A Joint Theoretical and Experimental Study of Phase Equilibria and

Dec 4, 2014 - The three-way catalyst (TWC) serves a critical role in automotive ..... the phase diagram at 300 °C features TiO2 (B), PtO2, and CaO as...
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A Joint Theoretical and Experimental Study of Phase Equilibria and Evolution in Pt-Doped Calcium Titanate under Redox Conditions Baihai Li,†,‡ Michael B. Katz,‡ Yingwen Duan,‡ Xianfeng Du,‡ Kui Zhang,‡ Liang Chen,§ Anton Van der Ven,∥ George W. Graham,‡ and Xiaoqing Pan*,‡ †

School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China ‡ Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States § Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, People’s Republic of China ∥ Materials Department, University of California, Santa Barbara, California 93106, United States S Supporting Information *

ABSTRACT: Pseudoternary phase diagrams of the PtOx− CaO−TiOx system were constructed using first-principles theoretical methods to interpret experimental observations of phase formation and evolution in Pt-doped CaTiO3 made by aberration-corrected scanning transmission electron microscopy. In this system, promoted as a self-regenerative automotive exhaust-gas catalyst, Pt precipitates as metallic particles from the doped perovskite under reducing conditions and tends to redissolve under oxidizing conditions. Due to the likely influence of kinetic limitations on experimental observations, we focus on a restricted (metastable) phase diagram in which single and other unobserved oxides of Pt are intentionally excluded. Various titanate phases appear, however, and their presence helps inform the calculation of the phase diagrams, which in turn confirm that the self-regenerative effect is a consequence of thermodynamic phase stability under the specific redox environments examined.

1. INTRODUCTION The three-way catalyst (TWC) serves a critical role in automotive emissions control by promoting the removal of harmful CO, NOx, and unburned hydrocarbons from the exhaust stream.1 This comes at the cost, however, of consuming the plurality of the world’s supply of Pt, Pd, and Rh, driving demand for these materials, raising their prices, and limiting their availability for other consumer and industrial applications.2 While these metals are essential ingredients in the TWC, significantly lower levels would suffice if only a long-standing problem, metal particle coarsening, which presently leads to an ultimate effective utilization efficiency of about 1%, could be somewhat alleviated.3 A decade ago, the development of a socalled “intelligent catalyst”, in which a perovskite oxide support supposedly helps to maintain a high metal dispersion by taking advantage of the cyclical redox environment present in the exhaust gas, was thus met with much scientific fanfare.4,5 Although it generated several follow-up reports from several groups in the intervening years,6−9 the intelligent catalyst has had little industrial utilization, possibly for reasons that have recently become clear from our experimental studies using advanced atomic-resolution transmission electron microscopy.10,11 The basic concept underlying the intelligent catalyst is not invalid, however, and we have subsequently endeavored to conduct a © 2014 American Chemical Society

more fundamental study of one of the prototypical systems, Pt supported on CaTiO3, to both more clearly understand the theoretical underpinnings of the original concept and explain some of the unexpected observations from our experimental work. In brief, we exploit density functional theory (DFT) and thermodynamic simulations in an attempt to model the phase equilibria of the Ca−Ti−Pt−O system and elucidate the thermodynamic processes by which the various phases appear and disappear under redox cycling.

2. METHODOLOGY 2.1. Thermodynamic Description. The mechanism of the intelligent catalyst relies on changes in thermodynamic phase stability with oxygen partial pressure. At high oxygen partial pressure (or equivalently, high oxygen chemical potential), Pt is expected to dissolve into the perovskite substrate, while at low oxygen partial pressures or high temperatures, the solubility of Pt in the perovskite substrate decreases, resulting in driving forces for Pt reprecipitation. In the ideal intelligent catalyst, Pt precipitation would only occur on the substrate surface and not within the substrate. This mechanism would allow the dissolution of coarsened Pt particles by increasing the oxygen partial Received: June 19, 2014 Revised: November 30, 2014 Published: December 4, 2014 18

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pressure, followed by the reprecipitation, but on a much finer scale, of new Pt particles upon reduction of the oxygen partial pressure. Phase stability in equilibrium is determined by minimizing an appropriate characteristic thermodynamic potential. The form of the characteristic potential is determined by the particular thermodynamic boundary conditions imposed on the system. We treat the orthorhombic CaTiO3 substrate with the symmetry of Pbnm, which is a stable phase at the temperatures below 1112 °C,12 together with the Pt particles as our system. Our system is therefore a quaternary one consisting of Ca, Ti, Pt, and O. Experimentally, we can control the pressure (kept at atmospheric pressure), the temperature, and the number of Ca, Ti, and Pt atoms. In contrast to the Ca, Ti, and Pt atoms, the oxygen concentration is not controlled. Instead, the oxygen chemical potential μO is controlled experimentally because the system is able to exchange oxygen with the gas phase, which is kept at constant oxygen partial pressure. The appropriate characteristic thermodynamic potential to be minimized is obtained by applying a Legendre transform to the internal energy for each intensive thermodynamic state variable controlled experimentally. In the present example, these intensive thermodynamic variables are T, P, and μO, and the characteristic thermodynamic potential reduces to a grand canonical free energy Λ = U − TS + PV − μONO

