- Nano Review
- Open Access
Self-organised synthesis of Rh nanostructures with tunable chemical reactivity
© to the authors 2007
Received: 30 March 2007
Accepted: 13 April 2007
Published: 22 May 2007
Nonequilibrium periodic nanostructures such as nanoscale ripples, mounds and rhomboidal pyramids formed on Rh(110) are particularly interesting as candidate model systems with enhanced catalytic reactivity, since they are endowed with steep facets running along nonequilibrium low-symmetry directions, exposing a high density of undercoordinated atoms. In this review we report on the formation of these novel nanostructured surfaces, a kinetic process which can be controlled by changing parameters such as temperature, sputtering ion flux and energy. The role of surface morphology with respect to chemical reactivity is investigated by analysing the carbon monoxide dissociation probability on the different nanostructured surfaces.
The control of the atomic step distribution of clusters and nanostructures is of utmost importance in determining, among others, their magnetic , electrical, and catalytic properties. Recent experiments and theoretical models have tried to elucidate the atomistic details underlying the enhanced surface chemical reactivity of these active sites of transition metals (TM). Among these, extensive studies of carbon monoxide chemisorption on TM surfaces have been a valuable resource for the development of surface chemistry. CO, a toxic molecule contained in the automotive exhaust gases, is object of conversion via catalytic oxidation reduction . The carbon monoxide dissociation process is a key step in the syngas reaction which is widely used in the industrial chemistry  for methane formation via the reaction or in the Fisher–Tropsch reaction  where CO and H2 are transformed in hydrocarbons via the (n > 2) reaction. This, along with the basic interest in understanding the mechanism involved in dissociative adsorption of heteroatomic molecules, has placed CO in the list of the most extensively studied adsorbed molecules . The room temperature interaction of CO with transition metal surfaces can be divided in two main groups. The first includes transition metals from the left side of the periodic table, such as Fe, W and Mo, which adsorb CO dissociatively, while the second is composed by elements from the right side of the periodic table such as Co, Ni, Ru, Rh, Pd, Ir and Pt, which tend to adsorb CO molecularly.
However CO dissociation can also occur on the latter metals, in particular Ru, Rh and Ni, under defined temperature, pressure and surface structural conditions, which allow the molecules to overcome the activation barrier for dissociation. Detailed experimental and theoretical investigations performed in the last 15 years report that the chemical reactivity strongly increases on corrugated surfaces and that CO dissociation is sensitive to the structure of the substrate: steps and kinks drastically modify the reaction paths on solid surfaces and appear to be the most active sites for the C–O bond breaking [6, 7].
To this respect a general relation between the chemical reactivity, the d-band center and thus the coordination number of surface atoms, has been established [8–10]: the lower the coordination number of TM surface atoms, the smaller the local bandwidth and the higher the d-band centre position relative to the Fermi level for metals like Rh with a more than half-filled d band. Detailed calculations  based on Density Functional Theory (DFT) report reaction barriers for the reaction which strongly decrease when passing from the flat Rh(111) surface (Ea = 1.17 eV) to steps (Ea = 0.30 eV) and kinks (Ea = 0.21 eV). Coordination numbers of these metal atoms range from n = 9, to n = 7 (steps) and n = 6 (kinks). Other DFT calculations by Mavrikakis et al.  have shown that the energy of the transition state for CO dissociation on Rh(211) is about 120 kJ/mol lower than on the (111) terrace. In this case the coordination of the atoms at the steps is 7.
Experimental investigations indeed report that CO dissociation is negligible on close packed (111), (110) and (100) Rh surfaces  and that it increases on stepped (211) , (210) Rh substrates . The dissociation process has been also extensively studied on Rh nanoparticles supported on thin Al2O3 films grown on a NiAl(110) single crystal, as a function of particle size [15, 16]. Maximum activity has been measured for particles containing about 1000 atoms, but the nature of the active sites was not explained.
It is a natural consequence of these detailed surface science studies to expect that promotion, enhancement, steering and control of CO dissociation can be reached by simply tuning surface morphology with the purpose of changing the density of reaction centers. Recently, it has been found that it is possible to tune the morphology and step distribution of a crystalline Rh(110) substrate by controlled exposure to a beam of noble gas ions: Xe ion irradiation at few hundreds eV leads to the formation of nonequilibrium periodic nanostructures such as nanoscale ripples, oriented either along  or [1–10] directions, mounds, and unexpected rhomboidal pyramids (RP) [17, 18]. The latter nanostructures are particularly interesting as candidate model systems for testing catalytic reactivity, since they are endowed with steep facets running along nonequilibrium directions, exposing a high density of undercoordinated atoms.
