Article pubs.acs.org/JPCC
Transport Properties in the CeO2−x(111) Surface: From Charge Distribution to Ion-Electron Collaborative Migration José J. Plata, Antonio M. Márquez, and Javier Fdez. Sanz* Departamento de Química Física, Facultad de Química, Universidad de Sevilla, E-41012 Sevilla, Spain ABSTRACT: Charge distribution and ion and electron migration have been theoretically studied in the reduced CeO2(111) surface by means of density functional calculations including on-site localization corrections (DFT+U). The analysis of the charge distribution shows that nearest-neighbor and next-nearest-neighbor configurations of Ce3+ and oxygen vacancies are the most stable arrangements for both surface and subsurface oxygen vacancies. Electron transfer between Ce3+ and Ce4+ centers corresponds to a polaron hopping involving the exchange of a 4f electron across the surface, with activation energies of about 0.3 eV. Activation barriers for oxygen atom migration on the surface strongly depend on the charge of the Ce ions surrounding the atom that actually moves. Namely, the migration is particularly facile when the migration occurs crossing the line through Ce4+ ions. The analysis also shows some coupling between polaron hopping and oxygen diffusion, suggesting that, for specific arrangements, the polaron hopping in some way assists the vacancy migration at the surface. The present results afford a quantitative illustration of the low barrier for the oxygen diffusion across the cerium oxide surface.
1. INTRODUCTION Cerium oxide or ceria (CeO2) has been one of the most studied materials during the past decade because of its outstanding properties in a variety of technological applications. This material is used as a catalyst in a diversity of processes such as automotive exhaust converters, water−gas shift reaction, production and purification of hydrogen, or crude oil refining.1−5 Initially, the promoting effect of ceria was attributed to the enhancement of the metal dispersion and the stabilization of the support toward thermal sintering.6,7 However, subsequent work has shown that ceria can act as a chemically active component as well, working as an oxygen reservoir able to release it in the presence of reductive gases and to stock it upon interaction with oxidizing gases.8−10 On the other hand, due to its relatively high oxygen ion conductivity, ceria is an interesting material as an electrolyte in hightemperature devices, such as solid oxide fuel cells or oxygen gas sensors.11,12 The suitability of ceria in this broad range of technological fields is due to the well-known ability of cerium to cycle between Ce3+ and Ce4+ oxidation states, on one side, and the easiness to create oxygen vacancies, on the other side. This ability, related to the reducibility of the material, is accompanied by a facile electron transfer across the bulk and surface, together with an easy oxygen transport, and later healing of the defects under oxidizing conditions. Understanding the behavior of surface reactive sites is essential to establish the reaction mechanisms, and a great effort has been made in recent years to describe the charge distribution in CeO2−x materials and thus rationalize the processes involved in ionic and electron migration.13 Electron mobility in ceria was first experimentally studied by Tuller and Nowick,14 who from electrical conductivity © 2013 American Chemical Society
measurements proposed a small polaron hopping mechanism in which electrons jump from a Ce3+ ion to a neighboring Ce4+ ion, according to the model developed by Holstein and Friedman.15,16 The mobility in CeO2−x was found to be activated, with an activation energy Ea = 0.40 eV at small x and increasing to 0.52 eV at x = 0.25. A similar conclusion was drawn from the work of Naik and Tien,17 though at very low vacancy concentration the activation energy reported was lower: 0.20 eV. From a theoretical point of view, the so-called hopping integral, t, a key quantity in the analysis of the electron mobility of a system, has been investigated. However, depending on the method to compute these values,18 a large discrepancy has been reported.13 In a recent work we have reported an ab initio prediction of this quantity based on quantum chemical calculations.19 The electron coupling matrix element, or hopping integral, was estimated to be 0.08 eV in bulk ceria, with an adiabatic activation barrier for the polaron hopping of 0.4 eV. Moreover the transmission coefficient κ was estimated to be 0.81, indicating that the electron transfer process is mainly adiabatic, confirming the earlier proposed adiabatic theory of small polaron and hopping conductivity in defective bulk ceria. Oxygen transport in ceria materials has been experimentally and theoretically studied too.1 On one hand, experiments have been performed to analyze the diffusion of oxygen vacancies in ceria and doped ceria. One of the most common techniques used to obtain activation energy for oxygen diffusion is the ac impedance analysis of the measured electrical conductivity. The barriers obtained range from 0.5 to 0.9 eV, a rather high value Received: July 5, 2013 Revised: October 17, 2013 Published: October 22, 2013 25497
dx.doi.org/10.1021/jp4066532 | J. Phys. Chem. C 2013, 117, 25497−25503
The Journal of Physical Chemistry C
Article
code solves the Kohn−Sham equations for the valence electron density within a plane-wave basis set and makes use of the projector augmented wave (PAW) method to describe the interaction between the valence electrons and the atomic cores.40,41 The valence electron density is defined by the twelve (5s25p66s25d14f1) electrons of each Ce atom and the six (2s22p4) electrons of each O atom. The plane-wave expansion includes all plane waves with kinetic energy smaller than a cutoff value set to 500 eV, which ensures adequate convergence with respect to the basis set. The GGA functional proposed by Perdew et al.42,43 (PW91) was selected. To take into account the on-site Coulomb correction, a Hubbard-like term was introduced according to the formalism due to Dudarev et al.,44 which makes use of a single Ueff parameter, hereafter denoted simply as Uf and Up, to design the effective values used for the Ce 4f and O 2p electrons, respectively. For Ce and O we have used a Uf and Up of 5 eV which leads to a moderately improved description of some critical aspects that concern structure, electronic properties, and thermochemistry of both CeO2 and Ce2O3.36,45 Forces on the ions were calculated through the Hellmann− Feyman theorem, including the Harris−Foulkes correction to forces.46 Iterative relaxation of the atomic positions was stopped when the forces on the atoms were
