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Comparison of surface structure and segregation in AgAu and NiPd alloys
Surface Science 566–568 (2004) 862–868 www.elsevier.com/locate/susc
Comparison of surface structure and segregation in AgAu and NiPd alloys G.N. Derry b
a,*
, R. Wan
b
a Department of Physics, Loyola College, 4501 N. Charles St., Baltimore, MD 21210, USA Department of Physics, University of Maryland-Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
Available online 15 June 2004
Abstract The structure and composition of a single-crystal AgAu(1 0 0) alloy surface was studied using low energy electron diffraction. The surface was found to be moderately enriched in silver, while the second atomic layer has an essentially bulklike composition. The first interlayer distance exhibits a small contraction, with a small expansion found in the second interlayer. This structure composition behavior is compared to that found in the low index surfaces of the NiPd alloy, which has compositional oscillations and a more complex surface relaxation behavior. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Low energy electron diffraction (LEED); Surface segregation; Surface structure, morphology, roughness, and topography; Low index single crystal surfaces; Gold; Silver; Nickel; Palladium
1. Introduction Surface segregation in alloys has long been considered an important scientific and technological problem, and a great deal of progress has been made in understanding the phenomenon by studying clean, well-characterized, single-crystal alloy surfaces [1–3]. There is an intimate relationship between the composition of the surface and its structure, and the use of clean, single-crystal surfaces allows us to measure both the structure and the composition simultaneously, given an appropriate measurement method. One such method is low energy electron diffraction (LEED), which has *
Corresponding author. Tel.: +410-617-2662; fax: +410-6172646. E-mail address: [email protected] (G.N. Derry).
emerged as an important technique in the study of alloy surfaces. A particular advantage of LEED is that it provides information about the structure and composition of several atomic layers in the near-surface region, as well as the actual surface layer. Although a considerable body of work exists on chemically ordered alloys and intermetallics, LEED has also been extensively applied to disordered alloy crystals, using the average t-matrix approximation [4,5]. The present article is a contribution to this literature, reporting the use of LEED with the average t-matrix approximation to measure the structure and composition of the surface (and near-surface region) of a 50 at.% AgAu(1 0 0) alloy. Silver/gold alloys are fcc crystals that form substitutionally disordered solid solutions for their entire composition range. The atomic radii of
0039-6028/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.022
G.N. Derry, R. Wan / Surface Science 566–568 (2004) 862–868
the constituent elements are almost equal, so there is very little lattice strain in this alloy. Also, excessive chemical interactions are not found [6], since the two elements are both noble metals. We will compare these results for the silver/gold system with a previously measured set of results for three low index surfaces of a 50 at.% NiPd alloy [7–9]. Nickel/palladium alloys also form fcc crystals and also are substitutionally disordered for all bulk compositions, but in contrast to silver/ gold the Ni and Pd atoms have atomic radii that are about 10% different, resulting in a large degree of lattice strain. This lattice strain can be expected to affect the structure and segregation behavior at the surface, making the comparison of Ni/Pd and Ag/Au alloy results instructive.
2. Experiment The measurements are done in an ultrahigh vacuum chamber with a base pressure of about 108 Pa. The chamber is equipped with a reverseview four-grid LEED optics, ion gun for surface cleaning, and a sample manipulator. The manipulator has three orthogonal directions of translational motion, and rotational motion about both the polar and azimuthal angle axes. The sample is mounted onto a ceramic button heater in the manipulator for sample annealing in vacuum. A video camera interfaced to an image acquisition system is used to collect the LEED intensity data. The sample is a single crystal of AgAu with 50 at.% bulk composition, in the form of a disk about 1 cm diameter and 1 mm thickness, cut to expose the (1 0 0) crystal face. The surface was mechanically polished with diamond compound, using successively smaller sizes until a final polish with 0.25 lm diamond. Annealing in vacuum caused visible roughening of the surface, and the polishing procedure had to be repeated twice before a suitable surface was obtained. With moderate heating, only very slight roughening occurred during the actual data acquisition period. The surface was cleaned in vacuum by cycles of sputtering and annealing, and appeared to be free of contamination using RFA Auger spectroscopy after only a few cleaning cycles. The LEED spots, however,
863