Morphological characterisation of nanostructures
The irradiation of transition metal surfaces with an energetic noble ion beam yields the self-organization of a great number of nanoscaled patterns. They originate from the surface instability induced by the ion sputtering as well as from the diffusion balance among the removed adatoms.
Here we show how the sputtering parameters, i.e. the substrate temperatureT, the ion fluxf, the impact energy ɛ may influence the structural features of the surface patterns in the case of a Rh(110) surface sputtered with energetic Xe ions at an incidence angle of 15° from the surface normal.
Experimental: Spot Profile Analysis-LEED
Structural characterization of nanoscale surfaces was performed by in situ spot profile analysis low energy electron diffraction (SPA-LEED) which provides information on large surface area by integrating the diffraction signal on the scale of the electron beam size (about 0.1 mm). As a general consideration on the electron diffraction from sample crystal surfaces, constructive (in-phase) and destructive (anti-phase) interference from the exposed terraces are identified respectively by integer and half-integer values of the vertical scattering phase S z = k z d/2π, k z and d being the vertical momentum transfer and the monoatomic step height .
If the intermediate temperature of 500 K is chosen, the out-of-phase diffraction profile in Fig. 2b is modified in a cross-like shape originating from the coexsistence of high symmetry 〈1−10〉 and oriented facets which bound the sides of the rectangular shaped islands constituting the Round Mouth (RM) pattern. The arrangement of the RM pattern actually appears as the interplay between the majority bounding steps in the two extreme cases of the LTR and HTR patterns. The temperature sequence of the surface patterns formed during Rh(110) sputtering is similar to that observed in the case of Ag(110)  and Cu(110) , apart from a shift to higher temperatures consistent with the larger diffusion barriers for Rh(110). The observation of the RM pattern was also reported in the homoepitaxial growth on Ag(110) .
The emergence of the LTR phase, for ɛ > 500 eV, can be rationalized from an atomistic viewpoint based on Scanning Tunneling Microscopy (STM) investigations of single ion impacts on the Ag(001) and Pt(111) surfaces [24, 25]. In those studies vacancy clusters with size of several nanometers are generated by the ion collisions and are coupled to several surrounding clusters which consist of the displaced adatoms. Within the crater width every correlation is reasonably suppressed due to the locally hyperthermal collision transient. The ascending character of the wavelength, observed in our data, can be thus regarded as a consequence of the increasing crater radius with the impact energy in agreement with molecular dynamics simulations . The LTR state arises then from the onset of impact-induced “hot spots” involving a local surface melting in the volume around the collision point [25, 27]. This assumption is corroborated by the slope relaxation intervening at higher impact energy (see Fig. 5), i.e. when the thermal spike affects wider areas of the surface . In addition, the loss of correlation for higher energy can be reasonably associated either to the stronger excitation transferred to the surface atoms from the impinging ions or to an increase of the lateral extension of the impact crater.
Let’s now consider the decrease of the correlation length Λ of the RP state, when ɛ ranges from 200 eV to 500 eV. Again, from the atomistic approach, this behavior can be understood in terms of the actual damage produced by the ion impact. Contrary to the “thermal spike” picture applied to the LTR case, decreasing the impact energy may have a critical role in the concentration of mobile defects at the topmost surface layer. This argument is supported by the observation of a monotonic increase of the adatom yield with the energy on the Pt(111) surface in the energy range 40–10,000 eV, as follows from STM analysis of single ion impacts  and from molecular dynamics simulations . The role of the impact energy is effectively analogous to that of the deposition flux in homoepitaxial growth: increasing the energy yields a higher concentration of mobile defects (mainly adatoms), which rearrange in stable nuclei after the ion impact. The higher density of stable nuclei on the surface and the lower correlation length between them, can explain the behavior of Λ in the RP regime (Fig. 5).
