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LEEDS studies of adsorbate-induced reconstruction of metal surfaces Grimsby, Đoan-Trang V. 1993

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LEED STUDIES OF ADSORBATE-INDUCEDRECONSTRUCTION OF METAL SURFACESbyDoan - Trang Vu GrimsbyB.A., Rice University, 1986A THESIS SUBMITTED IN PARTIAL FULFILMENTOF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJune 1993© Doan - Trang Vu Grimsby, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of (HEM i S T/2'y The University of British ColumbiaVancouver, CanadaDate  59oicikAut it r /Tei3 DE-6 (2/88)Abstract iiUsing the technique of low-energy electron diffraction (LEED), the structures ofthree systems have been investigated, where small, electronegative atoms chemisorb andinduce reconstruction at a metal surface; these surfaces are designated Ni(111)-(2x2)-0,Cu(110)-(2x3)-N, and Pd(100)-(V5x45)R27°-0. In each case, experimental data consistof a set of intensity-versus-energy (I(E)) curves measured at normal incidence with a videoLEED analyser. Multiple-scattering calculations were done for a number of proposedmodels of the surface structure, and comparisons were made between calculated andexperimental 1(E) curves. The objective in a LEED analysis is to find the geometry in thecalculations which leads to the best match between the two sets of intensity curves.Reliability indices are used to quantify the level of correspondence between experimentand theory; a lower R-value indicates better agreement, and consequently the model ismore likely to be correct. Two basic reliability indices were used in this work, and theyare the modified Zanazzi-Jona R-factor and the Pendry R-factor. In addition to the moreconventional LEED analysis, the recently-developed tensor LEED/directed search(TLEED) method was also used in the analyses of the N/Cu and 0/Pd surfaces. As wellas determining surface structure, this work has the further objective of using the detailsidentified to develop some principles of surface structural chemistry and to relate theseprinciples to the broader framework of structural chemistry.For the Ni(111)-(2x2)-0 structure, oxygen atoms chemisorb on 3-fold hollow siteswhich continue the fcc stacking of the nickel substrate. Top-layer Ni atoms which arebonding to 0 atoms are displaced both vertically toward (by 0.12 A) and laterally awayfrom (by 0.07 A in a rotated manner) the 0 atoms, while those Ni atoms not bonding to 0are displaced vertically toward the bulk. The determined surface O-Ni bond length of 1.83A agrees closely with the predicted value of 1.82 A for 3-coordinate 0 on Ni, and thesurface relaxations have been confirmed in a subsequent study with SEXAFS.iiiNitrogen, activated by an ion gun, chemisorbs on the Cu(110) surface to formCu(110)-(2x3)-N. Many techniques have been applied to study this surface, but littleconsensus exists as to its structure. Even structural conclusions from the present LEEDanalysis have been revised as new information, as well as TLEED program codes, becameavailable. Currently, TLEED appears to favour a reconstruction in which the topmostlayer is a pseudo-(100)-c(2x2)-N overlayer with substantial corrugation in the top twocopper layers. Large lateral displacements of both N atoms in the overlayer and Cu atomsin the topmost Cu(110) layer result in a total of three 5-coordinate adsorption sites perunit mesh (as compared to one when no lateral relaxations are allowed). Average N-Cubond lengths for the 5-coordinate sites (1.85 A) agree well with prediction based on thestructure of bulk Cu3N, while the bond lengths for the 4-coordinate sites (1.94 A) appearrather long. Very recently published STM images seem to suggest that nitrogenchemisorbs first on the 5-coordinate sites, before occupying the less favourable 4-coordinate sites, and that opens the possibility that the 4-coordinate sites may be onlypartly occupied under the experimental conditions of this work.The Pd(100)-(453015)R27°-0 surface is formed on extended 0-dosing with thesample temperature at greater than about 550 K. A tensor LEED analysis of 15independent beams supports a surface oxide model, as first postulated in outline by Orentand Bader. The detailed model which gives the best correspondence with experimentalintensity data has a PdO(001) overlayer stacked onto the Pd(100) surface such thatrumpling is induced in both the oxide and top two Pd(100) layers. The average 0-Pdbond length for 2-coordinate 0 on the Pd surface (1.73 A) is close to the predicted valueof 1.76 A based on the structure of bulk PdO. This analysis in particular highlights thepotential advantages of the TLEED approach in opening up LEED crystallography fordetermining a wider range of surface structures than has typically been the case until now.Table of Contents^ ivAbstract^ iiTable of Contents^ ivList of Tables viiList of Figures^ ixAcknowledgements xii^Dedication^ xiiiChapter 1 Introduction^ 1^1.1^Surface science and surface structure^ 11.2^Low-energy electron diffraction (TBED)^31.2.1 General principles^ 31.2.2 Multiple-scattering calculation of T ,F,RD intensities^91.2.3 Structural analysis and reliability indices (R-factors)^141.3^Auger electron spectroscopy (AES)^ 171.4^Outline^ 19Chapter 2 Tensor LEED (TLEED)^ 20^2.1^Introduction^ 202.2^General principles 202.3^Automated search procedure^ 252.4 Some tests of TLEED 272.4.1 Reproducibility of full-dynamical calculations^292.4.2 Lateral vs. vertical displacement^ 322.4.3 Interlayer spacings and Vor^342.4.4 Reference structure selection 372.5^General comments^ 38VChapter 3 Experimental methods^ 393.1^UHV equipment^ 393.2^Instrumentation for LEED and AES^ 413.3^Sample preparation and cleaning 463.4^LEED intensity measurement using a video LEED analyser (VLA)^46Chapter 4 Oxygen-induced substrate relaxation in theNi(111)-(2x2)-O surface^ 514.1^Introduction^ 514.2^Experiment 514.3^Calculation^ 534.4^Structural analysis 544.5^Comments on Ni(111)-(2x2)-S^ 634.6 Summary^ 65Chapter 5 Nitrogen-induced reconstruction of theCu(110)-(2x3)-N surface^ 665.1^Introduction^ 665.2^Experiment 675.3^Calculation^ 685.4^Structural analysis, I: conventional LEED^ 745.4.1 Initial comparison of 25 models 745.4.2 Further analysis of 100C2X2 and LBbMR^805.5^Structural analysis, II: tensor LEED^ 835.5.1 <110>-missing row models 845.5.2 <001>-missing row models^ 85vi5.5.3 Pseudo-(100) models^ 945.5.4 Anomalies in TLEED results 985.6^Summary^ 1015.7 Addendum 102Chapter 6 Surface oxide formation in thePd(100)-(I5x .V5)R27°-0 system^ 1046.1^Introduction^ 1046.2^Experiment 1056.3^Calculation^ 1086.4^Structural analysis: tensor LEED^ 1096.4.1 Reference structures 1096.4.2 Results^ 1116.4.3 Comparison with other models^ 1226.5^Summary^ 123Chapter 7 Concluding remarks^ 1257.1^Further work on Ni(111) 1257.2^Further work on Cu(110)-(2x3)-N^ 1257.3^Further work on Pd(100)-CV5x -V5)R27°-0 1267.4^Critique of the LEED analysis^ 127References 133List of Tables^ vii1.1^A selection of surface science techniques which have been applied to studythe three systems investigated in this thesis.^ 22.1^A test of the ability of the directed search/tensor LEED method forreproducing initially assumed structural details. "Experimental" curves werecalculated by FD methods for four types of atomic displacements (defined inFig. 2.3a) by two different magnitudes (DISP), and the optimization wasdone over all three Cartesian coordinates of the four 0 atoms and five top-layer Pd atoms. For both sets of results, initially assumed first-to-secondinterlayer spacing d12 = 1.94 A, and DISP = 0.10 and 0.20 A for the left andright sets, respectively. OVor is the difference between the TL-optimized V orvalue and that assumed initially. The values reported for the verticaldisplacements (Do and Dpd) do not correspond to a simple displacement ofthe particular atom under investigation (e.g., 0 for Do); hence theparentheses around these values. 304.1^Ranges of relaxation parameters considered for model (C)ABC... are given,along with optimized values; increment sizes are in parentheses, and rangeswere reduced as the structural search progressed.^ 585.1^General notation used to name structural models of the Cu(110)-(2x3)-Nsurface in terms of the chemisorption sites and types of reconstruction. Alsotabulated are model names, the figures (and page numbers) where the modelsare defined, and the section under which they are discussed. Models in boldare not defined in figures, but are described in the text (on the page noted)and are related to those for which there are schematic diagrams. 735.2^Ranges of structural parameters considered for those models for which I(E)curves are provided in Fig. 5.5. Included are increment sizes (in parentheses)and optimal values.^ 765.3^Ranges and optimized geometrical parameters, including those for the secondmetal layer, for model LBbMR during the conventional LEED analysis. Acomparison is made with results from the first study when no second layerrelaxations were allowed. 825.4^TLEED-optimized geometrical parameters for three <001>-missing rowmodels.^D and A correspond respectively to vertical and lateralviiidisplacements from the ideal positions (i.e., bulk for Cu or coplanar, long-bridge for N); negative displacement is toward the bulk or toward the originas specified in Fig. 5.7; d gives the center-of-mass interlayer spacings, and bthe N-Cu bond lengths. The initial reference structure, defined for LBbMR,fixed all parameters at zero except DN1 = +0.300 A, d12 = 1.080 A, d23 =1.280 A, and d34 = 1.278 A. 915.5 Geometrical parameters defining the initial reference structures, as well asoptimized values, for TLEED calculations of (100)-reconstruction models.D and A correspond respectively to vertical and lateral displacements fromthe ideal positions (negative displacement is toward the bulk or toward theorigin as specified in Fig. 5.7); d gives the center-of-mass interlayer spacings,and b the N-Cu bond lengths. 925.6 Comparison of N-Cu bond lengths for models 100G and UMRa for the I(E)curves shown in Fig. 5.11. DISP indicates the magnitude of maximumdisplacement in each set of calculation. 1016.1 Comparison of the level of agreement achieved between calculated andexperimental I(E) curves for the 12 models in Fig. 6.2, with the model givingthe overall best fit in bold. Values listed are for the final FD/TL cycle. Rayfor the final reference structure are included to verify the trend indicated byR. DISP indicates the level of convergence achieved within the context oftensor LEED, as given by the type and magnitude of maximum displacementin the final cycle. Only one cycle was performed for model PDOU since thevalue of DISP is within the range of validity of the tensor LEEDapproximation. 1136.2 Rp and maximum displacement (DISP) for the sequence of FD/TLcalculations done for PDOMA. Note the decrease in agreement, as indicatedby a higher value for RP, after the fourth cycle; R-values which are lower inthe previous cycles may be unreliable due to the large values of DISP inthose cycles. FD values are obtained from comparison with experiment offull-dynamical calculated I(E) curves, while TL values result fromoptimization of each reference structure. 1196.3 Some optimized structural parameters for model PDO; CM is center-of-massspacing. Other parameters are defined in Fig. 6.4.^ 119List of Figures^ ix1.1^Schematic diagrams of the real surface and diffraction pattern for the threesurface structures investigated in this thesis.^ 71.2^Schematic diagram illustrating the three steps to calculate LEED diffractedintensities.^ 111.3^De-excitation processes of atomic core holes: Auger electron emission andX-ray emission.^ 182.1^Schematic diagram showing scattering of a plane wave by a spherically and anon-spherically symmetric potential.^ 232.2^Directed search optimization scheme for structural analysis by tensor LEED.^262.3^Schematic diagram defining the 0/Pd reference structure model and the fourtypes of atomic displacement used to test tensor LEED.^ 282.4^Comparison of FD- and TL-calculated I(E) curves for the four types ofdisplacement illustrated in Fig. 2.3. See Table 2.1 for more details.^312.5^Comparison of the effect of different types of displacement on calculated I(E)curves.^ 332.6^Structural models of the type shown in Fig. 2.3 involved in tests of tensorLEED. 352.7^Two comparisons of FD- and TL-calculated curves for the structural modelsshown in Fig. 2.6.^ 363.1^Schematic diagram of the pump and gas line configuration of the Varian 240vacuum chamber used for the N/Cu experiment.^ 403.2^Schematic diagram of the UHV chamber used in the N/Cu study; Ref. 74.^423.3^Schematic diagram showing the (a) LEED and (b) ABS optics setup used inthe N/Cu study; Ref. 74.^ 433.4^The CMA setup used in the 0/Ni experiment; after Ref. 77.^443.5^Schematic diagram showing the He/Ne laser alignment of crystallographicand optical planes of the single-crystal sample.^ 473.6^Block diagram of the video LEED analyser (VLA) for collecting LEEDintensity data.^ 48x3.7^Example of the treatment of LEED experimental data for use in a structuralanalysis.^ 504.1^(a) Auger spectra for clean Ni(111) and Ni(111)-(2x2)-0. (b) Beam notationfor the (2x2) LEED pattern; experimental beams are indicated.^524.2^(a) Schematic diagram of the three basic models considered in theadsorption-site determination for the Ni(111)-(2x2)-0 surface. (b)Comparison of experimental and calculated I(E) curves for the modelsillustrated in (a). 554.3^Schematic diagram illustrating the types of metal relaxations considered forthe Ni(111)-(2x2)-0 surface. Positive displacements are indicated.^564.4^Comparison of experimental and calculated I(E) curves for model (C)ABC...of the Ni(111)-(2x2)-0 surface structure, which include relaxations of thetypes defined in Fig. 4.3.^ 595.1^Auger spectra for clean Cu(110) and Cu(110)-(2x3)-N and a schematicdiagram of the (2x3) LEED pattern; experimental beams are indicated.^695.2^A comparison of I(E) curves measured for the Cu(110)-(2x3)-N surface withN activated at 200, 350, and 500 eV.^ 705.3^(a) The bulk structure of Cu3N; (b) the ideal Cu3N(110) surface; and (c) theideal Cu3N(100) surface.^ 715.4^Schematic diagram for 21 out of the 25 models considered in the firstconventional T BED analysis.^ 755.5^Initial conventional LEED results comparing experimental with FD-calculated I(E) curves for the models listed in Table 5.2 and illustrated in Fig.5.4. 775.6^Six (100)-reconstruction models considered in the second conventionalI FED analysis.^ 815.7^Schematic diagram showing the atom-labelling scheme used in the tensorLEED analysis of the Cu(110)-(2x3)-N surface. Also shown are models100S1 and 100S2.^ 875.8^Top and side views showing explicitly TL-optimized displacements for three<001>-missing row and three (100)-reconstruction models of the Cu(110)-(2x3)-N surface structure.^ 88xi^5.9^Comparison of experimental and TL-calculated curves for the optimizedgeometry of two (100)-reconstructed models (100C2X2 and 100G) and two<001>-missing row models (LBbMR and UMR).^ 905.10 Comparison showing dramatic improvement in agreement betweenexperimental and calculated I(E) curves for model 100F after only oneFD/TL cycle. 955.11 Comparison of experimental data with TL-calculated curves for models100G and UMRa, illustrating the need to reset some TL-optimizeddisplacements. See Table 5.6 for structural details. 995.12 STM images (Ref. 130) of the Cu(110)-(2x3)-N surface at (a) low and (b)high N-dosages.^ 103^6.1^(a) The PdO bulk structure. (b) The Pd0(001) overlayer model of thePd(100)-('15 x A/5)R27*-0 surface; oxide layer Pd atoms are labelled toidentify their registry with respect to the Pd(100) substrate. (c) The distorted4F model of Simmons et al. 106^6.2^Beam notation for the LEED pattern from the Pd(100)-(V5 x -•15)R27°-0surface; experimental beams are indicated.^ 107^6.3^Schematic diagram of the initial reference structures for nine out of thetwelve models of the Pd(100)-(Ai5 x 45)R27°-0 surface.^110^6.4^Top views showing explicitly TLEED-optimized lateral displacements in thefinal cycle for two PdO(001)-reconstruction models (PDO and PDOS), abridge-site overlayer model (4B0), and a hollow-site overlayer model (4F).^114^6.5^TL-calculated I(E) curves for the optimized structures in Fig. 6.4.^116^7.1^Comparison of two sets of calculated I(E) curves with those from the N/Cuexperiment, illustrating the failure of R-factor analysis for these two beams.^129Acknowledgements xiiThe period during which the work in this thesis was performed has been a mosteducational one for me. I would like to thank my research advisor, Professor K.A.R.Mitchell, for directing me toward challenging surface structural problems and for his verycareful reading of this thesis.I thank Dr. H.C. Zeng and Ms. Y.K. Wu for introducing me to the LEEDcalculations, Prof. M.Y. Zhou for introducing me to the LEED experiment, and Mr. S.R.Parkin for providing the Cu(110) sample; I also acknowledge Ms. Wu for making LEEDintensity measurements used in the analysis of the 0/Ni system. I have greatly appreciatedmy interactions with Dr. Uwe Hess, Dr. J.R. Lou and Mr. Wei Liu and acknowledge inaddition Mr. K.C. Wong and Dr. P.C. Wong among the other members of our surfacescience group.The assistance of other members of the UBC community is gratefullyacknowledged. These include members of the electronic and mechanical shops of theChemistry Department, in particular, R. Hamilton and B. Snapkauskas; and members ofthe UBC Computing Centre, in particular, Dr. Tom Nicol, for helping with the manytransitions as computing facilities and policies were updated. Dr. E. Burnell is alsoacknowledged with respect to his assistance in the most recent change to the departmentalcomputer.Special thanks are directed at Dr. M.A. Van Hove (University of California,Berkeley) for providing not only the LEED program codes (co-authors of which are Dr.S.Y. Tong, Dr. A. Wander, Dr. P.J. Rous, and Dr. A. Barbieri), but also the insights intothe workings of and the approaches to the programs. Finally, Mr. 0. Warren and Dr. P.A.Thiel (Iowa State University, Ames) are acknowledged for providing the experimentaldata for the analysis of the oxygen-palladium system.Dedicationjfvio#41 Ltoo4, tiv÷i^pa"641,^truntial4 (34Ankki^wpfuyil^CdWaryJthilitattltait W471Z61)24, p.4. 3 Link ail^iny,ctincl^/94 161/ (4U •ii/n?^• in MQ,^642Q,^t tiv2, r.at2,t i/mpact^mv,lookliir ^umnfaithly, tmovAck&^ci,*nikatal^16 tom,, EgrD calculatiam. jo, AnkGBAdo!^cvnol lo, nu pongl&,, 3 eaviincIt  chwlical,t^thaie,.Chapter 1 : Introduction^ 11.1 Surface science and surface structureA surface represents the transition region between a bulk material and the externalenvironment. Whereas bulk atoms are surrounded on all sides by neighbours, surfaceatoms are surrounded by neighbours only on one side and thus have unsatisfied bondingcapacity. As a result, surface free energy is higher than that of the bulk, and surface atomsexperience a strong driving force to lower this energy either by bonding with foreignatoms, such as those from the gas phase, or by rearranging or reconstructing to increasetheir coordination number.Surface science studies this region, which includes not only the topmost atomiclayer, but also all those layers near the surface which may be involved in the reconstructionor reaction and which may be probed by a particular experimental method. Rapidprogress in this field in the last thirty years has been due both to instrumental andtheoretical improvements in the traditional methods, as well as the development of newtechniques for revealing the structure and chemical composition of surfaces on an atomicscale. Information gained from fundamental surface structural studies provides the basisfor the development of the theoretical framework for surface structural principles, which,when well established, can help increase understanding in a range of diverse fields oftechnological importance, including heterogeneous catalysis, corrosion, adhesion, andrnicroele,ctronics. 