Electrochemical and Electronic Properties of Platinum Deposits on Ru

Wei-Ping Zhou,† Adam Lewera,†,‡ Paul S. Bagus,*,§ and Andrzej Wieckowski*,†. Department of Chemistry, UniVersity of Illinois at Urbana-Champa...
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J. Phys. Chem. C 2007, 111, 13490-13496

Electrochemical and Electronic Properties of Platinum Deposits on Ru(0001): Combined XPS and Cyclic Voltammetric Study Wei-Ping Zhou,† Adam Lewera,†,‡ Paul S. Bagus,*,§ and Andrzej Wieckowski*,† Department of Chemistry, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Department of Chemistry, UniVersity of North Texas, Denton, Texas 76203-5070, and Department of Chemistry, Warsaw UniVersity, ul. Pasteura 1, PL-02-093 Warsaw, Poland ReceiVed: April 17, 2007; In Final Form: June 19, 2007

We report a combined X-ray photoelectron spectroscopy (XPS) and cyclic voltammetric study of Ru(0001) electrodes covered by platinum. The Ru(0001) surfaces were prepared in ultrahigh vacuum, transferred to an electrochemical cell, and covered with platinum using either spontaneous deposition or electrolysis tactics. The Pt 4f7/2 core level binding energies of the Pt/Ru(0001) electrodes prepared in this way were next studied as a function of Pt coverage. At 0.05 monolayer (ML), the binding energy is shifted by ca. 0.5 eV with respect to bulk Pt, but the shift decreases by 0.4 eV when the Pt coverage increases from 0.05 to 0.5 ML. The binding energy shifts are discussed in terms of the contributions from charge transfer and from lattice strain. We also studied the modes of growth of Pt islands on Ru(0001) by comparing estimates of the Pt coverage obtained from XPS and from cyclic voltammetry. At low Pt coverage, the islands have a monolayer height, but multilayer growth begins at a coverage of approximately 0.3 ML.

1. Introduction Surface modification by addition of submonolayer-to-multilayer amounts of noble metals to noble metal substrates (NM/ NM) has attracted considerable interest in this laboratory.1,2 The NM/NM systems show high reactivity to organic molecules, easily reacting them to CO2, and may be used as models for “real life” heterogeneous electrocatalysts, e.g., for use in fuel cells.3-6 Classic examples of appropriate model systems are electrodes obtained by deposition of platinum on ruthenium single crystals.7,8 Such electrodes closely approximatesin terms of both reactivity and composition of surface sitesthe alloy Pt/ Ru catalysts used in research and technology of a direct methanol fuel cell (DMFC).9-11 That is, the Pt/Ru systems display characteristic structure and electronic properties of catalytically modified surfaces of interest to electrochemistry and fuel cell science.7,8,12-17 This study makes use of results from previous scanning tunneling microscopy (STM)7 and reflection high energy electron diffraction (RHEED)8 research showing that the deposition of platinum on Ru(0001) yields Ru surfaces “decorated” with Pt nanoislands. (Our work in this field is reviewed in ref 2.) For the studies reported below, as well as in our earlier work, we use an ultrahigh-vacuum X-ray photoelectron spectroscopy (UHV-XPS) system connected to an electrochemical cell7,18-20 and our work emphasizes electronic aspects of electrode structure and reactivity. By doing so, we contribute to the worldwide efforts to connect catalytic activity to surface metal electronic properties. Specifically, the present work focuses on the core-level binding energy (BE) shifts,21-24 as measured by XPS. The sign and magnitude of these core-level BE shifts reflect the metal-metal chemical environment and bonding.24-28 * To whom the correspondence should be addressed. † University of Illinois at Urbana-Champaign. ‡ Warsaw University. § University of North Texas.

Figure 1. Cyclic voltammogram of the Ru(0001) electrode in 0.1 M HClO4. Scan rate: 50 mV/s.

