ORIGINAL PAPER Estimation on diffusion coefficient of lithium ions at the interface of LiNi 0.5 Mn 1.5 O 4 /electrolyte in Li-ion battery H. Seyyedhosseinzadeh & F. Mahboubi & A. Azadmehr Received: 28 August 2013 /Revised: 7 June 2014 /Accepted: 15 June 2014 # Springer-Verlag Berlin Heidelberg 2014 Abstract This research tried to estimate diffusion coefficient for lithium ions through the surface of the spinel LiNi 0.5 Mn 1.5 O 4 by spin-polarized total energy calculation. In addition, calculated result by this ab initio model was com- pared with a semi-empirical model. Both of these models predicted diffusion coefficient for lithium ions at the interface of the spinel LiNi 0.5 Mn 1.5 O 4 /electrolyte as 10 -8 cm 2 s -1 which is 3 orders of magnitude higher than the diffusion coefficient of lithium ions in LiNi 0.5 Mn 1.5 O 4 . Details of these two models have been explained in this paper along with calculated results for surface diffusion coefficient of LiNi 0.5 Mn 1.5 O 4 cathode material. Keywords Li-ion battery . Fickian transport approach . LiNi 0.5 Mn 1.5 O 4 . Ab initio calculation . Diffusion coefficient Introduction Manipulating active materials for Li-ion battery technology is still a challenging issue on developing the overall performance of battery. Therefore, any attempt of disclosing mechanism of atomic evolution and movement in active materials would be a necessary foundation of further researches on designing more efficient active materials during charging/discharging. Such kinds of attempts would be well-organized if computa- tional approaches work closely with experimental techniques. In general, physical concept computational models of Li-ion batteries are engaged in multiscale [1]. These kinds of multiscale models are efficient in modeling the overall perfor- mance of battery but less efficient in studying the physical mechanism in comparison to first principle simulations. It is not inequitable to claim that first principle simulations are more efficient to evaluate governing physical mechanisms than the other computational methods at higher length scales. But first principle simulations are limited to small atomic systems. Nevertheless, performing simulation at any desired length scale would be helpful to predict and discover governing physical mechanisms. There are some coarse grain thermodynamic models to simulate charging and discharging of Li-ion battery [2–7]. In addition, there are extensive first principle simulations particularly on designing active mate- rials by considering a small part of them [8–13]. In most cases that experimental techniques are expensive or hard to estab- lish, first principle simulations could be used efficiently as they are well-developed in material science and engineering physics. Any first principle simulation is started from Schrodinger equation (SE). SE governs the dynamics of the probability distribution of electrons [14]. SE is an equation which is derived from the minimization of the total energy of the atomic system. The total energy can be written in the quantum state by Eq. 1: Totalenergy ¼ φ Ã i X i -ℏ 2 2m e ∇ 2   þ V pp r ðÞ  ! φ i þ E XC þ E ee þ E ii ð1Þ In the minimum formalism of total energy, we have the following (Eqs. 2, 3, and 4): Time independent: E n φ n r ðÞ¼ - ℏ 2 2m ∇ 2 þ Vr ðÞ   φ n r ðÞ ð2Þ H. Seyyedhosseinzadeh (*) : F. Mahboubi : A. Azadmehr Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Hafez Ave., P.O. Box 15875-4413, Tehran, Iran e-mail: Hamed@uwalumni.com Ionics DOI 10.1007/s11581-014-1189-x