1-5 In particular, the connection should become better understoodbetween studies of well-defined, single-crystal surfaces under ultrahigh vacuum (UHV)and those of "real" systems such as in high-pressure, metal-on-support catalytic chambers.Of the many techniques now available to study surface structure (Table 1.1), low-energy electron diffraction (LEED) is the most developed surface crystallographictechnique, 29-32 and results from LEED studies are often used to test the accuracy of otherTable 1.1 A selection of surface science techniques which have been applied to study the three systems investigated in this thesis.Technique Acronym Probe Physical basisLow Energy Electron Diffraction LEED electron elastic electron back scatteringAuger Electron Spectroscopy AES electron secondary electron emissionX-ray Photoelectron Spectroscopy XPS photon core electron emissionPhotoelectron Diffraction PED photon diffraction of photoelectronSurface-Extended X-ray Absorption FineStructureSEXAFS photon interference effects ofphotoelectronsSurface-Enhanced Electron Energy LossStructureSEELFS electron interference effects of incidentelectronHigh-Resolution Electron-Energy Loss HREELS electron vibrational excitationSpectroscopyScanning Tunneling Microscopy STM electron tunneling of electrons between asharp probe and the sampleThermal Desorption Spectroscopy TDS, TPD heat desorption of adsorbate astemperature of sample is raisedIon Scattering HEIS, LEIS, NICISS ion ion scatteringX-ray Diffraction (and Reflectivity) XRD photon elastic X-ray back scatteringInformation gained^Ref.geometrical structure^[6-8]elemental composition^[9,10]composition, electronic states^[9-11]geometrical structure^[12,13]bond lengths [14,15]bond lengths^ [12,16]vibrational modes^[17,18]geometrical and electronic structure^[19,20]desorption energy, composition^[21-23]geometrical structure, composition^[24-26]geometrical structure,^[27,28]surface atom density3techniques. LEED is possible because of the wave-particle nature of the electron, an ideafirst proposed by de Broglie in 1924. Diffraction by electrons impinging on a solid wasfirst observed by Davisson and Germer in 1927, 33 but not until the 1960s, with advancesmade in UHV technology, did LEED become widely adopted as a surface characterizationtechnique. With theoretical development from around 1970 onwards, LEED has becomean ideal tool for studying the location of atoms on the surface because of its strongdependence on the electron ion cores and its low sensitivity to the specific surface electronwave functions, unlike other techniques such as photoemission and scanning tunnelingmicroscopy, which are sensitive to the electronic properties of the surface. 34 Initially,LEED studies have concentrated more on low-Miller-index unreconstructed surfaces ofmetallic single crystals, but with the advent of faster and more sensitive measuring devices,as well as approximative calculation schemes, LEED is now being increasingly applied tostudy more complicated systems such as those involving surface reconstruction,disordered chemisorption, alloyed surfaces, et cetera1.2 Low-energy electron diffraction (LEED)1.2.1 General principlesThe LEED analysis is, at least in principle, simple. A beam of low-energyelectrons is aimed at a single-crystal surface of known crystallographic orientation.Elastically back-scattered electrons are displayed on a fluorescent screen and form adiffraction (LEED) pattern if the surface is sufficiently well ordered. Diffraction occursbecause at typical LEED energies of 30 to 300 eV, the wavelengths of these electrons150.4 E (eV)X(A) = 11p =4are comparable to the lattice spacings in most materials (h is Planck's constant, and p is themagnitude of the electron momentum). The LEED pattern gives information with respectto the size and shape of the unit mesh for the surface region probed by the LEEDelectrons. But in order to determine atomic positions, the intensities of the diffractedbeams must be analyzed. It is most common to measure the intensity as a function of theincident electron energy to give intensity-versus-energy or I(E) curves. Based on anumber of chemically plausible models of the surface, theoretical I(E) curves are alsocalculated and then compared to experimental data. Reliability- or R-factors are used as aquantitative and objective measure of the agreement between experimental and calculatedI(E) curves; the lower the R-value, the better the agreement, hence, the more likely themodel is to be correct.44The very factors that make LEED a surface sensitive technique also make it moredifficult in practice than in principle. Strong inelastic scattering of low-energy electronsinside the target material limits the mean free path of the incident beam to the order of afew atomic layers, and this typically reduces the intensity of elastically back-scatteredelectrons to less than 2% of the incident beam current. The strong interaction betweenlow-energy electrons and the surface complicates the LEED theory compared with that forX-ray (or neutron) diffraction. Before escaping the surface and being detected, low-energy electrons will often have been elastically scattered several times by the ion cores.The positions of spots in a diffraction pattern are determined by symmetry, but thedistribution of intensity among different beams is affected by multiple scattering, and exacttheoretical reproduction of experimental I(E) curves cannot generally be achieved withouttaking account of this effect. Furthermore, because of multiple scattering, LEED istraditionally forced to work by the trial-and-error approach of testing "reasonable" modelsof surface structure; even when the field is narrowed to only a few models, an exhaustivesearch over parameter space of atomic positions for each model can still have large5demands on computing time. Finally, R-factors must be used with caution, especiallywhen the system being studied is complicated and no bulk structure exists to serve as aguide in predicting the surface structure. One problem is that R-factors can have localminima within parameter space, but the objective is always to find the global minimum. Inaddition, the choice of which R-factor to use can itself present a problem, there being noconsensus as to which is the most effective LEED reliability index, particularly foranalyzing completely unknown and complex surface structures.The first step in a LEED analysis is the interpretation of the diffraction pattern interms of the unit mesh basis vectors. The positions of spots on the screen, i.e., thedirection of interference maxima, is determined by the 2-dimensional Laue conditions(kd - ki) • s i = integer x 2rc^ (1.2)and(kd - ki) • s2 = integer x 2rc^ (1.3)where ki and kd are the wavevectors of the incident and diffracted beams, respectively, ands i and s2 are the basis vectors describing the surface unit mesh. The condition of elasticscattering is satisfied when the magnitude of the wavevectors kd = = 27.r/X. For a givenincident beam energy and direction, an increase in the magnitude of the surface unitvectors will cause the differences in the diffracted beam directions to get smaller; in otherwords, the spots on the screen will appear closer together. A (1x1) LEED pattern resultswhen the unit vectors s i and s2 are the same as the unit vectors a n and a2 of the substrate(i.e., bulk) planes parallel to the surface; that is, S I = a l and s2 = a2 . As often happens inthe case of chemisorption or reconstruction of the clean surface, the surface basis vectorsare related to those of the substrate by s i = ma n and s2 = nag (with m and n integers). The6resulting (mxn) pattern will have extra spots which appear in between those of the (1 xl)pattern. Diffracted beams corresponding to the (1x1) pattern are called integral beams,and extra beams in the (mxn) pattern are called fractional (or superstructure) beams. Insome cases, the surface basis vectors are rotated relative to the substrate (1x1) vectors byan angle a. The Wood notation 45 is commonly used to describe such a surface and hencethe accompanying LEED pattern:S(hk1)-i(mxn)Ra-riA,where S and A are respectively the chemical symbols of the substrate and adsorbate, (hkl)are the Miller indices describing the crystallographic orientation of the surface, (mxn)Rarelates the size and orientation of the surface unit vectors to those of the substrate, 11 givesthe number of adsorbed atoms in the surface unit mesh, and i is either p for primitive or cfor centered. For primitive unit cells, the "p" is often omitted. Figure 1.1 illustrates thesepoints for the three surface structures investigated in this work.While the LEED pattern results from the diperiodicity of the surface region, theintensity of the diffracted beams depends strongly on the periodicity normal to thesurface.46 In the single-scattering limit (e.g., for X-ray diffraction where kinematic theoryholds), 47 intensity in a direction determined by Eqs. (1.2) and (1.3) is maximized when thethird Laue condition(kd - ki) • s3 = integer x 2rc (1.4)is satisfied; s3 is the basis vector normal to the surface, defined in this work as +x in thedirection of the bulk. For the (0 0) beam at normal incidence, primary Bragg peaks areexpected whenCu(110)-(2x3)-N• 0 0 • 0 0 •0 0 0 0 0• 0 0 .--o 0 •0 0 0 0 0 0 0• 0 0 • 0 0 •Ni(111)-(2x2)-0•o• 0^•o ,D,o e: ▪:3*• 0^•o o•7Figure 1.1 Schematic diagrams of the real surface (left) and diffraction pattern (right) for the threesurface structures investigated in this thesis. For the real surface, large open circles represent thesubstrate atoms, while small filled circles represent adsorbed atoms; dark and light arrows give,respectively, the substrate and surface unit vectors. In the diffraction patterns, filled circlescorrespond to integral beams from the clean surface, with additional fractional beams (open circles)for the chemisorbed surface. Note that the observed diffraction pattern for the 0/Pd surface requiresthe presence of both domains on the real surface; 0 and o correspond respectively to diffractedbeams from domain A and domain B.Pd(100)-(45 x 45)R27°-0.^•^•• 0^• 0o^• o^•• 0^19,. ^00 •^: 1• .• oo^•^•• o •^oo •^o •• •^•Figure 1.1, continued009s3 (A) = n3 X = 150.4 E (eV) (1.5)In actual LEED experiments, however, intensity maxima are shifted by several voltstoward lower energies compared with expectation from Eq. (1.5) alone. This is amanifestation of the lowering in potential which an electron experiences on entering thesolid, and it relates to the concept of the inner potential. 6 Correspondingly, an electrongains kinetic energy inside the crystal so that its wavelength is effectively given by.11^150.4Xcrystal (A) =(E - V0 ) (eV)(1.6)as compared to the wavelength in vacuum as given by Eq. (1.1) (by definition, V 0 < 0). Inaddition, rather than having intensity maxima at sharply defined energies, Bragg peaks arebroadened by the uncertainty principle and the limited electron penetration depth, andmultiple scattering leads to the appearance in I(E) curves of much secondary Braggstructure, which is not predicted by Eq. (1.5).1.2.2 Multiple-scattering calculation of LEED intensitiesSince the kinematic theory is insufficient for calculating LEED intensity spectra forcomparison with experiment, a dynamical theory of diffraction is thus required.Mathematical details of the theory can be found in many references, 6-8,34,48 and only a briefoutline of the calculation schemes will be given here. In most LEED calculations, amuffin-tin model of the scattering potential is used, in which a spherically symmetricpotential is assumed around each atom and a constant potential is assumed in theinterstitial region outside of the spherical regions, which extend from each atomic nucleusto the appropriate muffin-tin radius. The latter are chosen to minimize the constantpotential volume for non-overlapping atomic spheres. The real part of the constant10potential, Vor, is treated as an adjustable parameter during the structural search, and itapproximates to the experimentally-determined inner potential. In addition, the constantpotential, Vo = Vor + iVoi , is given an imaginary component (Voi) which accounts for theremoval of flux from the elastic beam by inelastic processes.Calculation of LEED intensities (from squared amplitudes) is usually done in threesteps (Fig. 1.2), starting with scattering by a single atom, from which the scatteringproperties of a layer are calculated, and contributions from different layers are thensummed to give the total diffraction amplitude scattered by the surface. The sphericalsymmetry of the ion-core scattering potential favours a procedure whereby a plane waverepresenting the incident electron beam is decomposed into incoming and outgoingspherical waves, centered on each atom and characterized by angular momentum values= 0, 1, 2, .... For an incident plane wave given byei(jr^ (1.7)the scattered wave has the following asymptotic formik-r^eikire^+ .0.where t(0) is the scattering amplitude at scattering angle 0 and r is the distance from theatomic nucleus. The scattering amplitude is expanded in Legendre polynomials Pe ,t(0) = 47 -- (21 + 1) to Pe (cos 0)^ (1.9)kr (1.8)where tt is a t-matrix element given by11 1 11 1 111 1 1^1111111 111 1O 0 0 0/O 0 0 0/0 0 0 0111  \\\O 0 0 0/O 0 0 0/0 0 0 0/ll I IV It! 4//V(r)V, It t ///00/0000000/0 0 0I I Iatom scattering^layer diffraction^surface diffractionSt M(kgi' kg)^A(kg,ko)Figure 1.2 Schematic diagram illustrating the three steps to calculate LEED diffracted intensities interms of the phase shift (8k), layer diffraction matrix (M), and scattered amplitudes (A); after Ref. 32.12tt = iei4 sin8^ (1.10)Conservation of energy and angular momentum limits the difference betweenincoming and outgoing waves of the same e value to a phase factor, and the set of phaseshifts be calculated for each element (i.e., each atomic potential) accounts fully for theintraatomic scattering. Additionally, thermal effects are included by the use oftemperature-dependent phase shifts O t(T), calculated from multiplying t(0) by an effectiveDebye-Waller factore -m = exp 3(Ak)2 T)2mk B O2where T and CI are the real and Debye temperatures, m is the atomic mass, k B isBoltzmann's constant, and Ak = (k - k') is the momentum transfer due to diffraction fromone plane wave into another.Spherical waves which have been scattered by one atom can subsequently bemultiply scattered by other atoms in the same layer. The scattering matrix of an atomiclayer is obtained by combining and then transforming all partial waves into a set of planewaves, or diffracted beams, characterized by wavevectors k g . The two dimensionalperiodicity of a layer limits the number of wavevectors that need be considered; only thosebeams which can reach the next layer play a significant role in the diffraction process.Although it is possible to calculate exactly the total surface diffraction using onlyspherical waves by considering the surface as a thick slab consisting of a finite number ofsublayers, a more common approach is to stack the single layer diffraction matrices inorder to build up the surface slab. In the layer-doubling (LD) scheme, 49 diffractionmatrices are calculated exactly for a pair of layers from the diffraction matrices of the13individual layers; diffraction matrices for the pair are then combined to give diffractionfrom a slab of four layers; each step in the iterative process doubles the thickness of theslab by combining two identical slabs; and layers are stacked in this manner untilconvergence of reflected intensities is reached. An alternative perturbative method(Renormalized-Forward-Scattering or RFS) is based on the idea that backward diffraction(or reflection) is weak compared to forward diffraction (or transmission). 50 The incidentbeam is transmitted at each layer until the deepest layer is reached (in the presence ofinelastic scattering); waves reflected at each layer are forward diffracted out of the crystalto give the first-order beams; reflection of these first order beams back into and then outof the crystal create second-order beams; and the process is repeated until higher ordercontributions become negligible, at which point convergence is reached. RFS is the fastestmethod for stacking layers, but it may fail to converge when interlayer multiple scatteringis strong or when the interlayer spacing is small (— 1 A). LD can be used for interlayerspacings as small as 0.5 A.For interlayer spacings less than 0.5 A, as often occurs for chemisorption of smallatoms on the more open metal surfaces, the combined-space method 51 '52 is used. Thesurface layers where the small interlayer spacings occur are treated as a composite layerconsisting of two or more subplanes, each of which contain only one atom per unit mesh.Diffraction properties of the composite layer are calculated in the spherical-waverepresentation, while stacking of the composite layer onto the substrate is done in theplane-wave representation.When the rotational symmetry of the surface is lower than that of the substrate,rotationally related domains are to be expected (e.g., for the Pd(100)-('15x115)-R27°-0surface in Fig. 1.1). At normal incidence, it is only necessary to calculate diffractedintensities from one domain, but appropriate averaging of diffracted beams is required toeffect a summation of the different patterns from the different domains. The above14procedure assumes that domain sizes are large (compared to the instrumental transferwidth) and that different domains are equally populated. 6 These conditions are satisfiedexperimentally when a sharp diffraction pattern is observed, which contains fractionalbeams from all domains.1.2.3 Structural analysis and reliability indices (R -factors)The approach of LEED crystallography is to calculate theoretical I(E) curves fordifferent models of the surface, and comparison with experimental I(E) curves is doneboth visually and with reliability indices to determine the best match (hence, the mostlikely correct model of the surface). Ideally, R-factors should be more sensitive tostructural parameters such as atomic positions, and not so sensitive to nonstructuralparameters such as the Debye temperature and V oi ; in practice, however, Vor must beoptimized along with structural parameters. Two R-factors are especially used in thiswork: one is a modified form of that proposed by Zanazzi and Jona (R mzj)44,53 and theother proposed by Pendry (Rp).54 The latter emphasizes peak positions, weighing allpeaks in a spectrum equally; for each beam,Rp =f(Yexp Ycald2 dE(1.12)1 2^2Yexp + Ycalc dE whereLY = (1 + L2 Vol)^ (1.13)and L is the logarithmic derivative of the intensityRzj AzjexpfII " - cIcalce xpI II ' - cIcalc IlIexp I + maxlIexp Iwhere1 Azj 0.027fIexp dEis a reducing constant chosen so that RD — 1 for uncorrelated curves,53 andf'exp dEC = fIcale dE15d lnIL = dE (1.14)Voi is the imaginary part of the constant potential. The original Zanazzi-Jona R-factor(RD) uses both the first and second order derivatives of intensity (I' and I", respectively)and is designed to account for reproduction not only of peak positions, but also of relativepeak intensities. For a single beam,is a normalization constant to account for the different intensity scales between calculatedand experimental I(E) curves. Van Hove and Koestner 44 proposed a modified single-beamindex , RAJ , in which maxlcrealel replaces maxII'expI in Eq. (1.15), and the reducingconstant is redefined as1 Amzi =^ (1.18)p dEEAEiRiR=EAEi(1.19)16When comparing I(E) curves for more than one diffracted beam, as in LEEDcrystallographic applications, Zanazzi and Jona suggested an average R-factorwhereby individual beam R-values are weighted according to the energy range over whichthe comparison with experiment has been made. The summation in Eq. (1.19) is over eachindividual beam (i), and the multibeam index R can refer to either R p or Rmzj .All reliability indices have been defined so that their values are zero when identicalcurves are being compared, but often there is no clear meaning for a value when verydifferent curves are compared. This point has been discussed by Van Hove and Koestner,and they proposed a further factor of 1/2 in the definitions of both R p and Rmzj to ensure anupper value of — 1 when anticorrelated curves (sin2x and cos2x) are compared. This latterdefinition has been followed in this work, namely B_ p. Y2 Rp and Rmzj = Y2  Rte, and afurther index used is the average, defined as Ray = 1/2 (111, +1244/j).The first step in studying structure for chemisorption on metal surfaces is todetermine the adsorption site and the corresponding adsorbate-metal bond lengths. Theimmediate result is the adsorbate to topmost metal layer spacing, usually with the metalatoms initially in their bulk positions. But work in our laboratory and elsewhere hasshown that significant relaxations in the local metallic structure also occur, presumably tooptimize the total bonding (adsorbate-metal and metal-metal). Both vertical and lateraldisplacements of metal atoms from the ideal bulk-terminated positions can create a metalsurface layer with two-dimensional unit mesh different from that of the bulk, but the sameas that of the chemisorbed overlayer. In some cases, identification of the correctadsorption site requires a gross reconstruction of the substrate so that the atomic density17in the top metal layer (or layers) is different from that of the clean surface. Each step in ananalysis attempts to minimize the R-values in a search for the global minimum. Thetraditional trial-and-error method of LEED crystallography suffers from the uncertainty ofwhether a local or global minimum has been found at any stage, and this is combined withthe large computing demands resulting from the multiple-scattering challenge (diffractedbeams are coupled together so that, unlike X-ray diffraction, to calculate the intensity ofone beam requires the intensity of all to be determined at the same time). Tensor LEEDoffers a more efficient, and perhaps more reliable, approach to the structural optimization,and this topic will be discussed in Chapter 2.1.3 Auger electron spectroscopy (AES)AES is the primary technique used in LEED experiments for the purpose ofchemical identification of atoms in the surface region. 