It is important to point out that these BE shifts are complimentary to the shifts in metal d-band centers studied in the Norskov model of heterogeneous catalytic reactions.29-31 For Ru/Pt(111) electrodes, the Ru 3d BE shift as a function of Ru coverage was found barely measurable,18,32 as recently confirmed by a nanoparticle study.28 In contrast, the Pt 4f BE shifts are quite large.28 One of the origins of the BE shifts is lattice strain, which leads to bond distances different from the bulk as a function of the materials properties and environment, including particle composition and size.25-28 Rigorous theoretical studies have shown that the difference between Pt and Ru BE shifts can be related, in large part, to the different responses of Ru and Pt to lattice strain.28 In ref 28, some idealized models of pure Pt and Ru particles were used to study the BE shifts due to lattice strain by making uniform changes in the interatomic distances so that the particle expands or contracts.28 For equivalent changes in the lattice constants of Pt and Ru, we find that the changes in Pt 4f BE are much larger than those for the Ru 3d BE.28 These preliminary results show that involvement of d electrons in the bonding leads to smaller

10.1021/jp072993u CCC: $37.00 © 2007 American Chemical Society Published on Web 08/18/2007

Properties of Pt Deposits on Ru(0001)

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Figure 2. Cyclic voltammograms of the Pt/Ru(0001) electrode in a 0.1 M HClO4 solution in the potential range of 0.05-0.8 V. The Pt deposit (ca. 0.08 ML coverage) was obtained after a 30 s spontaneous deposition in 10-5 M H2PtCl4 + 0.1 M HClO4; see text. Scan rate: 20 mV/s.

its core level BEs increase, and, on the other hand, the BEs will decrease when the atom becomes negatively charged. However, one must use care to avoid confusing the BE changes due to bonding effects, in particular bond hybridization, with those that may be due to charge transfer.22 One of our longrange goals is to develop and apply theoretical criteria that permit the separation of these two mechanisms. Previously, electronic structures of Pt-decorated Ru nanoparticles and Pt in Pt/Ru alloys were studied by electrochemical-nuclear magnetic resonance (EC-NMR),33 synchrotron X-ray absorption spectroscopy,34 and XPS.19 All these studies demonstrated electronic modifications of Pt by Ru. In the present paper, we extend the previous work28 to Ru(0001) covered with platinum (Pt/Ru(0001)). This extension provides us with additional information needed for unified understanding of the Pt and Ru interactions in Ru-Pt mixed metal systems.18,19,28,32 Data on the Pt 4f core level BE shifts obtained as a function of Pt coverage were obtained and are reported. The relationship between Pt 4f BE and Pt coverage is interpreted according to the lattice strain25-28 and charge-transfer BE modification mechanisms.24 Figure 3. Pt 4f and Ru 4s spectra of the Pt/Ru(0001) electrode (a) after 30 s platinum spontaneous deposition in 10-5 M H2PtCl4 + 0.1 M HClO4 followed by rinsing in water and (b) after the electrode emersion at 0.13 V followed by five CV cycles (see above, also after rinsing in water). The Pt 4f7/2 peak position for pure Pt(111) is shown as the solid vertical line, while the positions of Pt 4f7/2 peaks for Pt/ Ru(0001) are shown as dashed vertical lines. (Also, see Experimental Section.)

changes in the effective number of d electrons for open-shell Ru than for Pt. Our analysis relates the BE shifts to the initial state electronic structure of the particles, especially to the extent of d hybridization.25-28 The net effect is that the BE is reduced when the interatomic distance is increased; we expect that changes in interatomic distances will be reflected in the distances in Pt islands on Ru(0001) (this work) with the Pt bond distance increasing toward the value for bulk Pt as the islands grow. Thus, lattice strain should contribute to the decrease in the Pt 4f BE as the island size increases. Another mechanism that leads to BE shifts is charge transfer between the interacting diverse atoms and their environment.22,24 It may be expected that when an atom becomes positively charged with respect to a reference,

2. Experimental Section Our EC-XPS apparatus that consists of a UHV chamber and an EC chamber with an electrochemical (EC) cell was described before.18,19 An electron spectroscopy for chemical analysis (ESCA) M-probe high-resolution multichannel hemispherical electron analyzer (Surface Science Instruments) equipped with a monochromatic Al KR line was operated at 110 W with a constant pass energy of 25 eV.18,19 The linearity of the BE scale of the detector was calibrated using Au 4f7/2 (84.0 eV), Ag 3d5/2 (368.25 eV), and Cu 2p3/2 (932.68 eV) lines.35 The reference values for the Ru 3d5/2 and Pt 4f7/2 BE’s are those for clean Ru(0001) and Pt(111): 280.10 and 71.10 eV, respectively.36,37 The S-probe version of 1.36 ESCA software (Fison Instruments) was used to monitor and process the XPS spectra. The background was subtracted using Shirley baselines.38 Mixed Gaussian-Lorentzian line shapes were chosen to fit the XPS spectra that are shown below. For the Pt 4f peaks, the choice of a 60% Gaussian-40% Lorentzian gave the best fit. The peak area ratio (1.33) and the spin-orbital splitting (3.33 eV) between