required a number of further cycles, with longer annealing times, before they became sharp and well-differentiated from the background. In fact, the diffraction spots never became highly intense compared to the background scattering, causing the LEED IV curves to remain somewhat noisy. To counteract this noise problem, all of the measurements were repeated multiple times and averaged, with further averaging being done over all symmetry equivalent beams. The final annealing temperature was 800 K prior to data acquisition at 300 K. LEED IV curves were acquired at four different incident beam angles to extend the total energy range (which was 3290 eV) and number of inequivalent beams (which was 24). The uncertainties in the angles were ±1° for h and ± 2° for u. The normal incidence data (h ¼ 0°, u ¼ 0°) are the most reliable because a large amount of symmetry equivalent beam averaging was possible, but they do not cover a large energy range. Two of the offnormal angles (h ¼ 8°, u ¼ 0°; h ¼ 12°, u ¼ 0°) also allowed significant symmetry averaging. The fourth angle (h ¼ 13°, u ¼ 40°) was problematic due to a misalignment of the azimuthal angle axis in the sample manipulator, however, and the quoted angle values have been adjusted from the intended nominal incident angle. Variation of the incidence angles in the scattering calculations suggests that the structure/composition parameters are relatively insensitive to the experimental angle uncertainties. The measured IV curves were compared to the results of parameterized scattering calculations using the Tensor-LEED method [10]. The implementation of this method that we employed was the TensErLEED software package [11]. Ten phase shifts were used, computed with a method devised by Rundgren [12], and chemical disorder was modeled using the average t-matrix approximation [4,5]. The best fit between the data and the computed IV curves was determined using both the Pendry R factor [13] (which emphasizes sensitivity to the peak positions) and R2 [14] (which is instead sensitive to the relative diffracted intensities). The final parameter values are taken to be the averages over all incident angles and R factors. The parameters that were varied are the compositions
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of the first two atomic layers, the first two interlayer distances, and the vibrational amplitudes in these layers (and also, as usual, the LEED inner potential).
3. Results To briefly summarize the main results of our analysis, we find that segregation in the AgAu(1 0 0) alloy is largely restricted to the surface monolayer, which is enriched with silver. Quantitatively, the surface composition is 76% ± 16% Ag while the second layer composition is 45% ± 18% Ag. Structurally, the first interlayer distance decreases by 0.003 ± 0.002 nm (i.e. a roughly 1.5% contraction) while the second interlayer distance increases by 0.005 ± 0.002 nm (a roughly 2.5% expansion). A comparison of the measured and calculated IV curves for the best fit using R2 is displayed for all four incident angles in Fig. 1 (the comparable curves using RP are slightly different in detail but the quality of the fits is visually similar). Quantitatively, the fits for three of the incident angles using R2 and two of the incident angles using RP are fairly good; two others (one angle using R2 and another using RP ) yield somewhat high but acceptable fit values, but the RP fit for one angle is too poor (and insensitive to parameter variations) to produce meaningful results. The R factors for all conditions are given in Table 1. Because of the limited energy range, the noise in the IV curves, and the fact that there are relatively few prominent features in each curve, results from any single incident angle are not highly precise and reliable. Table 1 illustrates the rather large degree of scatter in these individual incident angle results; note, however, that they do agree with each other well enough both to demonstrate broad trends in the results and to agree with each other within their substantial uncertainties. For all of the fitting results listed in Table 1, the vibrational amplitudes of the surface and second layer were fixed at 0.016 nm and 0.011 nm, respectively, based on the preliminary results of seven-parameter fits (the bulk vibrational amplitude was set as 0.009 nm based on the Debye temperature and atomic mass of the
alloy components). The physical interpretation of these vibrational amplitude values is unclear because of the mixture of static disorder with genuine thermal effects, but the other parameter values do not depend sensitively on the vibrational parameter values in any event. Results for all of the different incident angles were combined to obtain more precise and reliable values of the structure and composition parameters. This was first done separately for R2 and RP to make sure that the different R factors generate results that agree within their uncertainties. These separate parameter values were then averaged to obtain the final values listed in Table 2. Although the same data was used for both analyses, we believe that the averages represent more reliable values because the two different R factors are sensitive to different features of the data (peak positions in the RP case compared to actual diffracted intensities for R2 ). Uncertainties for the parameters found using RP were computed with the standard methods employed for this R factor and its variation [13]. Uncertainties for the parameters found using R2 were estimated with a technique, adapted from the work of Adams et al. [14–16], that relates R2 to the v2 statistic in order to determine the R2 cut-off corresponding to a standard deviation in the measured parameter. Fig. 2 shows the results of this method for the surface and second layer compositions, with results for all four incidence angles combined to generate a ‘‘global’’ R2 value for all of the data. Uncertainties computed using these two methods (with RP and R2 ) are quite comparable. The uncertainty values listed in Table 2 are those found using the R2 method.