9,10 When energetic electrons (orelectromagnetic radiation) strike atoms on the surface, electron emission can occur, whichcreates a hole in an inner electron shell. The ionized atoms may then relax to theelectronic ground state either by X-ray emission or by Auger electron emission (Fig. 1.3).While the incident beam may ionize atoms deep within the crystal, only Auger electronsfrom those atoms near the surface can escape and be detected without loss in energybecause of the short mean free path for low-energy electrons. 55 Furthermore, the kineticenergy of an Auger electron depends only on the three energy levels involved, which arecharacteristic of each element. Shifts in Auger peaks may be observed to reflectdifferences in an atom's chemical environment, but such effects tend to be small inmagnitude (a few eV) and usually do not affect the qualitative analysis aspect of AES.Chemical analysis is thus possible by assigning peaks in an Auger spectrum to a particularelement with the aid of listed Auger energies.56,57t--111-0---IIL111L 11L 1KKIlL inlipi Auger electron11—•-41-0-0—Auger electron emission•fI-*--9-40-tio-iExcitation-^- I/ • •I Kc-.1.--(1--i^1/ radiationII/• 4 X-ray emission-411-411-0-0-IKE . EK - ELI - ELIIIFigure 1.3 De-excitation processes of atomic core holes; KE is the kinetic energyof the Auger electron.191.4 OutlineThree systems of increasing complexity were investigated in this thesis, using thecombination of LEED and AES. Multiple-scattering calculations were done with thecomputer programs of Van Hove and Tong, as detailed in their book. 48 Additionally,tensor LEED calculations used programs provided by Barbieri and coworkers; 58-60 thetensor LEED approximation will be discussed in Chapter 2. Chapter 3 describes thegeneral experimental methods employed. Chapter 4 gives results from the simplest surfacestudied, that formed by the chemisorption of oxygen on the (111) surface of nickel to giveNi(111)-(2x2)-O. Chapters 5 and 6 discuss structural features of the Cu(110)-(2x3)-Nand Pd(100)-(V5x'■15)R27°-0 surfaces, respectively. In all cases, structural results werecompared to those from other surface science techniques, in particular those listed inTable 1.1, and discrepancies were addressed. Finally, Chapter 7 reviews the current statusof LEED crystallography and suggests directions for future research.Chapter 2 : Tensor LEED^202.1 IntroductionAs has been mentioned in the previous chapter, conventional full dynamical (FD)calculations of LEED intensities often have restricting requirements for computing (CPU)time, a large portion of which is spent in calculating the diffraction matrices for acomposite layer. The CPU time scales roughly as M 3 , where M is the number ofsubplanes in the composite layer. 48 An even more serious limitation of FD LEED is thetrial-and-error procedure for determining surface structure, where times required scaleroughly exponentially with the number of parameters being varied. 59,61 Human selectionof which structural parameter is to be studied in greatest detail limits not only the numberof parameters to be investigated, but also the parameter space over which the structuralsearch is done. Thus, the prospect of accurately determining the coordinates of more thanfive atoms is dim with the conventional procedure. Given the current interest inadsorbate-induced restructuring,42 often involving large unit cells containing many atoms,a new approach to LEED calculations is clearly needed to determine the many structuralparameters involved. The recently developed tensor LEED method offers an alternativeand faster approach to the standard LEED analysis. 62-682.2 General principlesTensor LEED is an approximative scheme for calculating diffracted beamintensities, which attempts to recover the simplicity of X-ray diffraction in the LEEDcontext. Weak atomic scattering of X-rays 47 allows treating scattering as a first-orderperturbation of the incident photon wavefield in vacuum. Furthermore, the probability ofan X-ray photon being scattered by more than one atom (multiple scattering) is muchlower than that of single scattering. Consequently, the amplitude of the scattered21wavefield can be expressed as a sum over all possible single-scattering events, and thediffracted intensity factorizes into the product of an atomic form factor f and a geometricalstructure factor SI(k,k') = If(Ak)12 IS(6.k)12^(2.1)s (Ak) = N^(2.2)J=1where (k,k') are respectively the wave vectors of the incident and diffracted waves and Ak= (k-k') is the momentum transfer. Intensity calculations for any number of arrangementsof atoms in the bulk unit cell can be accomplished by quick and simple resumming of thestructure factor in Eq. (2.2) over atomic coordinates of the N atoms in the unit cell.The above equations cannot be directly used in calculating LEED intensitiesbecause of the strong atomic scattering of low-energy electrons so that the electronwavefunctions must be solved from the SchrOdinger equation in which the crystalscattering potential is fully represented. 6 Multiple scattering of low-energy electrons linksthe arrangement of atoms with the scattered wavefield so that the calculated intensities canno longer be simply separated into a form factor and a structure factor. Tensor LEEDaddresses these problems by starting not with the electron wavefunction in free space, butwith the electron wavefield as calculated exactly for a reference surface using FD methodsas outlined in the previous chapter. Small atomic displacements away from the referencestructure can then be treated as a first-order perturbation of the reference structure, anddiffracted intensities for more complicated trial structures can be calculated much morequickly than with conventional means.Tensor LEED theory has been considered at three different levels of sophistication.The simplest, called Linear Tensor LEED, assumes that the change in the scattered22amplitude depends linearly upon the magnitude of atomic displacement; thisapproximation is accurate only for displacements of less than 0.2 A at energies greaterthan about 100 eV and is therefore not very useful for many LEED crystallographicapplications where intensity data often extend to 250 eV or higher. The mostsophisticated version, called Cluster-Corrected Tensor LEED, attempts to correct forsome multiple-scattering correlation between displaced atoms; this version has not beenimplemented, however, and will not be discussed here. The most widely available versionof tensor LEED theory, which is used in this work, is simply called Tensor LEED(TLEED); an outline of TLEED theory follows.First, an FD calculation is performed for a reference structure; the standardassumption of a spherically symmetric potential centered at each lattice point is made.Displacement of atoms from the reference structure positions is treated as a non-sphericaldistortion of the scattering potential (Fig. 2.1), as incorporated into the atomic scatteringt-matrix:t.' = t. + Sit .(8r. ), (2.3)Jwhere t.' and t. are respectively the t-matrices for the displaced and undisplaced atom j, Stis the change produced by the displacement Sr., all defined relative to the undisplacedatomic position r.. The change in each t-matrix element is given bySt^= EG^(Sr) tei G „ (-8r) - V N,tfibc 1 m,1^J^limpenb^Jwhere G is a spherical wave propagator, 6,69 which convertsr. to a set of spherical waves centered on rJ +Sr ., and 8 , is(2.4)a spherical wave centered onthe Kronecker delta (i.e., sr11111111111111111I 11111III11111111 111111111 111111111 11111Figure 2.1 Schematic diagram showing scattering of a plane wave (dashed lines) by an atom(solid circle) into spherical waves (open circles with arrows indicating some directions ofpropagation). The left panel corresponds to scattering by a spherically symmetric potentialwhere the origin is located at the atomic center, while atomic displacement in the right panelleads to a non-spherically symmetric potential.24equals 1 if e = e' and 0 if e * (). The change in scattering amplitude of a LEED beam ofparallel wavevector kis calculated from SitSA = E<'11+ (k) I Std ItP÷ (IQ>^ (2.5)which can be re-expressed65 as a product of a "form factor" F and a "structure factor" S jfor N displaced atoms as1SA = —NE (2.6)(-1) In1+1113 T j^t„gf""2,13"13 (C 6,C2 1/12.1 1711 C elml , In' 43'613^6e213)^(2.7)elm1 12m2i3m3S i t^= (4 2 i -G-G'^171-1-714' •7c)^(-1)^j (Or) Y (Sr) j (Or) Y (-Sr)Gm„tm, et cmTttn2,t3m3 = <IP+ (10 I ri ; t2m2 > < ri ; G37713 IT+ (IQ>je is a spherical Bessel function; Ye. is a spherical harmonic; C is a Gaunt coefficient; and'Ir.1. • 6, > is a state of angular momentum 6, centered on r .The tensors T, hence F, depend only on the property of the reference surface andneed only be calculated once. I(E) curves for any number of trial structures, each ofwhich would have required doing a new FD calculation in conventional LEED, can nowbe done quickly by reevaluating Eq. (2.8) (the CPU time now scales as N, where N is thenumber of displaced atoms). In addition, since the terms S contain a product of two(2.8)(2.9)25Bessel functions and je is a rapidly decreasing function of order e so that S 0 for +kOr, the sum in Eq. (2.6) can be truncated afterel-e Or,leading to a significant saving in CPU time. Previous tests 61-64 have shown that thisversion of tensor LEED can closely reproduce FD-calculated I(E) curves for atomicdisplacements less than 0.4 A, beyond which the theory becomes inaccurate as multiplescattering correlation between displaced atoms becomes important. For Sr = 0.4 A andmaximum incident energy of 252 eV, the sum in Eq. (2.6) need only to be performed for e+e' 5 4.2.3 Automated search procedureThe speed with which I(E) curves for a trial structure can be evaluated usingTLEED naturally suggests implementation of an automated search procedure: 59-61comparison between theoretical and experimental curves is done by the program, and theresulting increase or decrease in R-value is used to direct the choice of the next trialstructure. This process is repeated until an R-factor minimum is reached. Previous testsof the TLEED method have mainly been of clean metals and "simple" overlayer structures;for the work in Chapters 5 and 6, the emphasis is on reconstructed surfaces where, toincrease the likelihood of finding a global rather than local minimum, searches over manydifferent chemically plausible reference surfaces are done. Figure 2.2 illustrates theautomated search strategy as realized in the programs used in this work. 58-60Three steepest-descent optimization schemes were available: the simplex anddirection-set Powell algorithms are substantially modified versions of those contained inthe book by Press et al.,70 and a direction-set search similar to the Rosenbrook[Reference structure(FD) calculationTensorsstoredsm,imsI Disk file I26Choose initialtrial structureEvaluate I(E) spectrawith Tensor LEEDExpt.EvaluateDisk fileR-factor dataChoose nexttrial structure R-factordecrease?yes^ noR-factorminimum?yes"Global"minimum?yes ^TerminatesearchnoChoose nextreference structureFigure 2.2 Directed search optimization scheme for structural analysis by tensor LEED27algorithm71,72 which provides information about the local geometry around the minimumin parameter space. Additionally, a fourth set of routines supplies information withrespect to the explicit dependence of the R-factors on structural parameter variations inthe vicinity of the minimum. This work used the Powell algorithm, a brief description ofwhich follows.Consider a search for the 3N coordinates of N atoms. R-factor minimization isdone along 3N independent directions, initially chosen to be the Cartesian coordinates ofeach atom. Minimization along one direction begins by displacing an atom a distance s,calculating I(E) curves for this trial structure, and evaluating its R-factor. If the R-valuehas decreased relative to that for the initial structure, then a new trial structure is selectedin which the atom is displaced a distance as, where a > 1.0. Displacement in the samedirection continues until an increase in R-value is encountered, then the step length isreduced and the direction is reversed by Ps, where i3 < 1.0. Once this process has beenperformed for all 3N parameters, a new set of axes are defined in which one axis pointsalong the direction of steepest descent, and the others point along directions of minimalchange in R-factor. The minimization procedure is then repeated in the new coordinatesystem, and the search proceeds until no further significant variations could be observed ineither structural parameters or R-values.2.4 Some tests of TLEEDTo assess the ability of TLEED and an automated search procedure for determiningsurface structures involving more complex unit meshes than have previously beenconsidered, a number of tests were done using the TLEED program codes as provided byBarbieri et al.,58-6° with a simplified model of the 0/Pd surface (Fig. 2.3). For all tests, thereference structure was the ideal Pd(100) surface with an 0 overlayer at 1.30 A above theTOP VIEWAPdAoSIDE VIEWDoFigure 2.3 Schematic diagram of reference structure model used to test tensor LEED. Large open circlesand small shaded circles represent respectively Pd and 0 atoms. Four types of atomic displacement wereseparately considered, as indicated by arrows (top view) and dashed lines (side view).29surface and on bridge sites; the first-to-second Pd(100) layer spacing (d12) was initially setat the bulk value of 1.94 A. All FD calculations used an initial value of V o,. = -5.00 eV.2.4.1 Reproducibility of full -dynamical calculationsThe first test was of TLEED's ability to reproduce accurately full-dynamicalcalculations. I(E) curves were calculated by FD methods for four types of atomicdisplacement (A pd, 1o, Do , Dpd) by two different magnitudes (0.10 and 0.20 A). Thesetheoretical curves served as "experimental" curves; Table 2.1 summarizes the results fromthe TLEED calculations, and Figure 2.4 compares some TL vs. HD curves for this modelsurface. It is clear both from visual inspection of I(E) curves and from the low R p valuesthat TLEED can reproduce structural parameters to within 0.02 A for initially assumeddisplacements of 0.10 A or less. This is well within the error limit set by the uncertainty inexperimental data, estimated to be about 0.03 A,73 and, therefore, TL-calculated I(E)curves can be considered accurate for displacements in this range of values.Displacements of 0.20 A gave worse agreement between TL and FD calculations, but thisstatement applies not so much to visual analysis or even to the significant rise in R P, butrather to the lack of reproducibility in the magnitude of the atomic displacements. Lateraldisplacements were reasonably well reproduced by TLFF.D, the error being 0.03 A or less,whereas vertical displacements were somewhat underestimated, the error being as large as0.1 A. These observations are consistent with those of other workers61-63 and also serveas a guide as to how TLEED converges on the "correct" model:(1) generally, for displacements less than 0.20 A, structural results are the same fromTLEED and conventional (FD) LEED;(2) consequently, the difference in R p between an FD and TL calculation should be —0.05 or less;Table 2.1 A test of the ability of the directed search/tensor LEED method for reproducing initially assumed structuraldetails. "Experimental" curves were calculated by FD methods for four types of atomic displacements (defined in Fig. 2.3) bytwo different magnitudes (DISP), and the optimization was done over all three Cartesian coordinates of the four 0 atoms andfive top-layer Pd atoms. For both sets of results, initially assumed first-to-second interlayer spacing d 12 = 1.94 A, and DISP =0.10 and 0.20 A for the left and right sets, respectively. 8V or is the difference between the TL-optimized Vor value and thatassumed initially. The values reported for the vertical displacements (Do and Dpd) do not correspond to a simple displacementof the particular atom under investigation (e.g., 0 for Do); hence the parentheses around these values.DISP d12 6Vor (eV) —P DISP d12 6Vor (eV) --PApd 0.10 1.95 0.10 0.011 0.17 1.92 1.84 0.0520.12 1.94 0.53 0.013 0.22 1.95 -0.03 0.023Do (0.08) 1.93 1.14 0.017 (0.15) 1.91 2.58 0.055Dpd (0.09) 1.93 1.23 0.019 (0.16) 1.92 2.27 0.048(0.8 1.6) (0.6 1.8)__FD^TL( 0 1)DP260^80^100 120 140 160 180 200Cl)120 140 160 183 200( 0 2)(02 0.4)16080^100 120 140 160 180 200 20C(0.612) (0.4 1.8)130 160 1903180 100 120 140 160 160 200ENERGY (eV)Figure 2.4^Comparison of FD- and TL-calculated I(E) curves for the four types ofdisplacement illustrated in Fig. 2.3. "Experimental" FD curves were obtained by full-dynamical methods for a displacement of magnitude 0.20 A (LP2 corresponds to Apd,LO2 to .6,0 , DO2 to Do , and DP2 to Dpd). See Table 2.1 for more details.32(3 )^therefore, a new iteration of the TL search procedure starting from the last TL-optimized result is probably not necessary.2.4.2 Lateral vs. vertical displacementEven without the autosearch procedure, tensor LEED provides a very efficient,and hence powerful, method for correlating changes in calculated I(E) curves with aparticular displacement of a particular atom. Figure 2.5 illustrates this point. Comparisonwas made between real experimental data and FD-calculated curves for the referencestructure as well as four sets of TL-calculated curves (all displacements as defined in Fig.2.3), and the following conclusions can be drawn:(1) For normal incidence, vertical displacements generally have a greater effect thanlateral displacements of the same magnitude (e.g., beam (0 2)). This is to beexpected, since at normal incidence the momentum transfer Ak is mainly in thedirection perpendicular to the surface.(2) For the same number of atoms, displacement of a stronger scatterer (e.g., Pd) willchange calculated curves more than the same displacement of a weaker scatterer(e.g., 0, beams (0.2 0.6) and (0.6 0.8)). This, too, is as expected.(3)^In some cases, a lateral displacement can have a greater effect than vertical; beam(0.4 1.2) in Fig. 2.5 shows a significant change which is due solely to the lateraldisplacement of Pd.These observations are useful in cases where visual analysis suggests that aparticular change is needed to improve agreement between calculated and experimentalI(E) curves. Furthermore, as will be apparent in Chapters 5 and 6, the directed-searchprocedure relies solely on R-factors, but until there is a better understanding of the most480LP1tLO1tDO1tDP1t100 120 140 160 180 20040^60(0.2 0.6)(0.4 0.8)60^80^100 120 140 160 180 200(0.412)(0.6 0.8)60^80^100 120 140 160 180(0.8 1.4)160 200(0 2)33ENERGY (eV)Figure 2.5^Comparison of the effect of different types of displacement (defined in Fig.2.3) on calculated I(E) curves. 