Mechanical Stress Combined with Alloying May Allow Continuous

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Mechanical Stress Combined With Alloying May Allow Continuous Control Over Reactivity: Strain Effects on CO Dissociation and Subsequent Methanation Catalysis Over Ni(211), NiFe(211), and NiFe(112) 3

Michael F Francis, and William A. Curtin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12329 • Publication Date (Web): 21 Feb 2017 Downloaded from http://pubs.acs.org on February 26, 2017

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The Journal of Physical Chemistry

Mechanical Stress Combined with Alloying May Allow Continuous Control Over Reactivity: Strain effects on CO dissociation and subsequent methanation catalysis over Ni(211), Ni3Fe(211), and NiFe(112) Michael F. Francisa,b,†,*, William A. Curtina a

Brown University, Providence, Rhode Island, United States École Polytechnique Fédérale de Lausanne, Lausanne, Vaud, Switzerland

b

Abstract Mechanical stress combined with alloying as controlled by CO dissociation is investigated for the control of methanation activity. CO dissociation over strained Ni(211), Ni3Fe(211), and NiFe(112) is investigated. A continuous 0.62 eV range of CO reaction energy is achievable considering the examined alloys and strains. The CO dissociation energy spanned by the strained NixFey surfaces includes that of elemental Ni, Ru, Co, Rh, Ir. The linear relationship between activation energy and reaction energy is found to be the same under strain as under alloying, suggesting strain as a similar alchemical tool. Peak activity is achievable for each alloy depending on the selection of strain.

I. Introduction The design of a catalyst has traditionally focused on modifying structure and composition1-2. Whether research led to new catalytic materials or not, it became clear that the sampled alloys did not allow complete control over reactivity. Activity could be plotted as a function of a few key parameters, however, known and newly discovered materials were discrete points in this space with optimal catalyst performance often lying at an intermediate value3-10. To achieve optimal catalyst performance one possible strategy considered was a small perturbation of known catalysts using mechanical strain. The application of strain has the advantage that no change in structure or composition of the underlying catalyst is required, however, it was thought that changes in binding due to the application of stress would be small11-13. It was thought that binding to the surface was controlled by a fundamentally electronic picture which resulted from the mixing of orbital states with the bands of the underlying surface14-17. This electronic picture of binding created the anticipation that for the catalytically valuable late transition metals, tension (compression) would always lead to stronger (weaker) binding11, 14. The picture created was also that changes would be small and that as intermediate binding energies would move together, the resulting change in reaction energies would be yet smaller, leading to the limited applicability of strain in catalysis. 1 ACS Paragon Plus Environment


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When direct examination of contributions to changes in binding upon the application of strain were made it was found that a new, non-electronic, mechanical term existed18. When a molecule binds to a surface a structural relaxation occurs, equivalently an adsorbate induced

). When a stress is applied to the surface, strain, (

( ), the stress couples to the

strain and creates a mechanical work, ∆ , given as ∆ = ) (

( ) .

This mechanical work term is distinct from those previously considered electronic factors and demonstrated novel changes in chemical activity. It was found that the energy of intermediates could move more with applied strain than previously thought and furthermore that the energy of the intermediates states did not necessary move together. The energy of the intermediates moving differently with applied strain created the possibility of adding, not subtracting, strain effects and subsequently the possibility of large activity changes with applied strain. We here investigate the combination of alloying and applied strain in methanation catalysis to explore possible catalytic consequences of this novel mechanical energy term. Methanation serves as an excellent test ground for querying the range of activity that may be achieved by combining alloying and strain effects as a methanation model has been constructed19, tested9, and the controlling intermediates are known to be sensitive to both electronic and mechanical strain induced effects18. The methanation model has predicted and experiment confirmed Ni, Ni3Fe, and NiFe to be about the peak of methanation activity making study of these alloys readily analyzed by a tested model and any results relevant to industrial application9, 19. In this paper, we will show that, (i), for the CO reactant and the C+O product states there are significant contributions to changes in binding energy that are both electronic and mechanical in origin, (ii), that the application of strain does not perturb the Brønsted-EvansPolanyi (BEP) relationship for CO dissociation, (iii), that strain allows the continuous varying of the CO dissociation reaction energy and subsequent methanation catalysis, and (iv) that with the appropriate selection of strain, each of the Ni, Ni3Fe, and NiFe surfaces may be made to demonstrate at or near peak activity. The remainder of the paper is organized as follows: In section II, we define the density functional theory approach we use, and the terms used in analysis. In section III, we examine the binding energy of the CO and C+O intermediates, the aspect of their binding energy change that is electronic or mechanical in origin, and insert these results into a methanation model. In section IV, we consider the implications broader catalysis. This paper is a case demonstration that by combining alloying and strain, the engineering goals of continuous control over activity and peak activity with multiple alloys are achievable. II. Methods Defining Energetic Contributions 2 ACS Paragon Plus Environment

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The binding energy, Ebe, of a molecule, A, to a surface, S, is defined as ∗ ⁄ " = ∗ ⁄ " − $ " + &('()) *+.