13492 J. Phys. Chem. C, Vol. 111, No. 36, 2007 Pt 4f7/2 and 4f5/2 were fixed in the fits to be the same as for bulk Pt.36,37 For Ru 4s, the choice of the Ru 4s line shape as 90% Gaussian with a FWHM of 5.2 eV and a BE of 75.55 eV are taken from the measured values for pure Ru(0001). The relative intensity between Ru 4s and Ru 3d was 3 ( 0.5% for pure Ru(0001) and Ru(0001) covered with Pt, consistent with data reported by Scofield.39 This gave us the area of Ru 4s as a fixed parameter in the fitting. The error in the Pt 4f BE was (0.05 eV, as estimated from the measurements of the Au 4f peak (see above).38 However, at the lowest Pt coverage, the error in the binding energy was larger than (0.05 eV as the contribution from Ru 4s increases with decreasing Pt coverage, and, hence, the uncertainty of the deconvolution is larger when the Pt coverage is lower. The Pt total coverage from XPS measurements, θPt,XPS, was calculated using the formula given by Seah and others40-42 with the measured Pt 4f and Ru 3d peak intensities, which is appropriate in the coverage range considered. The Pt 4f XPS intensity was corrected for the Ru 4s intensity and the FWHM for single-crystal Pt was found to be 1.35 eV. The chemicals used were HClO4 (GFS Chemicals, double distilled from Vycor), H2PtCl4 (Alfa Aesar), and Millipore water. Ultrahigh-purity quality argon was supplied by Smith Welding. Electrochemical measurements were carried out using the PAR 273 potentiostat and associated auxiliaries. The Ag/AgCl/3 M NaCl electrode was used as a reference electrode, but potentials are quoted with respect to the reversible hydrogen electrode, RHE. All experiments were carried out at ambient temperature, 25 ( 2 °C. In the measurements reported below, a Ru(0001) disc (6 mm diameter and 2 mm thick, MaTeck) was mounted on the UHVXPS instrument sample holder12 by spot-welding a Pt wire to the back of the disc. While in UHV, the disc surface was cleaned by four to five cycles of argon ion bombardment and by hightemperature annealing (including repeated heating of the electrode in oxygen at 10-8 mbar).18 The surface cleanliness was controlled by XPS. After this processing, the Ru(0001) disc was transferred from UHV to the EC chamber, and platinum was deposited on the disc surface in the electrochemical cell using either spontaneous deposition or electrolysis.1 The spontaneous deposition was carried out by immersing the Ru(0001) electrode in a 1 × 10-5 M H2PtCl4 solution in 0.1 M HClO4 at open circuit (the open-circuit potential was 0.83 V).7,16,43 The electrochemical deposition of Pt was performed at 0.38 V using the same 1 × 10-5 M H2PtCl4 + 0.1 M HClO4 solution. 3. Results and Discussion 3.1. Characterization of Clean and Pt-Covered Ru(0001) Electrode. Figure 1 shows a cyclic voltammogram (CV) of the UHV-prepared Ru(0001) electrode obtained in 0.1 M HClO4 at 50 mV/s. The CV exhibits CV characteristics similar to those previously reported for Ru(0001) prepared either in UHV20,44,45 or by inductive heating in argon.46 On the positive-going scan, the key CV features are as follows: a peak for H desorption and OH adsorption at 0.23 V and the surface oxidation threshold at ca. 0.57 V. On the negative-going scan, the reduction of Ru surface oxides peaking at 0.5 V is followed by CV maxima due to reduction of adsorbed OH (at 0.17 and -0.01 V) and to H adsorption, also at -0.01 V.20,44-46 After 30 s of spontaneous deposition of platinum in H2PtCl4 and after rinsing with 0.1 M HClO4 at 0.10 V, the Pt/Ru(0001) electrode was examined by CV (Figure 2). The first scan is featureless, but a clear redox couple at 0.075/0.105 V develops along with further scans. This is typical behavior of reduction/

