Interplay between Subsurface Ordering, Surface Segregation, and

Article pubs.acs.org/Langmuir

Interplay between Subsurface Ordering, Surface Segregation, and Adsorption on Pt−Ti(111) Near-Surface Alloys Wei Chen,*,† P. Dalach,‡ William F. Schneider,§ and C. Wolverton† †

Department of Materials Science and Engineering and ‡Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, United States § Department of Chemical and Biomolecular Engineering and Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: Using the first-principles cluster expansion (CE) method, we studied the subsurface ordering of Pt/Pt− Ti(111) surface alloys and the effect of this ordering on segregation and adsorption behavior. The clusters included in the CE are optimized by a genetic algorithm to better describe the interactions between Pt and Ti atoms in the subsurface layer. Similar to bulk Pt−Ti alloys, Pt−Ti(111) subsurface alloys show a strong ordering tendency. A series of stable ordered Pt−Ti subsurface structures are identified from the two-dimensional (2D) CE. As an indication of the connection between the 2D and the bulk ordering, the CE predicts a ground-state Pt8Ti structure in the (111) subsurface layer, which is the same ordering as the close-packed plane of the bulk Pt8Ti compound. We carried out Monte Carlo simulations (MC) using the CE Hamiltonian to study the finite temperature stability of the Pt−Ti subsurface structures. The MC results show that subsurface structures in the Pt-rich range have higher order−disorder transition temperatures than their Ti-rich subsurface counterparts. We calculate the binding energy of different adsorbates (O, S, H, and NO) on Pt-terminated and Tisegregated surfaces of ordered PtTi and Pt8Ti subsurface alloys. The binding of these adsorbates is generally stronger on Tisegregated surfaces than Pt-terminated surfaces. The adsorption-induced Ti surface segregation is determined by two factors: (i) the unfavorable energy penalty for the Ti atom to segregate to the clean surface and (ii) the favorable energy decrease from stronger adsorbate binding on the Ti-segregated surface. The two factors introduce similar magnitude in energy change for the S and NO adsorption on Ti-segregated surfaces of PtTi subsurface alloys. We predict an adsorption-induced Ti surface segregation that is dependent on the atomic configurations of the Ti-segregated surfaces resulting from the competition of the two factors.

I. INTRODUCTION Bimetallic surface alloys play an increasingly prominent role in the effort to tailor the reactivity of heterogeneous catalysts through modification of surface composition and structure.1−11 As suggested by the Sabatier principle, the optimum rate of a catalytic reaction is achieved when the adsorbates bind to the surface neither too strongly nor too weakly.12 This principle points to the absorbate binding energy as a descriptor of catalytic performance and as a screen of potential bimetallic surface alloys.11 Because of the interactions between the adsorbates and the surface atoms the adsorption and desorption of adsorbates on an alloy surface can be substantially affected by the atomic arrangement of the metal atoms on the surface. An understanding of the stable atomic ordering of the bimetallic surface is essential to investigate the properties of adsorbate binding on the alloy surface quantitatively. The ordering of a bimetallic surface is not only a result of the interactions between the metal atoms in the surface but also influenced by the thermodynamic tendency of solute segregation to the surface. For example, Ru tends to segregate to the surface of Pt−Ru catalysts in an oxidizing environment but not in © 2012 American Chemical Society

vacuum. The composition of a Pt−Ru surface changes dramatically with the oxygen adsorbates, and the stable atomic ordering of the surface evolves as a function of oxygen chemical potential.13 To give an accurate description of the surface condition and adsorption properties of a surface alloy, both the surface segregation of the solute atoms and the ordering of the surface layers have to be considered. Pt−Ti alloys form a series of strongly ordered materials that are interesting for catalytic applications. These complex yet very stable Pt−Ti compounds have generated considerable interest in studying the bulk phase diagram of Pt−Ti.14−17 The stoichiometric phase A8B (tI18) was first discovered in Pt− Ti,18 and the existence of Pt8Ti prototype structure has been recently verified in a wide variety of binary alloy systems from first-principles calculations.18,19 It is well known that the atomic ordering in a two-dimensional (2D) system might be different from the ordering in the bulk.20,21 For example, Au−Pt is a bulk Received: December 8, 2011 Revised: February 15, 2012 Published: February 21, 2012 4683

dx.doi.org/10.1021/la204843q | Langmuir 2012, 28, 4683−4693

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of the Pt−Ti(111) subsurface, we use the first-principles cluster expansion (CE) formalism35−39 to investigate the ordering of Ti and Pt in the subsurface layer. The CE methodology is a powerful tool that has been used to study a wide range of material problems, such as ground-state structures and ordering,40−46 phase diagrams and order− disorder transition temperatures,42,47−49 short-range order in disordered systems,50−56 morphology of precipitates,57−60 intercalation voltages in battery materials,61−63 and also ordering in surface alloys.8,64−68 In this generalized Ising-like model, a subsurface site k occupied by a Pt atom is assigned a spin occupation variable Sk = +1 and a site occupied by a Ti atom is assigned Sk = −1. The total energy of any subsurface configuration σ of Pt and Ti can be expressed as

phase-separating system but forms ordered structures in the (111) surface.22−25 For the strongly ordered Pt−Ti system, we can ask the analogous question of whether a 2D Pt−Ti atomic layer preserves the bulk ordering or forms different ordered structures. Pt−Ti alloys are promising candidates for Pt catalyst in fuel cell applications because of their good activity for oxygen reduction reactions (ORR)26 and superior chemical stability.27 A number of experimental and theoretical studies have proved the surface compositions of Pt−Ti (111) or (100) facets to be a pure Pt layer.28−30 Some calculations also indicate a Ti segregation in the subsurface layer of Pt−Ti surface alloys in vacuum.31 The subsurface Pt−Ti layer below the Pt overlayer is therefore an ideal model system to study the 2D ordering of Pt−Ti. The subsurface ordering of Pt−Ti and its reactions with surface adsorbates are critical to the catalytic properties of Pt− Ti nanoparticles. However, while the bulk structures of Pt−Ti alloys have been widely studied, there is no systematic study of the subsurface ordering of Pt and Ti atoms. In this paper, we study the interplay between surface segregation, subsurface ordering, and adsorption on Pt/Pt− Ti(111) surface alloys from first principles. (i) We first confirm the energetic preference for Ti to segregate in the subsurface layer of Pt−Ti alloys in vacuum from DFT and focus on investigating the ordering in the Pt−Ti subsurface layers. (ii) We next use the cluster expansion (CE) method to search the vast configuration space for stable subsurface ordered Pt−Ti structures. A series of stable ordered structures is identified from the search. (iii) We last study the adsorption of several adsorbates (O, S, H, and NO) on the ordered Pt−Ti surface alloys. The segregation of Ti to the surface layer is considered due to the interaction of adsorbate atoms and metal atoms.31,32 We find the segregation tendency of Ti to the surface with adsorbates is related not only to the type of the adsorbates but also to the ordering of the surface layers.

