Vacuum 83 (2009) 1368–1375
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The adsorption of Ni on the Mo(111) crystal face C. Tomas, S. Stepanovskyi, Sz. Klein*, J. S´liwin´ski, J. Ko1aczkiewicz Institute of Experimental Physics, University of Wrocław, pl. M. Borna 9, 50-204 Wrocław, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 October 2008 Accepted 20 April 2009
STM, LEED, AES, TDS and Df measurements were performed to investigate the adsorption of Ni on the molybdenum (111) surface. The adsorption energy of Ni atoms on the Mo(111) surface was determined. At 300 K the layer-by-layer growth mechanism was observed. No faceting of the Mo(111) surface was observed after the annealing. Annealing leads to the adsorbate agglomeration and formation of Ni islands in the shape of pyramids. Ó 2009 Elsevier Ltd. All rights reserved.
PACS: 61.05jh 65.40gh 65.40gp 68.35bd 68.37Ef 68.43Fg 68.43Vx 68.55A Keywords: Reconstruction Faceting LEED TDS AES STM Work function
1. Introduction The W(111), Mo(111) and Ta(111) substrates represent morphologically unstable atomically rough surfaces, which under the influence of an adsorption layer can be reconstructed. It is massive transformation from planer morphology to microscopically faceted surfaces with two types of micro-faces {211} or {110}. The faceting of the W(111) surface was studied by Madey et al. [1–9]. They found that this effect can be observed for metals used as adsorbate characterized by electronegativity equal to 2 or higher on the Pauling scale. The faceting is observed when the surface is covered by one ‘physical monolayer’ (in such a case all ‘visible’ atoms on the W(111) surface are covered by adsorbate atoms when we look down on the surface) after annealing to 700 K. Theoretical works show that faceting results from a decrease of the surface free energy [10–14]. In this case the surface free energy is lower than before reconstruction, although the
* Corresponding author. Tel.: þ48 71 3759283; fax: þ48 71 3287365. E-mail address:
[email protected] (Sz. Klein). 0042-207X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2009.04.048
reconstructed surface exhibits larger area. According to Herring’s theory [15,16], the transformation of surface from {hkl} / {h0 k0 l0 } is favorable when ghkl > gh0 k0 l0 /cos q, where q is the angle between the [hkl] and [h0 k0 l0 ] directions and g represents the surface free energy per unit of area. Guan et al. [5] suggested that the adsorbate electronegativity is a decisive factor, although they claimed that only such metals as Pd, Pt, Rh, Ir and Au whose atomic radii are close to the atomic radius of W, cause this process. The adsorption of atoms with radii more than 5% greater (Gd) or more than 5% smaller (Cu, Co, Ni) does not cause faceting of the W(111) surface. The investigations of the Mo(111) and Ta(111) surfaces [17–27] led to similar conclusions. The adsorbate atoms whose size is much bigger (Sm, Gd) or much smaller (Fe, Ni) than: W, Mo and Ta atoms – do not cause faceting of the substrate. However, it was found that neither Au nor Ag (with the atom radius size similar to that for Au) cause faceting of the Ta(111) and Mo(111) surfaces [5,19,22,26]. Authors [27] suggest that the surface morphology is determined by the interaction between the adsorbate and the substrate. Adsorbate atoms which interact very strongly with substrate atoms cause the substrate transformation. This can explain the
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fact that there is no faceting in the case of Ag. However, there is no proof that the interaction of Au with the Mo(111) and Ta(111) surfaces is weaker than with the W(111) surface. The conclusion following from these investigations is that electronegativity does not affect faceting. Very important is whether the adsorbate wets the surface or not. Two conditions must be fulfilled: (1) the adsorbate must wet the surface and (2) the free energy must decrease. It was found that annealing of Fe and Ni layers on W leads to the adsorbate arrangement [27]. In thick Fe layers adsorbed on W(111), a non-wetting–wetting transition was observed. In the case of Ni on W(111) only the adsorption layer underwent reconstruction. The surface must consist of a more or less regular sequence of up and down steps within the limits of error for the width of three atomic row wide (111) terraces bounded by ½110 steps. These conclusions were drawn from LEED patterns and the work function measurements. In this work the properties of Ni on the Mo(111) surface were investigated with the use of LEED scanning tunneling microscopy (STM), Auger electron spectroscopy (AES), thermal desorption spectroscopy (TDS) and work function measurements Df. The question is whether the Ni adsorption on Mo(111) surface is similar to the W(111) case (Ni adsorption does not lead to faceting of W(111) surface) and whether the formation of the Ni–Mo alloy occurs after annealing up to 1175 K [8]. 