accounting for these configurational degrees of freedom, we can study the dissolution of Pt in the CaTiO3 perovskite and its subsequent reprecipitation as a function of oxygen partial pressure. Although contributions to the free energies from vibrational excitations can affect the prediction of phase stability, we neglect them here. We do not expect the inclusion of vibrational excitations to alter important qualitative predictions reported on here. The most important contribution to the dependence of phase stability on temperature and oxygen partial pressure arises from the solid to gas reaction entropy, where the entropy of the gas phase overwhelms other entropic contributions from the solid phases.13 2.2. Computational Methods. 2.2.1. Total Energies Determined from First-Principles. All first-principles total energy calculations were performed within the framework of density functional theory as implemented in the Vienna Ab Initio Simulation Package (VASP).24 Electron exchange and correlation were treated within the generalized gradient approximation (GGA) using the Perdew−Wang exchangecorrelation functional (PW91).25 The projector augmented wave (PAW) method26 was used for the treatment of the core electrons. A soft oxygen pseudopotential with valence configuration 2s22p4 and default cutoff energy of 250 eV was used. Pseudopotentials with valence configurations 3d0.014s2, 3d14s1, and 5d96s1 were chosen for Ca, Ti, and Pt, respectively. The cutoff energy for the plane wave basis was set to 400 eV. All calculations were performed spin polarized. The atomic positions and unit cell parameters were fully relaxed to minimize the total energy. Hence all calculations were performed at zero pressure. As reference states for the grand canonical free energies, we used the energies of the bulk phases of Ca, Ti, and Pt. We therefore work with grand canonical formation energies defined as

(1)

where U is the internal energy, S is the entropy and NO is the number of oxygen atoms in the system. Implicit in the above characteristic potential is an assumption that the substrate and Pt particles are under a hydrostatic stress state. We therefore neglect the role of anisotropic strain energy due to epitaxial coherency in our thermodynamic analysis of phase stability. We also neglect contributions from surface and interface free energies, which can become important when precipitates have sizes on the order of nanometers. The above potential is extensive (i.e., scales with the size of the system), and it is convenient to normalize it by the total number of Ca, Ti, and Pt, denoted by Ntot = NCa + NTi + NPt.13 The normalized characteristic potential becomes

λ = Λ/Ntot

Δλ α =

where E is the DFT total energy for the particular phase α. The reference energies eCa, eTi and ePt are the DFT energies of bulk Ca in the face-centered cubic (fcc) crystal structure, bulk Ti in the hexagonal close-packed (hcp) crystal structure and bulk Pt in the fcc crystal structure, all per atom. To relate the oxygen chemical potential to the oxygen partial pressure and the temperature, we use:27

This grand canonical free energy has as natural variables, T, P, xCa = NCa/ Ntot, xTi = NTi/Ntot, xPt = NPt/Ntot, and μO. The equilibrium state is determined by minimizing the total grand canonical free energy of the system with respect to internal degrees of freedom such as crystal structure and if several phases coexist, their phase fractions and solubility limits. Phase stability at fixed intensive variables, T, P, and μO, can be represented in a ternary composition phase diagram spanned by xCa, xTi, and xPt. Graphically, phase stability at fixed intensive variables is determined by the common tangent construction to the grand canonical free energies in ternary composition space.13 Having set up the thermodynamic framework, it is next necessary to calculate the grand canonical free energies, λ for all the phases competing for stability. At 0 K, the grand canonical free energy of a phase α reduces to

μO(T , p) = =

1 [μ (T ) + kT ln(p)] 2 O2

3/2 ⎧ ⎡ ⎤ ⎛ p⎞ 1 ⎪ ⎢⎛ 2π(m1 + m2)kT ⎞ kT ⎥ 8π 2IkT kT ⎨ − ln ⎜ + ln⎜⎜ ⎟⎟ − ln ⎟ 2 ⎠ p0 ⎥⎦ 2 ⎪ h 2h2 ⎝ p0 ⎠ ⎩ ⎢⎣⎝ ⎫ ⎪ |D | hv + + ln(1 − e−hv / kT ) − e − ln ωe1⎬ ⎪ kT 2kT ⎭ (5)

where k is the Boltzmann constant, m is the mass of an oxygen atom, h is Planck’s constant, p0 is the standard atmospheric pressure, I is the moment of inertia, and De is the energy of an O2 molecule as calculated with DFT. It is well-known that conventional first-principles methods based on DFT overestimate the binding energy of the O2 molecule, resulting in large errors in the calculation of redox energies.13,28,29 To compensate for this error, we add 0.33 eV to the total energy of O2 in our work, as suggested by Lee et al.30 We set De equal to −8.75 eV (the VASP calculated total energy is −9.08 eV) in our calculations, which is very close to the value obtained by Lee et al.30 In eq 5, the contribution from atomic vibrations and electronic excitations is negligible. Equation 5 can therefore be rewritten as

α

α

(4)

α

(2)

1 λ = (E α + PV α − μONOα) Ntot

1 α α (E α − NCa eCa − NTi e Ti − NPtα ePt − μONOα) Ntot

(3) α

where E is the energy of the phase at 0 K, V is the volume of the phase at 0 K, and NαO is the number of oxygen in the phase. At finite temperature, entropy becomes important and thermal excitations contribute to the thermodynamic averages of state variables and potentials. In crystalline phases the most important contributions to the entropy arise from vibrational and configurational excitations. Configurational excitations are especially important in multicomponent solids that form solid solutions but can often be neglected in solids that form line compounds. In this work, we use first-principles electronic structure methods based on density functional theory to calculate energies of all the phases that compete for stability in the Ca, Ti, Pt, and O quaternary. While we neglect the contributions of harmonic14 and anharmonic vibrational excitations15−19 to the grand canonical free energies, we rigorously account for configurational excitations associated with Pt dissolved over the Ti sublattice of the CaTiO3 perovskite crystal structure.20−23 By