E(σ) = N ∑ DF JF ∏̅F (σ) F

(1)

where N is the number of lattice sites, DF is the number of symmetryequivalent cluster figures F (the sum is over different pairs, triplets, quadruplets, etc.) per site, JF is the effective cluster interaction (ECI) associated with each figure, and ∏̅ F is a structure-dependent correlation function ∏̅F (σ) =

1 NDF

∑ S1(σ)S2(σ)...Sm(σ) f

(2)

Here, the spin products of all m sites of a figure f are summed over NDF equivalent figures of class F for the configuration σ. An optimal set of cluster figures and their corresponding ECIs can be obtained by minimizing the cross-validation (CV) score69 of the CE fitting across the DFT energies for a set of subsurface configurations. The predictive errors of the cluster expansion can be examined by the CV score, and a “leave-one-out” cross-validation is used in this paper, which is calculated as follows

CV =

1 n

n

∑ [Ei − Eî ]2 (3)

i=1

where Ei is the DFT energy of an input structure i and Ê i is the predicted energy of the structure i by the CE Hamiltonian from a leastsquares fit to the (n − 1) energies of the remaining structures used as input in CE fitting. The input Pt−Ti subsurface structures are chosen through an iterative method. If new low-energy structures different from any input structures of a certain composition are predicted from the CE Hamiltonian, DFT energies of these structures are calculated and included in the next iteration of CE fitting. The formation energies of these input structures are cluster expanded with 2D clusters. The end-point configurations of pure Pt(111) and Pt/Ti(111) [the element before (after) the slash is the surface (subsurface) layer; all layers below the subsurface layer are pure Pt] are used as references to calculate the formation energies of different configurations. The formation energy of a Pt−Ti subsurface structure is defined as follows

II. METHODS A. Density Functional Theory Calculations. Total energy calculations were performed for surfaces in the presence and absence of adsorbates. These calculations are based on density functional theory as implemented in the Vienna ab initio Simulation Package (VASP) using the projector augmented wave (PAW) method.33 The generalized gradient approximation of Perdew and Wang is used to approximate the electronic exchange and correlation.34 The plane wave basis set for the electronic wave functions is defined by a cutoff energy of 400 eV for clean surface calculations and 520 eV for surfaces with adsorbates. The Brillouin-zone integrations are sampled using Monkhorst-Pack k-point meshes corresponding to a 21 × 21 × 1 grid for a 1 × 1 surface unit cell. The k-point meshes for larger supercells are scaled with the size of the cell and keep the k points per reciprocal surface atom roughly constant. All DFT calculations are spin polarized. The dense k-point mesh is required to converge the energy to 1 meV per surface atom and distinguish the energy differences between competing ordered structures. We use a slab model with 5 atomic layers and a vacuum region of 10 Å in thickness for the surface calculations. The bottom two layers of the slab are fixed at the Pt bulk equilibrium positions with a lattice constant of 3.985 Å, and all other layers are fully relaxed. For the cluster expansion input structures, the subsurface layer consists of different 2D ordered structures of Pt and Ti atoms while the surface and substrate layers are all Pt atoms. B. Determining Stable Ordered Pt−Ti Subsurface Structures from Cluster Expansion. A bimetallic 2D system of N lattice sites has a total of of 2N arrangements of metal species on the surface. Even for a modest value of N, the configurational space is too big for direct exploration via DFT calculations. To find the stable ordered structures

EF (PtxTi1 − x) = E(PtxTi1 − x) − (1 − x)E(Ti) − xE(Pt)

(5)

where E(PtxTi1−x) is the total energy for a Pt−Ti subsurface structure with a Pt subsurface coverage of x and E(Pt) and E(Ti) are the energies for pure Pt/Pt(111) and Pt/Ti(111) subsurfaces. In all three energies of eq 5, the surface layer is always Pt and all layers below the subsurface are always pure Pt. All terms in eq 5 are defined as energies per subsurface atom. The CE formalism is exact in that the energy of a system is expanded in a complete and orthonormal basis if all cluster figures of the N lattice sites are included. In practice, the expansion is truncated with a limited number of clusters to achieve a rapidly converged expression. We apply a genetic algorithm (GA) search scheme to optimize the choice of clusters for the cluster expansion.70−72 With the help of CE Hamiltonians, the formation energies of a large number of the subsurface configurations can be efficiently evaluated, from which the ground-state structures can be accurately determined. C. Monte Carlo Simulations of the Finite Temperature Stability of Pt−Ti Subsurface Structures. Combining the CE 4684


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Hamiltonian with Monte Carlo simulations, we can assess the finitetemperature stability of the Pt−Ti(111) subsurface structures. Since we are interested in studying the order−disorder transition of the ordered Pt−Ti structure at a given subsurface concentration with temperature, we choose the canonical ensemble in the simulation. To study the equilibrium subsurface concentration one would need to use the grand-canonical ensemble, and thus, our MC calculations cannot be used to predict subsurface concentrations. The canonical simulations are carried out by fixing the composition of the subsurface layer and scanning over temperature. We run the simulations at compositions where stable ordered Pt−Ti structures are identified from the CE. The simulation cell has 40 × 40 sites, and the simulated temperatures are from 400 to 2000 K at a 50 K interval. The initial configuration for the simulation is a random Pt−Ti subsurface. We use 4000 MC steps for the equilibrium passes and 5000 MC steps for the sampling passes and monitor the energy change with temperature. We ran simulations both by raising the temperature and by cooling down from 2000 K. The MC simulation is able to stabilize the ground-state configurations from CE at low temperatures. The temperature of the order−disorder transition is determined from the peak in the specific heat as a function of temperature. D. First-Principles Calculations of Surface Segregation. To evaluate the surface segregation tendency of Ti atoms in Pt−Ti alloys, the segregation energy of Ti from the bulk to the Pt(111) surface is calculated as the difference between the total energy of a slab with a surface Pt atom replaced by a bulk Ti atom and the total energy of a slab with a pure Pt surface and a Ti atom in the bulk. A negative segregation energy indicates that the Ti atom energetically prefers to segregate to the Pt surface. We calculate the segregation energy of Ti to a clean Pt(111) surface using a slab model of 7 layers of atoms. The bottom three layers are fixed, and the remaining four layers are relaxed. A slab with Ti in the fourth layer from the surface is used to calculate the reference energy of Ti in bulk Pt. The segregation energy is calculated for both a 1 × 1 and a 2 × 2 supercell to simulate the condition of a 1 ML or 1/4 ML coverage of the solute Ti atoms in the surface layer. In addition to surface segregation energy, we also calculate the total energy of the Pt−Ti slabs with the Ti atoms situated at different layers to determine the preferred location of the Ti solute atoms in the Pt slab. E. First-Principles Calculations of Adsorbate Binding Energy. To study the effect of subsurface ordering on the surface adsorption, the binding energies of different adsorbates on the ordered Pt/Pt− Ti(111) subsurface structures are calculated both in the presence and in the absence of solute segregation to the surface. The adsorbates considered in the paper are atomic O, H, and S and the NO molecule. The dissociative binding energies of O and H are calculated by eq 6 Ebind(A) = EA/slab −