2. Experimental The measurements were carried out in two metal UHV systems at the pressure lower than 1 1010 Torr. One of them, Omicron apparatus, was equipped with a scanning tunneling microscope (STM) and a retarding field analyzer (RFA) used for Auger electron spectroscopy (AES) and low energy electron diffraction (LEED) pattern observations. The other apparatus consisted of an OCI retarding field analyzer (RFA) used for LEED/AES measurements, a quadrupole mass spectrometer (QMS) for temperature-programmed desorption spectroscopy (TDS) and an additional electron gun for measurements of the work function changes (Df). A sample of 5 N purity was cut perpendicular to the [111] direction with an accuracy of 0.05 . The Mo sample was cleaned by prolonged heating at 1300 K in an oxygen atmosphere (1 107 Torr), which was followed by flashing to 2300 K. The sample was considered to be clean when the Mo (186 eV) amplitude peak was at least 300 times higher than the carbon peak C (272 eV). The sample temperature was determined in two different ways depending on the UHV system. In the STM apparatus, where the sample was moved from the preparation chamber to the STM, the temperature was determined by an optical pyrometer. In the second one UHV system the temperature was determined by the W5%Rh–W26%Rh thermocouple spotwelded to the bottom of the sample. The sample was heated resistively by passing constant current directly through it. In this way the sample temperature was increased till 1700 K. In order to reach higher temperatures the sample was flashed by electron bombardment at energy 1 keV. The Ni was deposited from sources prepared from Ni wire (0.1 mm in diameter) wound onto tungsten wire (0.3 mm in diameter). Such a design of source is characterized by small thermal inertia and is relatively easy to degas. The measurements were performed after successive evaporations of the same adsorbate doses onto the sample. The thermal stability of the Ni layer was investigated by depositing a definite dose of adsorbate, which was followed by depositing time measurement. Then LEED and AES measurements were performed to verify the coverage and to check the sample cleanness. All STM measurements were carried out at 300 K. The tunneling current was usually 0.2 nA and the potential difference between the tip and the sample was usually
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2 V. The STM images were processed by using the WSxM program [28]. The change of the work function (D4) was measured by means of Anderson’s method, where electrons at the energy of 12 eV were directed onto the sample. TDS spectra were measured by the linear increase of temperature with the heating rate of 2.7 K/s. The Auger signal was measured with a 2% accuracy of a signal derived from the clean Mo surface, whereas the work function was measured with a 5 meV accuracy. For each coverage the desorption energy was determined by using the Arrhenius plot slope. The inaccuracy of measurement for specified coverage determined in several measurement series was 20 meV. The size of measurement points showed in the figures corresponds to the measurement error. 3. Results and discussion Fig. 1 shows the Auger amplitudes (AA) of Ni(61 eV) and Mo(186 eV) and work function changes as a function of the deposition time at 300 K. For the used modulation voltage (1 Vpp) two initial Ni doses do not result in appearance of visible peaks, because the Ni(61 eV) peak lies on the slope of the secondary electron peak. Additionally in the same figure a variation of the Auger amplitudes for Mo(186 eV) is presented as a function of the deposition time at 300 K, but with a lower deposition rate. The last dependence can be approximated by linear segments with the successively decreasing slope. The first slope-change occurs after 7.5 min and the Auger amplitude decreases to 75% of the initial value for the clean Mo surface (AA0). The next kinetic breaks are visible after 15 min and 22.5 min of the deposition time. After 15 min of evaporation AA(Mo) equals 56% of AA0, after 22.5 min AA(Mo) equals 43% of AA0. The ratios of slope of the linear segments (Snþ1/Sn) have constant value equal to 0.7 with an accuracy of 0.01. The first kinetic break of the (AA) 61 eV Ni and 186 eV Mo for a bigger deposition rate occurs after 3 min, and the next after 6, 9, 12, 15, 18 and 21 min. In the case of 3 min the (AA) 186 eV Mo peak equals 77% of the AA0 value. In the case of an adsorbate on the surface with low surface density, the slope changes of linear segments are not as clear as in the case of layers with high surface density. The work function initially increases and reaches the local maximum. It then decreases to reach the minimum after 3 min. Then the work function increases and after 11 min it reaches a value which is 0.7 eV higher than the value for the clean Mo(111) surface. For t > 11 min a decrease of the work function is observed, which depends on the layer deposition method. During deposition, the decrease grows with the value of a single dose. The largest decrease
Fig. 1. Auger amplitudes of Ni(61 eV), Mo(186 eV) and work function changes as a function of Ni deposition time at 300 K. The measurement points marked as empty squares correspond to lower deposition rate.
