Photoelectron spectroscopy of Tin− clusters - Chemistry Department ...

casey.brown.edu

Photoelectron spectroscopy of Tin− clusters - Chemistry Department ...

JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 5 1 FEBRUARY 2003Photoelectron spectroscopy of Ti n À clusters „nÄ1–130…Shu-Rong Liu and Hua-Jin ZhaiDepartment of Physics, Washington State University, Richland, Washington 99352and W. R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,MS K8-88, Richland, Washington 99352Miguel CastroDepartamento de Física y Química Teórica, Facultad de Química Universidad Nacional Autonomade México, Del. Coyoacán Cd. Universitaria, C. P. 04510, México D. F., MéxicoLai-Sheng Wang a)Department of Physics, Washington State University, Richland, Washington 99352and W. R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,MS K8-88, Richland, Washington 99352Received 13 September 2002; accepted 1 November 2002Photoelectron spectra of cold Ti n anion clusters for n1–130 were investigated at four detachmentphoton energies: 532, 355, 266, and 193 nm. Improved spectral resolution provides well-resolvedelectronic structures of the clusters, and the spectral evolution as a function of cluster size wasprobed systematically. Narrow and well-resolved spectral features were observed at n13, 19, and55, consistent with the high symmetry icosahedral structures proposed for these clusters. Themeasured electron affinities as a function of size in the studied size range do not extrapolate to thebulk work function, indicating that Ti clusters with n130 may not assume the bulk structure.© 2003 American Institute of Physics. DOI: 10.1063/1.1531999I. INTRODUCTIONIt is a central theme in cluster science to probe the evolutionof the electronic, structural and magnetic properties ofmetal clusters as a function of cluster size. Studies on thestructural and electronic properties of transition metal TMclusters are essential to understand their detailed physicaland chemical properties. However, due to the open d shells,TM clusters possess very complicated electronic structuresand high density of electronic states and studies on the propertiesof TM clusters have posed tremendous challenges bothexperimentally and theoretically. 1Photoelectron spectroscopy PES of size-selected anionshas emerged as a powerful experimental technique inproviding information about the electronic structure and excitationenergies of atomic clusters. Comparison of experimentalPES data with theoretical calculations has become avaluable means to determine the structures and low-lyingisomers for a variety of clusters. 2–7 However, due to theircomplexity, few such studies have been devoted to the TMclusters. 2,5 Experimentally, the dense low-lying electronicstates of TM clusters have generally resulted in rather diffusePES spectra. 8 Only very recently have we been able to obtainwell-resolved PES data for TM clusters, 9,10 as a result ofimproved experimental resolution and the ability to producecolder clusters, 6,11 opening an avenue for a more precisecomparison between the experimental spectra and computeddensity of states DOS.Studies on the properties of Ti clusters are relativelya Author to whom correspondence should be addressed. Electronic mail:ls.wang@pnl.govscarce compared to that of other TM clusters. 1 Collisioninduceddissociations of Ti n n2–22 clusters have beenreported. 12 A PES study was conducted previously in ourgroup on Ti n clusters from n3 to65at266nm. 13 Only onePES band was observed above n8 under the previous experimentalconditions and that observation was interpreted asan onset of the d band by comparing with bulk PES data.Theoretical studies using density functional theory DFTwere carried out for small Ti n n2–10 and Ti n n2–14,19, 55 clusters. 14,15 There has also been a study on Ti n n2–16 clusters using molecular dynamics. 