μO(T , p) =

⎧ 3/2 ⎛ p⎞ 1 ⎪ ⎡⎢⎛ 4πmkT ⎞ kT ⎤⎥ ⎜⎜ ⎟⎟ ⎜ ⎟ kT ⎨ ln ln − + 2 2 ⎪ ⎝ p0 ⎠ ⎩ ⎢⎣⎝ h ⎠ p0 ⎥⎦ − ln

19

⎪ |D | ⎫ 8π 2IkT − e⎬ 2 kT ⎪ 2h ⎭

(6)

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KrF excimer laser operated at 248 nm, with Pt:CaTiO3 films grown at both 600 and 750 °C. LaAlO3 (110) and SrTiO3 (100) single crystal substrates were supplied by MTI Corporation. Thermal processing was performed in a quartz tube in a tube furnace. Dry air was flowed through the tube at 450 sccm and 10% H2 (balance N2) at 100 sccm for oxidation and reduction treatments, respectively. These conditions mimic those in the original work.5 Cross-sectional transmission electron microscopy (TEM) specimens were then fabricated by mechanical thinning and polishing on diamond lapping media, followed by Ar-ion milling (Gatan PIPS, model 691) to electron transparency. Specimens were examined in a probe Cscorrected JEOL JEM-2100F electron microscope operated at 200 kV and equipped with electron energy-loss spectroscopy (EELS) and X-ray energy dispersive spectroscopy (XEDS) detectors. Wavelength dispersive spectroscopic (WDS) analyses of both PLD targets and films were performed on a Cameca SX-100 electron microprobe analyzer.

This expression for the oxygen chemical potential has a very similar dependence on temperature and oxygen partial pressure as that used by Reuter and Scheffler.31 Qualitatively, eq 6 indicates that a more positive μO corresponds to lower T, higher p, or both, while a more negative value corresponds to higher T, lower p, or both. Also, the oxygen chemical potential can be quantitatively converted to the temperature at a given oxygen partial pressure or to the oxygen partial pressure at a given temperature by this equation. 2.2.2. Cluster Expansion and Monte Carlo Simulations. The perovskite based CaTiO3 phase is capable of substitutionally dissolving Pt on the Ti sublattice. The resulting disorder over the Ti sublattice produces configurational entropy that contributes to the grand canonical free energy of this phase. To account for the configurational entropy, we use the cluster expansion formalism.22 Each B sublattice site i of the perovskite based (ABO3) form of CaTiO3 is assigned an occupation variable σi that is +1 if occupied by Pt and −1 if occupied by Ti. The collection of occupation variables, σ⃗ = {σ1,...,σi,...,σM} then uniquely specifies the arrangement of Ti and Pt within the perovskite phase. Any property of the crystal that depends on how the Ti and Pt are ordered can be expanded in terms of polynomials of the occupation variables according to22

E(σ )⃗ = Vo +

∑ Vγϕγ (σ )⃗

3. RESULTS AND DISCUSSION 3.1. Analytical Microscopy. The Pt:CaTiO3 epitaxial thin films, as grown, were apparently homogeneous and comprised a single perovskite phase. Scanning transmission electron microscopic (STEM) examination revealed no second phases, with the Pt well-distributed (Supporting Information, Figure S1). The high-temperature films (Tg = 750 °C) were smooth, whereas the low-temperature films (Tg = 600 °C) were lamellar, as we have previously reported,11 with the lamellae aligning along the beam direction, hence manifesting as an apparent columnar structure in the cross-sectional high angle annular dark field (HAADF) images. Morphology aside, the films appear identical at the atomic scale and behave in a congruent fashion upon redox aging. The thin films were exposed to reducing conditions (800 °C, 10% H2/N2, 1 h) in order to induce the extrusion of metallic Pt from the perovskite matrix. As we have reported previously, and as is shown in Figure 1, the metal does not exit the perovskite to a free surface (to any significant degree above that expected by random chance), as prior literature asserts, but coalesces into Pt clusters and particles of varying size and character within the oxide matrix itself. Most of the Pt clusters are 1−2 nm in diameter and appear in images simply as diffuse objects, but having definite increase in the HAADF contrast, though their chemical identity as Pt has been confirmed by XEDS. The phase identity of these smallest clusters, however, remains unknown because of the lack of a distinct crystal structure in the images. This alone does not discount the possibility of crystallinity, as it could simply be lacking a favorable zone axis alignment with the electron probe, but leaves open the possibility (through analysis of images alone) of the clusters being any of the following: a metallic Pt particle, any oxide of Pt, a high local concentration of PtTi-substituted perovskite (i.e., CaPtO3), or a cluster of interstitial Pt. Our assumption, however, owing to the reducing nature and high temperature of the reduction treatment, is that these clusters are indeed metallic. Also present are 1−3 nm fcc Pt particles that are epitaxial to the surrounding perovskite matrix with orientation relationships of either [100](010)Pt∥[100](010)CTO (cube-oncube epitaxy) or [100](011)Pt∥[100](010)CTO (45° rotation about a primary axis), with the CaTiO3 crystal treated for this purpose as pseudocubic. Finally, there is a population of 2−5 nm nonepitaxial fcc Pt particles that form both on the free surfaces (and interlamellar surfaces of the low-temperature film) and on internal defect surfaces. The oxide itself in the CaTi0.95Pt0.05O3 films also underwent significant local phase transformations in the vicinity of the Pt clusters that had nucleated upon reduction. Small 2−15 nm