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of the work function is observed during the single deposition of thick layers. It was found that during the deposition of Ni at 300 K for time shorter than 3 min, only the LEED pattern characteristic of the clean Mo surface was observed (Fig. 2a). For the deposition time from 3 min to 6 min the LEED pattern shown in Fig. 2b was observed. The next LEED pattern observed for the deposition time longer than 6 min is shown in Fig. 2c. In this pattern extra spots are present in the [110] direction of the substrate. The distance between basic spots of this pattern is divided by extra spots for six parts. A change of the next LEED pattern was observed at 300 K after 4 times longer time than for the first change. These LEED patterns (Fig. 2d–f) strongly suggest faceting of Ni. The pattern shown in Fig. 2b can be attributed to the Ni(111) layer whose [211] direction is parallel to the [211] direction of the substrate. Whereas the pattern in Fig. 2c shows the Ni layer with another orientation in relation to the substrate, where the [110] Ni direction is parallel to the [211] Mo direction. For higher thicknesses more complicated pattern was observed.
In the TDS spectra (Fig. 3) for low coverages (after up to 6 min of Ni deposition) as well as for higher coverages (3 min to 24 min of Ni deposition) two desorption peaks are visible. For low deposition doses the increase of the initial coverage causes the shift of the high-temperature peak towards lower temperatures, which is characteristic to desorption order greater than 1. This is in a good accordance with desorption order equal 1.5 obtained from the procedure described in subsequent paragraphs. This result whose physical reason seems to be unclear, we suggest to be a result of the superposition of more than one adsorption state. For higher coverages a shift of the dominating low energy peak towards higher temperatures is clearly visible. Such a shift is characteristic for a fractional order desorption which may indicate desorption from the three-dimensional clusters. Fig. 4a shows changes of high energy desorption peaks as a function of the deposition time. Fig. 4b shows changes of the full width at half maximum of desorption peaks and Fig. 4c shows the area of desorption peaks as a function of the deposition time. The
Fig. 2. The LEED patterns of Ni on Mo(111) deposited at 300 K: (a) clean Mo (111), Ep ¼ 90.7 eV; (b) Ep ¼ 64 eV, t ¼ 5.2 min; (c) Ep ¼ 69.5 eV, t ¼ 12 min; (d) Ep ¼ 50.1 eV, t ¼ 24 min; (e) Ep ¼ 60 eV, t ¼ 24 min; (f) Ep ¼ 90.7 eV, t ¼ 24 min.