16We have undertaken a more comprehensive PES studyof Ti n clusters n1–130 under well-controlled experimentalconditions and at various photon energies, 532, 355, 266,and 193 nm. The low photon energy data reveal more detailsof the electronic features of the small Ti n clusters, whereasthe high photon energy spectra probe more deeply into thevalence band of the clusters. In the accompanying paper, 17we report a theoretical study on Ti n and Ti n n3–8, 13and compare the theoretical results with the experimentaldata. The good agreement between the PES data and thecalculated DOS allowed us to establish the ground states andlow-lying isomers of Ti n and Ti n and provided insight intotheir structural and magnetic properties. In the present paper,we report the detailed PES results and the evolution of theelectronic properties of Ti clusters from one atom up to 130atoms at four detachment wavelengths with well-controlledcluster temperatures. Evidence of clusters with high symmetriesand the s/d nature of the PES features will be presented.Electron affinities EAs of the neutral clusters from atomicTi to Ti 130 and a possible structural transition will also bereported and discussed.0021-9606/2003/118(5)/2108/8/$20.00 2108© 2003 American Institute of PhysicsDownloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


J. Chem. Phys., Vol. 118, No. 5, 1 February 2003 Spectroscopy of Ti n clusters2111TABLE I. Adiabatic electron affinity EA of Ti n clusters n1–130.n EA eV n EA eV n EA eV1 0.0800.014 a 27 2.140.05 52 2.410.053 1.130.06 28 2.140.05 53 2.410.064 1.180.03 29 2.120.05 54 2.450.065 1.150.03 30 2.160.05 55 2.510.056 1.280.05 31 2.190.05 56 2.480.067 1.110.03 32 2.240.05 57 2.490.058 1.470.05 33 2.210.05 58 2.470.059 1.560.05 34 2.220.06 59 2.490.0510 1.700.05 35 2.240.05 60 2.510.0611 1.720.05 36 2.240.05 61 2.550.0512 1.710.05 37 2.270.05 62 2.570.0513 1.870.05 38 2.280.06 63 2.570.0514 1.870.05 39 2.290.05 64 2.600.0515 2.000.05 40 2.340.06 65 2.550.0516 1.960.05 41 2.330.05 66 2.580.0517 2.010.05 42 2.320.05 70 2.550.0618 1.970.05 43 2.360.05 75 2.630.0619 1.930.05 44 2.390.05 80 2.680.0620 2.060.05 45 2.400.05 90 2.660.0621 1.980.05 46 2.390.05 100 2.730.0622 2.040.05 47 2.410.05 110 2.750.08 b23 2.080.05 48 2.440.05 120 2.750.08 b24 1.970.05 49 2.400.05 130 2.830.08 b25 2.070.05 50 2.380.0526 2.100.05 51 2.410.05a From Ref. 21.b The masses of these clusters were not well separated and were estimated with an error of several atoms n4.266 nm data. Large clusters beyond Ti 56 were not measuredat 266 nm because a more systematic data set was obtainedat 193 nm see Fig. 7. At 266 nm, the most significant observationis the appearance of the PES band starting fromTi 12 at around 3 eV. This band has relatively weak intensityand shifts gradually to higher binding energies with theincrease of the cluster size. In our previous study on the Ticlusters at 266 nm, 13 this additional spectral feature was notclearly observed due to the relatively hot clusters and perhapshigh detachment photon fluxes, which both tended toenhance thermionic emissions and smeared out the higherbinding energy feature.D. Photoelectron spectra at 193 nmThe 193 nm spectra of Ti n n4–130 are shown in Fig.7. Although the spectral resolution deteriorated compared tothe lower photon energy spectra, the 193 nm data revealedthe electronic structure in a wider energy range. Startingfrom Ti 12 , the second PES band was clearly revealed ataround 3.3 eV. Significant electron signals were also observedat higher binding energies and the spectra becamealmost continuous in the higher binding energy side fromTi 20 to Ti 80 . However, the continuous spectral features werereplaced with a well shaped spectral band around 4.5 eVfrom Ti 90 to Ti 130 . Due to the isotope distributions and thelimited mass resolution, the spectra of the large clusters over100 atoms contained a range of cluster sizes of n4. TheEAs of Ti 110 ,Ti 120 , and Ti 130 were estimated from the 193nm spectra, as given in Table I.FIG. 4. Photoelectron spectra of Ti n n1–33 at 355 nm.Downloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


