Structure and composition of the NiPd(1 1 0) surface

Surface Science 603 (2009) 2193–2199

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Structure and composition of the NiPd(1 1 0) surface G.N. Derry a,*, R. Wan b,1, E. Krueger a,2, J. Waldt c,3, C. English a a b c

Physics Dept., Loyola College, 4501 N. Charles St., Baltimore, MD 21210, United States Physics Dept., University of Maryland-Baltimore County, United States Computer Science Dept., College of Notre Dame, Baltimore, MD 21210, United States

a r t i c l e

i n f o

Article history: Received 22 August 2008 Accepted for publication 10 April 2009 Available online 21 April 2009 Keywords: Low energy electron diffraction (LEED) Surface segregation Surface structure Low index single crystal surfaces Nickel Palladium

a b s t r a c t The NiPd(1 1 0) alloy surface was studied using low energy electron diffraction to measure the structure and composition of the first three atomic layers. The surface layer is highly enriched in Pd and has a significantly buckled structure. The second layer is also buckled, with displacements even larger than the surface layer. The second layer also exhibits intralayer segregation (chemical ordering), with alternate close-packed rows of atoms being Ni enriched and Pd enriched. The third layer has a structure and composition close to that of the bulk alloy. These results are compared with results for the other low index faces of NiPd, the extensive literature on NiPt alloy surfaces, and the growing body of theoretical literature for NiPd alloy surfaces. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Segregation at the surface of binary alloys has a long history of scientific and technological interest, and great progress has now been made in determining both the composition and also the structure of well-characterized single crystal surfaces [1–3]. An important technique in this effort has been low energy electron diffraction (LEED). More specifically, there have been a number of LEED studies of segregation and surface structure in substitutionally disordered alloys, modeling the disorder with the average t-matrix approximation [4–5]. Of particular interest in the present context, there is a substantial body of work on the structure and composition of the Ni/Pt alloys, for a variety of low index crystal faces and bulk compositions [4,6–23] . Motivated in part by these Ni/Pt studies, we have engaged in a series of measurements of the low index faces of a 50 at% NiPd alloy crystal, which makes an interesting comparison because the lattice constant mismatch of the constituent elements is similar and all three of these metals are in the same column of the periodic table. The Ni/Pd system has been much less studied than Ni/Pt alloys. An early series of studies using Auger spectroscopy to measure the compositions of poly-

* Corresponding author. Tel.: +1 410 617 2662; fax: +1 410 617 2646. E-mail address: [email protected] (G.N. Derry). 1 Present address: Kunming University of Science and Technology, Pudong New District, Postcode 201209, P.R. China. 2 Present address: Physics Department, University of Arkansas, Fayetteville, AR 72701, USA. 3 Present address: CareFirst of Maryland. 0039-6028/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2009.04.018

crystalline surfaces were undertaken [24–26], all showing significant Pd segregation to the surface over a wide range of bulk compositions. Palladium segregation for polycrystalline Ni/Pd surfaces was verified by [27,28] using ion scattering spectroscopy. The structure and composition of the single crystal Ni50Pd50(1 0 0) surface were measured by Derry et al. [29] using LEED. This work demonstrated that Pd segregates to the surface of this alloy, but that the second layer is highly enriched in Ni. The oscillatory composition profile is accompanied by contractions of both the first and second interlayer distances. The compositions of two single crystal surfaces, Ni92Pd8(1 1 1) and Ni92Pd8(1 1 0) were measured by Michel et al. [30] using ion scattering spectroscopy and X-ray photoemission, again demonstrating strong Pd segregation. The catalytic activity of these surfaces was measured, but no structural information was obtained. Structural information on Ni92Pd8(1 1 0) was obtained by Abel et al. [31] using scanning tunneling microscopy and by Saint-Lager et al. [32] using surface X-ray diffraction. The present paper reports the results of a LEED study of the structure and composition of the first three atomic layers of the single crystal Ni50Pd50(1 1 0) surface. NiPd is, as indicated, a substitutionally disordered alloy, which crystallizes in a fcc lattice. The large lattice constant mismatch (about 10%) between the constituent elements presumably gives rise to significant strain in the lattice, while the chemical interaction between the unlike atoms would be expected to be modest, consistent with the lack of ordered bulk phases. Our hope is that systematic study of the surface behavior of NiPd low index planes, especially in comparison with the extensive data on the similar (but not identical) Ni/Pt system, will illuminate the relative roles