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Fig. 3. The ion current as a function of annealing temperature with the heating rate 2.7 K/s. The curve parameter is the deposition time.
high desorption peaks were changed after 3 min and the next fundamental change was visible after 6 min. The area of desorption peaks is a linear function of the deposition time. It means that the measurement system worked correctly. The full width at half maximum increases gradually and obtains the maximum value after 6 min of the deposition time. This time corresponds to the situation when the heights of both low- and high-temperature peaks are comparable. For longer deposition times the low-temperature peak dominates and the full width at half maximum decreases. Over 12 min a change of the full width at half maximum is still visible. The results presented above were used to define the growth mechanism of Ni layers at 300 K and to determine the coverage
scale. The constant slope ratio of the successive linear segments describes AA(Mo) and AA(Ni) as a function of the deposition time, and fact that the Mo Auger amplitudes after 15 and 22.5 min are 0.752 ¼ 0.56 and 0.753 ¼ 0.42 of AA0 value (which is in agreement with the measured values), 0.75 is the value which the peak reaches after 7.5 min of the deposition time. These facts prove that the growth mechanism is layer-by-layer. The TDS results are partially correlated with the AES results. It is worth to reminding that TDS data describe the investigated system at a much higher temperature than the room temperature. The changes of the desorption peaks height observed after 3 min prove the appearance of a new adsorption state which does not produce a visible peak at the beginning. The next height change is observed
Fig. 4. (a) The height of the desorption peaks as a function of the deposition time; (b) Changes of the full width at half maximum of desorption peaks as a function of the deposition time; (c) The area of desorption peaks as a function of the deposition time.
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Fig. 5. The desorption energy and desorption frequency as a function of coverages. (1 ML ¼ 3 min of deposition time).
after 6 min of the deposition time, so 3 min of the deposition is needed to obtain one monolayer (Q ¼ 1 ML) Ni. On the basis of LEED patterns we can observe that one pseudomorphic layer was obtained at this time with the density 5.26 1014 at/cm2. The time intervals which correspond to the next linear segments are the same within the limit of error. However, the LEED patterns corresponding to the next layers differ from each other. The second monolayer is oriented, with regard to the substrate, in such a way that the [211] direction of adsorbed layer is parallel to the [211] direction of substrate. This arrangement is possible if Ni atoms are not situated at lattice sites. Probably the second monolayer of Ni atoms displace atoms of first monolayer from energy minima places and then together occupy hollow sites between Mo atoms consequently creating a layer observed in the LEED pattern. The TDS results shown in Fig. 3 were used to estimate the desorption energy (Ed). For this purpose, a computer program based on the desorption parameter calculation procedure proposed by Bauer [29] was used. This program contains the spectrum smoothing procedure, background subtraction procedure, procedure determining desorption order and the procedure for
Fig. 6. The LEED patterns observed for the annealed layer: (a) Ep ¼ 52.8 eV, t ¼ 5.2 min, T ¼ 1080 K; (b) Ep ¼ 47.6 eV, t ¼ 12 min, T ¼ 480 K; (c) Ep ¼ 52.9 eV, t ¼ 12 min, T ¼ 480 K; (d) Ep ¼ 72.5 eV, t ¼ 5.2 min, T ¼ 780 K; (e) Ep ¼ 116.8 eV, t ¼ 24 min, T ¼ 780 K.
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calculating desorption parameters for the estimated desorption order. The desorption order determination procedure is based on x the desorption equation dn=dt ¼ vd Q expðEd =kTÞ. The curve slope lnðdn=dtÞ ¼ lnQ can be determined in the way proposed in [30]. The measurements of the desorption parameters Ed – desorption energy and ad – desorption frequency were carried out with the assumed value x ¼ 1.5 and were restricted to coverages where this assumption was fulfilled (it means for Q < 0.8 ML). The calculated values for Q < 0.9 ML are shown in Fig. 5. With the increase of the coverage the value of both desorption parameters decreases. The desorption energy for low coverages (Q / 0) is 5.17 eV/at. In our opinion this value is connected with the desorption of Ni atoms from clean Mo(111). The final value of the desorption energy connected with the low-temperature peak with maximum about 1300 K equals 4.45 eV/at, which is in agreement with the value of Ni cohesion energy Ecoh ¼ 4.44 eV/at [31]. The value of desorption frequency corresponded to desorption of the Ni atoms from the first monolayer equals 6.31 1015 s1, which confirms the localized adsorption. To verify the faceting of Mo(111) under the influence of Ni adsorption, the LEED measurements were made at higher temperatures. The results of these measurements are shown in Fig. 6. The pattern in Fig. 6a was observed for coverages higher than 1 ML after the sample annealing to T 600 K. For coverages higher than 2 ML the LEED pattern observed after adsorption disappeared and after annealing to T 400 K new patterns were visible
