Thermodynamics of spinel Li x TiO 2 from first principles M. Wagemaker a, * , A. Van Der Ven b , D. Morgan c , G. Ceder b , F.M. Mulder a , G.J. Kearley a a Department of Radiation, Radionuclides and Reactors, Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands b Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, USA c Department of Materials Science and Engineering, University of Wisconsin – Madison, Madison, WI, USA Received 26 January 2005; accepted 4 May 2005 Available online 20 June 2005 Abstract The thermodynamic and structural properties of Li x TiO 2 spinel are investigated by means of a cluster expansion based on pseudopotential ground state energy calculations in the Generalized Gradient approximation (GGA). The cluster expansion enables a Monte Carlo simulation of configurational thermodynamics, giving the Li configurations, chemical potential and the insertion potential as function of Li composition at 300 K. For 1/2 < x < 1Li x TiO 2 we find a two-phase region, consistent with what is found experimentally. The two coexisting phases differ in the sites occupied by Li: in Li 1/2 TiO 2 and LiTiO 2 Li occupies the crystallographic 8a and 16c sites, respectively. This site occupation and the changes in the unit cell dimensions compare well with X-ray and neutron diffraction experiments. For x < 1/2 in Li x TiO 2 solid solution behavior is found and Li extraction can only occur at higher poten- tials. The potential step at Li 1/2 TiO 2 is calculated to be 1.4 V, in good agreement with experiment, but considerably higher than in the comparable Co and Mn-spinel. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Lithium intercalation; Battery material; First principles; Spinel, Li x TiO 2 1. Introduction The growing demand for energy resources has led to the development of renewable energy sources, including photovoltaics (solar cells), solar thermal, wind, biomass and several others. To resolve the discrepancy between the moments of supply and demand of the energy pro- duced, energy storage is required. For small scale appli- cations one option is to store energy in rechargeable batteries. Rechargeable batteries convert chemical en- ergy contained in the electrodes into electrical energy via electrochemical reactions. Transport of ions from one electrode to another through an electrolyte, causes an electrical current between the electrodes that can be used to power an application. In particular, lithium- ion batteries are very promising due to their stored en- ergy/weight ratio [1]. During the last decades, three- dimensional framework spinel transition metal oxides have appeared to be a very promising class of lithium- ion electrode materials. The use of spinel Li 1/2 TiO 2 (often represented as Li 1 Ti 2 O 4 ) as electrode material is based on its ability to host an additional amount of Li leading to composi- tion LiTiO 2 [2]. Other titanium oxide compounds stud- ied in relation to Li intercalation include anatase, rutile and brookite (all TiO 2 ) [3–5]. In particular the anatase and the spinel structures have been found to be suitable anode materials. In the starting compound, spinel Li 1/2 TiO 2 , neutron diffraction indicates that Li re- sides on the tetrahedral 8a sites, whereas it occupies the octahedral 16c sites in LiTiO 2 [6]. The latter structure 0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.05.011 * Corresponding author. Tel.: +31 152783800; fax: +31 152788303. E-mail address: m.wagemaker@iri.tudelft.nl (M. Wagemaker). www.elsevier.com/locate/chemphys Chemical Physics 317 (2005) 130–136