(1a)

Mechanical and electronic contributions to this binding may be readily decomposed. The mechanical energy is the elastic energy stored in the surface due to the adsorbate induced relaxation18. If we represent the structure of the relaxed surface due to the presence of the molecule A, but in the absence of the molecule, A, as ,- (), and the clean, unrelaxed surface as , the mechanical energy associated with the binding of A may be identified as ∗ ⁄ " = &

,- ()*

− ".

(1b)

The electronic contributions are then given as . ∗ ⁄ " = ∗ ⁄ " − $&

,- ()*

+ &('()) *+.

(1c)

When the substrate is strained, eqns 1 become strain-dependent. We analyze the strain contributions explicitly by subtracting the energy in the presence of strain from the value at zero strain. This gives the change in energy contribution as a function of strain as ∆ (/) = ∗ ⁄ "(/) − ∗ ⁄ "(/ = 0), ∆ (/) = ∗ ⁄ "(/) − ∗ ⁄ "(/ = 0), ∆. (/) = . ∗ ⁄ "(/) − . ∗ ⁄ "(/ = 0).

(2a) (2b) (2c)

In this convention, (2), a negative value is a contribution to stronger binding and a positive value is a contribution to weaker binding. Structural Model and Application of Strain We envision a biaxial stress applied to the surface, which induces corresponding strains in the structure. The strains are then computed by the application of Hooke’s law using the computed stiffness tensor of the bulk substrate.18 For each case the surface is two atoms wide in the direction of the step, and six atoms tall out of the plane of the step, with a vacuum layer of at least ten Angstrom. The bottom two layers of atoms, and the overall cell geometry, are held fixed at the positions dictated by the computed strain tensor. The top four layers of atoms are free to relax, subject to the constraints on the simulation cell geometry at the computed strain tensor.18 Computational Approach

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To compute binding energies, we use density functional theory as implemented in VASP . A Monkhorst-Pack automatic k-mesh generation scheme with 40 subdivisions along each reciprocal lattice lattice vector and shifted with respect to the origin by 0.5 reciprocal lattice vectors was used, resulting in k-mesh densities of 7x8x1 for Ni(211), 6x8x1 for Ni3Fe(211), and 8x7x1 for NiFe(112). Ni(211) and NiFe(112) each are well defined surfaces, whereas Ni3Fe(211) may show both Ni-Ni step termination and Ni-Fe step termnination; here, for Ni3Fe(211), only the Ni-Ni step termination is considered. Due to the inherent distortions associated with the application of strain, care was taken not to utilize symmetry based algorithms. A kinetic energy cut-off of 700 eV was used in all calculations20-22. Electronic structure calculations were converged to 1x10-5 eV; ionic relaxation calculations were converged to 1x10-4 eV. Standard stress minimization techniques were used to determine bulk lattice constants resulting in the values of 3.55 Å for Ni, 3.57 Å for Ni3Fe, and 3.58 Å for NiFe. We use spin-polarized Revised Perdew-Burke-Ernzerhof (RPBE)20-22. Energy barriers were calculated using the Nudged Elastic Band (NEB) method23-24. For interpreting electronic contributions to the binding energy, we will correlate the binding energy with the shift the d-band center, Ed. Defining Ei as the energy level of a d-band state, Ef as the Fermi-level, and nd(Ei) as the density-of-states of a d-band state at energy Ei, the d-band center Ed is computed as 20-22

+∞

Ed = ∑ ( Ei − E f ) nd ( Ei ) .

(3a)

−∞

The shift in the d-band center due to strain is defined as ∆, (/) = , (/) − , (/ = 0).

(3b)

III. Results Change in CO and C+O energies with Applied Strain The reaction pathway for methanation over the Ni(211), Ni3Fe(211), and NiFe(112) surfaces is known to be controlled by the binding of the CO molecule and subsequent dissociation, allowing us to focus on this single reaction2, 19. The reactant state for CO dissociation is the CO molecule bound to the bridge site of the step (Fig 1), the product state is the C atom in the hollow-4 within the step edge and the O atom in the hcp site on top of the step (Fig 2). In discussing the change in binding of the CO and C+O states with strain we first show the change in binding energy, ΔEbe. The electronic picture of binding to late transition metals predicts stronger (negative) binding with an upward movement in the d-band center position, ΔEbe~-ΔEd14. 4 ACS Paragon Plus Environment

