There is no relevant research on the relationship between the piezoelectric behavior of superlattice and the internal cations.In this paper,by the first-principles method of density-functional theory,we study the polarizations and piezoelectric contributions of cations A and B in three lead-free tetragonal perovskite ferroelectric superlattices (BaTiO3/SrTiO3,KNbO3/KTaO3 and BaTiO3/KNbO3).By calculating atomic structures and atomic Born effective charges of three superlattices under different axial strain conditions (-0.15-0.15),the polarization and piezoelectric coefficients of superlattices and internal cations are obtained.With the axial compressive strain changing from -0.15 to 0,the variations of displacements D(A) and D(B) of cations A and B in lead-free superlattices are very small, and displacements D(A) and D(B) significantly increase as the axial tensile strain (0-0.15) is applied,indicating that the axial compressive strain is not beneficial to the ferroelectric displacement in the tetragonal superlattice,especially in BaTiO3/SrTiO3 nor KNbO3/KTaO3 superlattices.The tetragonal ferroelectric superlattices BaTiO3/SrTiO3 and KNbO3/KTaO3 may be unstable under the condition of the axial compressive strain,and only the axial tensile strain can promote the existence of tetragonal phase in superlattice.As the axial strain is applied,Born effective changes of A-site cations in three lead-free tetragonal superlattices are small,and Z33*(B) gradually declines,and Zxy*(B) continually rises.The axial strain induced charges are transferred from the B-site cations to O atoms along the c-axis,and the charges are transferred from O atoms to B-site cations along the xy direction.The variation rate of Born effective charges under the condition of the axial tensile strain is greater than under the condition of the axial compressive strain, especially in superlattices BaTiO3/SrTiO3 and KNbO3/KTaO3,showing that the axial tensile strain is more beneficial to the redistribution of atomic charges in the superlattices.Under the condition of the axial compressive strain,the total polarizations of superlattices BaTiO3/SrTiO3 and KNbO3/KTaO3 are close to zero;while polarizations of superlattices BaTiO3/KNbO3 gradually increase with the axial compressive strain varying from -0.15 to 0.There are atomic ferroelectric displacements in superlattice BaTiO3/KNbO3,and the interaction between BaTiO3 ferroelectric layer and KNbO3 ferroelectric layer contributes to the generation of ferroelectric behavior.When the axial tensile strain (0-0.15) is applied,the polarization contributions of B-site cations in superlattices BaTiO3/SrTiO3 and KNbO3/KTaO3 increase significantly,especially the polarization contributions of B-site cations Ti,Nb and Ta,and the total polarization is obviously improved.The effect of the tensile strain on polarization of BaTiO3/KNbO3 is smaller than on polarizations of BaTiO3/SrTiO3 and KNbO3/KTaO3.The interaction between two ferroelectric layers in BaTiO3/KNbO3 contributes to the redistribution of atomic charges,and alleviates ferroelectric displacements of atoms to some extent.The polarization contribution of B-site cations is largest,because of their large Born effective charges and ferroelectric displacements. When the tensile strain reaches a certain threshold,tetragonal superlattices will present obvious piezoelectric behavior. With the tensile strain increasing,total piezoelectric coefficient d33 and piezoelectric contributions of A,B-site cations both increase.The piezoelectric behaviors of lead-free superlattices are mainly attributed to the B-site cations.