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of strain and chemical interactions in driving segregation in alloys and its accompanying structural effects. LEED is an extremely useful tool for this purpose, since it provides both the composition and the structure of several layers of atoms near the surface.

2. Experiment The experiments are performed in an ultrahigh vacuum chamber with a base pressure of about 108 Pa. The vacuum is produced by a turbomolecular pump augmented by a Ti sublimation pump, and the chamber is equipped with a reverse-view four-grid LEED optics, ion gun for surface cleaning, and a sample manipulator. The manipulator has three orthogonal directions of translational motion, and two independent rotation axes to vary both the polar and azimuthal angles. The sample is mounted onto a ceramic button heater in the manipulator for sample annealing in vacuum, with the temperature measured by a Pt/Pt10%Rh thermocouple spotwelded to the sample’s edge. A video camera interfaced to an image acquisition system is used to collect the LEED intensity data. LEED intensities are taken to be the integrated intensity within a region-of-interest containing the diffracted beam, with a background (taken to be the intensity at the boundary of the region-of-interest) subtraction and incident intensity correction automatically performed. Trim magnets are employed to null the earth’s magnetic field, and there is also magnetic shielding around the LEED optics. The sample is a disk, about 1 cm diameter by 1 mm thickness, cut from a single crystal of 50 at% NiPd alloy to expose the (1 1 0) surface. The surface is mechanically polished with successively smaller diamond grit, using 0.25 lm diamond for the final step. The surface is then cleaned in vacuum by repeated cycles of Ar ion sputtering and sample annealing. A difficult problem encountered during the cleaning procedure was the strong impurity segregation of sulfur from the bulk, which continued even after an extraordinarily large number of cleaning cycles. A clean surface (as judged by RFA Auger spectroscopy) was eventually obtained by lowering the annealing temperature. To insure that the sample was sufficiently equilibrated at this moderate temperature, LEED patterns at a variety of energies were examined for a wide range of annealing temperature/time conditions; no significant differences were observed, and we conclude that the surface is both clean and well-characterized for our final experimental conditions. The sample preparation protocol we followed to obtain these conditions was 1800 s of sputtering at 3 keV ion energy and 1 lA beam current, followed by 7200 s of annealing at 720 K. After annealing, the sample is cooled to room temperature for data acquisition. Since there is no observable sulfur contamination, it seems reasonable to assume the effects of contaminant cosegregation are negligible. Under these conditions, we observed sharp LEED spots and low backgrounds, although the elastic intensities decreased and the backgrounds increased (more than for other NiPd samples) as the incident beam energy increased. LEED IV curves were measured for two incidence angles, normal incidence (h = 0°, / = 0°) and one off-normal angle (h = 11°, / = 90°). Each experiment was repeated multiple times, with the results averaged for all experiments and averaged over symmetry-equivalent beams; these averaged IV curves are used in the analysis. LEED IV curves for a total of 21 inequivalent beams were obtained altogether for both angles, with a total energy range of 2580 eV. The LEED data was analysed using the Tensor LEED method [33] with the average tmatrix approximation [4,5] to account for chemical disorder. The particular implementation of Tensor LEED used in this work is the TensErLEED software package [34] developed at Erlangen. The phase shifts used in the analysis were calculated with methods

devised by Rundgren [35]. Eight phase shifts were used, and the phase shift calculations also generate an energy-dependent inner potential used in the LEED analysis. Twelve parameters were varied in the structure/composition model reported in the Results section (other models, with different parameters, were also tested). The fit between the experimental and calculated IV curves was measured using the R factor R2, because sensitivity to the actual intensities turned out to be important in this analysis.

