A scanning tunneling microscopy investigation of the structure of the Pt(110) and Au(110) surfaces

A scanning tunneling microscopy investigation of the structure of the Pt(110) and Au(110) surfaces

Surface Science 257 (1991) 297-306 Noah-Holl~d 297 A scanning tunneling microscopy investigation of the Pt(110) and Au{ 110) surfaces T. Gritsch I, ...

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Surface Science 257 (1991) 297-306 Noah-Holl~d

297

A scanning tunneling microscopy investigation of the Pt(110) and Au{ 110) surfaces T. Gritsch I, D. Coulman Fritz-~a~r-Insti~t

of the structure

2, R.J. Behm 3 and G. Ertl

der Max-Planck-Gesellschaft,

Faradayweg

4-6, D-1000 Berlin 33, Germany

Received 2 April 1991; accepted for publication 30 April 1991

The periodic and intrinsic defect structure of the (1 X 2) missing-row reconstructed Pt(ll0) and Au(ll0) surfaces was investigated by scanning tunneling microscopy. From the formation of extended, defect-free (1 x 2) domains, this phase is identified as the energetically most stable one for the clean surfaces. Structural defects such as steps were found to interact with the reconstruction. Tbe stabilization of (111) microfacets, at step edges, is found as a general principle governing the step terrace topography of these surfaces, The presence of trace impurities is correlated with an increase of (1 X 3) structural units along the [ITO]direction, leading at first to a decrease in (1 x 2) domain size and, at higher densities, to structures such as (1 x 7), (1 x 5) and finally a (1 x 3), which exhibit periodic arrangements of (1 X 3) units as the common building principle. The (1 X 3) troughs, with third-layer metal atoms missing as well, are equally formed by (Ill) microfacets.

1. Introducticm The clean (110) surfaces of the 5d metals Ir, Pt and Au are known to reconstruct into a (1 X 2) structure of the “missing-row” type with significant distortions extending even into deeper layers [l-7]. In addition, these structures were often found to exhibit considerable disorder [S]. In a number of cases more or less well-ordered (1 x 3) and even (1 X 5) structures were observed after prolonged annealing in oxygen [5,9] or in the presence of Ca impurities [lo]. These structures were often attributed to the presence of contaminants. But these observations, in com~mation with controversial theoretical results 111,141, still left considerable doubt in the actual periodic and intrinsic defect structure of the clean, reconstructed

i Present address: Teclmischer Uberwachungsverein Bayern, Westendstr. 199, W-8000 Mtchen 21, Germany. * Present address: E.I. DuPont, Experimental Station, P.O.Box 80356, Wilmington, DE 19880-0356, USA. 3 Permanent address: Institut fur Kristallograpbie und Mineralogie, Universittit Mtinchen, Theresienstr. 41, W-8000 Munchen 2, Germany. 0039-6028/91/$03.50

(110) surfaces of Ir, Pt and Au in their thermodynamically stable state. Previous investigations by means of scanning tunneling microscopy (STM) identified the surface disorder as resulting from coexistent (1 X 2) and (1 x n) (n > 2) structural units and from steps [15-181. We here present the results of an STM study on these structural properties of the Au(ll0) and Pt(ll0) surfaces. We were particularly interested in the impact of surface defects such as steps etc. on the (defect) structure of the r~onst~ction, as it was observed, e.g., on Pt(100) [19]. This includes the question of whether, by careful cleaning and surface preparation procedures, the intrinsic structure of the clean surfaces can be identified. This paper continues previous reports on the (1 x 2) -+ (1 X 1) structural transformation of Pt(ll0) initiated by the presence of adsorbates [20,21].

2. Ehperimental The experiments were performed with a pocket-size STM incorporated into a UHV system (base pressure about lo-’ Pa) with standard facilities