4B0 curves are FD-calculated curves for the referencestructure, while LP1 t, LO1 t, DO1 t, and DP1 t are TL-calculated curves for displacements ofmagnitude 0.10 A of type 6pd , Ao, Do, and Dpd, respectively.34appropriate R-factor to use in different contexts, it appears preferable to back an R-factoranalysis with visual comparison as well as by consistency with some general chemicalprinciples for structural results.2.4.3 Interlayer spacings and V0,Results of a third test qualify the last conclusion of Section 2.4.1. A new FDcalculation was done in which four out of the five Pd atoms in the first Pd(100) layer werevertically displaced toward the bulk, with a corresponding decrease of d12 to 1.74 A; TLcurves were also calculated by displacing the same atoms in the reference surface so thatall structural parameters in the two calculations are identical (Fig. 2.6a). When the twosets of calculated curves were compared to real experimental data, however, differentoptimized values of Vor were obtained (-10.23 eV for FD and -5.50 eV for TL), and visualinspection of the two sets of curves (Fig. 2.7a) showed similar profiles, but with asystematic shift in the energy scale of about 5 eV.Since comparison against an unknown real structure (i.e., using real data) seemsrather arbitrary, another series of tests similar to the first set of tests was done, using theFD-calculated curves as "experimental" data and allowing tensor LEED to find the "true"structure through the automated search procedure. Figure 2.6b shows that TLEED wasunable to locate the correct structure to within the experimental error limit of 0.03 A73when the search was done over all three Cartesian coordinates of the nine atoms; nor wasit able to locate the correct Vor value. Of particular concern is the fact that all atomicdisplacements were small (— 0.1 A), which suggests, in terms of the conclusions by Rous61that the calculations should have converged to the correct structure and that a newcalculation should not be needed. Clearly, this is not the case. When the search wasrestricted, however, to the vertical coordinates only (all lateral displacements being fixedat zero), the automated search procedure reproduced closely not only the correct structureacariaiaakIIPAPPIRIP(c) Vor = -9.76 eV, Bp 0.05790.110.100.111.83(b) Vor = -5.78 eV, Bp 0.1028 (d) Vor = -9.09 eV, Bp 0.0577(a) "real" structure; Vor = -10.23 eVFigure 2.6 Structural models of the type shown in Fig. 2.3 involved in tests of tensor LEED. FD-calculated curves for model (a) wereused as experimental data. The other models show results of three optimization schemes corresponding to (b) full optimization overthree Cartesian coordinates of all nine atoms; (c) optimization restricted to vertical displacements only (lateral displacements beingfixed at zero); and (d) full optimization after an initial Vor shift of -5.0 eV. Dashed lines show displacements relative to the referencestructure as indicated by solid lines.( 0 2 )1)( 1(0.4 1.8)(0.612)(0.6 1.8)36__FD^TL(0 I )80^100 120 140 180 180 200(0.412)__FD^TL( 0 1) 0 2)1)( 1(0.6 1.8)(0.412)40^60^80^100 120 140 160 180 200(b)/60^80^100 120 140 180 180 200 1.4■0•C•1._F-z>-wF-zENERGY (eV)Figure 2.7^(a) Comparison of FD- and TL-calculated curves for the assumedstructure shown in Fig. 2.6a; note the systematic shift in energy scale of about 5 eVdue to differences in the optimized V on value. (b) Comparison of FD-calculated curvesfor the model shown in Fig. 2.6a and TL-calculated curves for the optimized structureshown in Fig. 2.6c.37(Fig. 2.6c), but also the correct value for V or (-9.76 eV vs. the "true" value of -10.23 eV;Fig. 2.7b). The implication, then, is that an analysis of an unknown structure should beginby optimizing the vertical displacement of atoms (and consequently Var), with subsequentfine-turning of the structural details by allowing lateral displacements in the latter TLEEDcycles. A third test allowed displacements along all three coordinates but only after aninitial Vor shift of -5.00 eV; TLEED-optimized results are similar to those obtained fromnot allowing lateral displacements. This last test would not be useful in practice, however,since the real value of Vor is usually not known a priori. Nevertheless, it shows thatTI .F.ED can produce the essentially correct structure after only one cycle provided thatthe initial values of either V or or the interlayer spacings are not too far from the truevalues.2.4.4 Reference structure selectionA final test was performed to verify the claim that TLEED can producesuperstructure beams which are not present in the reference surface. 62 A missing-rowmodel of the Cu(110)-(2x3)-N surface was used (LBbMR in Chapter 5), where allremaining long-bridge sites were occupied by N atoms, effectively removing the "3"periodicity; relaxations in the top two layers were allowed. The optimization procedureproduced very small (< 0.05 A) displacements for Cu atoms which would effectivelyrestore the "3" periodicity in the <110> direction. Nevertheless, no intensity was obtainedfor any of the four fractional beams needed for comparison with experimental data. It willbe concluded, therefore, that while tensor LEED may be able to produce intensities insuperstructure beams for sufficiently large atomic displacements, the autosearch procedurecannot be relied upon to produce such displacements and that some care is needed inchoosing a reference structure which reflects the observed diffraction pattern.382.5 General commentsEach full dynamical calculation in Section 2.4 (as part of the TLEED programs)takes about 12800 CPU seconds on an IBM RISC/6000. With a conventional LEEDstructural search, each variation in atomic position would require almost the same amountof CPU time, such that a thorough structural search would tend to be very limited bycomputing resources and power. TLEED calculation takes only an additional 30 CPUseconds for each of the above variations, while even full optimization of the atomiccoordinates of nine atoms and Vor takes only 671 CPU seconds! For a more complicatedreal structure, e.g., an PdO(001) overlayer on Pd(100), the reference structure (FD)calculation takes about 5 CPU hours with an additional 1 CPU hour for the TLoptimization where the coordinates of 18 atoms were varied. Clearly, it would beextremely difficult to explore parameter space in sufficient detail during a trial-and-errorsearch of such a structure. This would in turn easily lead to identification of local ratherthan global minima in R-factors, and hence to incorrect conclusions (see Chapter 5 for Non Cu(110)). The power, validity, as well as the limitations of the combined tensor LEEDand automated search procedure have been assessed in relation to some model situations.Application of TLEED to two real systems will be discussed in Chapters 5 and 6.Chapter 3 : Experiment^ 393.1 UHV equipmentA modern surface science experiment requires the use of an ultrahigh vacuum(UHV) chamber, where the base pressure should be maintained in the range 10 -10 Torr orless. Although three different experimental chambers were used in this work, manyaspects are common to all chambers and will be described here. Figure 3.1 illustrates thepumping arrangement for the chamber that was used in the study of Cu(110)-(2x3)-Nsurface. UHV is achieved by a series of pumps connected to the non-magnetic stainlesssteel chamber; vacuum seals between flanges are made using copper gaskets pinchedbetween steel knife edges. Gas pressure inside the chamber and at the diffusion pump ismonitored with ionization gauges, whereas gas-line pressure is measured usingthermocouple gauges or the gauge on the small ion pump.Pump down from atmospheric pressure to UHV is done in stages:(1) A liquid nitrogen-cooled adsorption pump reduces the chamber pressure to about10-3 Torr.(2) A water-cooled, liquid nitrogen-trapped oil diffusion pump lowers the pressure toabout 10-7 Torr.(3) A sputter-ion pump is then turned on and maintained as the primary pump for thevacuum chamber. Before baking, a pressure of only about 10 -8 Torr is reached.(4) The chamber is baked at about 150°C for 12 hours or more to desorb and removegases from the chamber walls. After baking and while the chamber is still warm,all filaments used in the chamber are degassed thoroughly to avoid contaminatingthe surface during an experiment. The baking and degassing procedures arerepeated as necessary to lower the pressure to UHV range. Additionally, aSputterIon Pump200 Us DiffusionPumpTi-Getter......_ ____Variable LeakValve( LN2( H2OVacuum Chamber1BafflesOil-SealedMechanicalPumpSputterIon Pump20 Us0--LIkiSorptionPumpI IOilFigure 3.1 Schematic diagram of the pump and gas line configurationof the Varian 240 vacuum chamber used for the N/Cu experiment.41titanium sublimation pump (TSP) is available for use during degassing and normaloperations.The single-crystal sample sits inside a molybdenum sample cup, which is equippedwith a resistive heater and to which is attached a thermocouple for measuring crystaltemperature. The whole assembly is mounted on a manipulator to allow five degrees ofmovement for the sample: translation along three orthogonal directions (x,y,z), andvariation of the polar angle (0) and flip angle (iv). Gases used for cleaning and forchemisorption studies are introduced into the chamber from the gas side line through avariable leak valve. An ion-bombardment gun and the LF.FD/AES optics complete thebasic UI-1V chamber for surface study (Fig. 3.2 74).3.2 Instrumentation for LEED and AESThis work used a standard front-view LEED display system (Fig. 3.3a 74). Anelectron gun provides the incident electron beam of desired energy. Four concentrichemispherical grids located in front of the fluorescent screen work to repel inelasticallyscattered electrons, while elastically scattered electrons are accelerated onto the positivelybiased screen to form the diffraction pattern. The first of the four grids is grounded toprovide a field-free region around the sample. Linked together and biased at a negativepotential several volts below the accelerating voltage, the second and third grids act as anenergy selector. The fourth grid, grounded, isolates the positive screen potential from theretarding potential of grids 2 and 3, which in turn improves the resolution of the gridsystem, especially when it is being used as an energy analyzer for Auger electronspectroscopy.75TitaniumSublimationPumpWater CoolingManipulatorWindowThermocoupleSampleIon GunLeak Valve42Ion PumpFigure 3.2 Schematic diagram of the UHV chamber used in the N/Cu study;Ref. 74.GunExtractorFilamentcn^ ==0 racted Beam.§ 815 u.o7:-.^ \^ ,.CD ■■•••. ..."..CI .............. ••••=-1....[ M.CAFreq.Doublersin2cot si r(a) , .....,or o• ....0;,..*'......110"Fluorescent ScreenGrids43Sample(b)Scope< CD \ \ No.Figure 3.3 Schematic diagram showing the (a) LEED and (b) AES optics setupused in the N/Cu study; Ref. 74.C.M.A.GLANCING ANGLEELECTRON GUNw• ..."••PROGRAMMABLECRAMP)POWER SUPPLY^GEN.iVmsin onB•••••11•00.44^I—0SIGNALGEN.e - MULTIPLIERI ^N( PRE. ,_.i.LOCK-IN^iAMP^AMP.CSCOPE-. p X-YPLOTTER)Figure 3.4 The CMA setup used in the 0/Ni experiment; after Ref. 77.45The four-grid optics can also serve as the retarding-field analyzer (RFA) for AES,and the same gun used for LEED provides the primary electron beam with energy around2 keV (Fig. 3.3b74). In Auger mode, the retarding potential on the repeller grids (2 and 3)is modulated about the ramp voltage Vr and the spectrum is recorded in dN(E)/dE vs. Eformat in order to extract the Auger peaks from the background. Besides its obviousconvenience, the RFA system suffers from a number of disadvantages. It cannot be usedto study many kinetic processes occurring on the surface because of the relatively longtime required to obtain a full spectrum (several minutes). The large primary beam currentneeded (40 1.1,A in the current study) leads to heating of the surface, and care is needed toensure that the nature of the adsorbed layer is not significantly changed. Poor signal-to-noise ratio also makes difficult the detection of small impurity Auger peaks frombackground noise.The cylindrical mirror analyzer (CMA), introduced by Palmberg et al.,76 hasgreatly improved signal-to-noise characteristics compared with the RFA. Figure 3 .477shows the CMA set up for the Ni(111)-(2x2)-0 study. A glancing incidence electron gunenhances the Auger yield from the topmost atomic layer relative to that of the substrate. 75Emitted electrons enter the analyzer and are deflected by a potential V a applied betweentwo coaxial cylindrical electrodes. Only electrons with kinetic energy eV e will passthrough the exit slit and arrive at the collector. A small modulating voltage V msuperimposed on Va yields the dN(E)/dE vs. E spectrum, which can be recorded fastenough to be displayed on an oscilloscope. For the CMA, the relative resolution (AE/E) isconstant at all energies so that the resolution (AE) and consequently the sensitivity aregreater at high energies than low; by contrast, AE of the RFA is constant with energy for aconstant modulating voltage so that the sensitivity is greater at low energies than high. Infavourable cases, the sensitivity of a CMA can get down to around 0.1% of a monolayerof impurity and is generally an order of magnitude better than for the RFA.463.3 Sample preparation and cleaningSamples used in these studies were thin discs cut from single-crystal rods. LaueX-ray diffraction was used to orient the rods, and cutting by spark erosion exposed asurface of desired crystallographic plane (e.g., the (111) plane). Initial surface polishingwas done with a planetary lapping system with progressively finer grades of diamond paste(from 9 to 3 pm), while final polishing was done by hand with either 0.05 pm alumina or 1pm diamond paste on a deer skin-covered, flat glass plate. After polishing, optical facealignment was checked with a He/Ne laser (Fig. 3.5), and X-ray diffraction was again usedto ensure that the desired crystallographic plane and the optical face are parallel to eachother (to within 0.5°).For the purpose of LEED crystallography, the single-crystal surface must be cleanand well ordered. The sample was first degreased with trichloroethylene, acetone, andmethanol and rinsed with distilled water. Once inside the UHV chamber, surfaceimpurities were removed by Al .+ bombardment. Subsequent annealing induced surfaceordering as well as surface segregation of bulk impurities. Cycles of Al .+ bombardmentfollowed by annealing were repeated until AES indicated no impurity signals and LEEDshowed a sharp (1 x 1) pattern. After each chemisorption experiment, the clean, well-ordered surface was recovered by a shorter period of ion bombardment and annealing.3.4 LEED intensity measurement using the video LEED analyser (VLA)Experimental I(E) curves in the current study were measured at normal incidencewith a commercial VLA, 78 shown schematically in Fig. 3.6. A silicon-intensified TVcamera placed in front of the viewing window allowed the diffraction pattern to bedisplayed on a monitor. The camera defined the viewing area as a 256x256-pixel frameand recorded the intensity of each diffracted beam by summing the digitized intensitiesIIni 1thin-hole brass standscrystallographic i_0viI opticalplane^i plane//rsampleRHe / NelaserFigure 3.5 Schematic diagram showing He/Ne laser alignment of crystallographic and optical planesof the single-crystal sample. For large R, A (rads) = r/2R.TV monitor Video ND converterinterfaceISIT TVcameralenssampleLEEDunMain frameVideo signal^.*^Scope D/A converter LEEDMotorola interface controller^h_6800X-Y plotterTerminal Floppy disks ^[ModemFigure 3.6 Block diagram of the Video LEED analyser (VLA) for collecting LEED intensity data.49inside a 10x10-pixel window, which completely covered the spot and which automaticallytracked the moving spots as the incident electron energy was varied by a microcomputerunit. Theoretically, up to 49 beams can be measured at the same time, but typically onlyup to eight symmetry-equivalent beams were measured in one pass. Two or three passeswere made for each set of beams to improve the signal-to-noise ratio. In addition, it wasnecessary to use different gain level settings for integral-order and fractional-order beams,as the latter were often much weaker than the former.Measurement of LEED intensities in this work was made at normal incidence, andfixing of the direction was done by comparing spectra of symmetrically equivalent beams.At normal incidence, the LEED pattern has the highest rotational symmetry that oftencorresponds to the rotational symmetry of the substrate (see Section 1.2.2 for a discussionof rotationally related domains). The sample orientation was adjusted until the measuredI(E) curves reflected this symmetry.Further treatment of the experimental data was needed before they can be used in astructural analysis. First, raw intensities were normalized to constant incident beamcurrent (the experimental beam current increases linearly from low energy to about 100eV, at which point it becomes constant at approximately 1 pA). Second, symmetricallydegenerate beams were averaged together to minimize experimental errors such as slightmisalignment of the surface away from normal incidence. 79 Finally, the average I(E)curves were smoothed to reduce noise which would adversely affect the R-factoranalysis.44 In some cases, a correction for background intensity was also made, and datafrom different experiments can also be averaged together to reduce statistical error.Figure 3.7 illustrates these procedures as applied to the treatment of experimental data forthe N/Cu system.500.■Czwz(b)(2/3 1/2)(2/3 -1/2)avg .smoothexpt. #1expt. #2expt.(a)^I ^I^I40^60^80^100 120ENERGY (eV)I^I^1^40 60 80^100 120Figure 3.7 Treatment of LEED experimental data for use in the structuralanalysis of the Cu(110)-(2x3)-N surface. (a) Symmetrically equivalent beamsfrom one experiment are averaged and smoothed. (b) Data from differentexperiments are averaged to reduce statistical error.Chapter 4 : Ni(111)-(2x2)-O^514.1 IntroductionThe first structural analysis for the Ni(111)-(2x2)-0 surface, which was a LEEDstudy by Marcus et a/.,8° identified that the 0 atoms chemisorb at 3-coordinate hollowsites in the close-packed nickel surface, but that work was unable to make a choicebetween the two types of hollow site. Indeed, neither of the later studies on this surface,by high-energy ion scattering (HEIS) 81 and surface-enhanced electron energy loss finestructure82, clarified further the details of the adsorbate layer, although these analyses didsuggest that there are significant 0-induced relaxations in the metal structure. Forexample, Narusawa et a1.81 reported with HEIS that three quarters of the Ni atoms in thetop layer are relaxed outward by about 0.15 A in a direction perpendicular to the surface.Displacements of this magnitude could have significantly affected the results of the 1975LEED analysis. 8° Also, the structural parameters deduced by Marcus et al. 8° correspondto a O-Ni bond length of 1.88 A, which is somewhat longer than the prediction of 1.82A83 made with a bond length-bond order relation deduced for related bulk structures.These observations suggested the need for a new LEED crystallographic analysis for theNi(111)-(2x2)-0 surface structure.84 Furthermore, at the time this work was done, it wasby no means clear to what degree LEED could reliably identify relaxations in metalsurfaces induced by chemisorbed species. Such topics provide the subject of this chapter.4.2 ExperimentThis project used LEED intensity data measured by Y.K. Wu, 85 and the details forthese measurements are outlined here. The starting point was the preparation of a clean,well-ordered Ni(111) surface as characterized by the cylindrical mirror analyzer showingno detectable Auger signals for impurity elements (Fig. 4.1 a) as well as by LEED showing(a)52•0^0• 0^•(b) O 0^0(-1.1)• o0o^•o o^0^ao (-1 0) •^o^0 (01)^oo o^a^a• o^(0 0) •^a (1/2 1/2) ao o^a^ao (0 -1) •^o^0 (10)^oo o^0^a• o^•(1 -1)O 0^0• o^•O 0•Figure 4.1^(a) Auger spectra for clean Ni(111) and Ni(111)-(2x2)-0 taken with the CMA setup in Fig.3.4. (b) Schematic diagram of the (2x2) LEED pattern. Solid and hollow dots correspond respectively tointegral and fractional beams, and boxes indicate one beam from each symmetrically equivalent set forwhich I(E) curves were measured.00•53a sharp (1x1) pattern. 