2112 J. Chem. Phys., Vol. 118, No. 5, 1 February 2003 Liu et al.FIG. 5. Photoelectron spectra of Ti n n33–100 at 355 nm.Within the experimental uncertainty, the EAs obtained inthe current study Table I are consistent with our previousresults in the size range of Ti 3 to Ti 65 . The better spectralresolution in the current experiment resulted in slightly moreaccurate EAs.E. Photon energy dependent PES spectraFigure 8 shows the PES spectra of Ti 7 and Ti 8 at fourphoton energies in the same energy scale. The spectra of Ti 7and Ti 8 exhibit similar features with similar photon energydependence. For example, the relative intensities of peak Ain both systems decreased with the increase of photon energies,whereas those of features B and C increase with theincrease of photon energies. Figure 9 displays the PES spectraof Ti 25 and Ti 28 at three photon energies. It was observedthat for these two systems the relative intensities of the lowerbinding energy features decreased with increasing photon energies.Such photon energy dependence provides informationabout the nature of the electrons being detached and will befurther discussed later.IV. DISCUSSIONA. Evidence of highly symmetric clustersIn the accompanying paper, 17 a combination of PES andtheoretical study is reported on small Ti clusters, Ti 3 to Ti 8 ,and Ti 13 . Detailed electronic and structural information wasFIG. 6. Photoelectron spectra of Ti n n3–56 at 266 nm.obtained for these clusters based on the good agreement betweenthe computational and experimental results. We havepreviously observed structure effect on photoelectron spectrafor several 13-atom clusters. In our study of Al n clusters, 19we observed an abrupt change in the PES spectra from acomplicated multifeature spectrum for Al 12 to a simple singleband for Al 13 , which was confirmed to be an ideal icosahedronthrough a combined experimental and theoreticalstudy. 6,7 The PES spectra of Al 14 and Al 15 maintained themain feature of Al 13 and these clusters were shown to becapped icosahedra. Al 16 gave a quite different PES spectrum,indicating a significant structural transition from Al 15 toAl 16 . In Co and Ni clusters, we made similar observationsabout abrupt PES spectral changes and highly symmetricclusters. 9,10,22 For example, the PES spectrum of Co 13 becamevery sharp compared to that of Co 12 , consistent withthe icosahedral structure suggested for Co 13 . The spectra ofCo 14 and Co 15 were similar to that of Co 13 , except that theyare slightly more diffuse; similar icosahedral structures withone or two capping atoms were possible arrangements forCo 14 and Co 15 . Abrupt PES spectra change from Co 15 toCo 16 marks a possible structural transition from the icosahedralpacking. 9An ideal icosahedron was proposed for Ti 13 previously. 15Using DFT calculations, we obtained a slightly distortedicosahedron structure for Ti 13 and Ti 13 . 17 Based on the simi-Downloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


J. Chem. Phys., Vol. 118, No. 5, 1 February 2003 Spectroscopy of Ti n clusters2113FIG. 9. Photoelectron spectra of Ti 25 and Ti 28 at three detachment photonenergies.FIG. 7. Photoelectron spectra of Ti n n4–130 at 193 nm 6.424 eV.larity of the PES spectra of Ti 14 and Ti 15 to that of Ti 13 ,asimilar conjecture as for Al or Co clusters, could be drawnfor the Ti clusters. Ti 14 and Ti 15 may also possess icosahedralgeometry with one or two capping atoms. In fact, the icosahedralpacking may extend to even larger clusters on thebasis of their similar PES spectra to the basic pattern of theTi 13 PES spectra. Additional evidence of high symmetryclusters was also observed in other size regime. As seenin Fig. 4, the PES spectra from Ti 9 to Ti 10 display a transitionfrom a complex multipeak spectrum to a relativelysimple one, indicating that a structural transition might existfrom Ti 9 to Ti 10 .Ti 9 may possess a less symmetric structurethan Ti 10 , consistent with a previous theoretical study,showing a C 1h , and C 3v symmetry for Ti 9 and Ti 10 ,respectively. 