Since the ion fluxf defines the relaxation time between two subsequent collision events, a morphological variation of the surface structure similar to that observed in the T dependence of Fig. 6a–c, is expected even for different ion flux f. This is shown in Fig. 6d–f: here the out-of-phase diffraction maps of the (00) spot are reported for three different fluxes at ɛ = 400 eV and T = 230 K. Sputtering at a relatively low flux (f = 0.1 ML/min—Fig. 6f) results in a faint HTR pattern; in the intermediate range (f = 0.3–1 ML/min—Fig. 6e) the RP state emerges, while further increasing the flux (f = 3 ML/min—Fig. 6d) the transition to a well-resolved LTR state occurs. From this it can be concluded that, the decrease of the ion flux on the surface morphology corresponds to the increase of the substrate temperature, further confirming the kinetic and diffusive mechanisms underlying the pattern formation.
According to the atomistic approach proposed for the discussion of Fig. 5, a further question which has to be addressed is the role of the ion impact energy in the formation of the surface pattern. In Fig. 6g–i we show the dependence of the surface morphology of the Cu(110) surface on ion energy, for fixed f = 1 ML/min and T = 230 K. As already observed in Fig. 3 and 5, the LTR state transforms into the RP pattern when decreasing the energy from ɛ = 600 eV (Fig. 6g) to ɛ = 400 eV (Fig. 6h), whereas a further decrease of the impact energy down to 200 eV allows to revert the surface morphology into an HTR pattern (Fig. 6i). The sequence of Fig. 6g–i is consistent with the sequence of panels Fig. 6d–f, suggesting that an increase of the ion flux f is equivalent to an increase of the ion energy ɛ. Such behavior can be rationalised if we recall that both STM experiments  and molecular dynamics simulations of a single ion impact  show a monotonic increase of the adatom production yields when the impact energy is increased in the range 0.1–10 keV. Therefore an increase of the average production rate of adatoms can be achieved either through an increase of ɛ (which affects the number of adatoms produced per impact event) or through an increase of f (which modifies the rate of single ion impact events). This picture is fairly compatible with the atomistic discussion on Fig. 5 according to which the role of the energy can be regarded as that of the deposition flux, i.e. as source of mobile defects.
Furthermore, from the data in Fig. 5 and 6g–i, we can also conclude that the impact energy affects the formation process of the RP state not through a selective anisotropic etching of the surface, but by controlling the total number of adatoms emitted per collision event which constitute the mobile species that enter the destabilizing massive transport at the base of the self-diffusion in fcc(110) terminated metal surfaces.
Theory: the continuum model
The diffusion of the mobile species can be treated in a unified scheme both under erosion as well as growth conditions by considering a non-equilibrium, tilt-dependent flux of defects J up as responsible for the surface instability which gives rise to the pattern formation. In a continuum approach, the evolution of the surface profile h(x,y,t) obeys the conservation law described in terms of the total adatom current density J = J sd + J up (m), J sd being the curvature dependent surface diffusion term (vanishing in flat regions such as facets) and J up (m) the destabilising contribution which depends on the local slope vector and biases diffusion uphill, towards ascending step edges ; η(x,y,t) accounts for the randomness of the adatom (ion) arrivals.
We have studied CO interaction with the Rh nanostructured surfaces described in Sect. 2.1 by using High-Energy Resolution Core Level Spectroscopy with synchrotron radiation, to probe the coverage evolution and the molecular dissociation process. The photoemission studies were performed at the SuperESCA beamline [33, 34] of the Elettra third generation synchrotron radiation source in Trieste, Italy. The experimental chamber is equipped with a double pass hemispherical electron energy analyser with 96 channels detector . During the measurements the background pressure in the main chamber was always better than 2 × 10−10 mbar. The Rh(110) single crystal was cleaned by Xe ion sputtering at room temperature (E = 1 keV), flash to 1300 K, oxygen cycles in order to remove residual carbon (in the range 570–1070 K at PO2 = 5 × 10−8 mbar) and finally, hydrogen reduction to remove residual oxygen traces (PH2 = 1 × 10−7 mbar, T = 470–770 K). Surface cleanliness prior to nanostructures preparation was checked by measuring C1s, S2p and O1s signals. C1s and O1s spectra were recorded always at a sample temperature of 200 K in order to reduce temperature broadening of the peaks and in normal emission conditions. Photon energies of 400 and 650 eV were used for C1s and O1s spectra, with an overall energy resolution (X-ray monochromator and electron energy analyser) of 150 and 300 meV, respectively. In these conditions typical data acquisition time was 5 min/spectrum. Core level spectra binding energies have always been calibrated with respect to the Fermi level.