1 E A (g) − Eslab 2 2

III. RESULTS A. Subsurface Ti Segregation for Clean Pt Surface. The strong tendency of Ti not to segregate to the clean surface of Pt−Ti alloys is a well-known phenomenon from experimental studies. Both LEED28 and STM29 observations have verified the (111) surface of the ordered Pt3Ti alloy to be pure Pt, different from any (111) terminations of the ordered bulk Pt3Ti structure. The segregation energy determines the energetic preference for the solute atom to segregate to the surface or remain in the bulk. The segregation energy of Ti to the clean Pt(111) surface from our DFT calculations is +0.68 eV per Ti for the 1/4 ML Ti coverage and +1.5 eV per Ti for the 1 ML Ti coverage. The very positive segregation energy indicates a strong energy penalty for Ti to segregate to the top atomic layer. We find that a pure Pt-terminated surface is energetically stable for Pt−Ti alloys in vacuum, which is in agreement with experimental results. Although there is an energetic penalty for Ti segregation to the surface layer, we next investigate the segregation tendency of Ti to the subsurface layer. We find that Ti atoms are energetically favorable to segregate in the subsurface layer and form Pt−Ti subsurface alloys.74 In Figure 1, we show the

Figure 1. Segregation energy of a Ti atom to different (111) atomic layers of a Pt slab. (Inset) Schematic illustration of how the surface segregation energy is calculated. Negative values indicate an energetic preference for the Ti atom to segregate to the atomic layer from the bulk. Lowest energy position for Ti atoms is the subsurface layer under a clean Pt surface.

(6)

where the first term is the total energy of an adsorbate A (O or H atom) on the given slab, the second term is the total energy of A2 (O2 or H2) in the gas phase, and the third term is the total energy of the slab in vacuum. The binding energies of S and spin-polarized NO are referenced to H2S and NO as in eqs 6 and 7.

Ebind(S) = ES/slab − [E H2S(g ) − E H2(g)] − Eslab

(6)

Ebind(NO) = ENO/slab − ENO(g) − Eslab

(7)

change of segregation energy for a Ti atom to move from the bulk to different (111) layers with 1 ML and 1/4 ML Ti coverage. For the 1/4 ML Ti coverage, it costs 1.15 eV to move a subsurface Ti atom to the Pt surface and 0.49 eV to move the subsurface Ti atom deeper into the bulk. In both cases, the subsurface segregation of Ti gives the largest negative segregation energy, suggesting an energetic preference for subsurface segregation of Ti. Our results are in agreement with other DFT and modified embedded-atom method (MEAM) calculations.31 To study the 2D ordering of Pt−Ti near surface alloy, it is a reasonable simplification to focus on the subsurface layer. The slab model used to search the stable ordered 2D Pt− Ti structures in this paper only considers Pt−Ti ordering in the subsurface layer. Similar models have also been used to study other subsurface alloys.3,5 B. Ordering of Pt/Pt−Ti(111) Subsurface. Pt−Ti alloys are typical examples of a binary system showing a strong ordering tendency. The phase diagram of the bulk Pt−Ti

The binding energies of the adsorbates are calculated for the fcc sites of the (111) surface, which are usually the most stable adsorption sites for Pt alloys at low surface coverage.73 From the stable ordered Pt−Ti subsurface structure used in the clean surface binding energy calculations, we allow 50% or 100% of the subsurface Ti atoms to move to the Pt surface to simulate the adsorption-induced Ti surface segregation. To study the interplay between surface adsorption and surface segregation, the binding energies of the same adsorbates are calculated for the fcc sites of different configurations of the Ti-segregated surfaces. 4685


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Compared to the traditional methods, the genetic algorithm optimization approach is more effective in solving complex CE problems that require inclusion of many-body interactions and/ or long-range interactions.71 To aid our search for an optimum set of clusters for the CE, we adopt a genetic algorithm to improve cluster selection for the Pt−Ti subsurface. We use the same set of 118 Pt−Ti subsurface structures for the GA search. The GA optimization process starts with a pool of clusters (genes), from which several unique subsets of clusters (genomes) are chosen randomly as trial solutions. The fitness of each genome is evaluated by a CV score. Subsequent generations of “children” are generated by swapping genes between the fittest “parent” genomes or by randomly introducing mutations. We choose the pool of clusters to be optimized by setting a cutoff size for clusters of the same number points and including all clusters that are smaller than the cutoff size: pairs (18 Å), triplets (12 Å), quadruplets (10 Å), and quintuplets (8 Å). The size of a cluster is defined as the longest distance between two points of the cluster. The initial pool of clusters for the Pt−Ti subsurface has 17 pairs, 72 triplets, 75 quadruplets, and 63 quintuplets. The cutoff size for clusters is chosen for efficiency, and the pool of clusters does not change during the GA optimization. The GA optimization of cluster choice is not based on any physical rules, in contrast to conventional cluster choice algorithms. In Figure 2, we illustrate how the CV score of the CE decreases in the GA optimization process. The red line is the