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We first consider the change in the binding energy of the CO molecule at the bridge site over the Ni(211), Ni3Fe(211), and NiFe(112) surfaces (Fig 1 a1,b1,c1). Images of the CO bound to each surface is added as an inset (Fig 1 a1,b1,c1). For the case of CO binding to Ni(211) the trend with applied strain is weaker binding – positive slope with applied tensile strain. The binding energy response of CO on Ni(211) is also not readily described as linear. The change in binding energy of CO on Ni(211) is -0.25 eV at an applied strain of -0.03, peaks at 0.05 eV at 0.01, and reduces to ~0.0 eV at an applied strain of 0.03 (Fig 1 a1). For the case of CO binding to Ni3Fe(211) the trend with applied strain is again weaker binding with applied tensile strain. The change in binding energy with applied strain of CO on Ni3Fe(211) is nearly linearly, ranging from -0.0075 eV at -0.03 strain to 0.0025 eV at 0.03 (Fig 1 b1). For the case of CO binding to NiFe(112) the binding energy varies by ~0.02 eV over the range of applied strains, is close to the error of DFT, and has no distinct pattern (Fig 1 c1). For each surface the shape of the binding energy response to an applied strain was different, and in each case the binding energy response to an applied strain could neither be described as linear nor as stronger in response to the applied strain as would have been anticipated by an electronic picture. We now consider the change in the dissociative binding energy of the C+O state over the Ni(211), Ni3Fe(211), and NiFe(112) surfaces (Fig 2 a1,b1,c1). Images of the C+O bound to each surface is added as an inset (Fig 2 a1,b1,c1). For the case of the C+O state over Ni(211) the trend with applied strain is negative and linear with applied tensile strain (Fig 2 a1). As the applied strain goes from -0.03 to 0.03 to change in the dissociative binding energy moves from 0.1 to -0.21 eV. For the case of the C+O state over Ni3Fe(211) the trend with applied strain is negative and curved (Fig 2 b1). The shape of the change in binding energy with applied strain is curved, first beginning at 0.08 eV at -0.03 strain, moving subtly to a peak of 0.085 at -0.025 before dropping to -0.3 eV at 0.03. For the case of the C+O state over NiFe(112) the trend with applied strain is linear and negative (Fig 2 c1). The strain response moves from 0.12 eV at -0.025 strain to -0.09 eV at 0.025. The directionality and structure of the change in binding is what would be anticipated by an electronic picture of binding. Decomposition of CO and C+O Binding Changes into Electronic and Mechanical Components Before we consider the contributing factors to the change in binding energy under an applied strain, we can look back to the six cases of binding energy response under an applied strain and compare them to what would have been anticipated based on a purely electronic picture of bonding. In three of six of the cases the binding energy response to strain was negative (Fig 2 a1,b1,c1), two positive (Fig 1 a1, b1), and one flat (Fig 1 c1). Reiterating, an electronic picture of binding predicts the qualitative changes of binding under an applied strain, ε~ΔEd and ΔEbe~-ΔEd14. The electronic picture of binding would have been correct three out of six times. We now decompose the change in binding into electronic 5 ACS Paragon Plus Environment


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contributions, ΔEelec, and mechanical contributions, ΔEmech. We also show the shift in d-band center with applied strain, describing the shift of those two atoms to which the CO molecule binds to in the reactant bridge position. In order to facilitate comparison of the total binding energy shifts with their component contributions, we present them all together, taking care to show ΔEelec with -ΔEd (Fig 1,2). We now decompose the binding energy response of the CO state into electronic and mechanical contributions (eq 1), determine the change in contributions under strain (eq 2), and look at the d-band shift with strain (eq 3). For the case of CO binding to Ni(211) the change in the electronic contribution to binding with applied strain is largely flat or weakly negative, moving from 0.015 eV at -0.03 strain to -0.002 at a strain of 0.03; concurrently, the d-band center is moving upward with the applied tensile strain (-ΔEd, down), moving from -0.029 eV at -0.03 to 0.018 eV at 0.03 strain (Fig 1 a2). If we look at the mechanical contributions to the change in binding energy with applied strain we see a positive response with strain that curves downward at 0.01 strain and in fact the change in mechanical energy predicts the change in overall energy (Fig 1 a1,a3). For CO binding to Ni(211) the changes in binding under an applied strain are controlled by elastic effects. For the case of CO binding to Ni3Fe(211) the change in electronic contribution to binding with applied strain largely flat with applied strain (Fig 1 b2). The electronic contributions vary from -0.001 eV at -0.03 to 0.0014 eV at 0.03 strain. The CO molecule binding to the Ni3Fe(211) surface binds to both an Ni atom and an Fe atom meaning that there is no singular d-band center that may be used to describe the binding; the shift in the d-band center of both the Ni (squares) and Fe (triangles) atoms to which the CO binds is shown in figure (Fig 1 b2). When the pattern of d-band shift with applies strain of the Ni and Fe in the Ni3Fe(211) surface is examined it is seen that while there is a similar upward trend with applied strain; the d-band center shift at -0.03 strain is centered about ~0.00 eV and at 0.03 strain at about ~0.05 eV. If we look at the mechanical contributions to the change in binding energy we see a positive response with strain varying from -0.0065 eV at -0.03 strain to ~0.0 eV at 0.03 strain (Fig 1 b1,b3). For CO binding to Ni3Fe(211), the overall change in binding energy under the application of an applied strain is again controlled by the change in elastic energy. For the case of CO binding to NiFe(112) the change in electronic contribution to binding with applied strain is largely flat (Fig 1 c2). The step of the NiFe(112) surface is decorated only with Ni atoms allowing the shift in d-band center to be uniquely identified (Fig 1 c2). The NiFe alloy shows no clear trend in d-band shift (Fig 1 c2). If we look at the mechanical contributions to the change in binding energy with applied strain, we see again a relatively flat shift, ~0.03 eV over the domain of applied strains (Fig 1 c3). For CO binding to NiFe(112), the change in binding energy under the application of an applied strain is a mixed electronic, mechanical but small. We now decompose each C+O case into electronic and mechanical contributions (eq 1), determine the change in contributions under strain (eq 2), and look at the d-band shift with 6 ACS Paragon Plus Environment