The XPS analysis was done by fitting the core level spectra with a Doniach-Šunjić (DS) function , characterized by two parameters: the singularity index α (describing the asymmetry of the core level spectra due to electron–hole pairs excitations) and the Lorentzian width Γ (because of the natural core-hole lifetime), convoluted with a Gaussian, which takes into account the broadening due to unresolved vibrations, many-body effects and the instrumental resolution. A linear background was also included in the fit.
Chemical reactivity: experimental results on RP
It is well established that both oxygen and carbon 1s core-level signals are strongly sensitive to the local molecular and atomic adsorption sites, and can be used to determine the CO adsorption geometry. In particular, for a large number of carbon monoxide adsorption systems it was found that the binding energy (BE) decreases with increasing CO coordination to the substrate atoms, i.e. in the order BE(on-top) > BE(bridge) > BE(hollow), with a shift which is about twice as large for O1s than for C1s . The O1s BE on different TM single-crystal surfaces varies in the range 531.6–532.6 eV for on-top bonded CO and between 530.5 and 531.6 eV for bridge-bonded CO . The reason of this trend can be understood from total energy considerations, the major contribution to the shift originating from the changes in the energy of the core ionized final state. Indeed the difference of the CO adsorption energies between different adsorption sites for the neutral initial state is very small (∼100 meV) . Carbon and oxygen atomic species when chemisorbed on transition metal surfaces, usually produce core level components at lower BE. In particular carbon species are found at about 284 eV, while chemisorbed oxygen at about 530 eV.
The CO adsorption and the temperature evolution of the chemisorbed layer have been measured for HTR, LTR and RP nanostructures, produced using the procedures reported above.
The growth of the RP nanostructures was characterized in situ by low energy electron diffraction (LEED). The appearance of a fourfold splitting of the (00) diffraction peak along diagonal directions demonstrates the formation of the RP facets. The diffraction pattern is in agreement with the SPA-LEED results reported in Fig. 4. Carbon monoxide was firstly dosed on the Rh(110) nanostructured surface at T = 200 K, i.e. well before the CO desorption onset on the clean (1 × 1) Rh(110) surface [39–41], at different initial coverage, ranging from ∼0.03 ML for the RP to saturation.
However, the most interesting result of the heating process is that not all the CO desorbs but a minor fraction converts into atomic species already at ∼450 K, as evidenced by the increase of lower binding energy components in both, C1s (283.55 eV) and O1s spectra (∼530 eV). Indeed, after the removal of bridge-bonded CO, the on-top sites are gradually depopulated and the surface remains completely free of CO for T > 525 K. After heating to 563 K, 9.4 ± 0.5% of the initial CO has converted into atomic carbon. O1s spectra show the presence of a residual amount of atomic oxygen. Atomic oxygen species are expected to desorb as molecular oxygen at temperatures higher than 750 K. The lower amount of atomic oxygen is therefore interpreted as due to the CO + O→CO2 reaction followed by CO2 desorption .
The increase of CO dissociation probability on RP with decreasing the initial CO coverage is unambiguously confirmed by the temperature behavior of a very low CO coverage layer (0.03 ML) adsorbed at 200 K (Fig. 13b). In this case 80 ± 14% of the CO molecules adsorbed in on-top sites undergo dissociation.
Chemical reactivity: experimental results on HT and LT Ripples
The large set of inequivalent Rh nanostructured surfaces prepared under different experimental conditions, allowed us to investigate the CO dissociation process also on HTR structures.
The same annealing experiments have been performed after CO saturation of the (1 × 1) Rh(110) in order to make a detailed comparison with the nanostructured surfaces. We find evidence that in this condition only 2.4% of CO undergoes dissociation. This result can be explained as due to a residual density of surface defects on the (1 × 1) substrate. Indeed, even on a well prepared surface with a typical miscut of 0.2°, about 1% of the surface atoms reside at the steps.