0 1991 - Elsevier Science Publishers B.V. All rights reserved

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T. Gritsch et al. / A scanning tunneling microscopy investigation

for sample preparation and characterization [2023]. The surfaces were prepared by usual procedures. The Pt(ll0) sample was subjected to repeated cycles of oxidation (10e4 Pa O,, 800 K), Ar+ ion sputtering (800 eV, 1 h, 2 PA) and subsequent annealing to 1000 K. The Au(ll0) sample, which had previously been used for electrochemical experiments, was cleaned by cycles of Ar+ ion sputtering (500 eV) and subsequent annealing at 700 K. Higher annealing temperatures reproducibly led to much smaller terrace sizes for both the Pt(ll0) and Au(ll0) surfaces. The wellannealed and clean surfaces, as judged by Auger spectroscopy, exhibited a LEED pattern with sharp integral and only slightly elongated - in the [Ol] direction - half-order spots on a low background. The LEED pattern indicated a well-ordered (1 X 2) surface with domain widths in [OOl], normal to the

atomic rows in [liO], of at least 50 A which was confirmed by the STM results shown below. For STM imaging we used W tips of 0.7 mm diameter, which were electrochemically etched in 1N NaOH (2.5 V DC). The surface oxide layer was removed in vacuum by Ne+ or Ar+ ion sputtering (1 keV, p = 10e3 Pa) and subsequent field desorption. Prior to the experiments, the resolution was enhanced by applying short bias pulses (ca. 10 V) while scanning the Au(ll0) sample, similar to procedures described previously for high-resolution imaging of Au(ll1) and Al(111) surfaces [23,24]. For Pt imaging the sample was subsequently exchanged. The STM images were acquired in the constant current mode, with typical tunnel currents between 5 and 50 nA and tunnel voltages of 20 to 200 mV. Most of the images are displayed in a topview grey-scale repre-

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Fig. 1. Top-view images of perfect (1 X 2) areas on the missing-row reconstructed (110) surfaces. (a) Au(ll0) (600 A x 780 A); (b) Pt(ll0) (320 A X 420 A); (c) cut along the line in (b), indicating the corrugation normal to the [liO] rows.

T. Gritsch et al. / A scanning tunneling microscopy investigation

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3. Results and discussion The well-prepared and annealed surfaces consisted of large flat terraces, which exhibited a regular corrugation caused by parallel rows, around 8 A apart from each other (fig. 1). They reflect the atomic rows in the [liO] direction. The defect density on these terraces was found to be very low. The images typically exhibited a wellordered (1 x 2) arrangement of rows with few domain boundaries in between. This result contrasts earlier reports from an STM study where the (1 X 2) Au(ll0) surface was found to contain a large number of defects and hence only very narrow (1 x 2) domains [lS]. Along [liO] the rows mostly proceeded without any additional defects over the entire width of the terrace. An extremely low defect density in this direction was also concluded from results of recent ion scattering experiments [25,26]. The corrugation amplitude of STM scans across these rows, i.e., in the [OOl] direction, varied with the tunnel parameters. In general the amplitudes measured on Au(ll0) were about 15% larger than those found on Pt(llO), which is not far off from the difference in the geometrical heights of the surface atoms of ca. 7%. For a narrow parameter range (tunnel resistances around (0.5-l) x 10v8 Q), however, these differences were much larger and the corrugation amplitude could reach values of up to 1.0 A on Au(l10) and 0.6 A on Pt(llO) (fig. lc). The si~ific~tly higher value of the corrugation amplitude found for Au(ll0) under these conditions and the narrow parameter range for this enhancement effect, both point to a strong electronic contribution to the measured corrugation in the latter case. Typical values for the tunnel barrier were about 3 to 4 eV [23]. It should be noted in this context that the m~mum corrugation found on Au(ll0) exceeds that proposed from combined STM and field ion microscopy experiments for a monatomic tip [16]. This may be associated with the mode of tip preparation in our experiments [23,24]. The corrugation caused by

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(b) Fig. 2. (a) Large-scale STM image (1550 ax1800 A) of a Pt(ll0) surface area inclined in [OOl], exhibiting a sequence of [liO] oriented monatomic steps with a very low kink density; (b) cut along the line in (a), reflecting the downward sequence of terraces from foreground to background. Arrows mark the position of antiphase boundaries created by (1 x 3) structural units.

the densely packed atoms along the [liO] rows (distance - 2.9 A) could, however, not be resolved. (In very recent modulated measurements these atoms were reproducibly resolved in tunnel barrier images [27]). Typical step structures on these surfaces are displayed in figs. 2 and 3. A large-scale image (fig. 2a) shows a Pt(ll0) surface with extended flat terraces. The terraces are considerably more extended in the [ITO] than in the [OOl] direction, with typica dimensions of 4000 A x 100 A. The surface is slightly inclined in [OOl] direction, as evidenced by the sequence of monato~c steps of 1.3 A height along [liO] direction (fig. 2b). Surface areas with such large terraces were frequently observed. Terraces of up to 20000 A x 1000 A were found. The steps have a very low overall density of kinks and frequently run straight in the [liO]

