Rechargeable ion batteries based on the intercalation of multivalent ions are attractive due to their high energy density and structural stability. Surface of cathode materials plays an important role for the electrochemical performance of the rechargeable ion batteries. In this work we calculated surface energies of (001), (110) and (111) facets with different terminations in spinel MgMn2O4 and MgNi0.5Mn1.5O4 cathodes. Results showed clearly that atomic reconstruction occurred due to surface relaxation. The surface energies for the (001), (110) and (111) surfaces of the MgNi0.5Mn1.5O4 were 0.08, 0.13 and 0.11 J/m(2), respectively, whereas those of the Ni-doped MgMgMn2O4 showed less dependence on the surface structures. (C) 2016 Elsevier B.V. All rights reserved.