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Figure 4. (a) Steady-state cyclic voltammetric profiles for the Pt/Ru(0001) electrode in 0.1 M HClO4 solution after spontaneous deposition of Pt in 10-5 M H2PtCl4 + 0.1 M HClO4 for 15, 60, and 300 s. Scan rate: 20 mV/s. (b) Pt 4f core level XPS spectra for the Pt/Ru(0001) surface corresponding to deposition times of 15, 60, and 300 s. The Pt/Ru(0001) electrode was emersed at 0.13 V from 0.1 M HClO4 (after the CV scans shown in a). The Pt 4f7/2 peak positions are indicated by vertical lines, as in Figure 3b.

stabilization of the Pt deposit as a function of scan potential.32,47 The CV also includes a relatively weak feature at 0.2 V and a pair of broad peaks at 0.6/0.5 V. The CV reaches steady-state after five cycles. The 0.075/0.105 V couple (Figures 2, 4, and 5) is due to H adsorption/desorption and concomitant OH desorption/adsorption on the Ru sites.20 Notice that OH adsorption on the Pt surface starts at 0.58 V.48 Clearly, the Pt sites on Ruswhen reduced to metallic formssare electronically modified to the extent that no hydrogen (or OH) adsorption can occur.20 We therefore assume that the charge under the cathodic peak at around 0.075 V and the anodic peak at ca. 0.10 V originate from free Ru sites that were not covered by Pt (see below). After 30 s of spontaneous deposition, the Pt/Ru(0001) electrode was rinsed with water and transferred to UHV and

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Figure 5. (a) Cyclic voltammetric profiles of the Pt/Ru(0001) electrode in 0.1 M HClO4 after platinum electrodeposition at 0.38 V in 1 × 10-5 M H2PtCl4 + 0.1 M HClO4 for 30, 90, and 150 s. Scan rate: 20 mV/s. (b) Pt 4f core level XPS spectra for Pt/Ru(0001) after the deposition times of 30, 90, and 150 s emersed at + 0.13 V from 0.1 M HClO4, after the CV scans shown in a. See caption to Figure 3b.

the measured XPS are shown in Figure 3a,b. The data in Figure 3a correspond to the “scan 0” conditions in Figure 2. The XPS spectra in Figure 3a were fitted to three peaks, two for Pt 4f7/2 and Pt 4f5/2 (at 72.30 and 75.63 eV) and one for Ru 4s (at 75.59 eV). Figure 3b shows the XPS spectrum for Pt/Ru(0001) obtained after the fifth CV scan. The Pt adspecies with the Pt 4f7/2 peak at 72.23 eV (Figure 3a) is assigned to Pt(II).36,37,49 The 4f7/2 peak at 71.48 eV in Figure 3b is assigned to metallic Pt but is shifted by 0.4 eV to higher BE relative to bulk Pt (at 71.10 eV).36,37 This shift is due to a combination of the lattice strain and charge-transfer effects,24,25-28 as discussed below. From the data in Figures 2 and 3, we conclude that

the spontaneous deposition process produces Pt(II) adspecies and that the subsequent voltammetry reduces the Pt(II) to metallic Pt. 3.2. Ru(0001) with Different Pt Coverage. Figure 4a shows the effect of Pt spontaneous deposition time, 15, 60, and 300 s, on the steady-state cyclic voltammetric curves in 0.1 M HClO4 at 20 mV/s. The decrease in the amplitude of the 0.075 and 0.105 V peaks (or the reduction in charge in the 0.075/0.105 V peak areas) demonstrates that there is an increase in Pt coverage with increasing deposition time, as confirmed by XPS (Figure 4b). Additionally, the data in Figure 4b show that the Pt 4f7/2 peak shifts from 71.63 eV at 0.05 ML to 71.40 eV at 0.5 ML,

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θPt,charge ) ((275 µC cm-2) - Qcharge)/(275 µC cm-2)

Figure 6. The Pt coverage (left axis, θPt,charge) and the charge density (right axis) under the cathodic peak at 0.075 V as a function of Pt coverage obtained from XPS measurements (θPt,XPS). The straight line corresponds to θPt,charge ) θPt,XPS; see text. Error bars are estimates of uncertainties due to experimental scatter and deconvolution of the XPS data.