3. Results Several qualitative features are apparent in the LEED patterns. The most interesting feature is the presence of dim half-integer beams at relatively low incidence energies (100 eV), suggestive of some ordering mechanism beyond the simple (1X1) termination. In addition, there is a general lowering of the overall elastically scattered intensity (and a rise in the inelastic background) at higher incidence energies (300 eV), with few beams showing any structure or even being measurable above the background at these energies. Based on the presence of the half-integer beams, several structural models consistent with a (1  2) reconstruction (e.g., missing row and shifted row models) were tested, but none demonstrated good agreement with the data. (Adding row shifting to the unreconstructed model that was ultimately successful did not change the R factor appreciably for very small shifts, so strictly speaking this can not be ruled out.) Models in which the atomic planes can relax rigidly, changing the interlayer distances, were also tested and found to be unsuccessful. In order to obtain a good fit between the measured and calculated IV curves, buckling in the surface and in the second layer needed to be included in the model. Finally, to test whether chemical ordering is responsible for the half-integer beams, the compositions of the buckled sublayers were allowed to vary independently in the model. Surprisingly, it turned out that such chemical ordering was needed in the second layer to fit the experimental data, but not in the surface. Because the experimental curves are characterized by an overall decrease in elastically scattered intensity at high energies, we surmised that there is probably a high degree of static disorder in the crystal, in addition to the expected thermal disorder. To model this effect, we allowed the thermal vibration amplitudes to become somewhat higher than usual for purely thermal effects. In addition, we employed R2 instead of RPendry as a measure of the fit between calculated and experimental IV curves, thus gaining sensitivity to the diffracted intensities instead of just sensitivity to the peak positions. Assuming that we are correct, the physical interpretation of the vibrational amplitude parameter values is somewhat ambiguous, and we believe for this reason that it is safer to regard them as primarily fitting parameters rather than as actual sources of information about the surface. Having said that, the best-fit values for these amplitudes were found to be 0.016 nm for the surface, 0.016 nm for the second layer, and 0.011 nm for the third layer. The vibrational amplitude for the bulk atoms was set to 0.007 nm and not further varied. The more interesting parameters are those characterizing the structure and composition of the surface and near-surface region. The composition of the surface layer for the best-fit model is 85% ± 8% Pd, indicating fairly strong palladium enrichment in the surface. Details concerning the fit quality and uncertainty estimates will be presented below, but the experimental IV curves can be visually compared to the IV curves calculated using the best-fit parameters in Fig. 1. For the structure of the surface layer, a good fit was obtainable only by allowing the surface to buckle. In the model, this is accomplished by defining two sublayers in the surface layer. Each sublayer is composed of alternate chains of nearestneighbor atoms, as shown in Fig. 2. The vertical displacement from

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Fig. 2. Illustration of the sublayers defined in the structural model employed. Red atoms are sublayer 11, light blue atoms are sublayer 12, purple atoms are sublayer 21, and dark blue atoms are sublayer 22. Compositions and displacements of these sublayers are given in Tables 1 and 2.

Fig. 1. Experimental (solid lines) and calculated (dashed lines) LEED IV curves for the NiPd(1 1 0) surface at two different incidence angles (the (1,0) and (0,1) vectors correspond to the (0 0 1) and (1–10) directions).

a bulk termination can be independently varied in these two sublayers, modeling a buckled surface. The best fit is found to be a geometry with one sublayer displaced inward toward the bulk by 0.012 nm ± 0.003 nm. The other sublayer remains fixed with a displacement of 0.000 nm ± 0.004 nm. The second layer of atoms is also buckled. In fact, the buckling in the second layer is even more pronounced than in the surface layer. The first sublayer in this plane of atoms is displaced outward toward the surface by 0.015 nm ± 0.003 nm. The second sublayer, in contrast, is displaced by 0.016 nm ± 0.002 nm inward toward the bulk. Remarkably, the compositions of these two sublayers are also significantly different. The first sublayer has a composition of 73% ± 13% Pd, showing a high degree of palladium enrichment. The second sublayer, however, has a composition of only 10% ± 17% Pd, indicating strong nickel segregation into this sublayer. This chemical ordering, caused by intralayer segregation, accounts for the half-integer LEED spots discussed above.