86 Such a surface at room temperature was exposed to 0 2 gas atabout 1 x 10 -8 Torr,87 and I(E) curves were then measured at normal incidence for optimalsharpness of the (2x2) LEED pattern for the three integral and seven fractional beamsdesignated88 (Fig. 4.1b)(1 0), (0 1), (1 1), (1/2 0), (0 1/2), (1/2 1/2), (1 1/2), (1/2 1), (3/2 0), and (0 3/2).Intensity measurements were made with the VLA over a total energy range of about 1300eV.4.3 CalculationThe LEED multiple-scattering analysis for this system followed proceduresoutlined in Chapter 1 . The atomic potential in the substrate was characterized by phaseshifts up to 2 = 7 derived from a band structure calculation for nicke1, 89 and the real part ofthe constant potential (V() between all muffin-tin spheres was initially set at -7.2 eV.However, values of V or were effectively refined for each structural model during thecomparisons of the experimental and calculated I(E) curves, which were done bothvisually and with the LEED reliability indices Rmzj and R. The oxygen phase shifts werethose derived by Marcus et al. 80 from a superposition of charge densities model, and theimaginary part of the constant potential between all atomic spheres was equated to -0.9E l/3 eV (where E is the electron energy in eV). The Debye temperatures for nickel andoxygen were taken as 440 and 843 K, respectively. 80 Diffraction matrices for the relaxedtopmost nickel layer were calculated using the combined-space method, layer stackingbeing done with RFS routines.544.4 Structural analysisThe first part of the analysis aimed to determine the adsorption site, where allstructural parameters except the the oxygen-to-nickel top layer spacing (d 01 ) were fixed atbulk values. Three possibilities with 0 atoms chemisorbed in 3-coordinate hollow siteswere considered (Fig. 4.2a). The first two are represented as (C)ABC... and (B)ABC...,where 0 is identified by its registry in brackets with respect to the Ni layers; these twocases correspond respectively to 0 chemisorbed in "expected" 3f sites (which continue thefcc ABC... packing arrangement) and 0 chemisorbed in the alternative 3h sites whichcorrespond to the hcp stacking arrangement for the 0 and top two Ni layers. Alsoconsidered was a "graphitic" 0 layer which corresponds to (B+C)ABC..., and is thestructure proposed by Joebst1 9° for the Pt(111)-(2x2)-0 surface. Based on results fromother techniques for the Ni(111)-(2x2)-0 surface,91-95 no calculation was done for anymodel where oxygen dissolved into the substrate to form an underlayer, although thatcould be expected at higher coverages and/or temperatures when a surface oxidefor/m.91,92,96,97 Nor was any model tested where three rotationally related (2x1) domainsgive rise to the observed (2x2) pattern: the measured 92 oxygen coverage for the (2x2)surface is 00 = 0.25 ML, whereas that of a (2x1) structure is 0 0 = 0.50 ML. Theexistence of a higher coverage (0 0 = 0.33 ML) Ni(111)-03 x A/3)R30°-0 surface alsoprecludes a (2x1) model of the (2x2) surface.Visual analysis indicates clearly that the "expected" (C)ABC... model gives thebest fit with experiment; Figure 4.2b compares the experimental and calculated I(E) curvesfor these three basic model types. Furthermore, R-factor analyses arrive at consistent andbetter results for the 3f model compared with the 3h model: for the former, both R p(0.2326) and RAJ (0.2184) indicate an optimal value of dm . = 1.10 A, whereas twodifferent values were obtained for the latter (RP = 0.3026 for dol . = 1.30 A; Rmzj = 0.2383for dol . = 1.50 A). The best correspondence at this stage is still quite mediocre, consistent0° 0 0° 0 0 ®O® 0 ®Oe160 '180 200 220 240i100 120 140(b) ENERGY (eV)CI)zwF-z40 60 80 100 120 140I40 60 80 100 3f 3hCO."411000111040•ITTOP VIEWSIDE VIEWIJ3fh55(a)Figure 4.2 (a) Schematic diagram of the three basic models considered in the adsorption-sitedetermination for the Ni(111)-(2x2)-0 surface. (b) Comparison of experimental (dashed curves)and calculated I(E) curves for the models illustrated in (a).bulkd1256Arad^trotArad or trotFigure 4.3 Schematic diagram illustrating the types of metalrelaxations considered for the Ni(111)-(2x2)-0 surface.Positive displacements are indicated.57with observations from the earlier history of LEED crystallography that chemisorbed 0often did not immediately give as good a correspondence between experimental andcalculated I(E) curves as, for example, could be obtained with chemisorbed S. Since thiswas the situation on Ni(111), it was important to establish the reasons, and in particular toestablish whether the LEED method as used was limited in its scope for oxygenchemisorption, or whether the basic geometrical structure had simply not been fullyrefined.Figure 4.3 defines the structural parameters included in the refined analysis for theNi(111)-(2x2)-0 surface structure. A positive value of D 1 , 1 indicates a verticaldisplacement toward oxygen of those Ni atoms which are bonded to 0. Additionally, twotypes of lateral displacement were considered for the topmost Ni layer. That whichcorresponds to a radial displacement is designated A rad, while the twisted or rotateddisplacement is designated Arm. Table 4.1 summarizes the ranges of values considered foreach structural parameter, although the ranges were effectively reduced as theoptimization procedure developed; also tabulated are optimal values and thecorresponding Ray . The second-to-third interlayer spacing for nickel, and all below, werefixed throughout at the bulk value (2.03 A).The first part of this refined study emphasized Arad rather than Ardr for the lateraldisplacement, and indeed it was soon apparent that inclusion of both vertical and lateralrelaxations in the top layer of Ni were needed in the calculations in order to improveagreement between calculated and experimental I(E) curves. Figure 4.4 comparescalculated intensity curves for lateral and no vertical relaxation (Arad = 0.10 A, D 1 . 1 = 0.0,curves marked (c)), for vertical and no lateral relaxation (A rad = 0.0, D 1 , 1 = 0.10 A, curvesmarked (d)), and for vertical and lateral relaxation (Arad = 0.10 A, D 1 , 1 = 0.10 A, curvesmarked (e)). It was found that the correspondence with experiment improved on averagealong the progression of curves marked (c), (d), and (e) in Fig. 4.4, although problems doTable 4.1^Ranges of relaxation parameters considered for model (C)ABC... are given, along with optimized values;increment sizes are in parentheses, and ranges were reduced as the structural search progressed.D1,1 (A) dm, (A) d12 (A) Arad (A) Vor (eV) RayRange -0.10 (0.10) 0.20 0.90 (0.10) 1.35 1.90 (0.04) 2.14 -0.10 (0.05) 0.15 -13.2 (2.0) -1.2Optimal 0.12 A 1.10A 1.96A 0.09 A -6.8 eV 0.1560Dri (A) dol. (A) du (A) 4,4 (A) Vor (eV) RayRange^-0.20 (0.10) 0.20 1.08 (0.02) 1.14 1.94 (0.04) 2.14 0 (0.05) 0.15 -13.2 (2.0) -1.2Optimal^0.12 A 1.09 A 1.95 A 0.07 A -7.8 eV 0.1219I^1^1^10 40 80 120 160 200 80 120 160 200^12059Figure 4.4 Comparison^ofexperimental (dashed) withcalculated (solid) 1(E) curves(structural parameters arespecified in Fig. 4.3). Thosemarked (a) and (b) are formodels (B)ABC... and (C)ABC...,respectively, with no metalrelaxation and dol . = 1.10 A, d12= 2.03 A. The set of curvesmarked (c) (4,„ = 0.10 A, D1.1 =0.00 A), (d) = 0.00 A, Dr, =0.10 A), (e) (pm = 0.10 A Dv, =0.10 A), (f) (4„ = 0.10 A, D1 .,0.10 A) correspond to therelaxed model with do,. = 1.11 A,d,2 = 1.98 A. Calculated curvesmarked (g) give the bestagreement with experiment; withstructural parameters dor = 1.09A, du r: 1.96 A, Dr, = 0.12 A, 4,= 0.07 A.120 160 200 240 100 140 fli 2ENERGY (eV) 60I^11111160^100 140 180i^i 160 200 240 40 i 80^1^1 120 160 40^80^120ENERGY (eV)61still remain (e.g., for the (0 3/2) beam) and that suggested the need to try the other type oflateral displacement. The curves marked (f) in Fig. 4.4 are for A ra = 0.10 A and D 1 , 1 =0.10 A. This change had a negligible effect on the integral beams, while thecorrespondence with experiment for most of the fractional beams (except (3/2 0)) wasimproved.The average of the two R-factors mentioned above, namely R ay = 1/2 (Rmzj + Rp),was used for a full optimization of the structural parameters with the rotated lateralrelaxation in the topmost Ni layer. The best correspondence between the experimentaland calculated intensity curves was then obtained with the values d 01 . = 1.09 A, D I . = 0.12A , d12 = 1 .95 A , Arot = 0.07 A (the optimal value of Vor is -7.8 eV, and the values of RMZJand R, are 0.1087 and 0.1326, respectively); the uncertainty in these structural values isestimated at 0.03 A (the amount by which visual observation suggests the correspondencehas deteriorated, even if only slightly). Calculated I(E) curves corresponding to theseoptimal structural values are shown in Fig. 4.4, curves (g). In this structure, the topmostclose-packed layer of Ni distorts appreciably: specifically, those Ni atoms which neighbouran 0 atom relax in a way to emphasize the formation of a local Ni 30 cluster. The 0-Nibond length of 1.83 A agrees closely with the value (1.82 A) predicted by a relation whichrelates 0-Ni bond lengths to 0 coordination numbers in solid structures; 83 interestingly,the same predictive model suggests an 0-Ni bond length of 1.93 A for 0 chemisorbed onthe (100) surface of nickel, again very close to the latest experimental value of 1.92 A.98The radial relaxation, vertical relaxation, and radial combined with verticalrelaxation parameters were also applied to the (B)ABC... model. The match betweenexperimental and calculated I(E) curves, as observed visually and indicated by R-factoranalyses, was decreased when relaxation parameters were included. This is in constrast tothe improvements observed for the (C)ABC... relaxed models, and further supports thelatter as the correct structure of the Ni(111)-(2x2)-0 surface.62The finding here of a vertical relaxation (D 1 . 1 ) in the top Ni(111) layer of about0.12 A agrees to within the stated uncertainty with the value reported earlier by HEIS, 81although this latter technique did not identify the specific adsorption site. This relaxationcan be understood qualitatively by the strong bonding between the three Ni atoms and 0,and a consequent reduction in bonding between these Ni atoms and their other neighbours(including those below in the second layer). Previous works 81,82 did not detect, however,displacement toward the bulk of the non-oxygen-bonded Ni atoms, resulting in acontracted interlayer spacing of d 12 = 1.96 A. The net effect of the two displacements isto give for the center-of-mass distance between first and second Ni layers a value of 2.05A, which is only slightly greater than the bulk value of 2.03 A.The lateral relaxation of about 0.07 A had not been reported before in this context.At least two factors are involved in determining the direction of the lateral displacement.First, Ni atoms which are bonded to 0 will have partial positive charges due to the polarnature of the bonds to 0, and increased electrostatic repulsion between the three Ni atomswill lead to an expansion of the adsorption site. The second factor is related to the idealtendency for 0 to have bond angles near or greater than 90°, 99 and expansion of theadsorption site acts to increase the Ni-O-Ni bond angle. The Ni-O-Ni bond angle for theoptimal structure in this study is 88.3°, compared with an angle of 86.9° for the non-relaxed model.Lateral expansion of each occupied adsorption site is accompanied by contractionof an adjacent unoccupied site, associated with which is an energy penalty that increases asthe minimum Ni-Ni distance decreases. With the radial type of lateral displacement,groups of neighboring Ni atoms move directly toward one another, and for a givenmagnitude of displacement, the minimum Ni-Ni distance is shorter than with the rotated or"twisted" type of displacement. Thus, the energetics for A mt should be more favourablethan for Arad , an observation which is consistent with the results of this study. The63distortions found here in the topmost Ni layer can be expected to cause some furtherdisturbances in the second layer, and detailed considerations of such features may help toreduce the remaining discrepancies between the experimental and calculated I(E) curves.Nevertheless, 0-induced metal relaxations observed in here have been further confirmedby a more recent work using SEXAFS. 100Structural details of the (2x2) surface can also be compared to those subsequentlymeasured for the Ni(111)-(43 x 13)R30°-0 surface formed at higher oxygen coverage.LEED analysis of the latter -101 revealed no lateral relaxation, while a vertical buckling ofthe topmost layer was precluded by symmetry. A very slight uniform expansion of thetopmost nickel layer spacing (2.05 A), was observed, however, with an optimal second-to-third layer spacing (2.02 A) at essentially at bulk value. These spacings are comparable tothose from the current work, when the center-of-mass distance is used, and in addition,the oxygen height above its nearest nickel neighbours (on 3f sites) are the same in bothstudies, resulting in similar O-Ni bond lengths (d 01  = 1.08 A and bo_Ni = 1.80 A for the 13surface). Since phase diagram measurements as well as Monte Carlo simulations 102 havepredicted a restructuring during the p(2x2) (q3 x .q3)R30° phase transition, perhaps itis not surprising that the former is reconstructed while the latter is not. Furthermore,oxygen coverage on the -V3 surface (00 = 0.33 ML) is higher than that on the (2x2)surface, and in the limit of a monolayer coverage, no metal relaxation can be expected(other than a uniform metal interlayer spacing expansion).4.5 Comments on Ni(111)-(2x2)-SIn light of these results for the Ni(111)-(2x2)-0 system, it seemed appropriate toreanalyze the corresponding sulfur-nickel system since the correspondence betweencalculated and measured LEED intensities is now at a higher level for chemisorbed 0 than64for chemisorbed S, an observation contrary to that of earlier experience. A previousLEED study of the Ni(111)-(2x2)-S surfacelo reported a very small non-rotated lateralrelaxation of 0.03 A in the top Ni layer, accompanied by a uniform vertical expansion ofboth the first and second metallic layers. Second layer expansion has been questioned,however, since the commonly observed trend 104 is a contraction of second-to-thirdinterlayer spacing when the first-to-second spacing is expanded.Therefore, new models containing rotated lateral relaxation were tried. Some ofthese models included either uniform vertical expansion or contraction, or 3/4 MLexpansion or contraction, of the top metal layer. Unlike the 0-Ni system, calculated I(E)curves for these models for the S-Ni system did not change significantly as differentstructural parameters were varied by small amounts. Furthermore, results for the S-Nisystem indicate uniform rather than 3/4 ML expansion and non-rotated rather than rotatedlateral expansion. This is consistent with the previous report. 103In a further attempt to improve agreement between experiment and theory, modelswhich included hydrogen were considered. Coadsorption of hydrogen and sulfur fromhydrogen sulfide on Ni(111) at room temperature has been reported from a SIMSstudy.lo Thus, calculations were performed to stack a graphitic overlayer consisting ofone hydrogen and one sulfur per (2x2) unit mesh on a bulk-like Ni(111) surface. Sulfursits on the 3f site as before, and hydrogen sits on the adjacent 3h site. Rp is slightly lowerfor this structure (0.19) than for the corresponding structure without hydrogen (0.20), butas expected, calculated I(E) curves have not changed much visually, and the problembeams appear unaffected by the addition of hydrogen to the surface. Models in which ahydrogen remains bonded to the sulfur which is in turn chemisorbed onto the Ni(111)surface gave the same Rp as without hydrogen. Unlike the graphitic-overlayer model,however, the intensities of some of the peaks have changed enough to be discernible.654.6 SummaryEven with these new considerations, little progress was achieved with the S-Nisystem. The reported model 103 remains the best reached thus far, if the only criterion isthe lowest overall R-value. The fact that there was a decrease in agreement for five of theten beams in the relaxed model, however, is a problem that needs to be addressed. It ispossible that this problem can be solved by incorporating hydrogen into the bulk, ratherthan on the surface. Perhaps such a model can also explain why there is a uniform verticalexpansion of the substrate surface layers for the H 25 on Ni case, whereas 0 on Ni shows adifferential vertical expansion of the top Ni layer.The bonding geometry of chalcogen overlayers on Ni(111) has previously beendiscussed in terms of Ni3X clusters, where X is a member of the chalcogen family.106 Thismodel is perhaps most markedly illustrated in the case of 0 on Ni, where the interactionbetween oxygen and Ni atoms is so strong as to cause a lattice expansion of 3/4 ML of thetop Ni layer with a lateral displacement to increase the Ni-O-Ni bonding angle. Thus, thiswork not only has helped to increase knowledge of the structure of the Ni(111)-(2x2)-0surface, but also has confirmed the ability of conventional LEED methods to refinestructural details for 0 chemisorption on metal surfaces when sufficiently exhaustivestructural searches are undertaken in the calculations.Chapter 5 : Cu(110)-(2x3)-N^665.1^IntroductionChemisorption of activated nitrogen on to the (110) surface of copper yields asurface of (2x3) translational symmetry which shows high stability. 107-116 Such a surfacehas also been observed on the fcc(110) surface in other contexts including nitrogen onNi(110), 117-119 hydrogen on Ni(110) 120 and sulphur on Pd(110) 121 ; moreover, facets whichform on Cu(210) and Ni(210) under N chemisorption have also been interpreted ascorresponding to (110)-(2x3) surfaces. 122 Since the Cu(110)-(2x3)-N surface appearssignificant in the development of surface structural principles, both because of its highstability and its unestablished structure, the present work attempted to identify structuraldetails for it and provide some satisfactory explanation of the specific translationalsymmetry.Despite the large number of techniques 1 °7-116 which have been used to study thissurface, no consensus exists as to the correct structure of the Cu(110)-(2x3)-N surface.Studies using HREELS 107 and XPS 112 concluded that N atoms occupy only one type ofadsorption site, and that is the long-bridge site. 107 In addition, XPS data suggested thatthe nitrogen coverage ON = 2/3 ML (where 1 ML corresponds to 6 N atoms per (2x3) unitmesh), whereas Auger measurements from a different work 113 gave a value of ON < 1/4ML. Two separate low-energy ion scattering studies (LEIS 108 and NICISS 113) arrived atcompletely contrary structural models of the (2x3) surface, although each of theseconclusions have received support from other techniques. Specifically, with photoelectrondiffraction, 10 Ashwin, Robinson and coworkers proposed a pseudo-(100) reconstructionwhere the overlayer has four rows of copper atoms for every three on the clean surface inthe <110> direction; with STM images, 114 Spitzl et al. concluded that every third <110>row is missing so that the copper density in the topmost layer (O cu) is 2/3 that of the clean67surface. The most recent technique to be applied is X-ray reflectivity, which indicated that°Cu = 4/3, 116 supporting the (100)-reconstruction model of Ashwin et al.An initial conventional LEED crystallographic analysis (this work) suggested yetanother model, where every other <001> row is missing in the topmost layer (ecu =1/2), 115 but tensor LEED currently favours the pseudo-(100) model over that ofconventional LEED. Results from each analysis will be discussed separately in thischapter, along with summarizing remarks on the difference in conclusions between the twostudies.5.2 ExperimentThe UHV chamber is as described in Chapter 3. The Cu(110) sample was cutfrom a high-purity single-crystal rod 123 and cleaned under UHV by cycles of Al .