Development of a ReaxFF reactive force field for intrinsic point defects in titanium dioxide

doi:10.1016/j.commatsci.2014.07.056

Computational Materials Science

Volume 95, December 2014, Pages 579-591

https://doi.org/10.1016/j.commatsci.2014.07.056 Get rights and content

Highlights

•
We developed a ReaxFF force field for titanium dioxide.
•
The main focus is the influence of intrinsic point defects.
•
The diffusion barriers of oxygen are studied with the developed force field.

Abstract

A reactive ReaxFF force field is developed for studying the influence of intrinsic point defects on the chemistry with TiO₂ condensed phases. The force field parameters are optimized to ab initio data for the equations of state, relative phase stabilities for titanium and titanium dioxide, potential energy differences for (TiO₂)_n-clusters (n = 1–16). Also data for intrinsic point defects in anatase were added. These data contain formation energies for interstitial titanium and oxygen vacancies, diffusion barriers of the oxygen vacancies and molecular oxygen adsorption on a reduced anatase (1 0 1) surface. Employing the resulting force field, we study the influence of concentration of oxygen vacancies and expansion or compression of an anatase surface on the diffusion of the oxygen vacancies. Also the barrier for oxygen diffusion in the subsurface region is evaluated using this force field. This diffusion barrier of 27.7 kcal/mol indicates that the lateral redistribution of oxygen vacancies on the surface and in the subsurface will be dominated by their diffusion in the subsurface, since both this barrier as well as the barriers for diffusion from the surface to the subsurface and vice versa (17.07 kcal/mol and 21.91 kcal/mol, respectively, as calculated with DFT), are significantly lower than for diffusion on the surface (61.12 kcal/mol as calculated with DFT).

Graphical abstract

Introduction

Titanium dioxide (TiO₂) is the natural occurring oxide of titanium, which exists in various polymorphs. The three most stable polymorphs are rutile, anatase and brookite, in that order of abundance. Thanks to its high reactivity, anatase is widely applied in photocatalysis [1] and solar energy conversion [2]. Especially the surface is critically important for these applications, and for this reason the interest in the chemical and physical properties of the surfaces has increased significantly in the past decades. The reader is referred to a review [3] for a summary of the research on TiO₂ surfaces.

The higher catalytic activity of anatase with respect to rutile is due to the behaviour of its intrinsic point defects. It is indeed well known that point defects strongly affect the physical and chemical properties of metal oxides. In heterogeneous catalysis the defect sites act as an initiator for adsorption of molecules and/or metal particles. In photocatalysis the defects influence the surface reactivity, either favourably or detrimentally. A favourable effect occurs when oxygen vacancies act as trap sites for photoexcited charge carriers such that these carriers are transported to the surface. A detrimental effect occurs when these oxygen vacancies act as recombination centers for these carriers which will lower the reactivity. Not only the “chemistry” is influenced significantly by these defects, but the diffusion of point defects also plays a key role in the mass transport between the surface and the bulk during surface preparation techniques such as annealing or sputtering [4].

The location of the defect determines its role and its properties. Density functional theory (DFT) calculations demonstrated that for an anatase (1 0 1) surface, which is the lowest energy and most exposed surface [5], [6], the subsurface oxygen vacancies are 0.5 eV more stable than surface vacancies [7]. The diffusion barriers of these defects from the surface region to the subsurface region are around 1 eV [7]. This indicates that surface oxygen vacancies, once formed, diffuse relatively easily to the subsurface, which is consistent with the low density of surface defects found experimentally with scanning tunneling microscopy (STM) [8], [9] and the high density of O vacancies indicated by ultraviolet photoemission spectroscopy (UPS) [10] that also accesses the subsurface region. Therefore, the subsurface oxygen vacancies will play a more prominent role than the surface vacancies; this is in contrast with rutile where the opposite trend is observed, both theoretically [4] as well as experimentally with STM [8], [9] and UPS [10]. Because of the differences in these trends, anatase has a higher catalytic activity than rutile. The subsurface defects have a longer lifetime than surface defects, because the latter will be quenched by molecules in the environment.