The third atomic layer appears to be essentially bulklike. The displacement is measured to be 0.000 nm ±0.002 nm and the composition is 47% ± 14% Pd. All of these best-fit structure/composition parameters are summarized in Table 1, where ci (or cij) represents the composition and di (or dij) represents the displacement of the ith layer and jth sublayer. (The sign convention used in Tables 1 and 2 is the usual LEED convention in which + means in toward the bulk.) The foregoing results are averages of the parameter values for the two angles of incidence that were used. The analyses were conducted independently for each angle, and the results of these analyses are presented in Table 2. The R factors for these results are R2 = 0.083 for normal incidence and R2 = 0.11 for the offnormal data. Qualitatively, the two sets of results yield a consistent model: Pd segregation to the surface, buckling in both the surface and the second layer, chemical ordering in the second layer, and bulklike behavior in the third layer. Quantitatively, the agreement is excellent for several of the parameter values, and acceptable (i.e., the values agree within the uncertainties quoted above) in all but one case. For every parameter measured, the quoted average value and its uncertainty is in agreement with each of the individual values listed in Table 2, taken to have the same uncertainty. The uncertainties of the parameters are determined using a method that depends on the definition of R2 as a sum of squared differences between the calculated and measured IV curves. In principle, R2 can thus be related to the v2 statistic, since

Table 1 Final best averaged values for structure and composition parameters of NiPd(1 1 0) surface, along with their estimated uncertainties. See text for definitions of parameters.

Compositions (%Pd) Uncertainties (%Pd)

Displacements (nm) Uncertainties (nm)

c1

c21

c22

c3

85 8

73 13

10 17

47 14

d11

d12

d21

d22

d3

+0.012 0.003

0.000 0.004

0.015 0.003

+0.016 0.002

0.000 0.002

Table 2 Best-fit values for NiPd(1 1 0) structure and composition parameters from two independent sets of LEED IV curves for different incidence angles. Compositions (%Pd)

c1

c21

c22

c3

Normal incidence Off-normal incidence

79 90

73 72

13 6

54 40

Displacements (nm)