(7)

γ

where Vo and Vγ are expansion coefficients and ϕγ (σ )⃗ =

∏ σj (8)

j∈γ

are cluster basis functions constructed by taking the products of occupation variables of sites, j, belonging to differently sized clusters of sites, γ, such as pairs, triplets, quadruplets, and so on. While the expansion extends over all distinct clusters of sites, it must be truncated to be tractable. The expansion coefficients, Vo and Vγ, are referred to as effective cluster interactions (ECI) and can be determined by fitting a truncated cluster expansion to energies of different configurations as calculated with a first-principles electronic structure method. A genetic algorithm was used to determine the optimal set of clusters to be included in the cluster expansion32 that minimizes the cross validation score, a criterion for the quality of the cluster expansion in predicting energies not included in the fit. Converged cluster expansions are capable of predicting the energies of configurations not used in the fit with close to first-principles accuracy,20,21 making them ideally suited for Monte Carlo simulations. Grand canonical Monte Carlo simulations were employed to calculate thermodynamic averages, including the average Pt concentration, xP̅ t over the Ti sublattice of CaTiO3 as a function of temperature and difference in chemical potential, μ̃ = μPt − μTi. The Gibbs free energy at fixed temperature was calculated by integrating the relationship between xP̅ t and μ̃ according to g (x Pt ̅ , T ) = g (x Pt ̅ = 0, T ) +

∫x

x Pt ̅ Pt ̅ =0

μ ̃dx Pt ̅

(9)

The free energy of the reference state at xP̅ t =0 can be set equal to the energy of CaTiO3 where, due to perfect stoichiometry, configurational entropy is absent. The above free energy only accounts for configurational excitations and neglects contributions from vibrational excitations. The Gibbs free energy of CaTi1−xPtxO3 can be converted to a grand canonical free energy, eq 1, by applying a Legendre transform with respect to the oxygen chemical potential after renormalization. 2.3. Experimental Methods. Pulsed laser deposition (PLD) targets were constructed from CaTi0.95Pt0.05O3 and Ca1.1Ti0.9Pt0.1O3 powders, which were synthesized using the citrate method. Stoichiometric amounts of Ca(NO 3 ) 2 ·4H 2 O, Ti[O(CH 2 ) 3 CH 3 ] 4 , and PtC10H14O4 (Alfa Aesar) were dissolved in deionized water with citric acid, with nitric acid used to control the solution pH. The solution was dehydrated at 100 °C and held at 60 °C until gelation, after which it was calcined at 800 °C in flowing oxygen. The resultant powder was then pressed and sintered at 1200−1300 °C to form a dense PLD target. Film growth was performed in an ultrahigh vacuum growth chamber using a 20

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low-Ca regions corresponding to the TiO2 phase and disordered regions. We therefore sought to determine experimentally the stoichiometry of the thin film, as well as the originating PLD target by XWDS. Though the target had a nominal stoichiometry of Ca0.958Ti0.979Pt0.042O3 (cation concentrations normalized to a fully oxygenated state), close to the desired CaTi0.95Pt0.05O3, the resultant thin film had a stoichiometry of Ca0.858Ti1.057Pt0.014O3. It is apparent that Ti was less volatile or had a higher affinity for the substrate during growth than Ca and Pt. In contrast to the film with nominal composition CaTi0.95Pt0.05O3, the Ca1.1Ti0.9Pt0.1O3 film contained no such anomalous TiO2 or Ti-enriched semicrystalline regions. In this case, XWDS reveals the stoichiometries of the target and film to be Ca1.138Ti0.838Pt0.093O3 and Ca0.976Ti0.923Pt0.089O3, respectively (again, normalized to a fully oxygenated state). For ease of p resentat ion, we will refer to th ese films as A (Ca0.858Ti1.057Pt0.014O3) and B (Ca0.976Ti0.923Pt0.089O3), noting their actual compositions as needed below. The thin films were then exposed to a subsequent oxidation treatment (800 °C, 20% O2/N2, 1 h) to induce dissolution of the Pt clusters into the perovskite phase. Most of the very small (1−2 nm) Pt clusters have dissolved into the perovskite and no longer appear under HAADF-STEM imaging, as shown for film A in Figure 2. There still remain, however, some larger (2−3 nm) Figure 1. (a) Low-magnification HAADF-STEM images of the film with nominal composition CaTi0.95Pt0.05O3 after reduction treatment as well as high-magnification detailing (b) various types of epitaxial and indistinct Pt clusters, (c) TiO2 (A) and TiO2 (B) inclusions, and (d) an amorphous oxide inclusion surrounding a Pt clusters. (e) Conventional TEM image and corresponding Ca and Ti EFTEM images of the film showing Ti-enriched regions but no complementary Ca-enriched regions (the arrow points to the LaAlO3 substrate, from the direction of the film surface.) The actual composition of the film, approximately Ca0.858Ti1.057Pt0.014O3, was determined by XWDS, as discussed in the text.