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(Fig. 6b, c). Both patterns shown by the same layer were made with two different initial energies and spots moved are marked by arrows. After annealing to 950 K the pattern was changed (Fig. 6a). After annealing to T 600 K some spots became brighter (in Fig. 6d one of them is marked by arrow). The lattice constant for most of bright spots of the pattern is 2.42 Å. It is by 3% smaller than the lattice constant of Ni. Additionally, every second spot of the first diffraction order looks different, which proves the surface modification. For the highest measured coverages, where at 300 K a complicated pattern was observed, annealing made these spots sharper (Fig. 6e), which can be interpreted as deriving from narrow terraces analogically to what happens on the W(111) surface [27]. This pattern disappears after annealing to 1080 K. The STM results are shown in Fig. 7. Fig. 7a shows the Q > 2 ML layer of Ni after annealing up to 1000 K. The surface was covered by lots of pyramids with a triangle base. For the thickness Q > 5 ML after annealing up to 1200 K the layer looks as in Fig. 7c. There are visible big plane surfaces next to the surface covered by pyramids similar to the picture shown in Fig. 7a. The terraces visible in Fig. 7b are 0.95 Å high. This value corresponds very well to the distance between {111} planes in the bulk of Mo. Fig. 7d shows the surface with initially high coverage of Ni (7.4 ML), after annealing up to 1350 K, which causes that the coverage is lower than 1 ML. The coverage calculated from the Ni/Mo ratio is 0.6 ML. The distance between atoms visible in this image is 4.45 Å, so we can exclude the alloy formation at low coverages, although terrace edges in the presence of Ni atoms look different than in the case of clean surface.
Fig. 7. STM images of the Mo(111) surface covered by Ni layer: (a) t ¼ 7.8 min, T ¼ 1000 K; (b) t ¼ 7.8 min, T ¼ 1320 K; (c) t ¼ 15.5 min, T ¼ 1200 K; (d) t ¼ 22.2 min, T ¼ 1350 K. Scan angles are 0 .
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The STM results for annealed Ni layers, similar to the TDS results, suggest the intermixing of Ni with the Mo surface [8]. Especially the high-temperature TDS peak is not stabilized at Q > 1 ML and the temperature decreases, with the coverage increase. Although we cannot exclude that Ni does not wet the substrate at higher temperatures, especially at higher coverages the results suggest that visible pyramids are built solely of Ni atoms. The fact that the desorption energy starts decreasing already at 0.2 ML can be interpreted as a result of the intermixing of Ni with the Mo surface, which causes that Ni atoms which do not take part in mixing process are weakly bonded with the substrate, because Ni atoms interact not only with Mo atoms but also with the mixture of Ni and Mo atoms. An alternative explanation of Ed (Q) dependence can be that Ni atoms create several-layer islands, which is suggested by the STM images. Fig. 7b shows bright clusters two or three monolayers thick. This image was obtained after partial desorption of Ni. In order to check precisely the intermixing of Ni with Mo atoms, the Auger amplitude and the work function change were measured as a function of annealing temperature for layers with different thickness. The work function changes (Fig. 8a) indicate essential changes for thick layers as a result of annealing. Only for two coverages (Q < 2 ML) the course of the work function changes is converse to that for the measured changes for Ni deposition at 300 K. For these curves there is a minimum observed at high temperatures, even for the curve Q ¼ 0.8 ML where at 300 K minimum does not exist. Firstly there is no local minimum which corresponds to the first layer formation. Secondly there is a local minimum visible during annealing up to 570 K. The work function value that corresponds to this minimum depends on the initial coverage. The changes of (AA) 61 eV Ni and (AA) 186 eV Mo are shown in Fig. 8b. There are three temperatures at which changes of (AA) occur, first about 600 K, second about 1100 K and the last 1270 K. This last value corresponds very well to the desorption temperature. In the 1150–1300 K temperature range the Auger amplitudes of the Ni and Mo peaks have constant value, however the Auger amplitude of the Ni peak corresponds to the value at 0.9 ML coverage at 300 K, and the Auger amplitude of the Mo peak corresponds to Q ¼ 1.4 ML coverage. That means the adsorbate on the surface after annealing is arranged differently than after deposition at 300 K. The difference between the adsorbate location on the surface for annealed layers