A thermodynamic study on Li-poor vapor transport equilibration (VTE) in MgO-doped LiNbO3 crystal was carried out. A thorough thermodynamic VTE model is established that considers all of possible factors including the depth relative to crystal surface, VTE temperature and time. To solve the model, the composition on crystal surface was studied as a function of VTE temperature and time. To achieve that, a number of Li-deficient MgO(5 mol% in melt):LiNbO3 crystals were produced by the VTE under different temperatures from 1010 to 1130 degrees C for different durations up to 395 h, the crystalline phase contained was determined by X-ray powder diffraction and their surface compositions were determined from the measured birefringence. The results show that the Li-deficient crystal keeps the LiNbO3 phase. The surface Li2O-content has an Arrhenius relationship to the VTE temperature and a square-root dependence on the VTE duration. Based upon the VTE temperature and time dependences of surface Li2O-content, the solution to the thermodynamic VTE is obtained and verified experimentally. The solution is crucial to design and produce a Li-deficient MgO:LiNbO3 crystal with desired Li2O-content profile. By using the solution, one can predict the Li2O-content depth profile after a certain VTE time for a given VTE temperature. (C) 2013 Elsevier B.V. All rights reserved.