system exhibits a variety of ordered compounds and has been studied extensively from both experiment and theory. The equiatomic bulk PtTi phase is observed to undergo a reversible B2 α-PtTi (bcc-based) ↔ B19 β-PtTi (hcp-based) martensitic transformation.75 Within two layers of the close-packed planes, the local ordering of the low-temperature B19 phase is equivalent to the L10 (fcc-based) phase. Two stable compounds with Pt-rich compositions reported are Pt3Ti (hP16)76 and Pt8Ti (tI18).18 An L12 phase exists off-stoichiometry in the composition range of 20−25 Ti%.16 Although there are some disagreements about the Ti-rich side of the Pt−Ti phase diagram, one well-established phase is the A15 PtTi3 structure. The phase stability of bulk Pt−Ti ordered compounds has also been studied using computational approaches. Wolverton et al. studied the fcc-based phase stability of the Pt−Ti system using a cluster expansion approach and confirmed that L10 PtTi and L12 Pt3Ti compounds are fcc-based ground-state structures.77 Curtarolo et al. compared the formation energy of Pt−Ti compounds from first-principles and confirmed the experimental stability of A15 Pt3Ti and B19 PtTi intermetallic compounds.78 While the bulk structures of Pt−Ti alloys have been widely studied, one cannot generally predict 2D ordering directly from the 3D ordered structures. Hence, we next study the 2D ordering problem of the Pt−Ti(111) subsurface layer. 1. Obtaining a Predictive CE via a Genetic Algorithm Approach. We use a 2D cluster expansion to study the subsurface ordering of Pt−Ti. To construct a reliable CE Hamiltonian that describes the energetics of the system accurately, the choice of clusters has to be carefully optimized to capture the delicate interactions among the lattice sites. Common methods for choosing clusters for a CE are often based on physical intuition by implementing basic rules such as the following: (1) low-order clusters (fewer vertices in a cluster) are more important than higher order clusters, and (2) long-ranged clusters are generally assumed to have weaker interactions than shorter ranged ones.79 The purpose of these rules is to more efficiently search for an optimized CE by narrowing the number of clusters and considering only these “physically meaningful” clusters. Application of this “intuitive” cluster selection scheme has been successful for a wide range of bulk and surface ordering problems.47,64,68,80−82 We initially used the cluster choice algorithm based on these intuitive rules as implemented by ATAT to optimize clusters for the CE of Pt−Ti subsurface. The search algorithm includes a higher order cluster only when all its subclusters have been included.79 A total of 118 DFT energies of different subsurface configurations of Pt and Ti atoms are used in fitting the cluster expansion. We find that for Pt−Ti subsurface ordering the “intuitive” method is not effective in finding the optimum set of clusters for CE. Even though the best choice of clusters from this method (which include 27 pairs, 16 triples, and 27 quadruplets) gives a low CV score of 27 meV/surface site, the CE fails to reproduce the ground-state structures from DFT calculations and predicts high-energy structures to be ground states. The overall energy prediction error measured by the CV score is relatively small compared to the formation energy of the system, but the prediction error for individual structures is too big to give the correct ground-state structures. We attempted to solve this problem by increasing the weight of the low-energy structures in the CE fitting. In this case, although these high weights led to the low-energy structures described well by CE, the CV score became large, thereby undermining the predictive ability of the CE to describe the correct ordering of the system.

Figure 2. Cluster optimization by GA as measured by CV score. Solid red line is the lowest CV score achieved at each GA generation. Black dashed line shows the CV score using the default cluster selection method of ATAT.

lowest CV score achieved after each GA generation, and the black dashed line is the CV score from the conventional algorithm for cluster choice as implemented by ATAT.79 From this figure we see that the GA method is very effective in selecting appropriate clusters to reduce the CV score for the fitting. The CV score is below 4 meV after only 100 GA generations and is fairly stable after 250 GA generations. We stop the GA optimization at generation 338 when the set of clusters gives a CV score of 3.3 meV per subsurface site. The final set of clusters includes 8 pairs, 12 triplets, 22 quadruplets, and 11 quintuplets. Although fewer clusters are chosen from the GA optimization, these clusters give a much smaller CV score than the algorithm in ATAT. In Figure 3, we show the sizes and ECIs of the clusters selected for the Pt−Ti subsurface CE. As a sign of convergence of the CE, the ECIs of selected 4686


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formation energies predicted from CE in Figure 4. The CE formation energies are shown as blue circles, and the DFT energies are shown as blue dots. The formation energies predicted from the CE Hamiltonian are very close to the DFT energies for each input structure, reproducing the correct energetic hierarchy of input structures (including the groundstate structures). 2. Stable Ordered Subsurface Pt−Ti Structures. We identified a series of stable ordered structures for the Pt−Ti subsurface theoretically from both direct DFT calculations as well as from the 2D cluster expansion. We use the CE Hamiltonian to evaluate the formation energies of all subsurface Pt−Ti structures containing up to 11 subsurface sites. In Figure 4, the formation energies of these stable ordered structures are shown and compared to those of other Pt−Ti subsurface ordered structures. The gray dots are those ordered structures whose formation energies are predicted from the CE Hamiltonian. We then compare the formation energies of these structures with the convex hull and verify the groundstate structures. The atomic configurations for some of the stable ordered Pt−Ti subsurface structures are illustrated in Figure 5.

Figure 3. Clusters and their corresponding ECIs for the CE of the Pt− Ti(111) subsurface. Choice of clusters is optimized from GA. Set of clusters includes 8 pairs, 12 triplets, 22 quadruplets, and 11 quintuplets.

clusters converge to zero with the increase of cluster size. Inclusion of a relatively large number of many-body clusters is helpful to describe the complex ordering problem of Pt−Ti subsurface layer. It is possible to further decrease the CV score by GA optimization but only slightly so. In addition, decreasing the CV score below the numerical precision of DFT calculations is not physically meaningful. We carried out several GA runs with random starting genomes, and all these GA optimizations give similar results. Although the sets of clusters chosen are not identical in each run, the final CV score is very similar. The set of clusters chosen from the GA optimization gives the same ground-state structures as those obtained from DFT calculations. In Figure 4, we show the formation energies of stable ordered Pt−Ti structures at different compositions by red “×” symbols. Connecting these red “×” forms a convex hull (black solid lines) that indicates the ground-state diagram of the Pt−Ti subsurface. We also show the DFT formation energies of the 118 input structures with respect to their

Figure 5. Stable ordered Pt−Ti subsurface structures at (a) 1/3 (PtTi2), (b) 1/2 (PtTi), (c) 4/7 (Pt4Ti3), (d) 2/3 (Pt2Ti), and (e) 8/ 9 (Pt8Ti) ML Pt coverage. Ti atoms are shown in blue, and Pt atoms are in gray. Unit cells are shown in dashed lines.