+bombardment and annealing at 820 K. These cycles were repeated until the retarding fieldanalyzer showed no detectable Auger signal for impurity elements and LEED showed asharp (1x1) pattern.Such a cleaned and ordered surface was exposed at room temperature to (5-9) x10-5 Torr nitrogen activated by the ion gun for glancing incidence at 200, 350, or 500 eVfor varying lengths of time. The lowest dose which gave a sharp (2x3) pattern, afterannealing at 610-650 K, was 5 minutes at 200 eV and 2 1.1A at the surface (correspondingto 600 11C), and the highest was 20 minutes at 500 eV and 1 pA (corresponding to 1200ptC). These surfaces were stable over a period of some weeks at 4 x 10 -10 Torr vacuum.The (2x3) LEED pattern remained even when the surface was kept for several days atabout 10 -6 Torr, although it became less sharp and additional annealing did not improvethe pattern.68I(E) curves were measured at normal incidence for optimal sharpness of the (2x3)LEED pattern for five integral and four fractional beams designated(1 0), (0 1), (1 1), (2 0), (2 1), (2/3 1/2), (4/3 1/2), (4/3 1), and (5/3 1),using the beam notation indicated in Fig. 5.1. Intensity measurements were made at allthree activation energies over a total energy range of about 920 eV for each. Comparisonof experimental I(E) curves showed no significant differences among the three sets of data(Fig. 5.2), and the analysis was done using the averaged set of I(E) curves.5.3 CalculationThe combined-space formalism was used to calculate diffraction matrices for up tofour atomic layers, with N atoms being included in the topmost Cu layer. Layer stackingwas accomplished with either the layer doubling (conventional LEED) or RFS method(conventional and tensor LEED). Atomic potential in the substrate was characterized byphase shifts up to e = 7 derived from a band-structure calculation for copper, 124 whereasnitrogen phase shifts were those derived by Imbihl et a/. 125 from a superposition of free-atom potentials. Vor was initially set at -7.0, -10.0, or -12.0 eV, depending on the modeltype, and Vol was fixed throughout at -5.0 eV. Debye temperatures for copper andnitrogen were taken as 343 126 and 731 K, respectively; the latter was chosen to give aconstant root-mean-square vibrational amplitude for all atoms. 127Refined values of Vor were obtained during R-factor comparison of calculated andexperimental intensity curves, which was also done visually. Special care was taken in thetensor LEED analysis to ensure consistency between visually observed changes andchanges in individual beam R-factors. The average LEED reliability index Ray = 1/2 (Rmzj+ R, ) was used to assess overall agreement between experiment and theory.a (2 O)Cu (60)...^ .^ - -_  clean Cu(110)^CO,,^ , :T:777 j7 ,^, _ •^•=(21) -^(-21) • 0 0 • 0 0 aO 0 0 0 0 0 0 0 0 0 0D(DO)fa co •0 o•oo•oopooO 0 0 0 0 0 0 0 0 0 0 0 0-1 )(-2 -1) • 0 0 • 0 0 • 0 0 • 0 0 • a-1)•^..100 — 200c^I 300^400^500^6001^1^1700 800 900 -ENERGY (eV)Cu (105)--- N(381)Cu(110)-(2x3)-N69Figure 5.1 Auger spectra for the clean Cu(110) and Cu(110)-(2x3)-N surfaces taken with aCMA; two consecutive scans were made for the clean surface, whereas the scans for the (2x3)surface were made for two different experiments. The inset gives a schematic diagram of the (2x3)LEED pattern. Solid and hollow dots correspond respectively to integral and fractional beams, andboxes indicate one beam from each symmetry-equivalent set for which I(E) curves weremeasured.0 1) (4/3 1 )60 80 100 120(4/3 1/2)50^100^150^200^250^50 60 70 80 90100110200 eV350 eV500 eVavg70ENERGY (eV)Figure 5.2 A comparison of I(E) curves measured for the Cu(110)-(2x3)-N surfacewith N activated at 200, 350, and 500 eV. The average of the three experimentaldata sets was used in the comparison with theoretically calculated curves.71<1 To>^(b) (c)<00 1>Figure 5.3 (a) The bulk structure of Cu 3N; (b) the ideal Cu 3N(110) surface; and(c) the ideal Cu3N(100) surface. Small circles represent N atoms, while largecircles represent Cu atoms. Shading indicate atoms belonging to the same layer.72The bulk structure of Cu3N128 served as a guide for estimating the chemicalreasonableness of a particular model. In Cu3N (Fig. 5.3), each nitrogen atom bondsoctahedra)/ to six copper atoms with a bond length of 1.91 A, but a shorter N-Cu bondlength would be expected on a surface where the nitrogen atom bonds to fewer Cu atoms.Specific estimates can be made from bond length-bond order considerations, such asthrough Equation (5.1), deduced from bulk structural information. 83,129 Equation (5.1)relates the bond length of a bond of order s to the single bond length b 1 bybs = b 1 - 0.85 log s^ (5.1)For n non-equivalent bonds, there will be n different bond orders whose total s 1 + s2 +...+sn = valency v, insofar as the adsorbate species alone determines the total bondingcapacity. If all n bonds are equivalent, s = v/n. For nitrogen, v = 3, and b 1 = 1.65 A whenN is bonding to three Cu atoms. An average bond length value of 1.76 A would beexpected for four-coordinate nitrogen, which would occur, for example, when Nchemisorbs on long-bridge sites on the Cu(110) surface, or when N is held substantiallyabove its nearest copper neighbours on the (100)-reconstructed surface. In the latter case,a fifth bond can form between nitrogen and second layer Cu atoms when N is nearlycoplanar to the reconstructed layer; the average predicted bond length is then 1.84 A.Table 5.1 lists the names of all the models considered, along with the figures in which theyare illustrated, and calculational details will be given in the next two sections.73Table 5.1 General notation used to name structural models of the Cu(110)-(2x3)-Nsurface in terms of the chemisorption sites and types of reconstruction. Also tabulated aremodel names, the figures (and page numbers) where the models are defined, and thesection under which they are discussed. Models in bold are not defined in figures, but aredescribed in the text (on the page noted) and are related to those for which there areschematic diagrams.Type of site Type of reconstruction Variations of basic modelLB = long bridgeHOL = hollowU (ULB) = underlayer, "long bridge"MA = missing atomMR = missing row100 = pseudo-(100)a, b, c, ', A, B, C, D, E, F, GAnalysis Figures and Tables Model namesCom LEED, I;§ 5.4.1Fig. 5.4 (p. 75)Table 5.2 (p. 76)LBa ----) LBe, HOLa, HOLc, LBaMA --> LBcMA, LBaMR,LBbMR, LBaMR', LB2a, LB2b, LBM2R, ULBa (p. 78),ULBbMR, ULBbMR', 10002X2, PS100, PS100X2Cony. LEED, II;§ 5.4.2Fig. 5.6 (p. 81)Table 5.3 (p. 82)10002X2, 100A -4 100E, LBbMRTensor LEED; § 5.5.1 Fig. 5.4 (p.75) LBaMR', LB2a, LB2a' (p. 83)aTensor LEED; § 5.5.2 Fig. 5.7 (p. 87), Fig. 5.8(p.88),Table 5.4 (p. 91),Fig. 5.4 (p.75)LBbMR, MRa, UMR, UMRa (p. 84)b, ULBbMRTensor LEED; § 5.5.3 Fig. 5.7 (p. 87), Fig. 5.8(p.89),Table 5.5 (p. 92)10002X2, 100F, 100G, 100S1, 100S2Tensor LEED; § 5.5.4 Fig. 5.7 (p. 87), Fig. 5.8(p.89), Table 5.6 (p. 100)100G, UMRa (p. 84)b(a) LB2a' is the same as LB2a, except N atoms occupy all LB sites exposed by the missing row.(b) UMRa is the same as the <001>-missing row model illustrated in Fig. 5.7, except that the overlayer contains only 2 Natoms (labelled N 1 ) per (2x3) unit mesh.745.4 Structural analysis, I: conventional LEED5.4.1 Initial comparison of 25 modelsConventional LEED analysis of the Cu(110)-(2x3)-N surface was done in twoseparate stages. In the first study, 25 structurally distinct models were tested (Fig. 5.4).These cover a variety of local environment, with nitrogen coverage ranging from 1/6 to2/3 ML. Simple overlayer models include nitrogen chemisorption on long-bridge (LB)sites at 1/6 ML (LBa), 1/3 ML (LBb), 1/2 ML (LBc), and 2/3 ML (LBd, LBe) andnitrogen chemisorption on hollow (HOL) sites at 1/6 ML (HOLa) and 1/2 ML (HOLc).Multiple scattering calculations were done for these models with variations in the nitrogenheight relative to the top Cu layer and the first-to-second Cu interlayer spacing.Comparisons made with the experimental I(E) curves lead to the following conclusions:(1) Both visual and R-factor analyses show that LB models give a better account ofthe experimental I(E) curves than the HOL models. This appears to support theHREELS result 1 °7 that nitrogen chemisorbs on long-bridge sites.(2) The simple adsorption models seem unlikely to be correct. Reasonable agreementbetween experimental and calculated I(E) curves from simple LB-type modelscould be achieved only for integral beams, but not for fractional-order beams (e.g.,curves for LBd in Fig. 5.5).(3 )^In each simple adsorption model, Ray was greater than 0.280 at the geometrywhich minimized Ray. On visual analysis, none of these models showed a sufficientmatch between experimental and calculated I(E) curves to warrant consideringthem further.•.to*AOLuTable 5.2^Ranges of structural parameters considered for those models for which I(E) curves are provided in Fig. 5.5.Included are increment sizes (in parentheses) and optimal values.Model.^_Vertical parameters (A) Lateral parameters (A)Vor (eV) [Rav]DN-cu l D 11 d 12 ACui ANLBbMR Range -0.10 (0.10) 0.40 0 (0.10) 0.20 0.98 (0.10) 1.48 -0.10 (0.05) 0.10 -0.05 (0.05) 0.15Optimal 0.32 0.01 1.06 0.07 -0.01 -8.6 [0.2368]LBaMR Range -0.40 (0.10) 0.40 0 (0.10) 0.10 0.98 (0.10) 1.48 -0.10 (0.05) 0.10Optimal 0.25 0.03 1.06 0.06 -8.4 [0.2312]LBaMR' Range -0.10 (0.10) 0.10 -0.10 (0.05) 0.10 0.98 (0.10) 1.48 -0.10 (0.05) 0.05aOptimal 0.04 -0.02 1.10 -0.03 -12.2 [0.2565LBM2R Range -0.20 (0.10) 0.20 0.98 (0.10) 1.48 -0.05 (0.05) 0.25Optimal -0.10 1.48 0.19 -8.6 [0.2390]LB2b Range -0.10 (0.10) 0.10 -0.10 (0.10) 0.10 1.08 (0.10) 1.58bOptimal 0 0 1.58 [1.281b -9.2 [0.2486]LBd Range -0.10 (0.10) 0.10 0.98 (0.10) 1.48Optimal 0.10 1.20 -14.6 [0.2907]100C2X2 Range -0.20 (0.10) 0.20 1.68 (0.10) 2.18Optimal 0 2.18 -8.0 [0.3123](a) The range applies to displacement of either N-bonded Cu atoms only or the whole row of Cu atoms; optimal value corresponds to the latter displacement.(b) The same range was used for d 23, optimal value being given in brackets.40 60 80 100 120U)I-cciccwzE/380 80 100 120 140III^I^I^I120 140 160_ 180 200 220 240 260BO 100 120 1 140 16080 100 120 14 um Ho am zm zom am40 60 80 100 120\"41-tL/B'o`MIF\LJ2b-kt --1008282I^I^-(5/3 1) boom•xpt.LW.*LBOAR1.846.48'L81428LB2b77ENERGY (eV)Figure 5.5^Initial conventional LEED results comparing experimental with FD-calculated I(E)curves for the models listed in Table 5.2 and illustrated in Fig. 5.4. Only eight of the nine beamsused in the analysis are shown.78The restructured models considered comprise three types: the first has N in LBsites on the (110) surface supplemented by missing Cu atoms or missing rows of Cuatoms; the second has N in LB sites in overlayer/underlayer combinations; and the thirdhas an N environment like that established for hollow site chemisorption on the Cu(100)surface. The last type (100C2X2) was suggested by Ashwin et al.,108-110 while one of themissing-row models (LBaMR') was based on STM and NICISS results. 113,114 Geometricalvariations of the basic reconstructed models (Table 5.2) gave the following observations:(1) Of the pseudo-(100) models, 100C2X2 could better account for experimental datathan either PS 100 or PS 100X2. The last two maintain the total number of Cuatoms on an ideal Cu(110) surface and have N atoms at or near LB sites for totalcoverages of 1/3 and 2/3 ML, respectively. The optimal 100C2X2 structure, atthis stage, has N coplanar to a non-rumpled (100) overlayer with a first-to-secondinterlayer spacing (d 12) of 2.18 A. Visual comparison of calculated andexperimental I(E) curves showed problems for all fractional beams (e.g., (2/3 1/2)and (5/3 1) in Fig. 5.5) and verified the somewhat large value of R ay (0.312).(2) Calculated I(E) curves for models in which N atoms occupy LB sites both in theoverlayer and varying numbers of underlayers also gave poor correspondence withexperimental data. The underlayer is either unreconstructed (ULBa, not shown) oris of the missing-row type (ULBbMR and ULBbMR', Fig. 5.4). For ULBa, fourspecific models were considered corresponding to one, two, three and infinitenumber of N underlayers. In all cases, agreement with experimental I(E) curves,especially for the integral beams, was much worse than for the correspondingsingle overlayer models (i.e., LBa and LBbMR, respectively).(3)^All remaining restructured models in Fig. 5.4 have N in equivalent, 4-coordinateLB sites on the Cu surface. Initial comparison of I(E) curves suggested that79missing-row (MR) models can better account for experimental data than missing-atom (MA) models (c.f. LBbMR and LBbMA) and that the missing row is in the<001> direction, rather than in the <110> direction as proposed by Niehus et4,1013,114 f. LBaMR and LBaMR', respectively). Furthermore, models with alower N coverage tended to give lower values of Ray than those with highercoverage. For example, the minimum Ray for the basic (unrelaxed) LBaMR' (O N =1/6 ML) is 0.263 as compared to 0.287 for model LB2a (O N = 1/3 ML).(4) Metallic relaxations in the basic reconstructed LB models include rumpling (D,,)as well as lateral displacements (A ) of top-layer Cu atoms from the idealurCu(110) position. Also considered in model LBbMR was a lateral displacement(AN) of N from the ideal long-bridge position. R-factor and visual analysessupport two <001>-missing row models, which differ only in the number of Natoms on the surface (ON = 1/6 ML for LBaMR, and ON = 1/3 ML for LBbMR).Structural details were consistent between LBaMR and LBbMR, as well asbetween these models and Cu3N. The bulk structure of Cu3N has N atoms at the cornersof a cube with Cu atoms at midpoints on the cube edges, 128 and the ideal Cu3N(110)surface has rows of (Cu-N-Cu-N) x alternating with "missing rows" in the <001> direction(Fig. 5.2). In LBbMR, every third N atom is missing from the chain to give the surfaceunit (Cua-N-Cub-N-Cu.)., whereas every third site is occupied in LBaMR to give thesurface unit (Cub-Cu.-N-Cua-Cub).. Although LBaMR gives a slightly lower R ay valuethan LBbMR, the higher coverage model LBbMR does appear more consistent with thestoichiometry of Cu3N.In the optimized LBbMR surface structure, N atoms lie 0.32 A above the planecontaining those copper atoms (Cu.) which are bonded to only one nitrogen, while Cu. aredisplaced laterally away from the nitrogen atoms by about 0.07 A. The substrate80relaxation gives rise to asymmetric N-Cu surface bond lengths in the chain; specifically,b N_cua equals 1.90 A and bN_cab equals 1.83 A. The bond lengths of 1.88 A between each Natom and the two neighbouring Cu atoms in the second layer is achieved by a reduction inthe first-to-second copper interlayer spacing (dcaa_ca2) to 1.06 A from 1.15 A130 in theclean surface (1.28 A in the bulk).A small expansion of each occupied adsorption site is also observed as Cua atomsare displaced laterally away from the center. Thus, on the reconstructed missing-rowsurface, one out of three long-bridge sites in the (2x3) unit mesh is contracted and is,therefore, unoccupied. To have all sites occupied would require a substantial expansion ofthe (110) surface in the <001> direction to allow longer N-Cu bond lengths. Such anexpansion would destroy the (2x3) periodicity seen in the LEED pattern and maintained inthe optimized LBbMR model. The first stage of the conventional LEED analysis of theCu(110)-(2x3)-N surface structure thus favours an <001>-missing row model, similar tothe Cu3N(110) surface.5.4.2 Further analysis of 10002X2 and LBbMRSubsequent to the first study, X-ray reflectivity results became available,n 6supporting the (100)-reconstruction model. Structural details of the X-ray model weresignificantly different from those considered in the previous LEED analysis, however, andso a second series of FD calculations were done for five pseudo-(100) models notpreviously tested: the X-ray model included corrugation in the top four copper layers(100E), three models restricted buckling to the top two copper layers (100A, 100B,100C), and one had no rumpling but the top two copper layers were (100) reconstructed(100D). Additional calculations were also performed for model LBbMR, to allow second-layer relaxations. Figure 5.6 specifies the ranges and optimized values of structuralparameters for (100)-type models, while Table 5.3 lists those considered for LBbMR.lank-12.6 e 0.3115.0.20 .0.201-0.2011.58 • 2.18 (2.001aaa.,:riz,44kff1.58 - 2.18 [1.74^ II AIL ftRR 0.38150.28781.78 22811.9810.11501.08- 1.38 (1281V.0.3158028781.78 228[2.1410.11501.08- 1.3811.141TOP VIEW100C2X2. 100A„iligg_,INE^100BSIDE VIEW1.18- 1.38 [1.18)42S, 0.311610.85000.85001.18- 1.58(13810.18V1.13 1.38[1.2A02847 INFAL-00.98- 128 [1.24110.12271.08 - 1.3811 ' irmigwaaikeFigure 5.6 (100)-reconstruction models considered in the second conventional LEED analysis. Ranges of structural parameters are given Ink with optimized values in bracketsand Vor and Rr, under each model name. Calculations for models 100A, 100B, and 100C also induded second Cu layer relaxation in the opposite sense (Le.. Du 31. -0.1150 A).82Table 5.3 Ranges and optimized geometrical parameters, including those for thesecond metal layer, for model LBbMR during the conventional LEED analysis. Acomparison is made with results from the first study when no second layer relaxationswere allowed.Parameter Range Optimal I^Previous optimalD N1 (A) 0 (0.10) 0.30 0.20 0.32D 11 (A) 0 (0.05) 0.05 - 0 0.01Au., (A) -0.05 (0.05) 0.15 0.08 0.07AN1 (A) -0.05 (0.05) 0.05 - 0 -0.01D22 (A) -0.10 (0.05) 0.10 -0.05 0d 12 (A) 0.98 (0.05) 1.23 1.07 1.06d23 (A) 1.18 (0.05) 1.38 1.25 1.28Von (eV) -9.4 -8.6Rav 0.2305 0.236883Consistent with the previous LEED results, model LBbMR gave a lower R ay thanany of the (100)-type models; of the latter group of models, R ay was lowest for the singleCu(100)-c(2x2)-N overlayer, with N coplanar to the non-rumpled reconstructed Cu layer.Furthermore, optimized top-layer relaxation parameters in LBbMR were essentiallyunchanged by the inclusion of a small vertical splitting of the second Cu layer. Neither R-factor nor visual analysis could detect, however, any significant improvement in agreementbetween calculated and experimental I(E) curves for any of the models, as compared tothe previous work. Therefore, no new conclusions can be drawn at this time fromconventional LEED methods.5.5 Structural analysis, II: tensor LEEDThree model types were considered (Figs. 5.7 and 5.8): those based on LBbMR,which allowed relaxations of the top three Cu layers, those based on 100C2X2, whichrestricted relaxations to the top two Cu layers (set by currently available TLEEDprograms), and those based on the STM model, which included the top two Cu layers. Inthe following discussion, numerical subscript on each atom indicates the layer to which itbelongs, e.g., N1 represents a nitrogen atom in the first layer, Cu 3 a copper atom in thethird layer. Additionally, for (100)-type models, N t, No, and Nb refer respectively to Natoms which are on-top, off-top, and on bridge sites with respect to the topmost Cu(110)layer; and Cuh and Cui identify Cu atoms in the (100) layer which are farther away from(higher) and closer to the bulk (lower), respectively. Figure 5.7 specifies further theconvention for labeling atoms and structural parameters used in this section.845.5.1 <1 i 0>-missing row modelsReference structure (FL)) calculations were done for three models where everythird <110> row is missing: LBaMR', LB2a, and LB2a'. The first two are illustrated inFig. 5.4; the last is similar to LB2a, except that N atoms occupy all sites in the secondlayer exposed by the missing row. TLEED optimization gave the following preliminaryconclusions:(1) Similar displacements of top layer Cu atoms were observed for models LBaMR'and LB2a'. Specifically, those which are bonded to nitrogen are laterally displacedaway from the nitrogen to give bond lengths bNi _cui of 2.10 and 2.08 A,respectively.