regions of second phases formed epitaxially to the surrounding perovskite matrix. These phases were identified as the anatase phase and bronze phases of TiO2 [TiO2 (A) and TiO2 (B), respectively] by their crystal structure as imaged in HAADFSTEM and their stoichiometrythe absence of Ca relative to the surrounding matrixas probed by EELS. The bronze phase regions are heavily twinned due to the lattice mismatch with the surrounding perovskite. A further unexpected phenomenon was the appearance of small 2−10 nm regions in which the crystalline ordering has degraded. These disordered regions nearly universally surround or are adjacent to Pt clusters. Upon close examination, very small areas of the disordered regions, comprising only several atomic columns, appear to take on crystalline motifs resembling those of the TiO2 (A) and TiO2 (B) structures. ELNES reveals a decrease in Ca content with a commensurate increase in the fraction of Ti3+ relative to Ti4+. We should emphasize that these titanate phases formed only in the films synthesized from the CaTi0.95Pt0.05O3 target and not in those from the Ca1.1Ti0.9Pt0.1O3 target. The latter contained only the Pt-associated formations. It is notable that, while several phases of TiO2 and Ti-enriched regions were found and identified within the CaTi0.95Pt0.05O3 film, analogous regions of high Ca concentration were not identified. The most likely phase for Ca to take up would be the rock salt phase, none of which was identified from HAADFSTEM imaging. Furthermore, EFTEM imaging revealed no highCa regions in the film above the perovskite background, only

Figure 2. HAADF-STEM image of film A after reoxidation.

internal Pt clusters and most of the metallic Pt particles that had formed along internal surfaces during reduction. The metallic Pt particles that had formed on the free surfaces of the lamellar film have coarsened into larger particles, something that is expected given the well-known tendency of metallic Pt to coarsen under oxidizing conditions. Gone also are the disordered regions, having either formed into a TiO2 phase or reformed into the perovskite phase. The details of these transformations, after both reduction and reoxidation, are presented in our recent work.11 3.2. First-Principles Thermodynamic Phase Stability. The observed phases as a function of oxygen partial pressure and temperature are presumably those that form in either stable or metastable thermodynamic equilibrium. Equilibrium at constant oxygen partial pressure is determined by minimizing a grand canonical free energy (see the Methodology section). Kinetic limitations may suppress the formation of phases that are absolutely stable such that the system falls into a metastable equilibrium. Metastable equilibrium can be analyzed by 21

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Figure 3. (a) A comparison of the first-principles (VASP) calculated and cluster expansion predicted formation energies of different Pt−Ti arrangements over the B sites of the CaTi1−xPtxO3 having the perovskite crystal structure. The free energy at 100 °C as a function of Pt concentration as calculated using chemical potential versus concentration data from Monte Carlo simulations is also shown. (b) The chemical potential as a function of Pt concentration in CaTi1−xPtxO3 at 100 and 800 °C, calculated with grand canonical Monte Carlo simulations.

Figure 4. Calculated CaOx−TiOy−PtOz pseudoternary phase diagrams at various temperatures under reducing conditions. The blue line denotes the stability of the solid solution of CaPtxTi1−xO3 having the perovskite crystal structure. The red and blue points denote the compositions of experimental samples A and B, respectively.

minimizing the grand canonical free energy in the absence of phases that are deemed too difficult to form kinetically. We

calculated equilibrium and metastable equilibrium phase diagrams as a function of temperature and oxygen chemical 22

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Figure 5. Calculated CaOx−TiOy−PtOz pseudoternary phase diagrams at various temperatures under oxidizing conditions. The red and blue points denote the compositions of experimental samples A and B, respectively.

crystal. We calculated the energies of 135 different Ti−Pt configurations over the b-site of the perovskite crystal structure and used these to fit the coefficients of a cluster expansion. The resulting cluster expansion contains 28 clusters consisting of the empty and point clusters, 11 pairs, 9 triplets, and 6 quadruplets. The cross-validation score for the cluster expansion is 3.3 meV/ f.u. (formula unit) with a root-mean-square (rms) error of 1.4 meV/f.u. Figure 3 compares the formation energies of CaTi1−xPtxO3 configurations as calculated with DFT-PW91 (VASP) and as predicted with the cluster expansion (the formation energies in Figure 3a are relative to the energies of CaTiO3 and CaPtO3). Clearly, the cluster expansion is able to describe the first-principles DFT energies with high accuracy. The cluster expansion was subsequently subjected to grand canonical Monte Carlo simulations. Figure 3b shows the dependence of the chemical potential difference, μ̃ = μPt − μTi, as a function of average Pt concentration xP̅ t. The absence of kinks and plateaus in the chemical potential curve indicates that Pt dissolves into CaTiO3 as a solid solution above room temperature, without forming stoichiometric ordered compounds. The ordered ground states predicted to be stable at 0

potential (i.e., oxygen partial pressure) by minimizing the normalized grand canonical free energy with respect to all or a subset of the compounds reported to exist in the Ca−Ti−Pt−O quaternary, listed in Table S1 (Supporting Information). Phase stability at fixed T, P, and μO can be determined by applying the common tangent construction to the normalized grand canonical free energies within the ternary composition space spanned by xCa, xTi, and xPt.13 This was done by constructing the convex hull with respect to the grand canonical free energies of all considered phases in this ternary composition space. With the exception of the orthorhombic perovskite based CaTiO3−CaPtO3 mixture (Supporting Information, Figure S3), all phases were treated as line compounds and their grand canonical free energy was calculated using only 0 K DFT energies. Because a crucial component of the intelligent catalyst mechanism relies on the dissolution of Pt within the CaTiO3 phase, we need to account for the contribution of configurational entropy to the grand canonical free energy of this phase. To this end, we parametrized a cluster expansion describing the dependence of the energy of CaTi1−xPtxO3 on the arrangement of Ti and Pt over the b-site of the orthorhombic perovskite 23