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strain (eq 3). For the case of C+O to Ni(211) the change in electronic contribution leads to stronger binding (negative slope) with applied strain and the d-band center moves up (Fig 2 a2). The change in the electronic contribution to binding moves from 0.20 eV at -0.025 strain to 0.14 eV while the d-band center moves from -0.029 eV at -0.025 to 0.018 eV at 0.03 strain. When the mechanical contribution to the change in binding energy of the C+O state is examined it is seen that it is curvilinear, varying from -0.125 eV at -0.025 strain to 0.007 eV at 0.005 strain and then down to -0.07 eV at 0.03 strain. The binding energy response of the C+O state on Ni(211) is neither controlled by electronic nor mechanical factors but is a mixed picture. For the case of C+O binding to Ni3Fe(211) the change in electronic contribution leads to stronger binding (negative slope) with applied strain and the d-band center moves up (Fig 2 b2). The change in the electronic contribution to binding moves from 0.14 eV at -0.03 strain to -0.11 eV at 0.025 strain; the d-band centers has the qualitative upward trend previously discussed. If we look at the mechanical contributions to the change in binding energy with applied strain we see a curved structure starting at -0.06 eV at -0.03 strain, raising up to 0.007 eV at 0.005 strain, and then dropping to -0.125 eV at 0.023 strain (Fig 2 b3). For the C+O state on Ni3Fe(211) the binding energy response is a mixed electronic, mechanical picture. For the case of C+O binding to NiFe(112) the change in electronic contribution leads to stronger binding (Fig 2 c2). The electronic contributions range from 0.17 eV at -0.025 to -0.06 at 0.025 strain; the d-band centers of the Ni and Fe metal atoms have the upward trend previously discussed (Fig 2 c2). If we look at the mechanical contributions to the change in binding energy with applied strain we see a largely flat energy response with respect to strain, with the expectation of a single peak (Fig 2 c3). There is a peak in the mechanical contribution to changes in binding energy (Fig 2 c3), that is mirrored by a drop in electronic contributions (Fig 2 c2), however, we offer no physical interpretation for this effect. For NiFe(112), the C+O response to an applied strain is again controlled by a mixed electronic, mechanical picture. We can now look back to the results of the energy decomposition of the binding states and examine how expectations from a purely electronic picture of binding compare with results. Immediately it is observable that for CO cases binding changes were controlled by mechanical effects, and for C+O cases binding energy changes were controlled by mixed electronic, mechanical picture. The electronic picture of the C+O binding energy changes would have been correct, but for the wrong reasons. The component of the strain mediated interaction which was electronic in origin followed the anticipated trend - stronger binding with an applied tensile strain and an upward movement in the surface d-band center. While the electronic component followed the anticipated trend, it alone is an incomplete story. For CO dissociation over strained Ni(211), the linear relationship between activation barrier and reaction energy is maintained 7 ACS Paragon Plus Environment


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The model describing methanation as controlled by the CO dissociation reaction energy requires that there is a linear relationship between the activation energy and reaction energy of CO dissociation2, 19. We here investigate the change in activation barrier to CO dissociation and its relationship to the change in CO dissociation reaction energy under the application of strain over Ni(211). Shown in Fig 3 is the activation barrier and reaction energy for CO dissociation over Ni(211). Labelled in Fig 3 are the sampled strain states and shown as a dashed red line is a linear regression fit to the data. The literature values for the linear relationship, ( = 1∆234 + 5, is α=0.87±0.05,25 and is determined for a broad group of late transition metal steps; Fig 3 shows the linear fit coefficients under an applied strain to be α=0.893±0.169. The linear relationship between activation barrier and reaction energy, the BEP relationship, is a widespread phenomenon determined on an empirical basis and is relied upon in catalysis engineering2, 25. BEP relationships differ across interfaces of the same material and across compounds of the same material; BEP relationships are maintained for a given reaction over a given class of materials over a given type of structure of that material type26. No physics based arguments have been provided for BEP relationships; this empirical presentation of BEP complicates comparison, which is only further complicated by the variation of the relatively new term, the mechanical contribution. We therefore choose to compare the strain based BEP values with the BEP literature BEP values from compositional changes. The literature compositional change provides α=0.87±0.05 and the applied strain provides α=0.893±0.169 giving no statistical evidence of a difference. Empirically, the BEP due to strain at this structure is no different from that due to compositional changes. This result reiterates the observation that changes in chemistry due to composition and changes in chemistry due to strain are qualitatively similar. Strain enabled methanation catalysis Methananation has been successfully modelled as controlled by dissociative chemisorption19. The CO molecule binds and dissociates to form bound C and O states, with the overall reaction being readily described by the dissociative adsorption energy19 or CO reaction energy9. We have determined the change in binding behavior of the CO dissociation reactant state (Fig 1), product state (Fig 2), and change in activation energy of CO with respect to reaction dissociation reaction energy under strain (Fig 3). We now use this (Figs 1-3) to determine the change in reaction energy of CO dissociation under the application of strain (Fig 4a) and insert that reaction energy change into the methanation model (Fig 4b). The change in reaction energy of CO dissociation over Ni(211), Ni3Fe(211), and NiFe(112) under the application of a biaxial stress is shown in Fig 4a. The reaction energy has 8 ACS Paragon Plus Environment