and the adsorbate location after depositing at 300 K is also confirmed by LEED patterns. In the layer annealing process one does not observe the patterns showed in Fig. 2b–d. For annealed layers Fig. 6a dominates, after annealing up to about 1200 K spots from Fig. 2b are visible. The work function changes show that as an effect of annealing some adsorbate atoms are replaced. The change of (AA) observed after annealing up to 600 K is connected with the disappearance of the diffraction pattern observed after deposition and with the appearance of the pattern derived from the reconstructed surface. The spots are visible which move (during the change of primary energy) perpendicularly to the screen radius. This pattern disappears after annealing up to 1140 K. At this temperature the Ni desorption from the low-temperature states starts in the TDS spectra. The hightemperature peak begin to emerge at about 1200 K, which corresponds to the appearance of the pattern which is a superposition of Fig. 2b and Fig. 6a, and to the intensive decrease of the work function and Auger amplitudes. The final conclusion to be drawn from the results for annealed layers is that nickel agglomerates at higher temperatures, and probably only the first monolayer stays flat. The Ni agglomeration leads to the formation of pyramidal clusters. The pyramids observed in the STM images have the orientation of {211} facets.
Fig. 8. (a) The work function changes as a function of temperature at different coverages; (b) Auger amplitudes of Ni (61 eV) and Mo (186 eV) as a function of temperature.
However, the observed diffraction pattern does not correspond to the reconstruction with the formation of this kind of facets. Thus we can say that the adsorbate arrangement at the lateral wall of the formed pyramids corresponds to the Ni (111) surface packing. This kind of adsorbate arrangement at the substrate surface explains the observed dependence of the desorption parameters on coverage (Fig. 5). The constant value of these parameters for coverages Q < 0.2 ML indicates that only for small coverages Ni creates the mono-atomic layer. For Q > 0.2 ML the intermixing of Ni with Mo takes place, which leads to a weak interaction of Ni atoms with the modified substrate. In consequence the adsorbate forms severallayer islands. For higher coverages several-layer clusters, pyramidal in shape are formed, which results in the appearance of plenty of different adsorption sites with different bonding energies. 4. Conclusions At 300 K the growth mechanism of Ni layers on the Mo(111) surface is of the layer-by-layer type. A annealing leads to the
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agglomeration of clusters pyramidal in shape and with a triangle base. This surface is not observed to yield to faceting under the Ni layer influence. Diffraction patterns characteristic for the faceted Mo surface with {211} or {110} facets [5,21] were not observed. Whereas the adsorbate layer at high coverages nanofacets bounded by [110] steps, analogical to that observed on the W(111) surface [27]. We can say that in this case the Ni layer looks the same because the LEED patterns look the same, and it is built analogically. The agglomeration is a non-reversible process. At higher coverages even the first layer yielded to agglomeration, because local minimum of the work function at the coverage Q ¼ 1 ML was not observed. Probably intermixing takes place, which, can lead to a decrease of the desorption energy. The intermixing of Ni with Mo atoms leads to the surface modification and, as a result, to a change in relations between cohesion and adhesion forces, which in turn leads to changes of the growth mechanism. At 300 K when there are only Mo atoms on the surface, the adhesion dominates and Ni creates a flat layer and the Stranski–Krastanov growth mode is realized. However, in effect of the intermixing of Ni with Mo atoms the adhesion forces do not dominate and the growth mechanism is changed to the Weber– Volmer type. This modification is proved by the fact that desorption energy very quickly reaches the cohesion energy value at the coverage 2 ML before the complete physical layer is formed. The results for Ni/Mo(111) are partially similar to Ni/W(111) results [27]. The LEED patterns observed at 300 K are analogical for the W(111) and Mo(111) surfaces. Also the values of the work function changes at 300 K in both cases are similar, although in the case of Mo(111) there is no such a strong decrease of the work function value at Q ¼ 7 ML as in the W(111). However, for annealed layers differences are quite big as, for Q > 2 ML in the case of Mo(111) the minimum of the work function was not observed. In our opinion these differences are caused by a much stronger mixing of Ni atoms with the substrate atoms in Mo than in the case of W. It does not follow from our measurements whether the clusters in the shape of pyramids observed after annealing are composed of only Ni atoms or they are a mixture of Ni and Mo atoms.