14 In another theoretical study, 15 a bicapped anda tricapped pentagonal bipyramid structure were suggestedfor Ti 9 and Ti 10 , respectively, and the structure of Ti 10 isagain more symmetric.Resolved sharp peaks at the threshold of the Ti 17 andTi 19 spectra may also suggest a highly symmetric structurefor these two clusters. The previous theoretical study 15 indicateda double icosahedral ground state structure for Ti 19 ,which was found to be 5.89 eV lower in energy than that ofan octahedral structure. Theoretical structural information onTi 17 and Ti 18 is not yet available. Nevertheless, from itshighly resolved PES spectrum, a more symmetric structurefor Ti 17 is likely.In our previous studies, sharp peaks were resolved in thePES spectrum at and around Co 55 ,Ni 55 , and Fe 55 , 9,10,22,23suggesting highly symmetric I h structures for these clusters.The PES spectra of Ti 55 at all three photon energies showedmuch better resolved features, quite distinct from those of itsneighbors. This observation suggests that Ti 55 may also possessa highly symmetric I h structure. Indeed, a previous theoreticalstudy found that the I h structure was 1.65 eV morestable than a cuboctahedron for Ti 55 . 15FIG. 8. Photoelectron spectra of Ti 7 and Ti 8 at four detachment photonenergies.B. s–d hybridization and implication for the magneticproperties of Ti clustersIt is well established that small clusters of the late 3delements possess localized 3d electrons, leading to enhancedmagnetic moments. 1 Hybridization between the 4s and 3dorbitals was suggested to increase significantly as cluster sizeincreases, resulting in reduced magnetic moments in largerDownloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


2114 J. Chem. Phys., Vol. 118, No. 5, 1 February 2003 Liu et al.Stern–Gerlach experiment, in which no measurable magneticmoments were detected for Ti clusters. 26FIG. 10. a Electron affinities EA of Ti n as a function of n. b EA vsn 1/3 proportional to 1/r, r being the cluster radius. The unfilled circleindicates the bulk work function.clusters. 10,24 The electronic structure of Ti clusters is expectedto be different from those of the late 3d TM clustersbecause the 3d orbitals of Ti are delocalized valence orbitals.Therefore, s/d hybridization is expected for even the smallestTi cluster and this should have significant effect on the magneticproperties of these clusters. Figure 8 shows the photonenergy dependence of the detachment transitions of Ti 7 andTi 8 . Since detachment cross sections for different electronss, p or d should have different photon energy dependence, 25the peak intensity change provides information about the natureof the PES features. For both Ti 7 and Ti 8 , the intensityof peak A decreases and the intensities of peaks B and Cincrease with the increase of photon energies, suggestingpeak A should be from detachment of primarily s electronsand peaks B and C from primarily d electrons. This is consistentwith our theoretical analysis of the DOS of these clusters.Our theoretical analysis revealed the complexity of theelectronic structure of the Ti clusters and showed that, evenfor Ti 7 , the energy levels of the s and d electrons are alreadymixed. 17 The delocalization and the bonding nature of the 3delectrons should result in dramatically reduced magnetic momentsin small Ti clusters. 26Figure 9 shows that the intensities of the threshold PESfeatures of Ti 25 and Ti 28 decrease with increasing photonenergies. By comparing the spectra in Figs. 4–7, we notethat a number of small Ti n clusters with well resolvedthreshold peaks show s-like behavior, whereas such photonenergy dependence was largely unobservable in the largeclusters, indicating the complete s/d hybridization in thesesystems. This observation is consistent with a previousC. Electron affinity versus cluster sizeFigure 10 shows the measured EAs of the Ti n clusters asa function of size. The EAs exhibit strong size variation inthe smaller size regime from the atom to about Ti 25 . Some