(2) The magnitudes of displacements of second layer Cu atoms were different betweenLBaMR' and LB2a', although the direction was the same in each case. b N^fori -cu2LBaMR' and LB2a' are, respectively, 1.56 and 1.99 A .(3) For LB2a', displacements of N atoms in the second layer resulted in a rather shortbond length to copper atoms in the third layer (bN2_0,3 = 1.82 A).(4) R-factor analysis could not distinguish between LBaMR' and LB2a' (Ray = 0.235for both), although visual analysis showed some differences between calculatedI(E) curves for the two models. The previous LEED analysis for LBaMR' gaveRay = 0.256.It may be inferred from (4) above that the effect of the weakly scattering N atomson the LEED I(E) profiles is small compared with the effect of the gross rearrangement ofthe metal atoms. The optimized atomic displacements, especially in the topmost Cu layer,seem somewhat implausible in that they give a longer bN1 1 as compared to bNrcu2 . Thisis against expectation when the second layer Cu atoms must necessarily bond to more Cu85neighbours than those in the top layer (ten as compared to six). Since structural modelsmust ultimately be based on chemical principles, and since no significant improvement invisual or R-factor analysis could be observed, no further calculations were done for <110>-missing row models.5.5.2 <001>-missing row modelsTLEED calculations were performed for five different models where every other<001> row is missing, and they can be classified as follows: a single missing-row overlayerwith two or three N atoms on the remaining LB sites (LBbMR and MRa in Fig. 5.8), atwo-N-atom missing-row overlayer with two- or three-N-atom underlayer in an otherwiseunrecontructed Cu(110) surface (UMR and UMRa), and a two N-atom missing-rowreconstruction in both the first and third Cu layers (ULBbMR in Fig. 5.4). The last isbased closely on the ideal Cu 3N(110) surface, but with every third site empty; both thefirst and last models had been studied before (Section 5.4.1), while the remaining modelsarose as TL-optimized displacements suggested them as possibilities worth investigating.Relaxations in the top three layers were allowed so that the number of geometricalparameters being varied is similar between LBbMR-type and (100)-type models.Table 5.4 defines the reference structure coordinates and gives the TLEED-optimized geometrical parameters for the first type. Models LBbMR, MRa, and UMR canbe considered fully optimized within the context of tensor LEED, the magnitude ofdisplacements in the final TL cycle being S 0.1 A. Both ULBbMR and UMRa containlarge displacements in the range where TL fails to reproduce FD calculations.Furthermore, the displacements gave unreasonably short N-Cu bond lengths (as comparedto bulk Cu3N) so that no additional calculations were done for these two models; Section5.5.4 gives a more detailed discussion of the failure of the automated search procedurewith respect to UMRa.86Of the three optimized models, R ay indicates that agreement with experimentaldata is better achieved by having (1) every third LB site empty rather than all sites filledwith nitrogen (Ray = 0.194 and 0.204 for LBbMR and MRa, respectively) and (2) a singleN-overlayer rather than an overlayer/underlayer combination (R ay = 0.200 for UMR).Nevertheless, the differences among these models are not great in either R-factor or visualanalysis, and a possible explanation for this observation lies in the very similar atomiccoordinates obtained for each model (Table 5.4 and Fig. 5.8); this is consistent with resultsfrom the previous section where R-factor analysis could not distinguish between twomodels which differ essentially only in the number of N atoms on the surface. It is alsointeresting to note that MRa gives the observed (2x3) periodicity only because of the largedisplacement of a Cu atom in the third layer, in contrast to the test case results of Section2.4.4, where the periodicity in the <110> direction was not reproduced by atomicdisplacements of small magnitude.Further discussion of <001>-missing row models will be limited to LBbMR, firstbecause it gives the best account of experimental data among these types, and secondbecause it was favoured in the conventional LEED study. Full TL-optimization of the topthree layers in LBbMR gave first-layer displacements which differ not only in magnitudebut also in direction from those of conventional (PD) LEED. Specifically, from FDcalculations, Cu atoms which are bonded to only one N atom are laterally displaced awayfrom nitrogen (Acul = 0.07 A), whereas Acid = -0.06 A from TL, such that the unoccupiedthird site is expanded rather than contracted. Although the height of nitrogen above thefirst Cu layer is similar between the two analyses (D N — 0.3 A), TL indicated a movementof N atoms toward the center (AN = -0.04 A) where FD suggested none (or negligible at -0.01 A). Finally, first-to-second Cu interlayer spacing is somewhat longer from TL (1.10A) than from FD (1.06 A). The most significant difference among these three parametersis clearly Acul . Arguments for the empty site presented in Section 5.4.1 are no longerNa^Cu pCuo Cua Cur^Cu,100S2 +z87<001>-missing row type +zgsgug&:(100) jag+zFigure 5.7 Schematic diagram showing the atom-labelling scheme used in the tensor LEED analysisof the Cu(110)-(2x3)-N surface. Small filled circles represent N atoms. Large, hollow circles representtop-layer Cu atoms, while second-layer Cu atoms are filled. 10081 and 100S2 are (100)-reconstructionmodels which exhibit glide-line symmetry.foreground foregroundMRaLBbMRAft ab..APalliA"wWwilrwilr"IIIUMRFigure 5.8 Top views show explicitly TL-optimized lateral displacements of magnitudes specified in Tables 5.4 and 5.5 for sixmodels of the Cu(110)-(2x3)-N surface structure. Thick solid lines indicate the plane through which side views are taken. Solidlines in the side views locate the center of mass for each Cu layer, while broken lines indicate vertical displacements. Shading oftop-layer Cu atoms have been removed for darity.foreground1 00C2X2 agellialWaNalak _NW MP^111/foreground100F/Mk tat 6_0211,4%vt. lorquent ,■Sra■ WI AWN KWINIWWW100Gwr 11.-kilitsgiftFigure 5.8, continued100C2X21000expLBbMRUMR( 1 0) (5/3 1 ) (413 1 ) (4/31/2)^(2/31/2)—^—40 60 80 100 120LBbMRUMR40 60 80 100100 120 140 160( 0 1)SO 100 120 14i 180 180 200 220I0^ 240 SO 100 120 140 180 180 200 220 240( 2 0)80 100 120 140 100 180 200 220 24080 80 100 120 140 180 180100C21C21000exp90ENERGY (eV)Figure 5.9^Comparison of experimental and TL-calculated curves for the optimized geometryof two (100)-reconstructed models (100C2X2 and 100G) and two <001>-missing row models(LBbMR and UMR).91Table 5.4^TLEED-optimized geometrical parameters for three <001>-missing rowmodels. D and A correspond respectively to vertical and lateral displacements from theideal positions (i.e., bulk for Cu or coplanar, long-bridge for N); negative displacement istoward the bulk or toward the origin as specified in Fig. 5.7; d gives the center-of-massinterlayer spacings, and b the N-Cu bond lengths. The initial reference structure, definedfor LBbMR, fixed all parameters at zero except DN1 = +0.300 A, d12 = 1.080 A, d23 =1.280 A, and d34 = 1.278 A.Parameter (A)^LBbMR^I^MRa^I^UMRDN1D N1 ,DN3+0.379n/an/a+0.386+0.197n/a+0.373n/a+0.175D11 -0 +0.019 +0.014D22 -0.016 -0.028 -0.032DCuas -0.124 -0.146 -0.130DCu3b -0.087 -0.098 -0.106DCu3a , 0 +0.052 +0.012Dcu3b , +0.326 +0.286 +0.342AN 1 -0.043 -0.080 -0.082AN3 n/a n/a +0.048ACu la -0.061 -0.136 -0.077ACu2a +0.101 +0.192 +0.145Acu2a , -0.104 -0.029 -0.094ACu3b -0 -0.012 -0.079Acu3b, -0.093 -0.134 +0.038d12 1.096 1.086 1.112d23 1.241 1.223 1.257d34 1.364 1.365 1.364bN 1 Cut 1.804, 1.828 1.766, 1.794 1.762, 1.850bNi _cb2 1.903 1.935 1.917bN 1 , Cu t n/a 1.953 n/abNr-Cu2 n/a 1.930 n/abN3-Cup n/a n/a 1.812bN3-Cup n/a n/a 1.862, 1.805bN3-cu4 n/a n/a 1.903Vor (eV) [Ray] -7.34 [0.1943] -8.02 [0.2041] -7.09 [0.1997]92Table 5.5 Geometrical parameters defining the initial reference structures, as well asoptimized values, for TLEED calculations of (100)-reconstruction models. D and Acorrespond respectively to vertical and lateral displacements from the ideal positions(negative displacement is toward the bulk or toward the origin as specified in Fig. 5.7); dgives the center-of-mass interlayer spacings, and b the N-Cu bond lengths.Geometricalarameter ADNbD I11D NtD11DC1120DCu2o'Dr•.u2tDr.%JunANDCuhAcubAcub,d12d23bNb-cuhbN0-cuhbN0-cu ibN0-cubbNi-Cu dbNrcutfor (eV) [Ray]100C2X2Ref.^Opt.^0^-0.0350^+0.2270^-0.2400^0.0260^-00^-0.0270^+0.0390^+0.0220^+0.1040^+0.1130^+0.0940^-0.1590^+0.0552.170^2.2191.278^1.3501.863^1.8961.863^1.7721.863^1.879(3.383)^(2.096)1.863^1.958(2.170)^1.953-9.22 [0.2114]100FRef.^Opt.+0.650^+0.489+0.650^+0.767+0.650^+0.5540.650^0.497+0.056^+0.012+0.056^-0.024-0.112^+0.040-0.112^-0.016-0.159^-0.2900^+0.1570^+0.0720^-0.0730^-0.0551.709^1.8741.340^1.2941.973^1.7792.005^2.2651.997^1.907(3.119)^(2.812)1.973^1.972(2.797)^(2.140)-9.06 [0.2350]100GRef.^Opt. -0.130^+0.243+0.130^-0.112+0.130^+0.0680.640^0.494+0.055^+0.014+0.055^-0.022-0.111^+0.031-0.111^-0.014-0.159^+0.2150^+0.1510^+0.0230^-0.3360^-0.0601.985^1.8901.331^1.2891.868^1.9361.891^1.6781.782^2.024(2.200)^1.8731.868^1.8751.906^1.680-9.02 [0.1908]93valid (hence, the TL calculations for MRa). Nevertheless, it must be concluded that theTL-optimized geometry is more reliable. First, visual analysis supports the lower Rayvalue (0.194 vs. 0.237 from FD). Second, although a thorough structural search wasperformed in the FD study, the traditional trial-and-error method necessarily leaves muchof the parameter space unexplored, and the link between different atomic displacementscould be missed.It appears that the improvement in correspondence with experimental data is duein large part to a substantial rumpling in the third Cu layer. This observation was verifiedas follows. In the initial reference structure calculation for LBbMR, all Cu atoms (exceptfor the missing row) were kept at bulk positions. The first set of TL-optimizedgeometrical parameters was then used to calculate I(E) curves for displacements withineach separate layer. Relative to the undisplaced coordinates (Ray = 0.258), neither visualnor R-factor analysis showed any increased agreement between calculated andexperimental I(E) curves when first-layer, second-layer, or first-plus-second-layerdisplacements were considered individually (Ray = 0.274, 0.262, and 0.267, respectively).Ray dropped to 0.226 when only third-layer relaxations were included, first and secondlayers being fixed at the reference structure positions. Even with all displacements exceptone set at 0.00 A (D33 = 0.46 A), Ray decreased to 0.232. Full optimization of all threelayers gave the lowest Ray (0.190). Atomic coordinates obtained at this stage weresomewhat unreliable, however, since TL optimization gave a displacement of 0.46 A awayfrom the reference structure positions and this is beyond the range of validity of the tensorLEED approximation. Thus, a second calculation was done starting from the previousresult.After three FD/TL cycles, TLEED converges on an optimal set of geometricalparameters for LBbMR (Table 5.4). The asymmetric N-Cu surface bond lengths remain(bN-cu i = 1.80 and 1.83 A), although not as pronounced as in the conventional LEED94study. Metal relaxations appear chemically reasonable in that they tend to strengthen N-Cu bonding, Cu atoms in both the first and second layers moving toward nitrogen. Alonger bond length to the second layer (bN_cu2 = 1.90 A) gives an average N-Cu bondlength of 1.86 A, which is still rather long compared to the predicted value of 1.76 A.Nevertheless, having > bN_cul reinforces arguments put forth in Section 5.5.1 (that adelicate balance exists between bonding to nitrogen and bonding to its nearest neighbours,especially for second-layer Cu atoms). Missing from the first study are lateraldisplacements in the second and third metal layers and a significant rumpling in the third.5.5.3 Pseudo - (100) modelsFive models belonging to two diperiodic space groups (p2gg and p2mm) served asreference structures for (100)-reconstruction calculations (Figs. 5.7 and 5.8 and Table5.5). Initial optimization of structural parameters for models 100S1 and 100S2 indicatedthat the glide-line symmetry was being incorrectly treated by the automated searchroutines; for example, different displacements were obtained for the two top-layer Cuatoms marked 1 and 6 in Fig. 5.7, model 100S1. Furthermore, a vertical displacement of— 0.8 A for atom "1" gives a first-to-second Cu bond length of 2.01 A, which correspondsto a 21% contraction compared to the metallic distance of 2.556 A. Although significantinterlayer contractions are often observed on open surfaces, changes in metal bond lengthsare not as great (e.g., for clean Cu(110), d 12 = 1.15 A 13 0 is a 10% contraction relative tothe bulk value of 1.278 A, but the metal-metal bond length reduces to 2.49 A, only a 2.4%contraction from the distance in the bulk metal). Ray does not rule out 100S1 or 100S2 aspossible structures of the Cu(110)-(2x3)-N surface, but until the TLEED programsavailable can correctly treat surfaces exhibiting glide-line symmetry, additional calculationswill not be done for these models.70 80 90 100110120130(2/3 1/2)40 5 '0 6'0 70 8 '0 90100expTLOFDO25050 100 200expTLOcnzwI—zFDO!^1 100^150 200^25050( 0 1) (4/3 1 )95ENERGY (eV)Figure 5.10 Comparison showing dramatic improvement in agreement between experimentaland calculated I(E) curves for model 100F after only one FD/TL cycle. FDO are full-dynamicalcalculated curves, while TLO were obtained after optimization by the directed search method.96Two of the remaining three models contain metal corrugations of magnitudessuggested by X-ray reflectivity measurements " 6 (100F and 100G), while one maintained anon-rumpled (100) overlayer with N coplanar to the reconstructed layer (100C2X2) as inthe first LEED study. Dramatically improved agreement with experimental data wasimmediately achieved even after only one FD/TL cycle for the rumpled models. Forexample, FD calculated I(E) curves for 100F showed very poor correlation withexperiment, by both visual and R-factor analyses (R ay = 0.524); after TL optimization, Raydecreased to 0.196, and visual analysis confirmed the improvement (Fig. 5.10, e.g., beams(2/3 1/2) and (4/3 1)). TL displacements are still large at this stage, however, themaximum magnitude being 0.25 A, and so a second calculation was performed startingfrom the first TL results. After two FD/TL iterations, geometrical parameters for 100Fcan be considered closely optimized within the context of tensor LEED (maximumdisplacement — 0.10 A). Although the final TL-optimized Ray value of 0.235 is somewhathigher than that obtained after the first cycle, atomic coordinates from the second TLEEDcalculation should be more reliable because of the smaller shifts from the referencestructure positions. It is also important to note that, compared to conventional LEEDresults of Section 5.4.2, the directed search method had given significantly betteragreement between calculated and experimental I(E) curves so that the Cu(110)-(2x3)-Nsurface structure could now be considered as likely to be (100) reconstructed as <001>-missing row reconstructed.A similar, though not as dramatic, improvement was also observed for the non-rumpled, N-coplanar 100C2X2 model. Convergence to the optimal geometry wasachieved after two cycles, Ray dropping from 0.298 to 0.211. The slightly lower R ayvalue for 100C2X2 as compared to 100F appears to favour a nearly flat (100) overlayer toone which is highly corrugated (Table 5.5). Visual comparison of integral beam curves97supports R-factor analysis (Fig. 5.9, e.g., beams (1 0) and (2 0)), although problemsremain for fractional beams (e.g., (2/3 1/2)).Without rumpling in the topmost Cu layer, a (100)-reconstruction model isinconsistent with both STM images 114 and X-ray results. 116 Thus, a new series of TLcalculations was started from a reference structure where metallic corrugation is as inmodel 100F, but with N nearly coplanar to the reconstructed layer. The initial height of N(DN) above its local Cu neighbours gave an average N-Cu bond length of 1.87 A(predicted bond length is 1.85 A for 5-coordinate N); the Cu-Cu metallic distancedetermined the initial interlayer spacings (model 100G in Table 5.5 and Fig. 5.8).Observations regarding the failure of the automated search procedure in some instanceswill be discussed in the next section, and only a summary of the results will be given here.After eight FD/TL iterations, the coordinates of 18 atoms in the top two layers aresufficiently refined that all displacements in the final cycle are less than — 0.1 A.At this stage, 100G gives the best account of experimental data of the (100)-typemodels. Although R-factor analysis cannot distinguish between 100G and LBbMR (R ay =0.19 for both), visual analysis might favour the former (c.f. integral beams in Fig. 5.9).Further support for 100G as the correct structure of the Cu(110)-(2x3)-N surface comesfrom comparison with X-ray results. 