The Pt−Ti subsurface layer forms stable ordered structures with very negative formation energies. The formation energies of some structures are as low as −0.6 eV per subsurface atom. For Ti-rich coverages (cPt > 1/2 ML), the convex hull can be approximated as two segments of straight lines: 0−1/3 ML Pt and 1/3−1/2 ML Pt. There are several competing structures whose formation energies are virtually on the two tie lines. In the stable subsurface structure with 1/3 ML Pt (√3 × √3)R30 (Figure 5a), the nearest-neighbor atoms to Pt are all Ti atoms in the subsurface (111) layer. The stable ordered structures between 1/2 and 2/3 ML Pt have lower formation energies than other stable ordered structures on the convex hull. The structure with 4/7 ML Pt coverage (Figure 5c) has the lowest formation energy among all calculated ordered Pt−Ti subsurface structures. The atomic ordering of the 4/7 ML Pt structure is a variation of the 1/2 ML Pt structure (Figure 5b), which shows a herringbone pattern.83 The ordered structure with 2/3 ML Pt (Figure 5d) has the reverse ordering (positions of subsurface Pt and Ti atoms are switched) of the stable structure with 1/3 ML Pt. In this case, the subsurface Ti atom is surrounded completely by Pt atoms in all directions, and this

Figure 4. Ground-state diagram of the Pt−Ti(111) subsurface. For the input structures used to construct the CE, their formation energies from DFT calculations are shown as blue dots and the CE formation energy is shown as blue circles. Gray dots are ordered structures whose formation energies are predicted from the CE Hamiltonians. Red “×” symbol shows the ground-state structures. Diagram indicates the Pt− Ti subsurface forms some very stable ordered structures. 4687


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2D subsurface structure is similar to that of bulk Pt8Ti, with all Ti surrounded entirely by nearest-neighbor Pt atoms. C. Finite Temperature Stability of Pt/Pt−Ti(111) Ordered Subsurface Structures. We performed Monte Carlo simulations using the CE Hamiltonian to estimate the finite temperature stability of the Pt−Ti subsurface ordered structures. In Figure 6, the energy and specific heat are shown

structure contains the maximum possible number of Pt−Ti nearest-neighbor bonds for this composition. In the dilute Ti region, the convex hull indicates a stable structure with an 8/9 ML Pt (Figure 5e). The stable ordered structures at 1/3, 1/2, and 2/3 ML Pt coverages predicted from CE are among the general groundstate predictions for the 2D triangular lattice by Kaburagi et al.84 using a geometrical inequality method85 considering up to the third pair interactions. Kaburagi et al.84 calculated the ground-state structures of the triangular lattice for any possible set of first, second, and third nearest-neighbor interactions. These results can be used to make statements about which interactions are necessary to stabilize specific ground-state structures. The (√3 × √3)R30 structure can be determined as the ground state for 1/3 or 2/3 ML Pt coverage with only an ordering-type nearest-neighbor pair interaction.86 However, the herringbone structure at 1/2 Pt coverage is not a stable ground state with the nearest-neighbor pair only but rather requires 1− 3 nearest-neighbor pair interactions to be stabilized as a ground-state structure.87 Our approach to the ground-state problem is quite distinct from Kaburagi et al.: We use DFT to directly calculate the specific set of interactions that correspond to a particular alloy system (in our case, subsurface ordering in Pt/Pt−Ti(111)). Armed with the DFT-calculated set of interactions, we can then search for the ground-state ordering for that set of interactions. We have shown that Pt and Ti atoms in the subsurface (111) layer (similar to the Pt−Ti system in the bulk) exhibit a strong ordering tendency. This ordering tendency is also reflected in the dominant ECI of the CE. The set of clusters includes a dominant nearest-neighbor pair cluster, which has a very positive ECI of +0.11 eV (Figure 3). The very positive pair interaction indicates a strong preference for neighboring atoms to be dissimilar in the Pt−Ti subsurface layer. All of the structures shown in Figure 5 maximize the number of Pt−Ti bonds for that specific coverage. For example, moving a solute atom from its position in the (√3 × √3)R30 structure will inevitably form Pt−Pt or Ti−Ti bonds at the expense of Pt−Ti bonds and therefore will be energetically less favorable. The favorable Pt−Ti nearest-neighbor interaction alone is able to stabilize the (√3 × √3)R30 structure. Similarly, the (3 × 3) structure in Figure 5e not only has each Ti surrounded entirely by Pt nearest neighbors but also has the longest average Ti−Ti distance geometrically possible for the x = 1/9 Ti coverage. The equiatomic herringbone structure in Figure 5b has the same number of favorable Pt−Ti bonds per atom in the unit cell as an equiatomic striped structure.22 If only considering the nearest-neighbor interaction, the two structures have degenerate energies.86 The herringbone structure shows lower energy with the full set of interactions in the CE (striped structure −0.54 eV/site, herringbone structure −0.64 eV/site) . The ordered subsurface structures from the CE reveal some connections between the 2D subsurface and the 3D bulk ordering of the Pt−Ti system. In the bulk phase diagram, the Pt8Ti phase represents a superstructure of the fcc lattice with a specific ordered decoration of the fcc lattice sites.18 The similar preference is also found in the 2D ordering of Pt and Ti atoms. In the Pt-rich side of the 2D convex hull, a ground-state structure with a Pt8Ti unit cell exists (Figure 5e) from our CE prediction. The Pt8Ti subsurface structure has the same ordering as a close-packed plane of the experimentally observed bulk Pt8Ti phase. The local environment of the Ti atom in the

Figure 6. Change of energy and specific heat with temperature for the Pt8Ti subsurface structure. Peak in specific heat indicates the order− disorder transition at ∼577 °C (850 K). Curves for other stable ordered Pt−Ti subsurface structures have similar shapes.

as a function of temperature for Pt8Ti subsurface structure. For a first-order phase transformation, there is a discontinuity in the internal energy as a function of temperature. The peak of the specific energy in Figure 6 indicates the ordered Pt8Ti subsurface structure undergoes an order−disorder transition at ∼577 °C (850 K). We ran simulations to get the transition temperatures for other ordered Pt−Ti subsurface structures. The energy and specific heat vs temperature curves for these Pt−Ti structures have similar shapes as those for Pt8Ti. The calculated DFT+CE+MC order−disorder transition temperatures for these Pt−Ti subsurface structures are shown in Table 1. Table 1. Order−Disorder Transition Temperature for Pt−Ti Subsurface Ordered Structure from Monte Carlo Simulationsa structure

Pt coverage (ML)

transition temperature (K)

PtTi2 PtTi Pt2Ti Pt8Ti

1/3 1/2 2/3 8/9

450 950 1700 850

a Subsurface structures in the Pt-rich range have higher order−disorder transition temperatures than their Ti-rich subsurface counterparts.