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been determined and referenced to the Ni(211) case at zero strain (Fig 4a). The application of strain allows a reaction energy range of 0.44 eV over Ni(211), 0.39 eV over Ni3Fe(211), and 0.24 eV over NiFe(112). These reaction energy ranges are quantitatively significant but furthermore allow the continuous change of reaction energy. The reaction energy swept by Ni(211), Ni3Fe(211), and NiFe(112) using strain is 0.62 eV and is over the same reaction energy domain as the elemental metals of Ru, Co, Rh, and Ni 19. We now take the reaction energy changes due to the application of strain and insert it into the existing model by Andersson et al.19(Fig 4b). The existing model describes methanation activity in terms of the reaction energy to CO dissociation over steps9, 19. From more endothermic to exothermic CO dissociation, the activity changes by more than one order of magnitude. Noteworthy in Fig 4b is that peak activity is achievable by any one of the sampled alloys with an applied strain – Ni(211) at ε=0.03, Ni3Fe(211) at ε=0.015, NiFe(112) at ε=0.025. IV. Discussion and Conclusion In this paper we have demonstrated that strain may be used as a tool to gain fine control of methanation activity over NixFey catalysts. The sampled strains are those due to the application of a biaxial stress and are in the range of -0.03 to 0.03. The sampled strains both allow continuous control over activity about peak activity and demonstrate that each of the sampled alloys may be used to achieve peak activity – Ni(211) at ε=0.03, Ni3Fe(211) at ε=0.015, NiFe(112) at ε=0.025. The activity mediating strains are readily achievable using core-shell nano-particles27. These core-shell nanoparticles demonstrate controllable, static strains which are readily designable28, with strains of at least 4 % achievable29, allowing the designing of strain assisted catalysis. Seeing the possible meritorious application of strain to methanation catalysis it becomes natural to consider the possible broader application in catalysis. Descriptor theory plots, such as Fig 4, rely upon the existence of the BEP relationship, Fig 3, and scaling relationships2. The BEP relationship being the linear relation between the change in activation energy of a process, ( , and the change in reaction energy of that process, ∆234 , according to ( = 1∆234 + 5, and scaling relationships being the linear relationship between the valence binding energy of two species (AY and AX) that bind to a surface through the same element (A), 89 8; regardless of the ligands (X or Y)30, 67 = γ67 + ξ. The evidence provided here is not sufficient to comment on how strain may influence broader BEP or scaling relations. Two possible futures are imaginable, one in which both BEP and scaling is maintained under the application of strain and therefore strain becomes an alchemical tool, and a second in which one or both of these relations is not maintained and fundamentally new types of activity become available, again, an alchemical tool. Whichever of these two imaginable futures is the case, strain engineering of catalysis may create additional innovation opportunities. For 9 ACS Paragon Plus Environment


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these reasons the latest sets of studies have shown that strain engineering stands to make more meritorious contributions to chemical systems than previously imagined, however, the possible utility of strain engineering to other systems is, for the time being, something that must be determined on a case-by-case basis. Acknowledgements The authors acknowledge support from the US Army Research Office through the Grant No. W911NF-11-1-0353. Corresponding Author *(M.F.F.) E-mail: [email protected], [email protected] Telephone: +1.505.665.4689 Present Address Los Alamos National Laboratories, Los Alamos, New Mexico, 87545

†

Notes The authors declare no competing financial interest.


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Figures 0.010

CO*/Ni(211)

CO*/Ni3Fe(211)

∆Ebe

∆Ebe

0.000

-0.005

-0.2

(a1)

0.0

(b1) 0.1

0.0

(c1)

-0.04

0.05

Ni

0.04

0.005

-0.2

-0.2

-0.005

-0.3

-0.010

0.02

0.00

0.000

-0.1

(a2)

-0.02

0.05

0.010

-0.1

-0.3

0.00

-0.05

Fe

(b2)

0.00

0.00 -0.05

-0.02 -0.04

(c2)

-0.10

−∆Ed

-0.1

−∆Ed ∆Eelec

∆Ebe

CO*/NiFe(112)

0.02

0.1

∆Eelec

0.04

0.005

0.0

−∆Ed ∆Eelec

0.1

-0.10

0.04 0.005

∆Emech

0.000

-0.1

-0.005

-0.2

-0.3 -0.03 -0.02 -0.01

0.02

∆Emech

0.0

∆Emech

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a3) 0.00

ε

0.01

0.02

0.03

-0.010 -0.03 -0.02 -0.01

(b3) 0.00

ε

0.01

0.02

0.03

0.00 -0.02

(c3)