Chemical reactivity: discussion
Occupacy (in %) of the different sites labeledn l , according to the number of nearestn and next-nearest neighborsl for the different nanostructures (RP, HTR and LTR) and for the (110) flat terraces. The sites can be identified in the following way: 51 = upper step corner atom, 61 = upper step (100) facet, 71 = upper step (111) facet, 72 = (110) terrace atoms, 81 = lower step RP facets, 92 = lower step (111) facets, 92 = lower step (100) facets
Another interesting feature of our experimental results is the increased CO dissociation rate with smaller initial CO coverage on the RP. This can be correlated with the increased availability of undercoordinated atoms, with CO occupying on-top sites at the steps, i.e. the most probable adsorption site. The on-top CO adsorption geometries on the small (110) microterraces and steps can be very similar, but we expect that, as for the (211) stepped surface , CO is more stable at the steps. We associate this with the fact that the Rh 4d electrons are higher in energy and thus interact more strongly with the CO valence states as for CO on Rh stepped surfaces. With increasing the CO coverage only a residual amount of CO molecules can stay on the atoms at the steps. Moreover, the fact that also the adsorbed C and O strongly bind to the steps indicates that during the annealing experiment the products can poison the active sites and we expect that the reaction should stop when all step sites are occupied.
The increased chemical reactivity on nanoparticle catalysts supported on surface oxide is also connected to the presence of special defect configurations. This has been observed in core-level photoemission experiments on alumina-supported Rh particles as a function of particle size [15, 16]. The maximum dissociation rate of 50% was found for particles containing about 1000 Rh atoms, with the reactivity decreasing for larger clusters. The RP clusters produced in our experiments, formed by ∼3000 atoms, result in a dissociation fraction ranging from 10% up to 80%, which nicely compares with the 30% of Rh nanoclusters of similar dimension. These findings suggest that the role of the support in CO dissociation is marginal and that chemical reactivity is mainly governed by the density of undercoordinated surface atoms.
The growth of out-of-equilibrium morphological structures formed during Xenon ion irradiation on Rh(110) substrate is reported. The formation of rhomboydal pyramids and the transition to high temperature and low temperture ripple phases result from the interplay between different kinetic processes depending on temperature, flux and impact energy. Our results illustrate the close correlation between dissociation probability and surface morphology of nanostructured surfaces, a fundamental issue in surface chemistry and nano-catalysis. The RP strongly increase the CO dissociation probability because of the high density of under-coordinated Rh atoms. Detailed comparison of dissociation probability of different nanostructured surfaces shows that CO dissociation takes place in on-top configuration at the kinked step edges. This study shows that it is possibile to change in a controlled way the catalytic properties by changing the density of low coordinated atoms on nanostructured surfaces.
We thank U. Valbusa for useful discussion and suggestions. Financial support from the MIUR under the Programs PRIN 2003, FIRB 2001, from Fondazione CARIGE and from MAE under bilateral program Italia-Slovenia is acknowledged.