In the bulk Pt−Ti phase diagram, the Pt-rich compounds in general have higher melting temperatures than the Ti-rich side compounds. For example, compared to the high solidus temperature for bulk Pt3Ti phase (1860 °C), the solidus temperature for bulk PtTi3 phase is only 1310 °C.14 We find a similar trend in order−disorder transition temperatures for the Pt−Ti subsurface ordered structures. While the subsurface Pt2Ti structure is just a reverse ordering of Pt and Ti atoms in the subsurface PtTi2 structure, the calculated transition temperature for Pt2Ti (1700 K) is much higher than PtTi2 (450 K). Although the bulk transition temperatures are melting 4688


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atom is the nearest neighbor to the adsorbate at site 1 in Figure 7b. We calculate the binding energy of four adsorbates (O, S, H, and NO) for each fcc site of the Pt-terminated and Tisegregated Pt8Ti surfaces in Figure 7. The adsorbates have the same coverage of 1/9 ML on both surfaces as the Ti coverage. Table 2 shows the binding energy of the adsorbates on the fcc

temperatures and the transition temperatures we calculate are for order−disorder transitions, they both point to the increased stability of Pt-rich ordered compounds over Ti-rich compounds. The difference in stability is reflected in the odd-body ECIs. Even-body interactions give terms in the energy that are invariant to interchange of Pt and Ti (Si = −1 interchange with +1 and vice versa) and are thus symmetric about x = 1/2. Only odd-body interaction terms can introduce asymmetry in the convex hull about x = 1/2 or, in other words, can differentiate Pt-rich compounds from Ti-rich compounds. Considering eq 2, for example, a triplet with 2 Pt atoms and 1 Ti atom has a negative value of correlation function Π (we define spin variable as +1 for Pt and −1 for Ti), thus lowering the CE formation energy in eq 1 if the ECI for the triplet is positive. In Figure 3, the majority of odd-body ECIs, especially the shortrange triples, have positive values. Thus, these positive triplet interactions tend to favor Pt-rich compositions over Ti-rich compositions and explain the asymmetry in our calculated order−disorder transition temperatures. D. Adsorption-Induced Surface Segregation on Pt−Ti Ordered Subsurface Structures. Because of the strong affinity of the electropositive Ti atom to bond with electronegative adsorbates (such as O), the segregation tendency of the solute Ti atoms to the Pt surface is likely to change with the introduction of electronegative adsorbates to the surface. As a result, the binding properties of the adsorbates will also change on the Ti-segregated surface. We next discuss the interplay between adsorption and segregation of the ordered Pt−Ti subsurface structures. We will focus on the ordered Pt8Ti and PtTi subsurface structures identified from the CE. These two structures represent two distinct Ti subsurface concentrations: a dilute (Pt8Ti) and a concentrated (PtTi) Ti coverage in the (111) subsurface layer. 1. Segregation and Adsorption of Pt8Ti Subsurface Structure. We first study the adsorption on the ordered Pt8Ti subsurface structure, which has a low Ti subsurface coverage. To investigate possible adsorption-induced surface segregation of Ti atoms, we consider both the “unsegregated” Ptterminated surface with all Ti in the subsurface layer as well as the Ti-segregated surface with all Ti atoms in the surface layer (with the same Pt−Ti ordering). The atomic configuration of the surface and subsurface layer with the fcc adsorption sites for each structure is shown in Figure 7. There are three symmetrically inequivalent fcc sites for the Ptterminated and Ti-segregated surface. The numbering of these sites in Figure 7 increases with the distance between the adsorbate and the closest Ti atom either in the subsurface or in the surface layer, i.e., the subsurface Ti atom is the closest Ti atom to the adsorbate at site 1 in Figure 7a, and the surface Ti

Table 2. Binding Energies of Adsorbates on the fcc Sites of the Pt-Terminated and Ti-Segregated Pt8Ti Structures in Figure 7a Pt terminated (Figure 7a)

Ti segregated (Figure 7b)

ETi‑seg − EPt (eV/cell)

1.2

Ebind (eV/Ads)

site 1

site 2

site 3

site 1

site 2

site 3

NN Ti O S H NO

0 −1.2 −1.7 −0.5 −1.9

0 −1.2 −1.6 −0.4 −1.8

0 −1.1 −1.5 −0.4 −1.7

1 −2.2 −1.7 −0.6 −2.0

0 −1.5 −1.9 −0.5 −2.0

0 −1.4 −1.9 −0.6 −2.0

a

The second row shows the energy change of the Ti-segregated surface with respected to the Pt-terminated surface without adsorbates. The fourth row shows the number of the nearest Ti atoms to the adsorbate.

sites of the two surfaces. The binding of all adsorbates to the alloy surface is stronger when the Ti atoms segregate to the surface. The increase in binding energy from the Ti surface segregation is largest for the O adsorbate (∼1 eV increase at site 1) and smallest for the H adsorbate (∼0.1 eV increase at all three sites). For each adsorbate, the binding energy is similar among different sites of the Pt-terminated surface. On the Tisegregated surface, the binding energy at different sites is similar for H, S, and NO. However, oxygen binding shows big differences for different adsorption sites of the Ti-segregated surface: The binding energy of O is 0.7 eV larger for the adsorption site with a Ti nearest neighbor (site 1) than for the other sites with all Pt nearest-neighbor sites to the adsorbate. The stronger binding of O at the adsorption sites with Ti nearest-neighbor suggests a preference for Ti to bind with O. We can understand the trend in binding energy from the perspectives of the electronegativity of these elements. Ti has a lower electronegativity (1.54, revised Pauling values88) than Pt (2.28). The increase in binding energy due to Ti at the surface goes as O > S > H. The difference between the electronegativity of Ti and adsorbate also follows this trend: O (1.9) > S (1.04) > H (0.66). The electropositive Ti prefers to bind with the most electronegative O adsorbate, and therefore, the strongest binding for the system is oxygen adsorbates on the sites with Ti nearest-neighbor atom. Even though the binding of all four adsorbates is stronger on the Ti-segregated surface, this does not necessarily imply that segregation of Ti is energetically favored in the presence of adsorbates. The segregation energy of the Ti atom to the surface with adsorbates can be written as

Figure 7. fcc sites for binding energy calculation of (a) Pt8Ti subsurface structure and (b) Pt8Ti surface with all subsurface Ti atoms segregated to the (111) surface. Subsurface atoms are shown as rendered balls, and surface atoms are hollow circles. Ti atoms are shown in blue, and Pt atoms are in gray.