d11

d12

d21

d22

d3

Normal incidence Off-normal incidence

+0.013 +0.011

0.004 +0.004

0.019 0.009

+0.017 +0.015

0.001 +0.001

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R R2 ¼

½wIexp t ðEÞ  Icalc ðEÞ2 dE R ½wIexp t 2 dE

ð1Þ

and

v2 ¼

2 Z  ½wIexp t ðEÞ  Icalc ðEÞ dE rðEÞ

ð2Þ

where r(E)2 is the variance in the data and w is a scaling factor to match the experimental and calculated curves. This relationship can be used in turn to calculate confidence intervals for the parameters of the best fit, an idea that has been employed by other investigators to estimate parameter uncertainties in LEED analyses [36–38]. In practice, the procedure turns out to be difficult to do rigorously because the values of the measured points are not uncorrelated and the errors in the measured points are neither normally distributed nor the only source of uncertainty in the data. Nevertheless, such an analysis can still be performed in a heuristic manner to produce reasonable estimates of the parameter uncertainties. The variances in the diffracted intensity data can be found empirically using nominally identical IV curves, and these variances then used to compute v2 for the difference between the averaged experimental curves and the calculated best fit, using data points separated by 10 eV (the nominal peak width) to avoid statistical correlation. Knowing both R2 and v2 for the best fit, and making the approximation that R2 / v2, we then immediately have the desired proportionality constant for these numbers. We then can further assume that DR2 / Dv2 with this same proportionality constant for changes in R2 and v2 resulting from variation of the parameters away from the best-fit values. If we can establish the appropriate value of Dv2 corresponding to a 68% confidence interval around the best-fit parameter value, the value of DR2 associated with the uncertainty (taken to be one standard deviation) in this parameter follows trivially. For a model with the variation of only a single parameter, this change in the v2 statistic (for a 68% confidence interval) is well known to be Dv2 = 1; for the simultaneous variation of multiple parameters in a model, Dv2 can be computed using the incomplete gamma function [39]. When this method is applied to the normalincidence data for NiPd(1 1 0) with a full 13 parameter fit, we find Dv2/v2  0.09 which yields DR2  0.0076 for the change in R2 associated with a one standard deviation change in any parameter. Based on these approximations, we find the uncertainties in the structure and composition parameters by plotting R2 versus each parameter and finding the parameter values for R2 = R2,min + DR2. Such plots are shown in Figs. 2–6 for the analysis of the surface and second atomic layer. Clearly, given the assumptions and approximations involved in this procedure, one should not interpret these uncertainties as rigorous standard deviations. We believe, however, that they are still reasonable estimates of the genuine uncertainties in the measured quantities. In the analyses of other surfaces in our laboratory, for which both R2 and RPendry could be used, the uncertainties found using this method are quite comparable to those found using the conventionally employed method [40]. Finally, we explored the effects of altering the model, decreasing or increasing the number of parameters by requiring (or not requiring) the displacements or compositions within an atomic layer to be uniform (not allowing buckling, for example). If we restrict the surface layer to uniform rigid displacements, then R2 increases by DR2  0.02, which is roughly three times the DR2 for a standard deviation change in parameter value; thus, an unbuckled surface layer model yields a significantly worse fit to the data. The comparable results for a rigid second layer are similar, yielding an increase of DR2  0.03 (roughly four times DR2 for the standard

Fig. 3. Plot of R factor R2 versus surface Pd concentration for normal incidence data. Dashed horizontal line represents the R2 value corresponding to one standard deviation in all figures.

Fig. 4. Plot of R factor R2 versus vertical displacements for surface atoms in each sublayer (demonstrating buckling in surface) for normal incidence data.

Fig. 5. Plot of R factor R2 versus second-layer Pd concentration in each sublayer (demonstrating chemical ordering) for normal incidence data.

G.N. Derry et al. / Surface Science 603 (2009) 2193–2199

Fig. 6. Plot of R factor R2 versus vertical displacements for second-layer atoms in each sublayer (demonstrating buckling in second layer) for normal incidence data.

error). Turning to the compositions, if we restrict the composition to the second layer to be uniform (i.e. suppress the chemical ordering), then R2 increases by DR2  0.037, compelling evidence for intralayer segregation. None of these DR2 increases is simply a byproduct of decreasing the number of free parameters in the model. For example, if we increase the number of parameters in the model by allowing chemical ordering in the surface layer, the change in R2 is only a decrease of DR2  0.002, almost twenty times smaller than the comparable second layer result and about four times smaller than the DR2 for a standard deviation parameter change. Thus, there is little evidence for chemical ordering in the surface, and we can easily distinguish between DR2 changes that are fitting artifacts and those that reveal important information about the structure and composition. 4. Discussion The complex structure and composition results observed for the NiPd(1 1 0) surface present several points of interest. The open structure of this crystal face is associated with a higher surface energy, but also with more opportunity for structural changes at the surface to realize a lower-energy configuration. We can infer that the high degree of buckling observed here results from these considerations. The discovery of chemical ordering in the second layer, however, is unexpected. Understanding the details of both the structure and of the composition present a challenge to alloy surface theory. The strong segregation of Pd to the surface of NiPd(1 1 0), however, is easily understood based on elementary considerations, because Pd has a lower surface energy than does Ni. This behavior is also consistent with that of other low index faces of Ni/Pd alloys [29–31] and Ni/Pd polycrystalline alloy surfaces [24–28]. Understanding the surface composition quantitatively appears to be more subtle, though, based on a comparison of the results presented here with the previous results for single crystals. The more open (1 1 0) surface might be expected to show significantly greater Pd segregation based on simple broken bond arguments, but the 85% Pd reported here is only slightly higher than the 80% Pd previously measured for the NiPd(1 0 0) surface and the 82% Pd measured for the close-packed NiPd(1 1 1) surface [29,41]. Turning now to an alloy with the same crystal face but a different bulk composition, the surface of Pd8Ni92(1 1 0) was measured by ion scattering to be 81% Pd [30]. Thus, the surface compositions of an 8% and a 50% bulk alloy are almost the same. We would spec-