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Figure 6. Metastable phase diagrams as calculated without including oxides of Pt under reducing conditions. The red and blue points denote the compositions of experimental samples A and B, respectively.

calculated phase diagrams shown in Figures 4 and 5 are the full set of calculated CaOx−TiOy−PtOz pseudoternary phase diagrams in which we considered all thermodynamically stable oxides of Pt. Because it is not trivial to correlate an oxygen chemical potential in the energy calculations to a specific reducing atmosphere used in real experiments, phase diagrams were also calculated for extremely reducing atmospheres (Supporting Information, Figure S6). Under reducing conditions, as shown in Figure 4, the phase diagram at 300 °C features TiO2 (B), PtO2, and CaO as the ternary end members, with CaPtO3, CaTiO3, Ca2Pt3O8, Ca4PtO6, and CaTi5O11 [a TiO2 (B)-related structure] also appearing. The phase diagram also shows a solid solution along part of the line drawn between CaPtO3 and CaTiO3 with composition CaTi1−xPtxO3. This solid solution is denoted by the thick blue line in this and subsequent figures. The triangles in the phase diagram correspond to three phase regions. Any composition within a triangle will form a three-phase mixture in equilibrium consisting of the compounds that make up the corners of the triangle. Lines in the phase diagram denote twophase equilibria between the compounds defining the end points of the line. The measured compositions of films A and B are

K (i.e., the points on the 0 K convex hull in Figure 3a) disorder at temperatures below room temperature. Integration of the chemical potential difference using eq 9 yields the Gibbs free energy. An example of a calculated Gibbs free energy curve is shown in Figure 3a. Due to configurational entropy, the Gibbs free energy falls below the 0 K convex hull enveloping the ground state formation energies. The Gibbs free energies were converted to grand canonical free energies of the form of eq 1 by applying a Legendre transform with respect to the oxygen chemical potential followed by normalization to put it in the form of eq 2. 3.3. Comparison of First-Principles Predicted Phase Stability with Experiment. We primarily focus our attention on the evolution of phases at temperatures between 100 and 800 °C, mirroring those temperatures accessed during our experiments, and in oxygen partial pressures (PO2) of 0.2 and 1 × 10−8 atm, representing oxidizing and reducing conditions, respectively. Pseudoternary phase diagrams were calculated by minimizing the grand canonical free energies of all compounds reported to exist within the Ca−Ti−Pt−O system (Supporting Information, Table S1). Phase diagrams were calculated at intervals of 100 °C between 100 and 1200 °C for PO2 = 0.2 atm and between 100 and 800 °C for PO2 = 1 × 10−8 atm. The 24

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Figure 7. Metastable phase diagrams as calculated without including oxides of Pt under oxidizing conditions. The red and blue points denote the compositions of experimental samples A and B, respectively.

°C, respectively, with the perovskite phase with dissolved Pt existing even above 1100 °C, the highest temperature calculated. The Ca2Pt3O8 and Ca4PtO6 phases are stable until 1000 °C. These calculated phase diagrams of Figures 4 and 5 do not accurately reflect the experimental data presented above. The measured compositions of the thin films A and B put them slightly within or on the edge of the PtOx−CaTiO3−CaTi5O11 phase field under reducing conditions and within the Ca2Pt3O8− CaTiO3−CaTi5O11 phase field under oxidizing conditions at 800 °C in the calculated phase diagrams. This means that, independent of oxygen partial pressure, the films should consist of a stoichiometric CaTiO3 perovskite phase, without any dissolved Pt, along with CaTi5O11 and a either pure Pt or Ca2Pt3O8 at 800 °C. The experimental data would dictate that Pt is soluble in the perovskite phase under oxidizing conditions and insoluble under reducing conditions. Because we allow for all phases reported to exist within the Ca−Ti−Pt−O quaternary system to potentially appear in the phase diagrams, we consider that kinetics plays a role in preventing certain phases from forming. Single oxides of Pt, in particular, are well-known to be difficult to form,34 despite their relatively lower free energies. Because we furthermore cannot confirm experimentally that Pt exists as a single oxide or as

indicated by the red and blue dots, respectively, in this and subsequent figures. Our DFT-PBE calculations predict that TiO2 (B) has a lower energy than the anatase and rutile polymorphs. DFT methods are known to predict the anatase form of TiO2 to be more stable than the rutile form at low temperatures, contradicting experimental observations.33 It is likely that DFT also incorrectly predicts stability of TiO2 (B) relative to that of anatase and rutile. The shapes of the phase fields do not much change as temperature is increased, though the stable PtOx end member becomes Pt3O4 by 400 °C and Pt by 500 °C. Above 500 °C, the platinum rich form of CaTi1−xPtxO3 becomes more stable, with Pt gradually becoming more soluble in the perovskite CaTiO3 phase with increasing temperature, until by 700 °C, its stability goes to zero. Furthermore, by 700 °C, Ca2Pt3O8 and Ca4PtO6 are no longer stable. At all temperatures at which the CaTi1−xPtxO3 phase is stable, it can coexist in two-phase equilibrium with CaO, Ca2Pt3O8, or with the PtOx end member. A similar phase field configuration persists for the phase diagram evolution under oxidizing conditions, as shown in Figure 5; the low-temperature diagrams are identical to the reducing phase diagrams at even lower temperatures. In this case, though, the Pt3O4 and Pt phases do not appear until above 700 and 900 25