The first term on the right side of eq 8 is the unfavorable segregation energy of the Ti to the clean surface without adsorbates. The difference between the second and the third term in the parentheses of eq 8 is the favorable adsorbate 4689


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alloy surface is ∼1 eV. In the case of O adsorbates, the Ti−O bond is stronger than the Pt−O bond, but to segregate Ti to the surface, some Pt−Ti bonds have to be eliminated to create less favorable Pt−Pt bonds. The latter penalty is greater than the former benefit. The total energy of the Ti-segregated surface with stronger bound adsorbates increases by 0.2 eV. For other adsorbates, because the binding energy on the Tisegregated surface does not change as much as O, the Ti segregation energy to the surface with adsorbates has a more positive value than the O adsorbates. As a result, the Pt8Ti subsurface ordered structure is energetically stable with dilute adsorbate coverage on the Pt surface and Ti in the subsurface layer. a. Segregation and Adsorption of PtTi Subsurface Structure. Segregation of 1/4 ML Ti to Surface Layer. We next study the surface adsorption and segregation of the ordered subsurface PtTi structure as a model of a higher concentration of Ti (Figure 5b). We first discuss the condition where one-half of the subsurface Ti atoms segregate to the surface. This Ti-segregated surface has the same Ti coverage of 1/4 ML as the subsurface layer. We assume the surface and subsurface layer adopt the same p(2 × √3) Pt−Ti ordering, which maximizes the energetically favorable Pt−Ti bonds in each atomic layer. There are three different orientations for the surface Pt−Ti layer with respect to the subsurface Pt−Ti layer. The atomic configurations of the Pt-terminated surface, the Tisegregated surfaces, and their fcc adsorption sites are shown in Figure 8. In these figures, the color of the sites indicates the number of nearest-neighbor Ti atoms (in the surface layer) to the adsorbate, where red is 0 and green is 1. The shape of the sites indicates the number of the subsurface nearest-neighbor Ti atoms to the adsorbate, where a square is 0, a circle is 1, and a diamond is 2. We calculate the binding energy of the same four adsorbates on each fcc site in Figure 8. The adsorbates have a 1/4 ML coverage on the surface. We show the results in Table 4. On the

binding energy difference between the Pt-terminated and the Ti-segregated surface. The segregation tendency of Ti in the presence of adsorbates therefore depends on the balance between these two competing effects in eq 9: (i) the unfavorable segregation of Ti to the clean surface layer and (ii) the favorable increased adsorbate binding to Ti. We list the segregation energy of Ti (eq 8) to the surface with adsorbates at different sites of Figure 7b in Table 3. The Ti Table 3. Segregation Energy of Ti (eq 8) from Pt8Ti Subsurface Structure to the Surface Layer with Adsorbates at Different Adsorption Sites in Figure 7b segregation energy Ebind (eV/Ads)

site 1

site 2

site 3

O S H NO

0.2 1.2 1.1 1.1

0.9 0.9 1.2 1.0

0.9 0.7 1.1 0.8

segregation energy is positive for all four adsorbates, indicating the surface segregation of Ti is not energetically favorable for Pt8Ti with 1/9 ML adsorbate coverage. We can understand the positive segregation energy from eq 9. For the first term in eq 9, because of the dilute Ti concentration and the fact that each subsurface Ti is surrounded by Pt, the Ti segregation to the surface eliminates some of the favorable Pt−Ti bonds and is not energetically favorable. Our calculation shows that it takes +1.2 eV for each Ti atom to segregate from the Pt8Ti subsurface layer to the clean surface layer, similar to the segregation energy of a 1/4 ML Ti subsurface in Figure 1. For the second term in eq 9, because all adsorbates bind stronger to the Ti-segregated surface, their contributions are favorable to the Ti surface segregation. For the O adsorbates, which bind strongest to the Ti-segregated surface, the energy reduction for the system by forming stronger binding between O and the

Figure 8. fcc sites for binding energy calculation on (a) PtTi subsurface structure and (b−d) Pt−Ti surface of different configuration with one-half of the subsurface Ti segregated to the surface. Subsurface atoms are shown as rendered balls, and surface atoms are hollow circles. Ti atoms are shown in blue, and Pt atoms are in gray. Color of the sites indicates the number of nearest-neighbor Ti atoms to the adsorbate: red is 0 and green is 1. Shape of the sites indicates the number of nearest Ti atoms (in the subsurface layer) to the adsorbate: square is 0, circle is 1, and diamond is 2. 4690


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Table 4. Binding Energies of Adsorbates on the fcc Sites of the Pt Surface and Ti-Segregated Pt−Ti Surface in Figure 8a Pt-terminated (Figure 8a)

Ti-segregated 1 (Figure 8b)

Ti-segregated 2 (Figure 8c)

Ti-segregated 3 (Figure 8d)

0.8

0.4

1.0

ETi‑seg − EPt (eV/cell) Ebind (eV/Ads)

site 1

site 2

site 1

site 2

site 3

site 1

site 2

site 3

site 1

site 2

site 3

site 4

NN Ti O S H NO

0 −0.7 −0.9 −0.3 −1.2

0 −0.4 −0.5 −0.2 −1.0

1 −2.5 −1.7 −0.6 −2.1

0 −0.9 −0.9 −0.6 −1.7

1 −2.6 −1.8 −0.5 −2.0

0 −1.0 −1.3 −0.5 −1.6

1 −2.1 −1.2 −0.5 −1.9

1 −2.6 −1.8 −0.6 −1.9

1 −2.6 −1.5 −0.4 −2.0

1 −2.7 −1.6 −0.5 −2.0

0 −1.3 −1.6 −0.5 −0.5

1 −2.4 −1.7 −0.5 −2.1

a

The first row shows the energy change of the Ti-segregated surface with respect to the Pt-terminated surface. The sites with a bold binding energy indicate that the total energy of the Ti-segregated surface decreases with the adsorbates.

Figure 9. Segregation energy of Ti from the PtTi subsurface structure to the surface layer with adsorbates at different sites in Figure 8b−d. For the O and H adsorbates, the surface segregation tendency of Ti does not change with different atomic configurations of the Ti-segregated surfaces. For the S and NO adsorbates, the tendency of Ti surface segregation is dependent on the structures of the surface layers. Subsurface Ti does not segregate to the surface for configuration 3.