- Moroni R, Sekiba D, Buatier de Mongeot F, Gonella G, Boragno C, Mattera L, Valbusa U: Phys. Rev. Lett.. 2003, 91: 167207. COI number [1:STN:280:DC%2BD3srjsVeksw%3D%3D] 10.1103/PhysRevLett.91.167207View ArticleGoogle Scholar
- Crucq A. (Ed): Catalysis and Automotive Pollution Control II, Studies in Surface Science and Catalysis. Elsevier, Amsterdam; 1991.Google Scholar
- Newsome DS: Cat. Rev.-Sci. Eng. 1980, 21: 275. COI number [1:CAS:528:DyaL3cXitVShuro%3D] 10.1080/03602458008067535View ArticleGoogle Scholar
- Zhang Y, Jacobs G, Sparks DE, Dry ME, Davis BH: Catal. Today. 2002, 71: 411. COI number [1:CAS:528:DC%2BD38XhtFGqsLw%3D] 10.1016/S0920-5861(01)00468-0View ArticleGoogle Scholar
- Somorjai GA: Introduction to Surface Chemistry and Catalysis. Wiley, New York; 1994.Google Scholar
- Zubkov T, Morgan GA, Yates JT, Kuhlert O, Lisowski M, Schillinger R, Fick D, Jansch HJ: Surf. Sci.. 2003, 526: 57. COI number [1:CAS:528:DC%2BD3sXhtVagsb0%3D] 10.1016/S0039-6028(02)02655-9View ArticleGoogle Scholar
- Zubkov T, Morgan GA, Yates JT: Chem. Phys. Lett.. 2002, 362: 181. COI number [1:CAS:528:DC%2BD38XmtlWgsr0%3D] 10.1016/S0009-2614(02)00895-3View ArticleGoogle Scholar
- Hammer B, Nørskov JK: Surf. Sci.. 1995, 343: 211. COI number [1:CAS:528:DyaK28XnsFGq] 10.1016/0039-6028(96)80007-0View ArticleGoogle Scholar
- Hammer B, Nielsen OH, Nørskov JK: Catal. Lett.. 1997, 46: 31. COI number [1:CAS:528:DyaK2sXksFyrsb0%3D] 10.1023/A:1019073208575View ArticleGoogle Scholar
- Dahl S, Logadottier A, Egeberg RC, Larsen JH, Chorkendorff I, Tornqvist E, Nørskov JK: Phys. Rev. Lett.. 1999, 83: 1814. 10.1103/PhysRevLett.83.1814View ArticleGoogle Scholar
- Liu Z-P, Hu P: J. Am. Chem. Soc.. 2003, 125: 1958. COI number [1:CAS:528:DC%2BD3sXkvFKmtQ%3D%3D] 10.1021/ja0207551View ArticleGoogle Scholar
- Mavrikakis M, Bäumer M, Freund H-J, Nørskov JK: Catal. Lett.. 2002, 81: 153. D] COI number [1:CAS:528:DC%2BD38XlsVerur0%3D] 10.1023/A:1016560502889View ArticleGoogle Scholar
- Campuzano JC: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis.. Edited by: King D.A., Woodruff D.P.. Elsevier, New York; 1990:389.Google Scholar
- Rebholz M, Prins R, Kruse N: Surf. Sci.. 1991, 259: L797. COI number [1:CAS:528:DyaK38Xks12jtQ%3D%3D] 10.1016/0039-6028(91)90554-6View ArticleGoogle Scholar
- Andersson S, Frank M, Sandell A, Giertz A, Brena B, Bruhwiler PA, Martensson N, Libuda J, Baumer M, Freund H-J: J. Chem. Phys.. 1998, 108: 2967. COI number [1:CAS:528:DyaK1cXps1KnsQ%3D%3D] 10.1063/1.475684View ArticleGoogle Scholar
- Ertl G, Freund H-J: Phys. Today. 1999, 52: 32. COI number [1:CAS:528:DyaK1MXos1aktw%3D%3D]View ArticleGoogle Scholar
- Molle A, Buatierde Mongeot F, Molinari A, Fuerkaiti F, Boragno C, Valbusa U: Phys. Rev. Lett.. 2004, 93: 256103. COI number [1:STN:280:DC%2BD2M%2FnsFaqsQ%3D%3D] 10.1103/PhysRevLett.93.256103View ArticleGoogle Scholar
- Molle A, Buatier de Mongeot F, Molinari A, Boragno C, Valbusa U: Phys. Rev. B. 2006, 73: 155418. 10.1103/PhysRevB.73.155418View ArticleGoogle Scholar
- Rusponi S, Costantini G, Buatierde Mongeot F, Boragno C, Valbusa U: Appl. Phys. Lett.. 1999, 75: 3318. COI number [1:CAS:528:DyaK1MXnsVakt74%3D] 10.1063/1.125337View ArticleGoogle Scholar
- Buatierde Mongeot F, Costantini G, Boragno C, Valbusa U: Phys. Rev. Lett.. 2000, 84: 2445. COI number [1:CAS:528:DC%2BD3cXhs1Cms74%3D] 10.1103/PhysRevLett.84.2445View ArticleGoogle Scholar
- Rusponi S, Boragno C, Valbusa U: Phys. Rev. Lett.. 1997, 78: 2795. COI number [1:CAS:528:DyaK2sXisVWjtL0%3D] 10.1103/PhysRevLett.78.2795View ArticleGoogle Scholar