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Ca2Pt3O8 or Ca4PtO6 in any of the thin film specimens, we thus eliminate those phases from contention and recalculate metastable phase diagrams. Thus, we kept all phases that were experimentally observed in the three-phase and two-phase regions in which the experimental samples reside. The Ca-rich side was not explored in the experiments reported in this study. The phase field layout is substantially different in the metastable phase diagrams in which these oxides of Pt have been removed from consideration. Under reducing conditions at low temperatures, as shown in Figure 6, the CaTi1−xPtxO3 phase now forms two-phase coexistence regions with TiO2 (B) and CaTi5O11 rather than with Pt. This changes, though, above 300 °C when CaTi1−xPtxO3 begins to form two-phase regions with Pt. The Pt-rich end of the CaTi1−xPtxO3 perovskite solid solution gives way to more energetically favorable Pt and CaO above 500 °C, after which only the stoichiometric CaTiO3 perovskite remains stable by 700 °C. The phase diagrams are again largely the same for oxidizing conditions, as shown in Figure 7, though they are generally shifted to higher temperatures. This set of metastable phase diagrams (Figures 6 and 7) is in better agreement with our experimental observations than the true equilibrium phase diagrams (Figures 4 and 5) containing single oxides of platinum and the complex oxides Ca2Pt3O8 and Ca4PtO6. The most important feature in regard to the intelligent catalyst concept is the existence of a set of nominal compositions that, at 800 °C, are in phase fields in which Pt completely dissolves in host oxides under oxidizing conditions and are in phase fields where those oxides are in equilibrium with free Pt metal under reducing conditions. This change in the shape of the phase fields with varying oxygen partial pressure is the mechanism behind the self-regenerating effect. According to the metastable phase diagrams of Figures 6 and 7, a stoichiometrically exact CaTi0.95Pt0.05O3 catalyst formulation should form only perovskite and metallic Pt under reducing conditions and perovskite and CaTi5O11 under oxidizing conditions. This is somewhat contrary to the experimental results for our Ti-enriched thin film (film A), in which TiO2 (A) also appears, as well as the bronze B phase, referred to as TiO2 (B), which has a similar but simpler crystal structure as that of CaTi5O11. The occurrence of both phases can be partially explained by CaTi5O11 likely being kinetically more difficult to form, owing to its large unit cell, thereby resulting in the formation of the simpler TiO2 (B) variant. Additionally, both bronze-related phases have less suitable epitaxy with CaTiO3 than TiO2 (A). Therefore, though thermodynamically stable in the bulk, the formation of Ca containing bronze-related phases may not be as thermodynamically favored relative to the formation of TiO2 (A) when accounting for coherency strain energies. Our analysis neglects the role of anisotropic strain states due to epitaxial coherency that can alter the relative stability between different phases.35 Furthermore, we have also neglected the role of interfacial free energies in our analysis of phase stability. These are likely to be important for the very small precipitates where differences in interfacial free energies between the perovskite and the three candidate titanates could be sufficient to alter the phase stability predicted using bulk free energies alone. The appearance of the CaTi5O11 structure, which we discuss in detail elsewhere,36,37 and its TiO2-bronze progenitor, is also notable. CaTi5O11 forms out of the perovskite in small domains of order 10 nm in diameter, generally with its main crystallographic axes codirectional with those of the surrounding perovskite. Within these domains, however, about one-third to