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ulate that these results are due to Ni–Pd interactions limiting the degree of surface segregation in the 50% alloy while the much higher lattice strain in the 8% alloy serves to accentuate the segregation of the larger Pd atoms to the surface. One prominent feature of these results is the contrast between the behavior of NiPd(1 1 0) and that of NiPt(1 1 0) reported in the literature [9,11]. The NiPt(1 1 0) surface exhibits an unexpected reversal of the segregating species, with Ni enrichment seen instead of the Pt enrichment that occurs on the other low index surfaces of this alloy. This dramatic phenomenon has been the subject of several theoretical investigations [42–45]. Despite the many similarities between the nickel/platinum and nickel/palladium systems, we find here that NiPd(1 1 0) exhibits strong Pd segregation to the surface. A plausible explanation for this difference in the segregation behavior of the (1 1 0) surfaces of NiPd and NiPt is that the surface energies of Ni and Pt are fairly close to each other, whereas the surface energy of Pd is considerably lower; thus, the delicate energy balance found in the Ni/Pt system would not be operative for Ni/Pd alloy surfaces. This suggests that strain relief, though important, does not solely determine the behavior of these systems. In addition to the strong Pd segregation observed, the NiPd(1 1 0) surface exhibits chemical ordering in the second layer. The existence of chemical ordering here is consistent, in a general sense, with the behavior of other Ni/Pd alloy surfaces, but the specific form of the ordering is much different here. The NiPd(1 0 0) surface [29] and the NiPd(1 1 1) [41] surface, for example, both have oscillatory segregation profiles in the near-surface region, with Ni enriched second layers. Also, the Pd8Ni92(1 1 0) surface [31] shows evidence of chemical ordering accompanying its complex structural changes. There has been significant progress in understanding the source of chemical ordering and Pd segregation observed heretofore in the Ni/Pd alloys [46–52]. Rousset et al. [46] develop a model that is a sophisticated version of broken-bond ideas. The model employs bulk thermodynamic data as input but modifies the pairwise energies to account for the alloy lattice constant, layer-by-layer composition changes, and bond strength modifications at the surface. This model predicts strong Pd surface segregation and oscillating depth profiles for several Pd/Ni alloy systems, though no calculations were done for PdNi(1 1 0) surfaces. Christensen et al. [47] have performed ab initio total energy calculations for the NiPd(1 0 0) surface region, using the coherent potential approximation and effective cluster interactions. Their calculations also predict strong Pd surface segregation and oscillating depth profiles, and both of these phenomena can be interpreted in terms of the magnitudes and signs of the cluster interaction energies. These cluster energies identify the physical origin of the ordering tendency that results in oscillating layer-by-layer compositions. Poyurovskii et al. [48] employ a similar method to calculate the energetics and combine this with Monte Carlo techniques to compute the segregation profiles for all three low-index faces of NiPd. They find strong Pd segregation in all three surfaces, in agreement with experiment, and oscillatory segregation in the (1 0 0) and (1 1 1) surfaces caused by the Pd–Ni pair interactions. For PdNi(1 1 0), Poyurovskii et al. calculate roughly 50 at% for the second layer composition, which they attribute to a competition between the tendency of Pd to segregate to the this layer and the attractive interaction between Ni atoms and the Pd enriched surface. This result is, strictly speaking, in agreement with the experimental results reported here, and their physical reasoning seems consistent with the intralayer segregation that we observe, though they do not report such ordering. The embedded atom method has been applied to the Ni/Pd alloy system by Helfensteyn et al. [49], who computed composition depth profiles using Monte Carlo simulations for all three low index crystal faces; embedded atom method energies were used in Monte Carlo simulations at several temperatures. The surface composition