4. Discussion The results reported herein for the AgAu(1 0 0) surface form an interesting comparison both with the previous results reported in the literature for this alloy [17–24] and with a completed set of results for NiPd alloy surfaces that have been measured in our laboratory. These NiPd results, details of which are reported elsewhere [7–9], are summarized briefly in Table 2 along with the present AgAu(1 0 0) results.
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Fig. 1. Experimental (solid lines) and calculated (dashed lines) AgAu(1 0 0) LEED IV curves for all measured beams at all incidence angles. These curves are for the best-fit results using R2 .
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Table 1 Best-fit values of the structure/composition parameters for AgAu(1 0 0) determined for each angle of incidence, using both R2 and RP h (°)
u (°)
c1 (%Ag)
c2 (%Ag)
d12 (nm)
d23 (nm)
R type
R value
0 0 )8 )8 )12 )12 )13 )13
0 0 0 0 0 0 )40 )40
66 80 66 80 85 69 85 –
29 50 45 60 35 52 40 –
0.001 0.002 )0.005 )0.004 )0.006 )0.006 )0.002 –
0.004 0.003 0.006 0.004 0.007 0.007 0.006 –
R2 RP R2 RP R2 RP R2 RP
0.04 0.23 0.08 0.45 0.05 0.32 0.15 0.55
c and d denote the composition and the interlayer spacing change, respectively; subscripts indicate the relevant atomic layer(s).
Table 2 Final values, along with their uncertainties, for the compositions and interlayer spacing changes of the surface and second layer of AgAu(1 0 0) (also included are the comparable values for three low index surfaces of NiPd for comparison) AgAu(1 0 0) c1 (%Ag) 76% ± 16%
c2 (%Ag) 45% ± 18%
d12 (nm) )0.003 ± 0.002
d23 (nm) 0.005 ± 0.002
NiPd(1 0 0) c1 (%Pd) 80% ± 5%
c2 (%Pd) 0% ± 6%
c3 (%Pd) 64% ± 10%
d12 (nm) )0.005 ± 0.001
d23 (nm) )0.007 ± 0.001
NiPd(1 1 1) c1 (%Pd) 82% ± 7%
c2 (%Pd) 24% ± 9%
d12 (nm) 0.000 ± 0.002
NiPd(1 1 0) c1 (%Pd) 85% ± 8% D11 (nm) )0.012 ± 0.003
c21 (%Pd) 73% ± 13% D12 (nm) 0.000 ± 0.004
c22 (%Pd) 10% ± 17%
c3 (%Pd) 47% ± 14% D21 (nm) 0.015 ± 0.003
D22 (nm) )0.016 ± 0.002
Concerning the extant results for silver/gold surfaces, much of the early work was done using polycrystalline samples and tools such as Auger spectroscopy and ion scattering [17–22]. Despite some early controversies, the collective conclusion that can be drawn from this work is that silver segregates to the surface for all bulk compositions, though the amount of silver segregation was not always consistent between different experiments. Thus, the silver segregation observed in the present work is wholly consistent with the early conclusions. Subsequently, some Auger studies have been done using single-crystal samples [23,24]. For the (1 0 0) surface, Meinel et al. [24] were not able to obtain quantitative composition results, but King and Donnelly [23] measured the surface and
second layer compositions for Ag1 Au9 (1 0 0), Ag2 Au8 (1 0 0), and Ag3 Au7 (1 0 0). They report very strong silver segregation to the surface, and an oscillatory composition profile with gold enrichment in the second layer. Such a compositional oscillation is a surprising result given the substitutional disorder and lack of lattice strain in Ag/Au, and we had hoped to test that experimental conclusion for our AgAu(1 0 0) sample. Unfortunately, the large uncertainty in the second layer composition makes it difficult to form an unambiguous conclusion; there is some weak evidence for a slight gold enrichment in this layer, but the global average composition value of 45% ± 18% Ag is essentially equal to the bulk composition, and thus our results do not confirm
G.N. Derry, R. Wan / Surface Science 566–568 (2004) 862–868
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Fig. 2. Plot of the variation of R2 with changes in the surface and second-layer compositions, illustrating the method used to determine uncertainties in the structure/composition parameter values.