TABLE 1: Pt Coverage (θPt,XPS), the Core Level Binding Energy (BE), and the Full Width Half-Maximum (FWHM) of the Pt 4f7/2 Peaks (from Figures 4b and 5b) for Platinum Deposited on Ru(0001) Spontaneously and Electrochemicallya deposition time/s θPt,XPS/ML BE of Pt 4f7/2/eV fwhm of Pt 4f7/2/eV 15 b 60 b 300 b 30 c 90 c 150 c

0.05 0.2 0.48 0.58 1.23 2.08

71.63 71.47 71.40 71.26 71.24 71.23

1.85 1.5 1.45 1.48 1.45 1.4

a

b

The FWHM for a Pt(111) single crystal of platinum was 1.35 eV. Spontaneous deposition. c Electrochemical deposition.

and the FWHM of the Pt 4f7/2 feature narrows from 1.85 eV at 0.05 ML to 1.45 eV at 0.5 ML (Table 1). After 300 s, the Pt deposit obtained by spontaneous deposition has a maximum coverage of ca. 0.5 ML (the Pt coverage is derived from XPS; see Experimental Section). The surfaces with Pt coverage higher than 0.5 ML were therefore obtained using electrochemical deposition at 0.38 V (see Experimental Section). Figure 5a shows characteristic cyclic voltammetric curves for the Pt/Ru(0001) electrode obtained from electrolysis at 30, 90, and 150 s. Figure 5b shows the corresponding XPS spectra in the Pt 4f region. Between the coverage of 0.5 and 0.6 ML (the spontaneous deposition and electrolysis, Figures 4b and 5b, respectively), there is a 4f7/2 BE shift to the lower BE of 0.14 eV. However, with a further increase in the electrolysis time, the additional reduction in BE is small, only ca. 0.03 eV between θ ) 0.58 and 2.1 ML (Table 1). 3.3. Growth of 2D and 3D Pt Islands. The analysis of the Pt island growth was made using a correlation between the Pt coverage (θPt,charge) obtained from the charge density under the cathodic peak at 0.075 V (Qcharge) and the coverage of Pt obtained from XPS (θPt,XPS). The assumption is that Pt is site blocking for Ru in the hydrogen adsorption/OH desorption reactions:20

(1)

where 275 µC cm-2 is the initial charge density for the Ru(0001) surface, free of the Pt additive.20,46 In Figure 6, Qcharge (left axis) and the Pt coverage from Qcharge (right axis) are plotted as a function of Pt coverage obtained from XPS. For Qcharge, the integration was carried out in the 0.075 V peak range, assuming that the integration background is constant (see caption to Figure 6). If the measured data fall on the straight line with θPt,charge ) θPt,XPS, the Pt islands are monolayers. In contrast, if the points fall above the line, the Pt islands are multilayers. From the data in Figure 6, we conclude that spontaneous deposition of Pt initially leads to formation of the monolayertype islands (the Pt coverage below 0.2 ML), but multilayer islands prevail at and above ca. 0.3 ML. The XPS signal increases as a function of the electrolysis time showing an increasing uptake of platinum with the progress of electrolysis. At the same time (Figures 4a and 5a) at high Pt coverage there are still Ru sites that are free of the deposited Pt. This is evidence for a columnar multilayer (Volmer-Weber) growth50 of Pt on Ru(0001), confirming previous reports.7,8 3.4. Dependence of the Pt 4f7/2 BE Shift on Pt Coverage. In Figure 7, the core level binding energy of Pt 4f7/2 is plotted as a function of θPt,XPS (the Pt coverage obtained from XPS). At the lowest coverage, the BE is the highest and is 0.5 eV higher than that for bulk Pt (71.10 eV36,37). With further increase in Pt coverage, the difference in BE is lower than 0.5 eV but is large enough to be clearly measured. At θPt,XPS ) 2.1 ML, the BE is only 0.15 eV higher than for bulk Pt. The sign of the BE shift (positive vs bulk Pt) could be consistent with charge transfer from Pt to Ru. This direction of charge transfer is then in accord with the results of previous XPS investigations of adsorption of I on the Ru/Pt(111) surface,18 with results of the EC-NMR study,33 and with results obtained by X-ray absorption near-edge spectroscopy.34 Another and perhaps the main origin for the positive BE shifts (see above) is the lattice strain associated with the shorter Pt-Pt bond distance on Ru(0001) than in bulk Pt.25-28 Schlapka et al.51 reported that lattice compression of the pseudomorphic Pt layer on Ru(0001) can lead to significant perturbation in the electronic structure of Pt adatoms and that the perturbation due to Pt deposited on Ru remains operative up to at least four monolayers of platinum. This is most likely what we observe in this study. The Pt BE shift to the above-reported large values was also observed for bimetallic Ru-Pt nanoparticle samples.28 It was then argued that the observed BE shifts were consistent with lattice compression for the Pt atoms induced by the Ru matrix. The distinction between charge transfer and lattice strain is important if we are to correctly understand the significance of core level BE shifts in terms of their chemical origin.18,27,31,33,52 Along these lines, we notice that when the Pt coverage increases from 0.2 to 0.5 ML, that is, where the Pt islands are larger and become multilayer (Figure 6), a decrease in BE of only ca. 0.2 eV from the maximum BE value (Figure 7) is observed. This drop in BE could be ascribed to changes in charge transfer and, more generally, to changes in the Pt-Ru direct interaction. The changes are such that the Pt-Ru direct interaction is less important when 3D Pt islands form. However, the Pt islands may still have a large lattice compression and hence through the lattice strain may have BEs larger than the BE for the Pt reference. This is consistent with the prior work on the effects of lattice strain on the core level BE’s.25-28 Above 0.5 ML, where mainly multilayer islands are present, the Pt 4f7/2 BEs are roughly constant at ∼71.25 eV or about 0.15 eV higher