-0.04 -0.03 -0.02 -0.01

0.00

0.01

0.02

0.03

ε

Figure 1. Change in binding energy as a function of strain for CO bound to, (a), Ni(211), (b), Ni3Fe(211), and (c), NiFe(112). An image of the CO bound states is added as insets. For each surface, (1), the total change in binding energy (ΔEbe, black), (2), electronic contribution to change in binding energy along with the negative of the shift in d-band energy (ΔEelec, red; -ΔEd, blue), and the (3), mechanical contribution to the shift in binding energy is given (ΔEmech, green). For the case of the d-band shifts of Ni3Fe, the CO molecule is coordinated both to Ni and Fe; the dband center shifts of Ni and Fe are both shown with Ni labeled as squares and that of Fe as triangles. Vertical axes are in units eV.



0.3

(C*+O*)/Ni(211)

(C*+O*)/Ni3Fe(211)

0.1

0.2

0.2

(C*+O*)/NiFe(112)

0.0

0.0 -0.1 -0.2

(a1)

0.3

∆Ebe

∆Ebe

∆Ebe

0.1 -0.1 -0.2

(b1)

-0.3 0.3

0.05

0.1

(c1)

0.0

-0.1

0.05

0.1

0.1 0.0 -0.1

-0.2

-0.2

(a2)

-0.3

−∆Ed ∆Eelec

∆Eelec

0.0 -0.1

Ni

0.00

-0.1 -0.2

0.00 0.1

-0.05

Fe

-0.3

(b2)

-0.3

-0.10

(c2)

0.0

-0.1

-0.05

−∆Ed

0.2

0.1

−∆Ed ∆Eelec

0.2

0.2 0.0

-0.10

0.1 0.2

0.2

∆Emech

0.0 -0.1 -0.2 -0.3 -0.03 -0.02 -0.01

(a3) 0.00

ε

0.01

0.02

0.03

∆Emech

0.0 0.1

∆Emech

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 21

-0.1 -0.2 -0.3 -0.03 -0.02 -0.01

0.1

(c3)

0.0

(b3) 0.00

0.01

0.02

0.03

ε

-0.1 -0.03 -0.02 -0.01

0.00

0.01

0.02

0.03

ε

Figure 2. Change in binding energy as a function of strain for C+O bound to, (a), Ni(211), (b), Ni3Fe(211), and (c), NiFe(112). An image of the C+O bound states is added as insets. For each surface, (1), the total change in binding energy (ΔEbe, black), (2), electronic contribution to change in binding energy along with the negative of the shift in d-band energy (ΔEelec, red; -ΔEd, blue), and the (3), mechanical contribution to the shift in binding energy is given (ΔEmech, green). As for CO binding to Ni3Fe, C+O is coordinated both to Ni and Fe; the d-band center shifts of Ni and Fe are both shown with Ni labeled as squares and that of Fe as triangles. Vertical axes are in units eV.


Page 13 of 21

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Fig 3. Activation barrier to CO dissociation over Ni(211) as a function of change in reaction energy. The dashed line is a linear regression fit to the data which gives a slope of 0.893±0.169. The inset images are the reactant, CO, and product states, C+O.



0.4

Ediss[CO/S(hkl)(ε)] -Ediss[CO/Ni(211)(ε=0)]

0.3 0.2 0.1

Ni

0.0 -0.1

NiFe

-0.2 -0.3

(a)

-0.4 -0.03 -0.02 -0.01

16

0.00

0.01

0.02

0.03

Ni3Fe

14

Ru

12 10

Ni3Fe

ε

18

Activity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 21

NiFe

Co

8 6 4 2

Rh

(b)

Ni

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Ediss[CO/S(hkl)(ε)] -Ediss[CO/Ni(211)(ε=0)] Fig 4. (a) Change in CO dissociation reaction energy as a function of applied strain, using the unstraind Ni(211) as a 19 reference, and (b), the subsequent methanation activation based on the Andersson model . Shown in grey in (b) are the reaction energy positions of Co, Ru, and Rh and their activity according to the Andersson model. The unit of activity is mmol/(mol*s).