the previous measurement of a compositional oscillation. The surface silver composition of 76% ± 16% that was measured here also indicates weaker segregation than the 72% ± 6% Ag measured by King and Donnelly for a 30% bulk Ag alloy. We cannot compare our structural results with any previous work, since none of the published studies reported surface structure measurements; we believe that this work is the first such surface structural measurement for the Ag/Au alloys. AgAu(1 0 0) results can also be compared to the structure and composition of low index faces of 50 at.% NiPd alloys, as summarized in Table 2. The most direct comparison is to the results for NiPd(1 0 0). The surface composition of this alloy is about 80% Pd, which is very similar to the 76% Ag content of the AgAu(1 0 0) surface. The second layer compositions are radically different, however, since the NiPd(1 0 0) second layer is virtually pure Ni. This extremely strong compositional oscillation is in stark contrast to the bulklike composition of the AgAu(1 0 0) second layer. Considering the surface structure, the two alloys
are again similar in that the first interlayer distance contracts by a moderate amount. The second layer behavior is once again much different, however, since second interlayer distance in the NiPd(1 0 0) alloy exhibits another robust contraction, while the second interlayer distance in the AgAu(1 0 0) alloy expands. It’s interesting to note that such an alternating contraction and expansion of the nearsurface interlayer distances is fairly common behavior in pure metals, in contrast to the somewhat singular double contraction observed in NiPd(1 0 0). We would speculate that the similarity of the AgAu(1 0 0) structural behavior to pure metal behavior is related to the absence of lattice strain in this alloy, but a theoretical study of the two systems will be needed to illuminate these issues. Comparisons of AgAu(1 0 0) to the (1 1 1) and (1 1 0) surfaces of NiPd are less direct but still of some interest. NiPd(1 1 1), for example, has a compositional oscillation similar to the (1 0 0) case but has a much different surface structure in which very little interlayer relaxation occurs. This bulklike termination is once again quite different
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from typical pure metal behavior, which AgAu(1 0 0) seems to exhibit. Direct comparisons are most difficult in the case of NiPd(1 1 0), which has a very complex behavior consisting of strong buckling in both the surface and the second layer, strong Pd segregation to the surface, and chemical ordering (i.e. intralayer segregation) in the second layer. Perhaps the most interesting comparison is simply to contrast that rich array of phenomena with the relatively straightforward behavior of AgAu(1 0 0): single monolayer segregation of Ag to the surface and pure-metal-like relaxations of the near-surface interlayer distances. Finally, it is worth noting that for both of these alloys, the element that segregates to the surface is the one that is predicted by simple surface energy and bond-breaking arguments, despite the many subtleties in the details of their structure/composition behavior.
Acknowledgements We wish to thank V. Blum, K. Heinz, and their colleagues for generously sharing the TensErLEED code package, and especially to thank Dr. Blum for sharing his expertise in the proper use of the code. We are also grateful to J. Rundgren for sharing his phase shift calculation code and advice on its use. Conversations with P. Rous have provided several important insights in the interpretation of the data. Finally, we wish to thank the National Science Foundation for funding this work under grant DMR-9903108.
