Article pubs.acs.org/JPCC
Microscopic View of Nucleation in the Anatase-to-Rutile Transformation Ya Zhou† and Kristen A. Fichthorn*,†,‡ †
Department of Chemical Engineering and ‡Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: We use molecular simulation techniques to investigate the anatase-torutile transformation in TiO2 nanocrystals. A thermodynamic analysis indicates that edge and corner atoms significantly influence the critical size at which rutile nanocrystals become energetically preferred over anatase. We use molecular dynamics simulations to probe kinetics of the transformation in individual anatase nanocrystals as well as in nanocrystal aggregates. We follow structural evolution using simulated Xray diffraction. Additionally, we develop a local order parameter to distinguish individual Ti ions as anatase, rutile, or anatase {112} twin-like. We apply our local order parameter to track the formation and growth of rutile nuclei. Anatase {112} twins form easily at surfaces and interfaces of nanocrystal aggregates, and we observe that rutile forms among the twins. Stable rutile nuclei maintain {101} facets during growth as a result of nucleation from layers of alternating anatase {112} twins. Our results are in agreement with experiment and indicate the central role of {112} twinlike anatase in the transformation.
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INTRODUCTION Nanocrystalline titania (TiO2) has attracted considerable attention because of its high photocatalytic activity, which is beneficial for applications in green energy technologies, such as electrolysis and solar cells.1−5 Among the three well-known, naturally occurring polymorphs of titania, rutile is the equilibrium phase in the bulk form,6,7 whereas anatase becomes the most stable phase on the nanometer size scale because of its lower surface energy.8−11 In single-phase nanoparticles, there is evidence that the photoactivity of TiO2 is enhanced as the nanocrystal size is reduced due to the high density of localized electron states and the resultant high capacity to adsorb reactive species at the surfaces of small particles.12,13 Between the two competing phases, it is generally considered that the performance of anatase is superior to that of rutile as a result of larger specific surface area and higher photoactivity per unit area on the anatase surfaces.14 However, some mixed-phase TiO2 nanoparticles with coexisting anatase and rutile exhibit enhanced photoactivity, possibly due to the separation of charge carriers in different phases that suppresses electron− hole recombination.15 This points to the possibility of achieving optimized performance through careful control of phase composition. To achieve precise control of the phase composition of nanocrystalline titania, a comprehensive understanding of the structural transformation between anatase and rutile is useful. Experimentally, factors such as particle size and morphology, surface chemistry, concentration of intrinsic defects and impurities, and temperature have been observed to influence the transformation.16−24 On the theoretical side, first-principles calculations can be utilized to predict Wulff shapes and the crossover size at which the free energy of a rutile nanocrystal © 2012 American Chemical Society
becomes lower than that of anatase as the nanocrystal size increases.19,25−28 It is difficult, however, to characterize kinetics of the anatase-to-rutile transformation using first-principles calculations. Kinetic aspects of this transformation can be probed in molecular dynamics (MD) simulations based on semiempirical potentials. To date, studies of this type have focused on simulated X-ray diffraction (XRD).29,30 Whereas XRD patterns provide a measure of the overall ordering within a nanostructure, they do not reveal local structure or directly indicate the mechanisms of the structural transformation. In this study, we define a local order parameter to resolve structural units of TiO2 that are relevant to the anatase-to-rutile transformation. We employ our local order parameter in classical MD simulations to track the nucleation and growth of rutile in single anatase nanoparticles and nanoparticle aggregates. These detailed studies shed light on the microscopic aspects of this transformation.
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METHODS We perform MD simulations using the DL_POLY package, version 2.20.31 To describe Ti and O interactions, we use the Matsui−Akaogi force field, which treats Ti and O ions as partially charged spheres in the form32 ⎛ r ⎞ C qiqj ij ij U (rij) = A ij exp⎜⎜ − ⎟⎟ − + rij rij6 ⎝ ρij ⎠
(1)
Received: February 7, 2012 Revised: March 22, 2012 Published: March 23, 2012 8314
dx.doi.org/10.1021/jp301228x | J. Phys. Chem. C 2012, 116, 8314−8321
The Journal of Physical Chemistry C
Article
where U(rij) is the interaction potential between ions i and j that are separated by distance rij, and the partial charges q are +2.196 and −1.098 for Ti and O ions, respectively. The values of parameters A, ρ, and C can be found in ref 32. Considering accuracy and efficiency, the Matsui−Akaogi force field is considered to be a good choice among available force fields for MD simulations of TiO2.33−35 We perform simulations in the canonical ensemble with a time step of 1.0 fs using the Nosé− Hoover thermostat to control the temperature. No periodic boundary conditions are imposed, and every atom interacts explicitly with all other atoms in the system.
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RESULTS Thermodynamic Analysis. Similar to experimental and first-principles studies, the Matsui−Akaogi force field that we use for our simulations predicts that anatase will be the most stable phase of TiO2 for small particles and that rutile will be favored for sufficiently large particles. To determine the critical size at which rutile is preferred over anatase, we characterize energies of anatase and rutile nanocrystals with low-energy Wulff shapes. Wulff-shaped anatase nanocrystals have been observed experimentally, with sizes down to