T. Gritsch et al. / A scanning tunneling microscopy investigation

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direction over several hundreds of angstroms. In the topmost terrace three deeper grooves are resolved and marked by arrows. These correspond to individual (1 x 3) structural units, which separate different (1 x 2) domains and hence act as antiphase domain boundaries. Previous calculations concluded that, for larger gap widths, the STM trace could not clearly distinguish between a flat (1 X 3) trough formed by removal of two adjacent [liO] rows of metal atoms in the second layer and a deep (1 x 3) trough where an additional row is missing in the third layer [5,28]. In the present experiments, the much larger corrugation amplitude of both the (1 x 2) and the (1 X 3) (cf. fig. 5) indicates a much better resolution. The measured amplitude of the (1 x 3) troughs of up to 2 A can only be explained by the deep structure, which is terminated by (111) microfacets. In contrast, steps along the [OOl] direction, which were found on different areas of the surface, exhibit a quite different morphology. As can be seen from the overview image in fig. 3, where a number of [OOl] oriented steps proceed over the imaged area of 480 A X 850 A, these steps are strongly structured. They often form a large-scale

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zig-zag pattern with high densities of kinks. This leads to a diamond-like shape of the terraces and despite an average terrace width of around two hundred angstroms in this image, neigboring steps often nearly meet (cf. fig. 4). The steps are formed by the rather random termination of individual (1 x 2) rows, leading to the large number of observed kinks. Apparently there is only little interaction between neighboring [liO] rows and their terminating atoms and hence there is no noticable tendency for the formation of extended straight steps along the [OOl] direction. In other words, the formation of [OOl] microfacets appears to be energetically not very attractive. However, the negligible tendency to stabilize (001) microfacets alone does not explain the characteristic structure of these steps, since the total number of terminated [liO] rows here is not different from that in a linear [OOl] step. Hence they must originate from other physical effects, which may be identified by closer inspection of these structures. Fig. 4 allows a closer look at the details of these irregular patterns. The frontmost corners of the upper terraces along the zig-zag stepline often coincide with antiphase boundaries in the lower terrace. The presence of antiphase bounda-

T Griisch et ai. / A seaming tunneling ~i~r~~o~y inuestig~t~~n

ries, i.e., local (1 X 3) units, apparently plays an important role for the development of the step shape. On terraces exhibiting a perfect (1 x 2) periodicity the step shape often changes into an asymmetric, sawtooth-like configuration, with a long [liO] step on the one side and the usual kink structure on the other (cf. fig. 5a). In contrast, terrace ledges overgrowing (1 x 2) terraces with a (1 X 3) structural unit in general exhibit a more symmetric shape (cf. fig. 5b). These observations can be rationalized in terms of simple structural concepts, which are based on stability considerations of the resulting step edges, For the (1 x 2) missing-row reconstructed surface,

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there are two different possible phase relations between domains on different terraces. The (1 X 2) rows on adjacent terraces can be displaced by ;f.of a missing row unit cell, i.e., by a,/2 (with a0 being the bulk lattice constant), or by $ equivalent to 1.5~ with respect to each other. The long straight steps along [Ii01 are always terminated by extended (111) microfacets, i.e., the domains on the upper terrace are displaced inwards by 4 of the (1 X 2) unit cell. This arrangement reflects the high stability of the close-packed surface orientations, as had already been pointed out in an earlier STM study in connection with the observed (1 x 3) structural units [15]. The significant stabili-

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Fig. 5. Details of the kink structure of [OOl] oriented steps on a Au(ll0) surface. (a) STM image (top view) of a (1 x 2) terrace perfect (1 x 2) substrate; (b) cut along line I in (a); (c) structural model of the surface along cut I, structure along line II is identical (extra atoms of next bigber terrace are filled, microfacets at terrace edges as indicated); (d) STM image of a (1 x 2) terrace protruding on a (1 X 2) substrate with a single phase jump due to a (1 X 3) unit; (e) cut along lines I {top) and II (bottom); (f) model of(d) along cut I (empty circles) and cut II (f&d circles).