References [1] P.A. Dowben, A. Miller (Eds.), Surface Segregation Phenomena, CRC Press, Boca Raton, 1990. [2] U. Bardi, Rep. Prog. Phys. 57 (1994) 939. [3] G.N. Derry, in: H.S. Nalwa (Ed.), Handbook of Surfaces and Interfaces of Materials, vol. 1, Academic Press, San Diego, 2001, p. 329. [4] Y. Gauthier, Y. Joly, R. Baudoing, J. Rundgren, Phys. Rev. B 31 (1985) 6216. [5] S. Crampin, P.J. Rous, Surf. Sci. Lett. 244 (1991) L137. [6] B. Schonfeld, J. Traube, G. Kostorz, Phys. Rev. B 45 (1992) 613. [7] G.N. Derry, C.B. McVey, P.J. Rous, Surf. Sci. 326 (1995) 59. [8] G.N. Derry, R. Wan, E. Krueger, J. Waldt, in press. [9] R. Wan, G.N. Derry, F. Strauch, in press. [10] P.J. Rous, J.B. Pendry, D.K. Saldin, K. Heinz, K. Muller, N. Bickel, Phys. Rev. Lett. 23 (1986) 2951. [11] V. Blum, K. Heinz, Comput. Phys. Commun. 134 (2001) 392. [12] J. Rundgren, private communication. [13] J.B. Pendry, J. Phys. C 13 (1980) 937. [14] D.L. Adams, H.B. Nielsen, M.A. Van Hove, Phys. Rev. B 20 (1979) 4789. [15] D.L. Adams, V. Jensen, X.F. Sun, J.H. Vollesen, Phys. Rev. B 38 (1988) 7913. [16] M.M. Nielsen, J. Burchhardt, D.L. Adams, Phys. Rev. B 50 (1994) 7851. [17] S.C. Fain, J.M. McDavid, Phys. Rev. B 9 (1974) 5099. [18] R. Bouwman, L.H. Toneman, M.A.M. Boersma, R.A. van Santen, Surf. Sci. 59 (1976) 72. [19] S.H. Overbury, G.A. Somorjai, Surf. Sci. 55 (1976) 209. [20] G.C. Nelson, Surf. Sci. 59 (1976) 310. [21] M.J. Kelley, D.G. Swartzfager, V.S. Sundaram, J. Vac. Sci. Technol. 16 (1979) 664. [22] M. Yabumoto, K. Watanabe, T. Yamashina, Surf. Sci. 77 (1978) 615. [23] T.S. King, R.G. Donnelly, Surf. Sci. 151 (1985) 374. [24] K. Meinel, M. Klaua, H. Bethge, Physica Status Solidi A 106 (1988) 133.
Comparison of surface structure and segregation in AgAu and NiPd alloys G.N. Derry b
a,*
, R. Wan
b
a Department of Physics, Loyola College, 4501 N. Charles St., Baltimore, MD 21210, USA Department of Physics, University of Maryland-Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
Available online 15 June 2004
Abstract The structure and composition of a single-crystal AgAu(1 0 0) alloy surface was studied using low energy electron diffraction. The surface was found to be moderately enriched in silver, while the second atomic layer has an essentially bulklike composition. The first interlayer distance exhibits a small contraction, with a small expansion found in the second interlayer. This structure composition behavior is compared to that found in the low index surfaces of the NiPd alloy, which has compositional oscillations and a more complex surface relaxation behavior. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Low energy electron diffraction (LEED); Surface segregation; Surface structure, morphology, roughness, and topography; Low index single crystal surfaces; Gold; Silver; Nickel; Palladium
1. Introduction Surface segregation in alloys has long been considered an important scientific and technological problem, and a great deal of progress has been made in understanding the phenomenon by studying clean, well-characterized, single-crystal alloy surfaces [1–3]. There is an intimate relationship between the composition of the surface and its structure, and the use of clean, single-crystal surfaces allows us to measure both the structure and the composition simultaneously, given an appropriate measurement method. One such method is low energy electron diffraction (LEED), which has *
Corresponding author. Tel.: +410-617-2662; fax: +410-6172646. E-mail address: [email protected] (G.N. Derry).
emerged as an important technique in the study of alloy surfaces. A particular advantage of LEED is that it provides information about the structure and composition of several atomic layers in the near-surface region, as well as the actual surface layer. Although a considerable body of work exists on chemically ordered alloys and intermetallics, LEED has also been extensively applied to disordered alloy crystals, using the average t-matrix approximation [4,5]. The present article is a contribution to this literature, reporting the use of LEED with the average t-matrix approximation to measure the structure and composition of the surface (and near-surface region) of a 50 at.% AgAu(1 0 0) alloy. Silver/gold alloys are fcc crystals that form substitutionally disordered solid solutions for their entire composition range. The atomic radii of
0039-6028/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.022
G.N. Derry, R. Wan / Surface Science 566–568 (2004) 862–868
the constituent elements are almost equal, so there is very little lattice strain in this alloy. Also, excessive chemical interactions are not found [6], since the two elements are both noble metals. We will compare these results for the silver/gold system with a previously measured set of results for three low index surfaces of a 50 at.% NiPd alloy [7–9]. Nickel/palladium alloys also form fcc crystals and also are substitutionally disordered for all bulk compositions, but in contrast to silver/ gold the Ni and Pd atoms have atomic radii that are about 10% different, resulting in a large degree of lattice strain. This lattice strain can be expected to affect the structure and segregation behavior at the surface, making the comparison of Ni/Pd and Ag/Au alloy results instructive.