Pt-terminated surface, the adsorption sites with two subsurface Ti nearest neighbors (e.g., site 1 in Figure 8a) have stronger adsorbate binding than those sites with only one subsurface nearest Ti neighbor (e.g., site 2 in Figure 8a). Some of the other trends in binding energy from the more dilute Pt8Ti structure still hold for the PtTi structure: (i) binding of all adsorbates is stronger on the Ti-segregated surface than the Ptterminated surface; (ii) except for H, the other three adsorbates show stronger binding to the adsorption sites with a Ti nearest neighbor; (iii) among the four adsorbates, the increase in binding energy from Ti surface segregation is largest for the O adsorbate. The adsorption-induced Ti surface segregation for the PtTi subsurface is also governed by the two effects in eq 9. For a more Ti-concentrated subsurface such as PtTi, the subsurface Ti atoms have Ti neighbors and hence some unfavorable Ti−Ti bonds. When Ti segregates to the surface in this case, the penalty is smaller, because the segregated structures do not eliminate as many Pt−Ti bonds as the dilute Pt8Ti structure. As a result, the energy penalty from the Ti segregation to the clean surface, the first term in eq 9, is smaller for the PtTi structure than Pt8Ti. However, the first term in eq 9 shows a strong dependence on the configuration of the Ti-segregated surface for PtTi due to the difference in the number of the energetically favorable Pt−Ti bonds. The surface Ti atom has all nearest neighbors to be Pt for the configuration in Figure 8c but has to form some energetically unfavorable Ti−Ti bonds for the configurations in Figure 8b and 8d. Therefore, the first term in eq 9 differs from +0.4 eV for the configuration in Figure 8c to +1.0 eV for the configuration in Figure 8d. The energy gain from the strong adsorbate binding, the second term in eq 9,

does not depend strongly on the configuration of the Tisegregated surfaces. Considering the strongest binding sites, the adsorbate binding energy differences between the Pt-terminated and the Ti-segregated surfaces are larger for PtTi than Pt8Ti but similar among different configurations of the Tisegregated surfaces of PtTi. In Figure 9, we use a blue−red color scale to show the Ti segregation energy (eq 9) to the surface with adsorbates at different sites in Figure 8b−d. Blue indicates a negative Ti segregation energy, and red indicates a positive value. For the O adsorbate, the strong binding of O on the Ti-segregated surface makes the effect of the second term in eq 9 much bigger than the first term. Hence, when O occupies the strong binding sites on the Ti-segregated surface, the Ti segregation energy to the surface is negative in all three segregation configurations. Meanwhile, for the weaker binding H adsorbate, Ti segregation is disfavored in all three segregation configurations, because the energy cost for Ti segregation to the clean surface (first term in eq 9) is more than the increase in H binding on the Tisegregated surface (second term in eq 9). The adsorption-induced surface segregation of Ti for PtTi is not only related to the adsorbate type but could also be dependent on the atomic configuration of the segregated surfaces. The two effects in eq 9 are similar in magnitude for S and NO, and the segregation tendency of Ti in the presence of S and NO depends on the balance between these two competing effects. As shown above, the segregation energy of Ti to the clean Pt surface (first term in eq 9) is positive but varies with the atomic configurations of the Ti-segregated surface (from +0.4 to +1.0 eV). The change in binding energy between the Ti-segregated and the Pt-terminated surface 4691


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(second term in eq 9) is from −0.7 to −0.9 eV at the strong binding sites for S and NO. For the segregation configuration in Figure 8d, the energy decrease for the increased Ti− adsorbate bond is not enough to compensate for the energy penalty for the loss of Pt−Ti bonds from Ti surface segregation, and therefore, the Ti surface segregation is not energetically favorable with S or NO adsorbates. Because fewer Pt−Ti bonds are lost when Ti segregates to the surface for the configurations in Figure 8b and 8c, the energy penalty for the first term in eq 9 is smaller for these two configurations. The smaller energy penalty leads to the combined effects in eq 9 to be negative in energy, which indicates the Ti surface segregation is energetically favorable for the S and NO adsorbates on these two surface configurations. b. Segregation of 1/2 ML Ti to the Surface Layer. We now compare segregation of all Ti atoms from the PtTi subsurface to the surface with these adsorbates. We assume the Pt and Ti atoms adopt the same low-energy subsurface ordering at the surface, which maximizes the favorable Pt−Ti bonds in the surface layer. Because more Pt−Ti bonds are lost when all subsurface Ti segregate to the surface, the energy penalty from the first term in eq 9 is 1.63 eV per Ti, larger than any of the segregation configurations in Figure 8. At the same time, all adsorbates also bind stronger at the strong binding sites (two Ti nearest-neighbor atoms to the adsorbates) of the Tisegregated surface at the 1/4 ML adsorbate coverage, giving a larger energy reduction for the second term in eq 9. Segregation of all subsurface Ti is energetically favorable only for the O adsorbates (−0.46 eV/Ti), with positive segregation energies for the other three adsorbates. In Figure 9, the segregation energy for one-half of the subsurface Ti to the surface with O occupying the strong binding sites ranges from −1.0 to −1.4 eV per Ti. With the same O adsorbate coverage, the lower segregation energies indicate it is energetically preferred for one-half of the subsurface Ti, rather than all subsurface Ti, to segregate to the surface with the O adsorbates. From both Pt8Ti and PtTi results, we explain the adsorptioninduced Ti surface segregation in terms of two competing factors: the unfavorable segregation energy of the Ti atom to the clean surface and the favorable energy decrease from adsorbate binding on the Ti-segregated surface. The Ti atoms remain in the subsurface layer when the first factor dominates but segregate to the surface when the second factor becomes important. When the two factors introduce similar magnitude in energy change, the atomic configurations of the segregated surface layers would affect the tendency of the adsorptioninduced Ti surface segregation.

the Pt-rich range have higher order−disorder transition temperatures than their Ti-rich subsurface counterparts. We also conducted a detailed study of the binding energy of different adsorbates (O, S, H, and NO) on Pt-terminated and Ti-segregated surfaces of ordered PtTi and Pt8Ti subsurface alloys. The binding of these adsorbates are generally stronger on Ti-segregated surfaces than Pt-terminated surfaces. The energy preference for the adsorption-induced Ti surface segregation depends on the energetic competition between the favorable increased adsorbate binding to Ti and the unfavorable segregation of Ti to the clean surface. When the two factors introduce similar magnitude in energy change, such as in the case for the S and NO adsorption on Ti-segregated surfaces of PtTi subsurface alloys, the adsorption-induced Ti surface segregation is dependent on the atomic configurations of the Ti-segregated surfaces.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the support for this work by the National Science Foundation under contract nos. CBET0730841 and CBET-0731020.

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REFERENCES

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