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zation of the (111) microfacets is found only for the reconstructed (110) surfaces. If on Pt(ll0) the reconstruction is removed, e.g., by adsorption of CO at T > 300 K, the islands of Pt atoms created during this transition exhibit a rather isotropic shape [22]. The [liO] oriented edges of these monolayered islands equally consist of (111) microfacets, which, however, are less wide than those formed at step edges of the reconstructed surface. No preferential formation of [liO] steps and hence stabilization of (111) microfacets was reported for the clean, nonreconstructed Cu(ll0) and Ni(ll0) surfaces [29,30]. Hence, the experimental data provide strong evidence that the stabilization of the (111) microfacets is a result only of the reconstruction of the surface. The (111) stabilization is in accordance with the interpretation of the antiphase (1 X 3) units as deep troughs, i.e., with a [liO] row in the third layer missing as well. The shapes of the [OOl] oriented steps are equally governed by the tendency to maximize the fraction of these microfacets. This is demonstrated in fig. 5, where high-resolution images of the two different structural types are presented together with structural models. A narrow (1 X 2) terrace or even a single [liO] row of Pt atoms cannot be placed on top of a perfectly ordered (1 X 2) surface such that (111) microfacets are formed on both sides. Instead, termination by both a (111) and a (331) microfacet will take place. This becomes evident from the cut along line I in fig. 5a as shown in fig. 5b and the corresponding structural model in fig. 5c. The highly asymmetric shape of the terraces protruding on a perfect (1 X 2) substrate (fig. 5a) becomes now easily plausible: The terrace side terminated by a (111) microfacet is more stable than the other one formed by a (331) facet. This agrees well with results of recent embedded-atom calculations which found an increase in energy of 9.5 meV per unit length for the (331) step, while the (111) step was only 1.8 meV higher in energy than the ideal (1 X 2) phase [31]. As a consequence, the former leads to an extended [liO] step, whereas the latter results in the highly kinked step edges, thus the sawtooth pattern of fig. 5a. Termination of a terrace by (111) facets on both sides becomes possible only if the lower (1 x 2)

investigation

terrace exhibits an antiphase boundary in this range as demonstrated in the image in fig. 5d. The antiphase domain boundary manifests itself as a broader dark area in the upper half of the image and the cut along line I reveals the presence of a deep trough (fig. 5e) which is characteristic for a (1 x 3) spacing. In the second cut along line II the next Pt terrace becomes visible. Now the edges at both sides of the terrace are similar, reflecting the identical (111) termination at both terrace sides (fig. 5f). Consequently the step edges are equally stable which results in a symmetric overall shape of the protruding terrace. At higher temperatures, where the metal atoms can at least migrate freely along step edges, the upper terraces at [OOl] steps can grow along (1 X 3) troughs on the lower terrace, forming a single or double row, which is (111) terminated on both sides. Such structures were indeed frequently observed. For compensation, other areas of the upper terrace, between two different (1 X 3) units, have to retract. This leads to the observed zig-zag pattern. In turn, the tendency for minimization of the surface free energy by creation of densely packed (111) microfacets can be considered as driving force for the formation of (1 x 3) antiphase domains, whose existence is not simply a consequence of the phase shift of [liO] rows at monatomic steps along the [OOl] direction as had been suggested by Robinson [7] on the basis of X-ray diffraction data. The fact that the missing-row (1 x 2) structure indeed represents the most stable configuration of the Pt and Au(ll0) surfaces does not follow from simple arguments concerning the mean coordination of the surface atoms, since this number would be the same also for (1 X 1) as well as (1 x 3) (1 X 4), etc., configurations. According to an ab initio total-energy calculation for Au(llO), the (1 X 2) surface is more stable than the (1 X 1) phase by about 7% of the surface energy [ll]. Other (more approximate) theoretical treatments predicted that structures with even larger periodicities should be at least similar if not even more stable than the usually observed (1 x 2) structure [12-141. So far there exists, however, no clear experimental evidence of the occurrence of (1 x n ) reconstructions (n > 2) over larger regions of the