2. Experiment The measurements are done in an ultrahigh vacuum chamber with a base pressure of about 108 Pa. The chamber is equipped with a reverseview four-grid LEED optics, ion gun for surface cleaning, and a sample manipulator. The manipulator has three orthogonal directions of translational motion, and rotational motion about both the polar and azimuthal angle axes. The sample is mounted onto a ceramic button heater in the manipulator for sample annealing in vacuum. A video camera interfaced to an image acquisition system is used to collect the LEED intensity data. The sample is a single crystal of AgAu with 50 at.% bulk composition, in the form of a disk about 1 cm diameter and 1 mm thickness, cut to expose the (1 0 0) crystal face. The surface was mechanically polished with diamond compound, using successively smaller sizes until a final polish with 0.25 lm diamond. Annealing in vacuum caused visible roughening of the surface, and the polishing procedure had to be repeated twice before a suitable surface was obtained. With moderate heating, only very slight roughening occurred during the actual data acquisition period. The surface was cleaned in vacuum by cycles of sputtering and annealing, and appeared to be free of contamination using RFA Auger spectroscopy after only a few cleaning cycles. The LEED spots, however,
863
required a number of further cycles, with longer annealing times, before they became sharp and well-differentiated from the background. In fact, the diffraction spots never became highly intense compared to the background scattering, causing the LEED IV curves to remain somewhat noisy. To counteract this noise problem, all of the measurements were repeated multiple times and averaged, with further averaging being done over all symmetry equivalent beams. The final annealing temperature was 800 K prior to data acquisition at 300 K. LEED IV curves were acquired at four different incident beam angles to extend the total energy range (which was 3290 eV) and number of inequivalent beams (which was 24). The uncertainties in the angles were ±1° for h and ± 2° for u. The normal incidence data (h ¼ 0°, u ¼ 0°) are the most reliable because a large amount of symmetry equivalent beam averaging was possible, but they do not cover a large energy range. Two of the offnormal angles (h ¼ 8°, u ¼ 0°; h ¼ 12°, u ¼ 0°) also allowed significant symmetry averaging. The fourth angle (h ¼ 13°, u ¼ 40°) was problematic due to a misalignment of the azimuthal angle axis in the sample manipulator, however, and the quoted angle values have been adjusted from the intended nominal incident angle. Variation of the incidence angles in the scattering calculations suggests that the structure/composition parameters are relatively insensitive to the experimental angle uncertainties. The measured IV curves were compared to the results of parameterized scattering calculations using the Tensor-LEED method [10]. The implementation of this method that we employed was the TensErLEED software package [11]. Ten phase shifts were used, computed with a method devised by Rundgren [12], and chemical disorder was modeled using the average t-matrix approximation [4,5]. The best fit between the data and the computed IV curves was determined using both the Pendry R factor [13] (which emphasizes sensitivity to the peak positions) and R2 [14] (which is instead sensitive to the relative diffracted intensities). The final parameter values are taken to be the averages over all incident angles and R factors. The parameters that were varied are the compositions
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of the first two atomic layers, the first two interlayer distances, and the vibrational amplitudes in these layers (and also, as usual, the LEED inner potential).
3. Results To briefly summarize the main results of our analysis, we find that segregation in the AgAu(1 0 0) alloy is largely restricted to the surface monolayer, which is enriched with silver. Quantitatively, the surface composition is 76% ± 16% Ag while the second layer composition is 45% ± 18% Ag. Structurally, the first interlayer distance decreases by 0.003 ± 0.002 nm (i.e. a roughly 1.5% contraction) while the second interlayer distance increases by 0.005 ± 0.002 nm (a roughly 2.5% expansion). A comparison of the measured and calculated IV curves for the best fit using R2 is displayed for all four incident angles in Fig. 1 (the comparable curves using RP are slightly different in detail but the quality of the fits is visually similar). Quantitatively, the fits for three of the incident angles using R2 and two of the incident angles using RP are fairly good; two others (one angle using R2 and another using RP ) yield somewhat high but acceptable fit values, but the RP fit for one angle is too poor (and insensitive to parameter variations) to produce meaningful results. The R factors for all conditions are given in Table 1. Because of the limited energy range, the noise in the IV curves, and the fact that there are relatively few prominent features in each curve, results from any single incident angle are not highly precise and reliable. Table 1 illustrates the rather large degree of scatter in these individual incident angle results; note, however, that they do agree with each other well enough both to demonstrate broad trends in the results and to agree with each other within their substantial uncertainties. For all of the fitting results listed in Table 1, the vibrational amplitudes of the surface and second layer were fixed at 0.016 nm and 0.011 nm, respectively, based on the preliminary results of seven-parameter fits (the bulk vibrational amplitude was set as 0.009 nm based on the Debye temperature and atomic mass of the