- Rusponi S., Costantini G., Boragno C., Valbusa U. Phys. Rev. Lett. 81735 (1998)Google Scholar
- Golubovic’ L, Levandovsky A, Moldovan D: Phys. Rev. Lett.. 2002, 89: 266104. 10.1103/PhysRevLett.89.266104View ArticleGoogle Scholar
- Costantini G, Buatierde Mongeot F, Boragno C, Valbusa U: Phys. Rev. Lett.. 2000, 86: 838. 10.1103/PhysRevLett.86.838View ArticleGoogle Scholar
- Michely Th, Teichert C: Phys. Rev. B. 1994, 50: 11156. COI number [1:CAS:528:DyaK2MXhslSgur4%3D] 10.1103/PhysRevB.50.11156View ArticleGoogle Scholar
- Bringa EM, Nordlund K, Keinonen J: Phys. Rev. B. 2001, 64: 235426. 10.1103/PhysRevB.64.235426View ArticleGoogle Scholar
- van Dijken S, de Bruin D, Poelsema B: Phys. Rev. Lett.. 2000, 86: 4608. 10.1103/PhysRevLett.86.4608View ArticleGoogle Scholar
- Ghaly M, Averback RS: Phys. Rev. Lett.. 1994, 72: 364. COI number [1:CAS:528:DyaK2cXhslCitLg%3D] 10.1103/PhysRevLett.72.364View ArticleGoogle Scholar
- Villain J: J. Phys. (France). 1991, 1: 19. 10.1051/jp1:1991114View ArticleGoogle Scholar
- M. Siegert and Plischke, Phys. Rev. Lett. 73, 1517 (1994)Google Scholar
- Levandovsky A, Golubović L, Moldovan D: Phys. Rev. E. 2007, 74: 061601. 10.1103/PhysRevE.74.061601View ArticleGoogle Scholar
- Boragno C, Buatier de Mongeot F, Costantini G, Molle A, De Sanctis D, Valbusa U, Felici R, Ferrer S: Phys. Rev. B. 2003, 68: 094102. 10.1103/PhysRevB.68.094102View ArticleGoogle Scholar
- Baraldi A, Barnaba M, Brena B, Cocco D, Comelli G, Lizzit S, Paolucci G, Rosei R: Electron Spectrosc. Relat. Phenom.. 1995, 76: 145. COI number [1:CAS:528:DyaK28XisVSmsrc%3D] 10.1016/0368-2048(95)02490-5View ArticleGoogle Scholar
- Baraldi A, Comelli G, Lizzit S, Kiskinova M, Paolucci G: Surf. Sci. Rep.. 2003, 49: 169. COI number [1:CAS:528:DC%2BD3sXivVKgurk%3D] 10.1016/S0167-5729(03)00013-XView ArticleGoogle Scholar
- Baraldi A, Dhanak VR: J. Electron Spectrosc. Relat. Phenom.. 1994, 67: 211. COI number [1:CAS:528:DyaK2cXjtVOrsbY%3D] 10.1016/0368-2048(93)02038-NView ArticleGoogle Scholar
- Doniach S, Šunjić M: J. Phys. C. 1970, 3: 185. 10.1088/0022-3719/3/2/010View ArticleGoogle Scholar
- Mårtensson N, Nilsson A: Springer Series in Surface Science. Edited by: Eberhardt W.. Springer-Verlag, Berlin; 1994.Google Scholar
- Dhanak VR, Baraldi A, Comelli G, Paolucci G, Kiskinova M, Rosei R: Surf. Sci.. 1993, 295: 287. COI number [1:CAS:528:DyaK2cXhsFygtg%3D%3D] 10.1016/0039-6028(93)90275-OView ArticleGoogle Scholar
- Baraldi A, Dhanak VR, Comelli G, Prince KC, Rosei R: Surf. Sci.. 1993, 293: 246. COI number [1:CAS:528:DyaK3sXls1yhurs%3D] 10.1016/0039-6028(93)90318-EView ArticleGoogle Scholar
- Dhanak VR, Baraldi A, Comelli G, Paolucci G, Kiskinova M, Rosei R: Surf. Sci.. 1993, 295: 287. COI number [1:CAS:528:DyaK2cXhsFygtg%3D%3D] 10.1016/0039-6028(93)90275-OView ArticleGoogle Scholar
- Baraldi A, Comelli G, Lizzit S, Cocco D, Paolucci G, Rosei R: Surf. Sci.. 1996, 367: L67. COI number [1:CAS:528:DyaK28XnsVyrsrY%3D] 10.1016/S0039-6028(96)01126-0View ArticleGoogle Scholar
- Smedh M, Beutler A, Ramsvik T, Nyholm R, Borg M, Andersen JN, Duschek R, Sock M, Netzer FP, Ramsey MG: Surf. Sci.. 2001, 491: 99. COI number [1:CAS:528:DC%2BD3MXntVyktb8%3D] 10.1016/S0039-6028(01)01357-7View ArticleGoogle Scholar
- Baraldi A, Lizzit S, Cocco D, Comelli G, Paolucci G, Rosei R, Kiskinova M: Surf. Sci.. 1997, 385: 376. COI number [1:CAS:528:DyaK2sXmvVGru78%3D] 10.1016/S0039-6028(97)00264-1View ArticleGoogle Scholar