Page 15 of 21

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References 1. Vojvodic, A.; Nørskov, J. K., New design paradigm for heterogeneous catalysts. National Science Review 2015, 2 (2), 140-149. 2. Nørskov, J. K.; Abild-Pedersen, F.; Studt, F.; Bligaard, T., Density functional theory in surface chemistry and catalysis. Proceedings of the National Academy of Sciences 2010, 108 (3), 937-943. 3. Besenbacher, F.; Chorkendorff, I.; Clausen, B. S.; Hammer, B.; Molenbroek, A. M.; Nørskov, J. K.; Stensgaard, I., Design of a Surface Alloy Catalyst for Steam Reforming. Science 1998, 279 (5358), 19131915. 4. Jacobsen, C. J. H.; Dahl, S.; Clausen, B. S.; Bahn, S.; Logadottir, A.; Nørskov, J. K., Catalyst Design by Interpolation in the Periodic Table: Bimetallic Ammonia Synthesis Catalysts. Journal of the American Chemical Society 2001, 123 (34), 8404-8405. 5. Jacobsen, C. J. H.; Dahl, S.; Boisen, A.; Clausen, B. S.; Topsøe, H.; Logadottir, A.; Nørskov, J. K., Optimal Catalyst Curves: Connecting Density Functional Theory Calculations with Industrial Reactor Design and Catalyst Selection. Journal of Catalysis 2002, 205 (2), 382-387. 6. Toulhoat, H.; Raybaud, P., Kinetic interpretation of catalytic activity patterns based on theoretical chemical descriptors. Journal of Catalysis 2003, 216 (1–2), 63-72. 7. Strasser, P.; Fan, Q.; Devenney, M.; Weinberg, W. H.; Liu, P.; Nørskov, J. K., High Throughput Experimental and Theoretical Predictive Screening of Materials − A ComparaYve Study of Search Strategies for New Fuel Cell Anode Catalysts. The Journal of Physical Chemistry B 2003, 107 (40), 1101311021. 8. Greeley, J.; Nørskov, J. K.; Kibler, L. A.; El-Aziz, A. M.; Kolb, D. M., Hydrogen Evolution Over Bimetallic Systems: Understanding the Trends. ChemPhysChem 2006, 7 (5), 1032-1035. 9. Andersson, M. P.; Bligaard, T.; Kustov, A.; Larsen, K. E.; Greeley, J.; Johannessen, T.; Christensen, C. H.; Nørskov, J. K., Toward computational screening in heterogeneous catalysis: Pareto-optimal methanation catalysts. Journal of Catalysis 2006, 239 (2), 501-506. 10. Sehested, J.; Larsen, K.; Kustov, A.; Frey, A.; Johannessen, T.; Bligaard, T.; Andersson, M.; Nørskov, J.; Christensen, C., Discovery of technical methanation catalysts based on computational screening. Topics in Catalysis 2007, 45 (1-4), 9-13. 11. Schnur, S.; Groß, A., Strain and coordination effects in the adsorption properties of early transition metals: A density-functional theory study. Physical Review B 2010, 81 (3), 033402. 12. Akhade, S. A.; Kitchin, J. R., Effects of strain, d-band filling, and oxidation state on the surface electronic structure and reactivity of 3d perovskite surfaces. The Journal of Chemical Physics 2012, 137 (8), 9. 13. Nørskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H., Towards the computational design of solid catalysts. Nature Chemistry 2009, 1 (1), 37-46. 14. Mavrikakis, M.; Hammer, B.; Nørskov, J. K., Effect of Strain on the Reactivity of Metal Surfaces. Physical Review Letters 1998, 81 (13), 2819-2822. 15. Kitchin, J. R.; Nørskov, J. K.; Barteau, M. A.; Chen, J. G., Role of Strain and Ligand Effects in the Modification of the Electronic and Chemical Properties of Bimetallic Surfaces. Physical Review Letters 2004, 93 (15), 156801. 16. Abild-Pedersen, F.; Greeley, J.; Nørskov, J. K., Understanding the Effect of Steps, Strain, Poisons, and Alloying: Methane Activation on Ni Surfaces. Catalysis Letters 2005, 105 (1-2), 9-13.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

17. Ruban, A.; Hammer, B.; Stoltze, P.; Skriver, H. L.; Norskov, J. K., Surface electronic structure and reactivity of transition and noble metals. Journal of Molecular Catalysis A: Chemical 1997, 115 (3), 421429. 18. Francis, M. F.; Curtin, W. A., Mechanical work makes important contributions to surface chemistry at steps. Nature Communications 2015, 6, 1-7. 19. Bligaard, T.; Nørskov, J. K.; Dahl, S.; Matthiesen, J.; Christensen, C. H.; Sehested, J., The Brønsted–Evans–Polanyi relation and the volcano curve in heterogeneous catalysis. Journal of Catalysis 2004, 224 (1), 206-217. 20. Zhang, Y.; Yang, W., Comment on “Generalized Gradient Approximation Made Simple”. Physical Review Letters 1998, 80 (4), 890-890. 21. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77 (18), 3865-3868. 22. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Physical Review Letters 1997, 78 (7), 1396-1396. 23. Jonsson, H. M., G; Jacobsen, KW, Classical and Quantum Dynamics in Condensed Phase Simulations. 1998. 24. Olsen, R. A.; Kroes, G. J.; Henkelman, G.; Arnaldsson, A.; Jonsson, H., Comparison of methods for finding saddle points without knowledge of the final states. Journal of Chemical Physics 2004, 121 (20), 9776-9792. 25. Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Bahn, S.; Hansen, L. B.; Bollinger, M.; Bengaard, H.; Hammer, B.; Sljivancanin, Z.; Mavrikakis, M.; Xu, Y.; Dahl, S.; Jacobsen, C. J. H., Universality in Heterogeneous Catalysis. Journal of Catalysis 2002, 209 (2), 275-278. 26. Viñes, F.; Vojvodic, A.; Abild-Pedersen, F.; Illas, F., Brønsted–Evans–Polanyi Relationship for Transition Metal Carbide and Transition Metal Oxide Surfaces. The Journal of Physical Chemistry C 2013, 117 (8), 4168-4171. 27. Strasser, P.; Koh, S.; Anniyev, T.; Greeley, J.; More, K.; Yu, C.; Liu, Z.; Kaya, S.; Nordlund, D.; Ogasawara, H.; Toney, M. F.; Nilsson, A., Lattice-strain control of the activity in dealloyed core–shell fuel cell catalysts. Nature Chemistry 2010, 2 (6), 454-460. 28. Moseley, P.; Curtin, W. A., Computational Design of Strain in Core-Shell Nanoparticles for Optimizing Catalytic Activity. Nano letters 2015. 29. Brochard, S.; Hirel, P.; Pizzagalli, L.; Godet, J., Elastic limit for surface step dislocation nucleation in face-centered cubic metals: Temperature and step height dependence. Acta Materialia 58 (12), 41824190. 30. Peterson, A. A.; Nørskov, J. K., Activity Descriptors for CO2 Electroreduction to Methane on Transition-Metal Catalysts. The Journal of Physical Chemistry Letters 2012, 3, 251-258.