alloy components). The physical interpretation of these vibrational amplitude values is unclear because of the mixture of static disorder with genuine thermal effects, but the other parameter values do not depend sensitively on the vibrational parameter values in any event. Results for all of the different incident angles were combined to obtain more precise and reliable values of the structure and composition parameters. This was first done separately for R2 and RP to make sure that the different R factors generate results that agree within their uncertainties. These separate parameter values were then averaged to obtain the final values listed in Table 2. Although the same data was used for both analyses, we believe that the averages represent more reliable values because the two different R factors are sensitive to different features of the data (peak positions in the RP case compared to actual diffracted intensities for R2 ). Uncertainties for the parameters found using RP were computed with the standard methods employed for this R factor and its variation [13]. Uncertainties for the parameters found using R2 were estimated with a technique, adapted from the work of Adams et al. [14–16], that relates R2 to the v2 statistic in order to determine the R2 cut-off corresponding to a standard deviation in the measured parameter. Fig. 2 shows the results of this method for the surface and second layer compositions, with results for all four incidence angles combined to generate a ‘‘global’’ R2 value for all of the data. Uncertainties computed using these two methods (with RP and R2 ) are quite comparable. The uncertainty values listed in Table 2 are those found using the R2 method.
4. Discussion The results reported herein for the AgAu(1 0 0) surface form an interesting comparison both with the previous results reported in the literature for this alloy [17–24] and with a completed set of results for NiPd alloy surfaces that have been measured in our laboratory. These NiPd results, details of which are reported elsewhere [7–9], are summarized briefly in Table 2 along with the present AgAu(1 0 0) results.
G.N. Derry, R. Wan / Surface Science 566–568 (2004) 862–868
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Fig. 1. Experimental (solid lines) and calculated (dashed lines) AgAu(1 0 0) LEED IV curves for all measured beams at all incidence angles. These curves are for the best-fit results using R2 .
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Table 1 Best-fit values of the structure/composition parameters for AgAu(1 0 0) determined for each angle of incidence, using both R2 and RP h (°)
u (°)
c1 (%Ag)
c2 (%Ag)
d12 (nm)
d23 (nm)
R type
R value
0 0 )8 )8 )12 )12 )13 )13
0 0 0 0 0 0 )40 )40
66 80 66 80 85 69 85 –
29 50 45 60 35 52 40 –
0.001 0.002 )0.005 )0.004 )0.006 )0.006 )0.002 –
0.004 0.003 0.006 0.004 0.007 0.007 0.006 –
R2 RP R2 RP R2 RP R2 RP
0.04 0.23 0.08 0.45 0.05 0.32 0.15 0.55
c and d denote the composition and the interlayer spacing change, respectively; subscripts indicate the relevant atomic layer(s).
Table 2 Final values, along with their uncertainties, for the compositions and interlayer spacing changes of the surface and second layer of AgAu(1 0 0) (also included are the comparable values for three low index surfaces of NiPd for comparison) AgAu(1 0 0) c1 (%Ag) 76% ± 16%
c2 (%Ag) 45% ± 18%
d12 (nm) )0.003 ± 0.002
d23 (nm) 0.005 ± 0.002
NiPd(1 0 0) c1 (%Pd) 80% ± 5%
c2 (%Pd) 0% ± 6%
c3 (%Pd) 64% ± 10%
d12 (nm) )0.005 ± 0.001
d23 (nm) )0.007 ± 0.001
NiPd(1 1 1) c1 (%Pd) 82% ± 7%
c2 (%Pd) 24% ± 9%
d12 (nm) 0.000 ± 0.002
NiPd(1 1 0) c1 (%Pd) 85% ± 8% D11 (nm) )0.012 ± 0.003
c21 (%Pd) 73% ± 13% D12 (nm) 0.000 ± 0.004
c22 (%Pd) 10% ± 17%
c3 (%Pd) 47% ± 14% D21 (nm) 0.015 ± 0.003
D22 (nm) )0.016 ± 0.002
Concerning the extant results for silver/gold surfaces, much of the early work was done using polycrystalline samples and tools such as Auger spectroscopy and ion scattering [17–22]. Despite some early controversies, the collective conclusion that can be drawn from this work is that silver segregates to the surface for all bulk compositions, though the amount of silver segregation was not always consistent between different experiments. Thus, the silver segregation observed in the present work is wholly consistent with the early conclusions. Subsequently, some Auger studies have been done using single-crystal samples [23,24]. For the (1 0 0) surface, Meinel et al. [24] were not able to obtain quantitative composition results, but King and Donnelly [23] measured the surface and
second layer compositions for Ag1 Au9 (1 0 0), Ag2 Au8 (1 0 0), and Ag3 Au7 (1 0 0). They report very strong silver segregation to the surface, and an oscillatory composition profile with gold enrichment in the second layer. Such a compositional oscillation is a surprising result given the substitutional disorder and lack of lattice strain in Ag/Au, and we had hoped to test that experimental conclusion for our AgAu(1 0 0) sample. Unfortunately, the large uncertainty in the second layer composition makes it difficult to form an unambiguous conclusion; there is some weak evidence for a slight gold enrichment in this layer, but the global average composition value of 45% ± 18% Ag is essentially equal to the bulk composition, and thus our results do not confirm
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Fig. 2. Plot of the variation of R2 with changes in the surface and second-layer compositions, illustrating the method used to determine uncertainties in the structure/composition parameter values.