ofthe EA variations in the large size regime correlate to structuraleffect. For example, the EA of Ti 55 exhibits a localmaximum Fig. 10a, which correlates to its highly symmetricstructure mentioned above. Beyond Ti 25 , the EAs essentiallyfollow a straight line versus 1/n 1/3 , which is proportionalto 1/r, r being the radius of the clusters Fig. 10b.According to the classical metallic droplet model, 27 the EAsof finite spherical metallic particles are proportional to 1/rand should extrapolate to the bulk work function at infinite r.However, the EA versus 1/n 1/3 of the Ti clusters extrapolatesto a value of around 3.80 eV at infinite size, which is significantlysmaller than the bulk work function 4.33 eV of apolycrystalline Ti film. 28 Previously, we have obtained consistentagreement between the extrapolated EAs at infinitesize and the bulk work functions for all other TM clustersystems including V, Cr, Fe, Co, and Ni. 8,9,22,23,29,30 The disagreementbetween the extrapolated EA and the bulk workfunction in the Ti system might suggest that the Ti clusters inthe studied size regime may possess structures other than thebulk and that there must be a structural transition at evenlarger sizes, from thereon the EA versus 1/n 1/3 curve shouldexhibit a different slope.D. Comparison to other 3d metal clusters and furtherimplications for cluster packingThe most interesting observation in the 193 nm spectrais the higher binding energy transitions starting from Ti 12 ,which emerge as a well-defined band starting from Ti 60 .These spectral features are quite different from the bulk photoemissionspectra of Ti, which only show a single band inthe valence range. 31,32 However, we have observed previouslyfor V clusters that PES spectra starting from V 60began to resemble those from the bulk body-centered-cubicBCC crystal. 29 Surprisingly, the two-band features observedfor the PES spectra of the Ti n clusters are very similarto those observed for the V clusters.Vanadium is next to Ti in the periodic table, but theyhave different bulk crystal structures. Vanadium has a BCClattice, whereas Ti and the other group IVB elements Zr andHf adopt the hexagonal-closed packed HCP lattice at roomtemperature. However, it is well known that there is HCP toBCC solid-to-solid phase transition for the group IVB metalsat high temperatures. 33,34 In fact, there was a previous PESstudy of the HCP to BCC phase transitions for the GroupIVB metals, but due to the low resolution of the experimentand the high temperature conditions, no observable differencewas obtained between the BCC and HCP structures. 35Our current observation of the similarity between the PESspectra of Ti clusters and those of V clusters might suggestthat they both have similar cluster packing, i.e., the small TiDownloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


J. Chem. Phys., Vol. 118, No. 5, 1 February 2003 Spectroscopy of Ti n clusters2115clusters possess BCC-type structures, rather than the HCPtypestructures. This conjecture is consistent with the EAsversus 1/n 1/3 trend, which does not extrapolate to the bulkwork function of the HCP crystal, as discussed above. Thecoldest clusters produced from our cluster source are aroundroom temperature, as shown previously for small Alclusters. 6 Our current observation suggests that the HCP toBCC phase transition in small Ti clusters occurs at muchlower temperatures than the bulk. This is a tentative conclusion,which warrants further theoretical verifications.V. CONCLUSIONSWe reported an extensive PES study of Ti n n1–130clusters at four photon energies. Spectral evidence was observedfor highly symmetric icosahedral Ti 13 and Ti 55 , whichboth show an abrupt spectral narrowing compared to the PESspectra of their neighbors. Due to the improved experimentalconditions, well resolved data were observed, allowing moredetails in the PES spectra to be obtained for the small clusters.The high photon energy data revealed high bindingenergyvalence-band transitions. It was