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Page 17 of 21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.010

-0.005

1

0.000

Ni

0.00 -0.02

(c1)

-0.04

0.05

0.05

0.04 0.02

0.00

-0.05

Fe

(b2)

-0.010

-0.10

0.00

0.00 -0.05

-0.02

(c2)

-0.04

-0.10

0.04 0.005

∆Emech

∆Emech

3

-0.005

(b1)

−∆Ed ∆Eelec

0

0.005

−∆Ed ∆Eelec

1

2

∆Ebe

0.000

0.010

CO*/NiFe(112)

0.02

∆Ebe

0.005

CO*/Ni3Fe(211)

0.04

0.000

-0.005 -0.010 -0.03 -0.02 -0.01

(b3)

ε

0.00

0.01

0.02

0.02 0.00 -0.02

(c3)

-0.04

0.03

-0.03 -0.02 -0.01

ACS Paragon Plus Environment

0.00

ε

0.01

0.02

0.03


Page 18 of 21

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0.1

∆Ebe

-0.2

-0.1 -0.2

(a1)

0.3 0.2

0.3

0.0

−∆Ed ∆Eelec

0.1

0.0

0.0

-0.1

-0.2

-0.2

-0.2

-0.3

-0.3

-0.3

-0.1

Ni

-0.05

Fe

(b2)

-0.10

∆Emech

∆Emech

∆Emech

-0.2

-0.2

(a3) 0.00

ε

0.01

0.02

0.03

(b3)

-0.3 -0.03 -0.02 -0.01

0.1

(c2)

0.0

-0.05

-0.10

0.2

-0.1

-0.1

0.00

-0.1

0.1 0.0

0.0

0.05

0.00

0.2 0.1

(c1)

0.0

0.2

-0.1

-0.1

(a2)

0.05

0.1

0.2

0.1

(b1)

-0.3

0.1

−∆Ed

∆Ebe

-0.1

0.0

-0.3 -0.03 -0.02 -0.01

(C*+O*)/NiFe(112)

0.0

0.1

∆Eelec

0.2

∆Ebe

0.2

(C*+O*)/Ni(211)

(C*+O*)/Ni3Fe(211)

−∆Ed ∆Eelec

0.3

0.00

ε

0.01


0.02

0.03

0.1

(c3)

0.0

-0.1 -0.03 -0.02 -0.01

0.00

ε

0.01

0.02

0.03

Page 19 of 21


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Activation Barrier

2.1

ε=0.00 2.0

ε=0.02 p o l s

1.9

= e

9 8 . 0

1 . 0 ± 3

ε=−0.01

9 6

ε=0.03

1.8 -0.2

-0.1

0.0

Ediss[CO/Ni(hkl)(ε)] -Ediss[CO/Ni(211)(ε=0)]


0.1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ediss[CO/S(hkl)(ε)] -Ediss[CO/Ni(211)(ε=0)]

0.4 0.3 0.2 0.1

Ni

0.0 -0.1

NiFe

-0.2 -0.3

(a)

-0.4 -0.03 -0.02 -0.01 18 16

Ni3Fe

Activity

14 12 10

Co

Ru

Ni3Fe 0.00

0.01

ε

0.02

0.03

NiFe

8 6 4 2

(b)

Rh

Ni

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Ediss[CO/S(hkl)(ε)] [CO/Ni(211)(ε=0)] -E -Ediss [ CO/Ni(hkl) ( ε=0 )] diss


Page 20 of 21

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Catalyst Activity

Page 21 of 21

Strain enables continuous control over activity

ε+ ε+

ε+

Alloy 3

Alloy 1

ε-

Alloy 2

ε-

ε-

Surface Reaction Energy ACS Paragon Plus Environment

Mechanical Stress Combined with Alloying May Allow Continuous

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