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Acknowledgements We would like to thank to dr Maciej Kuchowicz for support with STM results. We thank also to Dominika Grodzin´ska for help in preparation of figures, and for linguistic assistance. This work is sponsored by Wroc1aw University from fund 2016/2008. References [1] Song K-J, Demmin RA, Dong C, Garfunkel E, Madey TE. Surf Sci Lett 1990;227:L79. [2] Song KJ, Dong CZ, Madey TE. Langmuir 1991;7:3019. [3] Dong CZ, Shivaprasad SM, Song K-J, Madey TE. J Chem Phys 1993;99:9172. [4] Madey TE, Guan J, Dong C-Z, Shivaprasad SM. Surf Sci 1993;287/288:826. [5] Guan J, Campbell RA, Madey TE. Surf Sci 1995;341:311. [6] Nien C-H, Madey TE. Surf Sci 1997;380:L527. [7] Nien C-H, Madey TE, Tai YW, Leung TC, Che JG, Chan CT. Phys Rev 1999;B59:10335. [8] Dong CZ, Zhang L, Diebold U, Madey TE. Surf Sci 1995;322:221. [9] Madey TE, Nien C-H, Pelhos K, Ko1odziej JJ, Abdelrehim IM, Tao H-S. Surf Sci 1999;438:191. [10] Chen SP. Surf Sci Lett 1992;274:L619. [11] Che JG, Chan CT, Kuo CH, Leung TC. Phys Rev Lett 1997;79:4230. [12] Che JG, Chan CT. Surf Sci 1998;401:L432. [13] Chan CT, Che JG, Leung TC. Prog Surf Sci 1998;59:1–11. [14] Chen JG, Chan CT. Phys Rev 2003;B67:125411. [15] Herring C. Phys Rev 1951;82:87. [16] Williams ED, Bartelt NC. Ultramicroscopy 1989;31. [17] Song K-J, Lin JC, Lai MY, Wang YL. Surf Sci 1995;327:17. [18] Che JG, Zhang KM, Xie XD. Surf Sci 2001;472:179. [19] Song K-J, Chen WR, Yeh V, Liao Y-W, Tsao PT, Lin MT. Surf Sci 2001;478:145. [20] Tomas C, Ossowski T, Ko1aczkiewicz J. Surf Sci 2001;494:183. [21] Szukiewicz R, Ko1aczkiewicz J. Surf Sci 2003;547:L837. [22] Ko1aczkiewicz J, Kuchowicz M, Szukiewicz R. Surf Sci 2004;548:246. [23] Ko1aczkiewicz J, Kuchowicz M, Szukiewicz R. Surf Sci 2004;548:259. [24] Szukiewicz R, Ko1aczkiewicz J. Vaccuum 2004;74:55. [25] Dan´ko DB, Kuchowicz M, Ko1aczkiewicz J. Surf Sci 2004;552:111. [26] Dan´ko DB, Kuchowicz M, Szukiewicz R, Ko1aczkiewicz J. Surf Sci 2006;600:2258. [27] Ko1aczkiewicz J, Bauer E. Surf Sci 1999;420:157. [28] Horcas I, Fernandez R, Gomez-Rodriguez JM, Colchero J, Gomez-Herrero J, Baro AM. Rev Sci Instrum 2007;78:013705. [29] Bauer E, Bonczek F, Poppa H, Todd G. Surf Sci 1975;53:87–109. [30] Schlatterbeck D, Parschau M, Christmann K. Surf Sci 1998;418:240. [31] Kittel Ch. Introduction to solid state physics (polish edition). Warszawa: PWN; 1999.