T. Gritsch et al. / A scanning tunneling micr~evpy ~nvest~gatjon

clean surface and our data and procedures for sample preparation strongly indicate that the perfect (1 x 2) phase corresponds to the ideal state of the clean Au(ll0) and Pt(ll0) surfaces. In the second part, reconstructions with higher periodicity shall be discussed. It is well-known that such structures can be induced in these surfaces by small amounts of a variety of adsorbates. Low concentrations of alkali adsorbates for example can lead to (1 X 3) reconstructions on various fcc(ll0) surfaces [32], including Au(l10) [33,34]. In the present study, Pt(ll0) surfaces exhibiting larger domains with (1 X 3) periodicity could be prepared by prolonged heating in oxygen at 1000 K. This is identical to the method described by Fery et al. [S] and by Salmeron and Somojai [9] for the production of (1 x 3) surfaces. In our case, these surfaces generally still exhibited detectable levels of impurities such as Ca, C or 0 ( < 5% of a monoiayer). The corresponding LEED pattern was somewhat diffuse and showed elongated extra spots at positions characteristic for a (1 x 3) superstructure. The STM image reproduced in fig. 6 was recorded on a Pt(ll0) surface after similar treatment. In this surface only a few

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(1 x 2) units intersect the prevailing (1 x 3) periodicity. The corrugation amplitude measured in the (1 x 3) regions was around three times as large as that observed for the (1 X 2) units in this measurement, which points to a similar structure as that shown in fig. 5f, with a [liO] row of Pt atoms in the third layer missing as well. This surface differs from the usual (1 x 2) surface also in another respect. An extended [OOl] step progresses linearly over many hundred angstroms over the surface. Actually, this is a double step, and at locations where the double step splits up into two single-height steps a highly kinked shape again develops. Double steps in [OOl] have never been observed on clean surfaces and hence represent a structural feature only typical for these “modified” surfaces. It is not clear whether the stabi~tion of double steps along [OOl] solely results from the presence of impurity atoms or whether it also indicates a size effect. In many aspects, it resembles the stabilization of (111) facets along [ITO] rows in the presence of the reconstruction, which was described above and which is equally accompanied by an increase in the size of the microfacets. STM images of these surfaces often revealed higher order (1 X n) reconst~~tions with n > 3. Following Salmeron and Somorjai, they can be produced by exposing a (1 x 3) surface to the residual gas for longer periods of time 191. Fig. 7 shows, as an example, a section of the Pt(ll0) surface exhibiting 5 repeating (1 X 5) units with neighboring (1 x 7) and (1 x 9) units. These larger structural units are composed of a (1 x 3) channel (= wide, dark strings in the grey-scale image and deep valleys in the line cut) plus (n - 1)/Z elements of the (1 X 2) structure (= pairs of bright strings and shallower valleys). As a consequence, only building blocks with odd values for n appear. The dark holes in the line pairs represent first (1 x 1) nuclei created by adsorption of CO from the residual atmosphere, as described in refs. [20,21]. Earlier LEED observations led to somewhat controversial reports in the literature about the influence of CO adsorption on the (1 X 3) structure on Pt(ll0). Fery et al. [5] found that these were transformed into the (1 x 1) phase upon CO

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T. Gritsch et al. / A scanning tun~efing microscop!yinuesi~gation

Fig. 8. Top-view image (330 A x 600 .&t)showing two neigboring screw dislocations with opposite spin on a (1 x2) reconstructed Au(ll0) surface. Fig. 7. Pt(ll0) with coexisting (1 X5), (1 X7) and (1 X9) domains, created by periodic arrangement of (1 X2) and (1 X3) structural units. (a) Top-view image (380 AX290 A), the square “defects” represent nuclei of (1 X 1) due to CO adsoTtion from the background; (b) cut along the line indicated in (a).

adsorption, similar to the behavior of the (1 X 2) phase. The Cu induced (1 X 3) reconstructions described by Shek et al. [35] were equally removed by CO adsorption at 370 K, which may be regarded as evidence for a ~mmon origin in these experiments. In contrast, Salmeron and Somorjai [9] reported them to be stable in the presence of a CO atmosphere, in agreement with findings of the present study. We observed that only the (1 X 2) structural elements were affected by CO, but not the (1 X 3) units, as becomes evident from fig. 7. If, however, a (1 x 3) string is adjacent to a (1 X 2) unit which is broken up by adsorbed CO, then also the (1 x 3) periodicity will be changed. The physical origin for the observed stabilization of (1 X n) structural units, with n > 2, is still unclear. Surfaces exhibiting these features frequently contain a higher concentration of impurities, as analyzed by Auger spectroscopy. In the