the previous measurement of a compositional oscillation. The surface silver composition of 76% ± 16% that was measured here also indicates weaker segregation than the 72% ± 6% Ag measured by King and Donnelly for a 30% bulk Ag alloy. We cannot compare our structural results with any previous work, since none of the published studies reported surface structure measurements; we believe that this work is the first such surface structural measurement for the Ag/Au alloys. AgAu(1 0 0) results can also be compared to the structure and composition of low index faces of 50 at.% NiPd alloys, as summarized in Table 2. The most direct comparison is to the results for NiPd(1 0 0). The surface composition of this alloy is about 80% Pd, which is very similar to the 76% Ag content of the AgAu(1 0 0) surface. The second layer compositions are radically different, however, since the NiPd(1 0 0) second layer is virtually pure Ni. This extremely strong compositional oscillation is in stark contrast to the bulklike composition of the AgAu(1 0 0) second layer. Considering the surface structure, the two alloys
are again similar in that the first interlayer distance contracts by a moderate amount. The second layer behavior is once again much different, however, since second interlayer distance in the NiPd(1 0 0) alloy exhibits another robust contraction, while the second interlayer distance in the AgAu(1 0 0) alloy expands. It’s interesting to note that such an alternating contraction and expansion of the nearsurface interlayer distances is fairly common behavior in pure metals, in contrast to the somewhat singular double contraction observed in NiPd(1 0 0). We would speculate that the similarity of the AgAu(1 0 0) structural behavior to pure metal behavior is related to the absence of lattice strain in this alloy, but a theoretical study of the two systems will be needed to illuminate these issues. Comparisons of AgAu(1 0 0) to the (1 1 1) and (1 1 0) surfaces of NiPd are less direct but still of some interest. NiPd(1 1 1), for example, has a compositional oscillation similar to the (1 0 0) case but has a much different surface structure in which very little interlayer relaxation occurs. This bulklike termination is once again quite different
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from typical pure metal behavior, which AgAu(1 0 0) seems to exhibit. Direct comparisons are most difficult in the case of NiPd(1 1 0), which has a very complex behavior consisting of strong buckling in both the surface and the second layer, strong Pd segregation to the surface, and chemical ordering (i.e. intralayer segregation) in the second layer. Perhaps the most interesting comparison is simply to contrast that rich array of phenomena with the relatively straightforward behavior of AgAu(1 0 0): single monolayer segregation of Ag to the surface and pure-metal-like relaxations of the near-surface interlayer distances. Finally, it is worth noting that for both of these alloys, the element that segregates to the surface is the one that is predicted by simple surface energy and bond-breaking arguments, despite the many subtleties in the details of their structure/composition behavior.
Acknowledgements We wish to thank V. Blum, K. Heinz, and their colleagues for generously sharing the TensErLEED code package, and especially to thank Dr. Blum for sharing his expertise in the proper use of the code. We are also grateful to J. Rundgren for sharing his phase shift calculation code and advice on its use. Conversations with P. Rous have provided several important insights in the interpretation of the data. Finally, we wish to thank the National Science Foundation for funding this work under grant DMR-9903108.
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