Properties of Pt Deposits on Ru(0001)

J. Phys. Chem. C, Vol. 111, No. 36, 2007 13495 Poland, under a BW-175606 grant and by the Ministry of Science and Higher Education, Poland, under Grant N204 164 32/4284. References and Notes

Figure 7. Pt 4f7/2 binding energy as a function of Pt coverage on Ru(0001). Platinum was deposited either spontaneously or electrochemically (see text). Error bars are estimates of uncertainties due to experimental scatter and deconvolution of the XPS data.

than BE for the bulk Pt, 71.10 eV.36,37 This BE shift is, most likely, due only to the contribution of the remaining lattice strain, since the electronic influence of the Ru substrate decays rapidly with Pt layer thickness, while the lattice strain for the growth of multilayers of Pt persists to coverages over four Pt layers.51 Apparently, due to the cumulative effects of lattice strain and charge transfer, Pt shows significant 4f core level BE shifts when Pt islands are predominantly monolayer. The electronic influence of the Ru substrate on the Pt core level BE shifts becomes less when the Pt islands are transformed from the monolayer to multilayer heights, while the lattice strain retains its contribution to the BE shift51 until the end of these measurements. Further theoretical studies of the isolated Pt and Ru particles and of Pt atoms and particles on Ru(0001) surfaces will allow us to determine the importance of the different mechanisms that contribute to the observed BE shifts. It will then be possible to quantitatively separate the contributions from charge transfer, lattice strain, and surface to bulk shifts. Work is in progress to provide such information. 4. Conclusions The key result of this study is the demonstration that the Pt 4f BE shifts of the Pt/Ru(0001) electrodes at low Pt coverage is as high as 0.5 eV vs the bulk Pt reference. We have discussed two chemical mechanisms that are the principle origins of these shifts: charge transfer and lattice strain. In particular, we have argued that the contributions of these two mechanisms are different for the cases where monolayer Pt islands are formed and at higher coverage where the islands are multilayers. The observed core level BE shifts in Pt islands on Ru may help us to understand the role of Pt/Ru electronic structure in electrocatalysis, with reference to fuel cells. Theoretical studies are in progress to determine the relative importance of lattice strain and charge transfer for the Pt BE shifts, and the results of these studies will be reported. We also studied the growth mode of Pt islands on Ru(0001) by comparing Pt coverage obtained from XPS and from cyclic voltammetry. We conclude that, at low coverage, the islands are of a monolayer height; the multilayer growth begins at approximately 0.3 ML. Acknowledgment. This work is supported by the National Science Foundation under Grant No. CHE-0651083 and by the Department of Energy Grant E-FG02005ER46260. A.L. acknowledges partial support by Warsaw University, Warsaw,

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