloys and the equilibrium open-circuit voltage were calculated,which were agreement with the experimental work.The elastic properties of the Li-Sn alloys such as the orientation-averaged bulk,Youngs moduli,shear moduli and the Poissons ratios for the crystalline alloys were presented.According to Eshelbys ellipsoidal inclusion theory,the elastic-strain energies during the lithiation processes were obtained.Our calculated results demonstrate that the amorphous or distorted Li7Sn3 phases tend to form in order to decrease the large elastic-strain energy.In addition,we suggest that the whole lithiated processes under the elastically constrained condition could be classified into two groups.The first group is the two-phase equilibrium process.In this case,the thermodynamic driving force is large enough to facilitate the phase conversion and the plateau voltage could be determined.The second group was considered to be the selective equilibrium.In this case,the thermodynamic driving force is not enough to facilitate the nucleation of the new equilibrium phase due to the elastically constrained conditions and the plateau voltage unformed.Besides,we found that in the Li0.4Sn matrix the nucleation of the α-Sn is more preferential than the β-Sn due to the effects of the elastic-strain energies.