shown that the EAsof the Ti clusters do not extrapolate to the bulk work function,indicating that the clusters in the observed size rangemay not possess the bulk packing. This observation is corroboratedby the surprising observation that the PES spectraof the larger Ti clusters resemble those of V clusters, suggestingthat the Ti clusters may possess BCC-type structuresas the V clusters, rather than the HCP-type structure expectedfrom the bulk lattice.ACKNOWLEDGMENTSThis work was supported by the National Science FoundationCHE-9817811 and was performed at the W. R.Wiley Environmental Molecular Sciences Laboratory, a nationalscientific user facility sponsored by DOE’s Office ofBiological and Environmental Research and located at thePacific Northwest National Laboratory, operated for DOEby Battelle. M.C. acknowledges financial support fromCONACYT-México under Project 34845-E and fromDGAPA–UNAM under Project PAPPIIT-IN-101901. Theaccess to the supercomputer SG Origin 2000/32 at DGSCA–UNAM is greatly appreciated.1 J. A. Alonso, Chem. Rev. 100, 637 2000.2 C. Massobrio, A. Pasquarello, and R. Car, Phys. Rev. Lett. 75, 21041995.3 N. Binggeli and J. R. Chelikowsky, Phys. Rev. Lett. 75, 493 1995.4 J. Muller, B. Liu, A. A. Shvartsburg, S. Ogut, J. R. Chelikowsky, K. W. M.Siu, K. M. Ho, and G. Gantefor, Phys. Rev. Lett. 85, 1666 2000.5 H. Kietzmann et al., Phys. Rev. Lett. 77, 4528 1996.6 J. Akola, M. Manninen, H. Hakkinen, U. Landman, X. Li, and L. S. Wang,Phys. Rev. B 60, R11297 1999.7 J. Akola, M. Manninen, H. Hakkinen, U. Landman, X. Li, and L. S. Wang,Phys. Rev. B 62, 13216 2000.8 L. S. Wang and H. Wu, in Advances in Metal and Semiconductor Clusters.Vol. 4, Cluster Materials, edited by M. A. Duncan JAI, Greenwich, CT,1998, p.299.9 S. R. Liu, H. J. Zhai, and L. S. Wang, Phys. Rev. B 64, 153402 2001.10 S. R. Liu, H. J. Zhai, and L. S. Wang, Phys. Rev. B 65, 113401 2002.11 L. S. Wang and X. Li, ‘‘Temperature effects in anion photoelectron spectroscopyof metal clusters,’’ in Clusters and Nanostructure Interfaces, editedby P. Jena, S. N. Khanna, and B. K. Rao World Scientific, NewJersey, 2000, p. 293.12 L. Lian, C. X. Su, and P. B. Armentrout, J. Chem. Phys. 97, 4084 1992.13 H. Wu, S. R. Desai, and L. S. Wang, Phys. Rev. Lett. 76, 2121996.14 S. H. Wei, J. Q. You, X. H. Yan, and X. G. Gong, J. Chem. Phys. 113,11127 2000.15 J. Zhao, Q. Qiu, B. Wang, J. Wang, and G. Wang, Solid State Commun.118, 157 2001.16 A. Taneda and Y. Kawazoe, Mater. Trans., JIM 41, 635 2000.17 M. Castro, S. R. Liu, H. J. Zhai, and L. S. Wang, J. Chem. Phys. 118,21162003, following paper.18 L. S. Wang, H. S. Cheng, and J. Fan, J. Chem. Phys. 102, 9480 1995.19 X. Li, H. Wu, X. B. Wang, and L. S. Wang, Phys. Rev. Lett. 81, 19091998.20 L. S. Wang, J. Conceicao, C. Jin, and R. E. Smalley, Chem. Phys. Lett.182, 51991.21 C. S. Feigerle, R. R. Corderman, S. V. Bobashev, and W. C. Lineberger, J.Chem. Phys. 74, 1580 1981.22 S. R. Liu, H. J. Zhai, and L. S. Wang, J. Chem. Phys. 117, 9758 2002.23 L. S. Wang, X. Li, and H. F. Zhang, Chem. Phys. 262, 532000.24 G. Gantefor and W. Eberhardt, Phys. Rev. Lett. 76, 4975 1996.25 S. Hufner, Photoelectron Spectroscopy Springer-Verlag, New York,1995.26 D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, Phys. Rev. B 45, 63411992.27 D. M. Wood, Phys. Rev. Lett. 46, 749 1981.28 Handbook of Chemistry and Physics, 67th ed. CRC, Boca Raton, FL,1986.29 H. Wu, S. R. Desai, and L. S. Wang, Phys. Rev. Lett. 77, 24361996.30 L. S. Wang, H. Wu, and H. Cheng, Phys. Rev. B 55, 12884 1997.31 P. J. Feibelman and F. J. Himpsel, Phys. Rev. B 21, 1394 1980.32 D. M. Hanson, R. Stockbauer, and T. E. Madey, Phys. Rev. B 24, 55131981.33 I. Bakonyi, H. Ebert, and A. I. Liechtenstein, Phys. Rev. B 48, 78411993.34 A. Aguayo, G. Murrieta, and R. de Coss, Phys. Rev. B 65, 092106 2002.35 Y. Fukuda, G. M. Lancaster, F. Honda, and J. W. Rabalais, Phys. Rev. B18, 6191 1978.Downloaded 25 Mar 2007 to 130.20.226.164. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

Similar magazines