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of 50 at% NiPd(1 1 0) at 800 K was found to be 91% Pd, in good agreement with the present results. Oscillatory depth profiles are also reported for the (1 0 0) and (1 1 0) surfaces, again consistent with an ordering tendency due to attractive Ni–Pd interactions, but not in agreement with the present results for NiPd(1 1 0). The energetics of several metals, including Ni, alloyed with Pd for (1 1 1) surfaces have been calculated by Lovvik [50] using density functional band structure methods. In these calculations, Pd segregation is predicted and Ni is once again found to be energetically favorable in the second layer. Bozzolo and Noebe and Bozzolo et al. [51,52] performed Monte Carlo simulations on Ni/Pd alloys for all three low index crystal faces at a variety of bulk compositions and temperatures, using the BFS method to compute the energies. The energetics were examined carefully for various environments of individual Pd and Ni atoms. A pronounced ordering tendency was again found, with Pd segregation to the surfaces of all crystal faces and a Ni-enriched second layer for the (1 0 0) and (1 1 1) faces, as found by experiment. The potentially puzzling lack of ordered bulk phases in experimental Ni/Pd phase diagrams was addressed by the finding of stable bulk ordered phases forming in their simulations at very low transition temperatures, where kinetics prevent the occurrence of such phases in nature [51]. The NiPd(1 1 0) predictions were not entirely consistent with the present results, however, because both the second layer and the surface were found to be Pd enriched, with Ni enrichment in the third layer. The structural models used by Bozzolo et al. did not allow for any lattice relaxation, however, whereas the experimental results presented here have considerable buckling. Since the results of Christensen et al. [47] showed that lattice relaxations can have major effects on the layer compositions, we hypothesized that the inclusion of buckling in the BFS calculations might lead to chemical ordering and performed such calculations to test the hypothesis. Although the buckled surfaces are indeed lower in energy, this did not affect the compositions greatly. Also, even though the chemically ordered second layer has a slightly lower energy than a disordered layer of the same composition, the BFS method computes a much lower energy for Pd enrichment of this layer. In summary, then, three different theoretical approaches all consistently predict strong Pd enrichment in the NiPd(1 1 0) surface and five different theoretical approaches find that ordering is expected in Ni/Pd alloys. Despite the finding of a strong ordering tendency in the Ni/Pd system in all of these theoretical studies, however, none have predicted the actual second-layer chemical ordering in NiPd(1 1 0) reported here, and it is unclear exactly what the physical explanation is for this ordering. Most of the theoretical work, though, has assumed a bulk termination for the surface structure, in contrast with the large observed buckling, and this may account for the discrepancy between the experimental and computed depth profiles. We have some reason to believe that strain relief mechanisms are involved, since the only two other alloy systems that we are aware of having lateral chemical ordering within the second layer of the (1 1 0) face are the Pt10Ni90(1 1 0) surface [8] and the Cu85Pd15(1 1 0) surface [53–55], both of which share a large atomic size mismatch with the Ni/Pd case. Such chemical ordering in the second layer is uncommon, and so it is intriguing that all three of these systems have the same open structural termination along with a significant atomic size mismatch in their constituents. In addition, the structure of Pd layers deposited on the Ni(1 1 0) surface also exhibits a large buckling amplitude as part of the strain relief mechanism in that system [56] (although this structure also has other complications like row pairing and vacancies). In the present case, however, we do not understand the details of the strain relief mechanism or its relationship to the ordering tendency, even though the high degree of buckling reported here is likely related to the details of the surface region compositions. Understanding

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