present study, the formation of these structures often coincided with small Ca signals, in agreement with earlier findings [lO], The absence of any detectable impurity levels was reported in papers reporting the formation of (1 x 3) structures by annealing in an oxygen atmosphere [5,9]. This treatment, however, is well-known to lead to segregation of Ca from the bulk to the surface [36]. It is thus very likely that the formation of these (1 X n) structures is stabilized by impurities, probably by subtle modifications of the electronic structure. In consequence, although their origin could not be clarified in the present study, their building principle could be clearly resolved. Screw dislocations were the only type of buIk defects which were found to manifest itself at the surface and which were observed on both metal surfaces in the present study. Fig. 8 reproduces an STM image from a well-annealed Au(ll0) surface where two screw dislocations emerge within the imaged area of about 330 A x 600 A. Their presence is indicated by the two steps which appear in the middle terrace and extend to the left side of the image. They result from the displacement of

T. Gritsch et al. / A scanning tunneling microscopy i~ve~t~gatio~

the horizontal layers along a vertical slip plane which originates at the dislocation line. In contrast to microscopic observations on other metal surfaces, e.g., Ni(lOO) [37] or Mo(ll0) [38], the steps do not proceed linearly over large distances, but exhibit the same high density of kinks as other steps along the [OOl]. The two screw dislocations are of opposite spin and hence the surface between the two slip planes rises gradually, without ad~tion~ distortions, in the area between them. In the vicinity of the emerging screw dislocation the positions of the [liO] rows in the upper plane are not laterally displaced by a,/2 with respect to those in the lower one. Rather, over an area of about 50 A in diameter, these rows are not perfectly straight but deformed. Further away the usual lateral displacement is exhibited. These deformations can result from substrate distortion within this area or from the tendency for the formation of [HO] strings, over the slip plane. The overall tendency for the (1 X 2) reconstruction, as well as for the highly kinked shape of [OOl] steps, appears to be preserved. That means that even in the strain field surrounding the dislocation line, there is not sufficient stabilization of the unreconstructed (1 X 1) bulk structure to make it more stable than the reconstructed phase. Similar observations were reported for the r~onst~cted Au(ll1) surface, where the [“_: i] reconstruction was equally found to be present in the direct vicinity of screw dislocations [23].

4. Conclusions Based on direct observation by STM, we could show that after careful cleaning procedures the (1 X 2) reconstructed Pt(ll0) and Au(ll0) surfaces form large, defect-free domains of the (1 X 2) missing-row structure. These data provide clear evidence that this structure represents the energetically most stable phase of the clean surfaces and does not result from stabilization by traces of impurities. Even in the strain field of screw dislocations emerging at the surface is the stability of the (1 x 2) reconst~ction preserved. The long, linear steps in [liO] direction with their very low kink densities, which were not ob-

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served on (1 x 1) Pt(ll0) or on other nonreconstrutted fcc(ll0) surfaces, suggest a stabilization predominantly of the larger (111) microfacets formed along [l’iO] step edges on the (1 x 2) reconstructed surfaces. The highly structured [Ofjl] steps, formed by individually terminated [llO] atomic rows, reflect the negligible stabilization of (001) microfacets. The zig-zag pattern of these steps is rationalized by a preferential growth of the upper terraces along local (1 x 3) units, i.e., antiphase boundaries in the lower terraces, which leaves (111) microfacets exposed on both sides of the protruding terrace ledge. Similar terrace ledges on a perfect (1 X 2) lower terrace are ter~nated by a (111) and a less stable (331) microfacet, which results in an asymmetric, saw tooth-like shape of the ledge, with an extended, linear (111) side and a highly kinked (331) side. The stabilization of ]OOl] steps by indi~du~ (1 x 3) units is suggested as the driving force for the formation of these antiphase boundaries. In the presence of impurities such as alkali or earth alkali atoms (ill), facetted (1 X 3) structural units are increasingly formed, leading at first to a decrease in (1 X 2) domain size and, at higher densities, to structures such as a (1 x 7), a (1 X 5) and finally a (1 X 3), which exhibit a periodic arrangement of (1 X 3) units as a common building principle.

Acknowledgement D.C. gratefully acknowledges a fellowship by the Alexander v. Humboldt foundation.

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