one-half of the volume is the simple TiO2 bronze structure, of which CaTi5O11 is a twinned, augmented variant with a layer comprising one ion each of Ca, Ti, and O separating each twin plane. It is likely that the small size of the domains along with the large size of the CaTi5O11 unit cell and its existing crystallographic template allows the otherwise slightly more unfavorable TiO2 bronze to easily form. The more stoichiometrically balanced film (film B) with its slight Ca enrichment, to the contrary, again exhibited none of these secondary TiO2 phases. Given that this formulation sits very close to the tie line between CaTiO3 and the Pt end-member corner, we would expect, and indeed do observe, that this film only ever contains the perovskite crystal structure and metallic (or possibly oxidized) Pt under reducing conditions. After oxidation, though, the expectation from the calculated phase diagrams is that the Pt will dissolve into the host oxide. However, under the present conditions, much of the Pt remains in clusters within the matrix. It may be that the dissolution kinetics are too slow with the increased Pt content of this formulation relative to the previous film and that, given enough time, the Pt will indeed fully dissolve. It is worth noting that the assumed oxygen partial pressure of 1 × 10−8 atm during reduction may be higher than that of the real reducing condition in our experiments (i.e., flowing 10% H2/N2). We therefore investigated the evolution of phase diagrams with decreasing oxygen partial pressure at fixed 800 °C (Supporting Information, Figure S6). Our calculations show that there is no phase disappearing or new phase appearing in the range of 1 × 10−8 to about 1 × 10−20 atm until the bimetallic structure Pt8Ti1 shows up at 1 × 10−20 p0. Under even more aggressively reducing condition, the Pt−Ca bimetallic alloy (Ca1Pt5 and Ca2Pt4), followed by Pt5Ti3 appear in the phase diagrams gradually. TiO2 (A) can be reduced to Ti2O3 while CaTi5O11 disappears at 1 × 10−28 atm. CaTiO3 could be reduced to be CaTi2O4 at extremely low oxygen partial pressure, but as this was not seen in our experiments, we can take that as a lower bound to the oxygen content. 3.4. Informed Synthesis of a TWC. Using the knowledge gained from this study, specifically from the calculated phase diagrams, a self-regenerative catalyst may be designed to contain the maximum Pt loading that could be expected to be stabilized by the CaTiO3 support. That is, the phase diagrams may be used as a guide to maximally utilize the support for a prescribed amount of Pt at the expected use temperature without oversaturating the support during oxidation-induced dissolution. For the purposes of this discussion, the operating temperature will be taken as 800 °C. If a catalyst could be made with a stoichiometry of exactly CaTi1−xPtxO3, i.e. on the line precisely between CaTiO3 and CaPtO3, any amount of Pt, up to the amount of Ca, could, in principle, be used. This would result in an oscillation between a microstructure that consists only of perovskite and a three-phase mixture of CaTiO3, Pt, and CaO under oxidizing and reducing conditions, respectively. Alternatively, one could simply add Pt to an already stoichiometric formulation of CaTiO3. This scenario is, in fact, closer to the materials discussed in this report. In this case, Pt could be added to the extent such that the nominal stoichiometry (assuming it is fully oxygenated) is CaTiPt0.18O3.36, that is, Pt comprising 8% of all cations. In this situation, the reduced catalyst would, according to the phase diagrams, comprise CaTiO3, Pt, and CaTi5O11, and the oxidized catalyst would comprise CaTixPt1−xO3 and CaTi5O11. The perovskite could support more Pt at lower operating temperatures as the Pt 26

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solubility in the CaTixPt1−xO3−CaTi5O11 two-phase coexistence region is increased, but this may or may not be useful. In general, it should be pointed out that thermodynamics offer little insight into the rate of Pt exchange with the perovskite host. A crucial kinetic process during the dissolution and reprecipitation of Pt particles is presumably substitutional diffusion38,39 of Pt over the Ti sublattice of the perovskite. An analysis of thermodynamic phase stability also cannot provide much insight into the spatial distribution of the various phases relative to each other, that is, whether the Pt will form on the surface of perovskite host particles or will nucleate within, as we have observed. To take advantage of any cyclical self-regeneration of supported Pt particles in this system, we must pay special attention to the morphology of the working catalyst. Because Pt precipitates from the perovskite in a high density of small particles, one might surmise that if the length scale of the perovskite film or particle support were small enough, then Pt particles would have some chance of forming at a free surface. It is to this end that we propose as a promising morphology for this catalyst system a thin, conformal coating of CaTi1−xPtxO3 on the surface of a stable, high-surface-area support (e.g., alumina). A thin enough coating, on the order of a few nanometers, should it remain stable against agglomeration, could provide a useful platform for a practical self-regenerative catalyst. 3.5. Additional Observations. One additional series of phenomena arose in these Pt-doped CaTiO3 thin films that merits some discussion, though it does not directly pertain to the phase interactions discussed above. In a few of the reoxidized B films, we observed by HAADF-STEM small regions of ordered Pt substitutions on perovskite cation sites (Supporting Information, Figure S7). The extent of these regions was generally 1−10 nm, throughout which a set of cation sites were much brighter in the HAADF-STEM, corresponding to the presence of a heavy ion, namely, Pt. Curiously, the regions generally had Pt substituting on a-sites, which is, of course, counter to the central notion of this catalyst system−that Pt will substitute onto the b-site, replacing Ti. Because the population of samples showing this phenomenon was relatively small, we are unable to make any conclusions as to what might cause this local ordering of Pt. Although we included in our DFT modeling calculations the energies of these phases, none were energetically favorable relative to other phases present in any of the conditions to which the specimens were subjected.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key Basic Research Program of China under grant 2013CB934800, the Natural Science Foundation of China under grants 11104287 and 51472254, Ford Motor Company under a Ford−University of Michigan Innovation Alliance grant, and the National Science Foundation under grants DMR-0723032 and CBET-115940.

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4. CONCLUSIONS In summary, we have considered the phase evolution of Pt-doped CaTiO3 induced by redox cycling, as observed experimentally by advanced atomic-resolution transmission electron microscopy, within the context of density functional theory calculations of phase equilibria in the pseudoternary PtOx−CaO−TiOx system. With the assumption that single Pt oxides do not form in the system due to kinetic limitation, our theoretical results account for most of the phases appearing in our experimental thin film samples, including anatase TiO2 and CaTi5O11, as well as Pt metal and CaTiO3. We confirm the basic validity of the intelligent catalyst concept while highlighting important shortcomings.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org. 27

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