Because of the accuracy and speed of modern quantum mechanical (QM) methods, they can be used to calculate the energy and the geometry of molecules and solid state systems. Ab initio MD has also been extensively used to model dynamical processes of relatively large molecules adsorbed on solid state substrates. However to reach larger time and space scales, classical molecular dynamics simulations may be used as a complimentary technique. In this work, we developed a classical reactive force field for titanium dioxide for the ReaxFF method developed by van Duin and coworkers [11]. The main focus of this force field is the correct description of intrinsic point defects, oxygen vacancies and titanium interstitials in anatase. The developed force field thus allows larger spatial scale and longer time scale simulations of the titanium dioxide system compared to DFT, with comparable accuracy. For instance, in the LAMMPS implementation of ReaxFF [12], it is possible to simulate systems with 10⁶atoms at nanosecond timescales [13], [14], [15], [16]. Within LAMMPS there is also another variable-charge reactive force field implemented, namely the charge-optimized many-body potential (COMB) developed by Sinnott, Phillpot and coworkers [17], [18], [19], [20], [21], [22]. Also for COMB a parametrization for the titanium dioxide system has been developed [23].

Section snippets

ReaxFF

ReaxFF is a generic bond order dependent force field. In this method the forces are derived from the following energy expression: $E_{system} = E_{bond} + E_{over} + E_{under} + E_{lp} + E_{val} + E_{vdWaals} + E_{coulomb}$

The energy expression for the system consists of different partial contributions: bond energies (E_bond), energy penalties for over-coordination (E_over) and (optionally) stabilize under-coordination of atoms (E_over and E_under), lone-pair energies (E_lp), valence angle energies (E_val) and terms to handle non-bonded van

Results and discussion

In this section we will compare the ReaxFF calculated data, the data added to the training set and the data as calculated with other ReaxFF force fields [30], [31], [32]. These data consist of the equations-of-state, relative phase stabilities, TiO₂-cluster stabilities, formation energies of interstitial titanium and oxygen vacancies, diffusion barriers of the oxygen vacancies and oxygen adsorption energies on a reduced anatase (1 0 1) surface. This comparison between the data as calculated with

Conclusions

We developed a ReaxFF reactive force field for studying the influence of intrinsic point defects on the chemistry of TiO₂ condensed-phases. The ReaxFF parameters were fitted against DFT and experimental data to reproduce the equations-of-state, TiO₂-cluster stabilities, defect formation energies, defect diffusion barriers and oxygen adsorption energies. All important data are reproduced quite satisfactory. In comparison with two other recently developed ReaxFF force fields for TiO₂, the current

Acknowledgements

Stijn Huygh is funded as aspirant of the Research Foundation Flanders (FWO, Brussels, Belgium). This work was carried out in part using the Turing HPC infrastructure at the CalcUA core facility of the Universiteit Antwerpen (UA), a division of the Flemish Supercomputer Center VSC, funded by the Hercules Foundation, the Flemish Government (department EWI) and the UA.

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Development of a ReaxFF reactive force field for intrinsic point defects in titanium dioxide

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

ReaxFF

Results and discussion

Conclusions

Acknowledgements

Surf. Sci. Rep.

Surf. Sci.

Catal. Today

Comput. Mater. Sci.

Surf. Sci.

Surf. Sci.

Mater. Sci. Eng. A

Surf. Coat. Technol.

J. Chem. Rev.

Nature

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. B

J. Phys. Chem. A

J. Comput. Phys.

Phys. Rev. Lett.

Phys. Rev. Lett.

Appl. Phys. Lett.

J. Phys. Chem. A

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

J. Phys.: Condens. Matter

Annu. Rev. Mater. Res.

J. Am. Chem. Soc.

J. Phys. Chem. A