116 TL-optimized first-layer corrugation D 11 = 0.494A is close to the stated error limit of 0.639 ± 0.089 A from the latter work. Additionally,first-to-second ((In) and second-to-third (d23) interlayer spacings equal 1.890 and 1.289A, respectively; X-ray reflectivity measurements give d 12 = 2.006 ± 0.153 and d 23 = 1.304± 0.064 A. Similar magnitudes were obtained for second-layer rumpling (D 22) and Nvertical height between the two techniques, although the details of the displacementsdiffer. For example, TL indicates three different values for DN ranging from 0.068 to0.284 A and corresponding to nitrogen being in three different local environments, whereX-ray suggests only one (0.75 ± 0.5 A). Perhaps it is not surprising that LEED is more98sensitive than X-ray scattering to the position of a weak scatterer such as nitrogen, whilecoordinates of Cu atoms were more closely reproduced between the two techniques.TLEED also gave other structural parameters not observed in the X-ray study.Most notable of these are lateral displacements of N o and second-layer Cu atoms to allowthe formation of a fifth N-Cu bond, which is not significantly present in the absence ofthese relaxations (Fig. 5.8). Consequently, three out of the four nitrogen atoms become 5-coordinate as they would be on the true Cu(100)-c(2x2)-N surface. One N atom remains4-coordinate resulting from the need to maintain a physically reasonable CurCu 2 metallicdistance. The average N-Cu bond lengths of 1.836 (N t) and 1.855 A (No) for 5-coordinate nitrogen are close to both the expected value and that obtained for Cu(100)-c(2x2)-N, 131 while the value of 1.936 A for 4-coordinate nitrogen (Nb) is somewhat longcompared to the predicted value of 1.76 A. Nevertheless, these bond lengths appear moreconsistent with prediction than those (1.93 and 2.08 A) reported by Baddorf et a/., 116 asthe latter are rather longer than the value of 1.91 A for 6-coordinate nitrogen in bulkCu3N. 1285.5.4 Anomalies in TLEED resultsThe last two sections noted concern with respect to TLEED results in twoinstances: those for 100G and for UMRa. An intermediate TL calculation of 100G, forexample, gave a nitrogen-to-second layer Cu bond length which is much shorter than thatto first-layer Cu atoms (bNicui = 1.71 Avs. tt = 1.93 A), and since this contrasts withthe N-Cu bond lengths observed on the true Cu(100)-c(2x2)-N surface (b N_cu2 = 2.00 A,bN-cu, = 1.81 A), the question arises whether the TLEED analysis got misdirected in thiscase. For example, visual analysis showed a substantial decrease in agreement for thefractional beam (2/3 1/2) (c.f. curves marked opt3 and opt4 in Fig. 5.11), with only amarginally improved correspondence in the integral beams (1 1) and (2 0). These99(5131)100 120 140 100(55 1)(44 1)00 80 MO UM 140(44 1)SO SO UM MO UM(4414)40 00 80 100 120(4/3 1/2)40 GO 80 100 120(2,31/2)(2/31/2)60 00 100 120 140 160 100Mtpalt4opt41000:(I 0)60 80 100 120 140 160 100UMRa:(1 0)140 100100 120ENERGY (eV)Figure 5.11^Comparison of experimental data with TL-calculated curves for models 100G and UMRa, iustratingthe need to reset some TL-optimized displacements. For 100G, opt3 are TL-optimized curves for the third FD/TL cycle;opt4 are TL-optirnized curves for the fourth FD/TL cycle; alt4 are TI-calculated curves with some atomic displacementsfrom the fourth cycle reset Note the improved agreement with experimental beam (21312) going from opt4 to alt4. ForUMRa, TL-catulated curves with (a) hi optimization of al atomic coordinates, inducing a vertical displacement of N. 3 (DN,3)by 1.13 A; (b) as (a) with D fixed at zero; (c) partial optimization, atomic cisplacement being reset to give chemicalyplausble N-Cu bond lengths. See Table 5.6 for structural details.100observations together suggested that it may be worth resetting some atomic positionsduring the analysis to increase bNccut , decrease bNccui, and at the same time improvecorrespondence between calculated and experimental intensities for the beam (2/3 1/2).Table 5.6 gives bond lengths for one such set of alternate coordinates, and Fig. 5.11indicates that the match was indeed better for the alternate positions (curves marked alt4)than for the fully optimized model (curves marked opt4) for beam (2/3 1/2), with noobservable change in other beams (consequently, R ay remains comparable between thetwo calculations at 0.171 and 0.165, respectively). Thus, based on visual analysis as wellas bond-length considerations, the subsequent FD/TL cycle was started from thealternative set of atomic positions.Calculations for model UMRa also revealed the need to check the directed searchresults for chemical reasonableness. (Refer to Fig. 5.7 for atomic labels.) Fulloptimization (Ray = 0.173; Fig. 5.11, curves a) gives two physically implausible N-Cubond lengths in the underlayer: vertical displacement of N3, (DN3,) by 1.13 A produces anitrogen-to-fourth layer Cu bond length of 1.31 A, and a lateral displacement of N3 by0.48 A gives a value of 1.51 A for bm r a' Neither R-factor (Table 5.6) nor visualanalysis (Fig. 5.11, curves b) could detect any significant decrease in agreement betweencalculation and experiment when DN3, was fixed at zero, while resetting this displacementgave an N-Cu bond length more consistent with six-coordinate nitrogen (b N3 ,_ cu4 = 1 .91A). Figure 5.11 also shows calculated I(E) curves (marked c) corresponding to bm =1.81 A (Ray = 0.183). Visual comparison of the three variations appears to suggest thatTL-optimized displacements of large magnitude may not always be necessary (or evenreliable) and that chemical input may be useful in resetting atomic positions. Finally, thelow Ray value for the fully optimized model UMRa (a in the table below) can certainly bedismissed as unreliable due to the large displacements beyond the range of validity oftensor LEED.101Table 5.6^Comparison of N-Cu bond lengths (in A) for models 100G and UMRa forthe I(E) curves shown in Fig.5.11. DISP indicates the magnitude (in A) of maximumdisplacement in each set of calculation.100G DISP Nt-Cud bNt-Cut I^Rayalt4 0.24 1.88 1.86 0.1713opt4 0.24 1.93 1.71 0.1650opt3 0.43 1.85 1.69 0.1786UMRa DISP bN3.cu3a bN3,.cu4 Ray(a) 1.13 1.51 1.31 0.1731(b) 0.48 1.51 1.91 0.1711(c) 0.35 1.81 1.91 0.18335.6 SummaryResults from this chapter clearly illustrate the limitations of the conventionalLEED method compared with the tensor LEED method. First, even with an extensivesearch in parameter space using the trial-and-error procedure, structural details weremissed in the calculations for the <001>-missing row model LBbMR. Second, modelswhere the topmost Cu layer is (100)-reconstructed were ruled out simply because thegeometrical parameters had been insufficiently refined by conventional means, as there hadbeen no indication to encourage further investigation of these models. At the presenttime, the R-factor analysis from tensor LEED and the directed search method appears tofavour both model types equally (Ray around 0.19), although the latter, in particular model100G in Fig. 5.8, appears more likely to be the correct structure of the Cu(110)-(2x3)-Nsurface for a number of reasons.A highly corrugated pseudo-(100)-c(2x2)-N reconstruction model with N nearlycoplanar with the topmost Cu layer can account not only for LEED data (Fig. 5.9) in thecurrent work, but also for results from other techniques. Specifically, the copper densityin the topmost Cu layer has been indicated to be increased relative to that on the cleansurface (X-ray reflectivity, 116 PED and LEISios - lio), while a nitrogen coverage of 2/3 MLagrees with XPS measurements of Baddorf and Zehner." 2 Rumpling of the pseudo-(100)102layer by 0.494 A is consistent with observations of Baddorf et al., 116 and can perhapsreconcile an added-row model with STM images by Neihus, Spitzl and coworkers.'" Inaddition, average N-Cu bond lengths in model 100G (— 1.85 A) generally agree withprediction83,129 based on the bulk structure of Cu3N; two aspects remain to be resolved,however: (1) the rather long N-Cu bond length for 4-coordinate, "bridge-site" N atoms,and (2) bond lengths which are shorter to second-layer Cu atoms than to first-layer Cuatoms for "on-top" N. The second point may not present a serious problem, however,since bonding to second layer Cu atoms is constrained in part by the short Cu(110)interlayer spacing on the pseudo-(100) surface in contrast to the longer interlayer spacingson the true Cu(100)-c(2x2)-N surface. It is expected that structural details for 100G canbe further refined, and an improved account of experimental data be achieved, as futureversions of the tensor LEED programs allow more complete calculations, for example, toinclude third and fourth metal layer relaxations as suggested by X-ray reflectivitymeasurements.5.7 AddedumAfter this chapter was completed, a new high resolution STM study of theCu(110)-(2x3)-N surface became available; 132 Figure 5.12 identifies the structures seen.At low N dosage, Leibsle et al. observed the paired rows of bright spots (labelled as Bfeatures by the authors) in the <110> direction, like those seen previously by Neihus etapia Additional bright spots (labelled A) appeared, however, at the center of the fourlocal B features, the surface density of A features increasing with the N dosage. Alsoimportant is the imaging of atoms (labelled C) in the dark bands between the paired rows,previously attributed to a missing row in the <110> direction. These features can beexplained in terms of model 100G as follows, if it is the N atoms which are principallyimaged. The B and C features correspond respectively to N atoms which are off-bridge103(No) and on-top sites (N t) with respect to the Cu(110) surface. There are two N o atomsin every (2x3) unit mesh, imaged as pairs of bright spots, and N t atoms are less brightbecause they are lower than No atoms (i.e., closer to the bulk). "Bridge-site" Nb atomsare highest on the surface and are thus most brightly imaged as the A features. STMshows the (2x3) surface structure exists even when the density of the A features is verylow, which is consistent with the Nb sites being occupied only at higher dosages sincechemisorption on the 4-coordinate "bridge-site" would be less favourable than on theother two types of sites, where the coordination is five. Furthermore, the rather long Nb-Cu bond length obtained in the current LEED analysis may perhaps indicate that the Nbsites are not occupied, or only partly occupied, under our experimental conditions. Theseobservations give strong evidence that the model which can best explain the structure ofthe Cu(110)-(2x3)-N surface, and which is most consistent with the multitude oftechniques which have been applied to study this system, is a highly corrugated, pseudo-(100) reconstruction of the topmost copper layer.(a)^(b)Figure 5.12^STM images (Ref. 130) of the Cu(110)-(2x3)-N surface at (a) low and (b) high N-dosages.Chapter 6 : Pd(100)-(V5x -V5)R27°-0^1046.1 IntroductionConsidering that palladium plays an important catalytic role in certain oxidationreactions, for example of CO and NO in catalytic converters, it is surprising how very littlequantitative structural work has been done on 0/Pd chemisorption systems comparedwith, for example, 0/Ni systems. Previous LEED studies on low Miller index surfaces ofpalladium have been restricted to observations of patterns and suggestions of models toaccount for the observed patterns. 133-135 The additional techniques most often employedare HREELS and TPD, but these only give indirect evidence for the surface structurethrough comparison with similar systems. For example, Stuve et al. 136 compared the losspeak at 370 cm -1 measured for the Pd(100)-p(2x2)-0 surface to those of 0 chemisorbedon Ag(1 10) and Pt(1 1 1) and concluded a 4-coordinate (hollow) adsorption site for 0atoms.Oxygen chemisorbs on Pd(100) to form four ordered surface structures: p(2x2),c(2x2), p(5x5), and (/5xV5)R27°. 135-142 Room-temperature chemisorption results in onlythe p(2x2) and c(2x2) surfaces, with respective ideal coverages (0 0) of 0.25 and 0.50 ML,where 1 ML corresponds to one oxygen per palladium surface atom. The p(5x5) structure(proposed 137 00 = 0.64 ML) develops with extended 0 2 dosing and sample heating above— 400 K, while a temperature of 550 K is needed to create the ('I5x/5)R27° surface(proposed137 00 = 0.80 ML). The oxygen coverages for the latter two surfaces have beenestimated using Auger and TDS, assuming ideal 0 0 values for the p(2x2) and c(2x2)surfaces. 138,139,142 He diffraction study of the p(2x2) structure places 0 atoms in hollowsites on the unreconstructed Pd(100) surface, 143 which supports the interpretation givenby the HREELS results. 136,140,141 No structural analysis exists for the latter two surfaces,although two very different models have been postulated. In an earlier energy loss study,Orent and Bader137 suggested that the two high coverage structures correspond to105reconstructions with the formation of a PdO layer on top of the Pd(100) substrate,specifically, Pd0(110) for the p(5x5) surface and PdO(001) for the (45)0/5)R27° surface(Fig. 6.1). Such oxide overlayer reconstruction is commonly observed for high-temperature oxygen chemisorption on metal surfaces, e.g., for the 0/Ni(110) system.'"An alternative interpretation for both structures was suggested by Simmons et al. ;142 theauthors reported a HREELS loss peak at 430 cm -1 (in addition to that at 350 cm -1 ) andproposed a model where oxygen atoms chemisorb on distorted 4-fold hollow sites, withsignificant lateral displacements of both 0 and surface Pd atoms to give 0-Pd bondlengths of 1.576, 2.460, 2.504, and 3.138 A for each chemisorbed 0 atom. The need foran independent analysis is clearly indicated, especially since knowing the surface structureis fundamental and prerequisite to understanding catalytic reactions occuring at thesurface. Thus, a LEED structural analysis has been undertaken for the Pd(100)-(/5x .V5)R27°-0 surface, and the results are reported in this chapter.6.2 ExperimentExperimental data at normal incidence were provided by Oden Warren at AmesLaboratory, Iowa, for 15 independent beams (Fig. 6.2) corresponding to(0 1), (1 1), (0 2), (0.2 0.4), (0.2 0.6), (0.6 0.8), (0.4 0.8), (0.4 1.2),(0.6 1.2), (0.6 1.8), (0.4 1.8), (0.2 1.4), (0.2 1.6), (0.8 1.6), (0.8 1.4).Briefly, the Pd(100) sample was cleaned by a three step process. First, Ar -E bombardmentduring heating in UHV removed impurities, such as sulfur and phosphorus, whichsegregated to the surface. Second, the other main contaminant, carbon, is removed byreaction with oxygen to form CO. Finally, any excess oxygen is removed by annealing thesurface in vacuo at 1150 K for about 2 min. The (V5xI5)R27° surface was formed by(a)^ (b)^ (c)Q Pd 0 0 Figure 6.1 (a) The PdO bulk structure; Ref. 145. (b) The Pd0(001) overlayer model of the Pd(100)-(45x45)-R27°-0 surface, as proposedby Orent and Bader; Ref. 137. Oxide Pd atoms have been labelled to identify their registry with respect to the Pd(100) substrate: Pdt andPdh correspond respectively to "on-top" and "hollow-site" Pd atoms, while Pd bt and Pdbh refer to "bridge-site" Pd atoms along the stringcontaining Pdt and Pdh, respectively. (c) The distorted hollow-site model of Simmons et al.; Ref. 142. Additional legend in Fig. 6.3.(-2 2)•000000•o 000(-2 0)0 0•0 0000 0•0 000(-2 -2)0 0•^(0 2)^ (2 2)^M •^•(0 0)•°^et)(0.6 0.2) •0 0(2 0)•0 0 0 00 0 0 00 0 0 00 0 0 0• • •0 0 0 00 0 0 00 0 0 0(0 -2)•0 0•0 0(2 -2)•1070 0O 0^0O 0^00 0•0 0O 0^0O 0^00 00 0^ra M^0 00^0^0^0^E^0^00^0^0^02^0^0^00 0 IR ".3 0 0• M (0.40.8)^LE (1 .2 0.6)^•0 0^di EI0 0O 0^0^E^0^0^0O 0^0^IM^0^0^00 0•Figure 6.2 Schematic diagram of the LEED pattern from thePd(100)-(45x45)R27°-0 surface, showing beams from two domains whichare mutually rotated by 90° (see Fig. 1.1). Solid and hollow dotscorrespond respectively to integral and fractional beams, and boxesindicate one beam from each symmetrically equivalent set for which I(E)curves were measured.108dosing 02 at 5 x 10 Torr onto the cleaned Pd(100) surface for 15 min. with the crystaltemperature being held at about 570 K. Intensity measurements were made for a total of81 beams before averaging (30-200 eV, 1-eV grid), and background subtraction wasperformed locally during the measurement.6.3 CalculationOxygen phase shifts were the same as those used by Marcus et al.80 in their ONcalculations, while substrate phase shifts up to E = 7 were calculated from the Moruzzi-Janak-Williams atomic potential for metallic palladium.124 The real part of the constantpotential between muffin-tin spheres was initially set through visual comparison at V orequals -10.0, -5.0, or 0.0 eV depending on the basic model type, but was always refinedduring the structural search; the imaginary part was fixed at V 01 = -5.0 eV. Debyetemperatures of 270 and 696 K were used for Pd and 0, respectively.Initial analysis used the conventional LEED programs as provided by Van Hoveand Tong.48 Because structural models of the Pd(100)-N5x45)R27°-0 surface generallyhave a large number of parameters to be varied, however, this procedure was abandonedin favour of the tensor LEED method (see Chapter 2), as working TLEED computercodes became available. This system, in turn, served as a test case for assessing theefficiency of the tensor LEED method for determining a challenging surface structure, forwhich no hard information is available. As discussed in Section 2.4.1, the cycle of FDcalculation followed by directed search was repeated until the final TL-optimized structurecontained displacements away from the current reference structure which were all lessthan — 0.1 A, the amount within which TL accurately reproduces FD results. For theanalysis of the Pd(100)-(q5xq5)R27°-0 surface structure, Rp was used to assess theagreement between calculated and experimental I(E) curves.1096.4 Structural analysis: tensor LEED6.4.1 Reference structuresA range of chemically plausible models of the Pd(100)-N5x -q5)R27°-0 surfacestructure was proposed. Relaxations in the top three Pd layers were allowed, and eachoxygen layer contained either four or two 0 atoms. Bulk Pd-Pd distances andparametrized O-Pd bond lengths (see, e.g., Section 5.3) determined the atomiccoordinates in the first reference structure, while subsequent reference structures weretaken from TL-optimized displacements. All models except one (2BU1, 0 0 = 0.40 ML)have an oxygen coverage of 0.80 ML, as suggested by Orent and Bader and measured byother workers. 137-139 . 142 Figure 6.3 illustrates schematically the twelve basic model typeswhich were considered in some detail and which can be roughly divided into three groups:(1) 0 overlayer on Pd(100). Three adsorption sites were considered on theunreconstructed surface: symmetrical 4-coordinate hollow (4F), symmetrical 2-coordinate bridge (4B0), and off-bridge (4FB), where 0 atoms were initiallyplaced exactly half way between the hollow and bridge sites. An alternative 4-coordinate hollow site (4FMA) is created by having 0 nearly coplanar with areconstructed top layer where one out of every five Pd surface atoms is missing.The distorted hollow-site model of Simmons and coworkers 142 (Fig. 6.1) was nottested explicitly, as it is only a variation of 4F.(2) 0 underlayer in Pd(100). One-underlayer models (4BU and 2BU1) have 0 atomsin tetrahedral holes between the first and second Pd layers; a two-underlayer model(2BU2) has an additional 2-0-atom layer between the second and third substratelayers. One model (2BOU) combines a bridge-site overlayer with an underlayerbetween first and second Pd layers.LEGEND". overlays: + ^layer Pdunderlayer 02BOU 4FB 4B0PDOS4FPDOMA4FMAPDOoverlayer 0underlayer 01st layer on topof 2nd layer Pd(--"' missing atom Pd,2114 layerYer DA^/1St or 2nd layer1st layer PdFigure 6.3 Schematic diagrams of the initial reference structures for nine out of the twelve models of thePd(100)-(J5 x N/5)R27°-0 surface. Models 4BU and 2BU1 have an oxygen underlayer between the first and secondPd layers with 0 atom positions directly below the positions shown in models 4B0 and 2BOU, respectively; model2BU2 has two 0 underlayers between the first-and-second and the second-and-third Pd layers.110111(3) Pd0(001) reconstruction. The slightly expanded Pd0(001) overlayer can bestacked onto the substrate in two ways: one (PDO) has Pd atoms in the oxide layeron three different sites (top, bridge, and hollow) and is that proposed by Orent andBader, 137 while the other (PDOS) has all overlayer Pd atoms in equivalentenvironments relative to the Pd(100) surface. A variation of the latter (PDOMA)has one out of every five atoms missing in the first Pd(100) layer. Finally, a two-layer reconstruction model (PDOU) consists of an 0 layer between two oxide Pdlayers. (Figure 6.1 illustrates the bulk structure of Pd0.)For model PDO, the difference in adsorption sites of Pd atoms in the oxide layergives hard-sphere stacking distances of 1.94, 2.38, and 2.75 A, respectively, for hollow-site (Pdh), bridge-site (Pdbh and Pdbt), and on-top Pd atoms (Pd) (Fig. 6.1). Therefore,four separate initial reference structures were considered, corresponding to (1) norumpling in either the oxide or the Pd(100) layers and a value of 2.75 A for the interlayerspacing (d 12) between the oxide and topmost Pd(100) layers; (2) corrugation restricted tothe oxide layer (i.e., Dht, defined as the difference in height between Pd h and Pdt) ofmagnitudes 0.80 A (d12 = 1.94 A) and (3) 0.40 A (d 12 = 2.34 A); and (4) rumpling withinboth the oxide and topmost Pd(100) layers by 0.40 A, for an effective Dht = 0.80 A. Initialanalysis favoured the last type, and thus subsequent calculations were based on type (4) ofmodel PDO.6.4.2 ResultsFull optimization, as determined by convergence within the tensor LEEDapproximation, was achieved for all models but one (Table 6.1); after six FD/TL cycles,calculations were discontinued for model PDOMA for two reasons. First, rather thanconverging toward smaller displacements with increasing numbers of iterations, themagnitude of maximum displacement was still 0.17 A at this stage. Furthermore,112agreement between experimental and calculated I(E) curves decreased during the lattercycles; for example, R. = 0.3101 for the fourth reference structure, while Rp = 0.3186 forthe sixth. Decrease in agreement was also observed for the TL-optimized geometries(Table 6.2). This would appear to indicate that the optimization procedure was divergingrather than converging toward an optimal set of geometrical parameters for this model,thus suggesting that PDOMA is unlikely to be the correct structure of the (45)0/5)R27°surface.Of the remaining 11 models, R-factor analysis indicates that model PDO gives thebest account of experimental data. That is to say that the most likely structure of thePd(100)-0/5)0/5)R27°-0 surface is an oxide reconstruction with a single PdO(001)overlayer on top of the Pd(100) substrate (Fig. 6.4). R p equals 0.2323 for fully optimizedPDO, while the next closest minimum Rp value of 0.2514 (for PDOS) is sufficiently higherto rule out the other models tested. Although only Rp was used during the optimizationprocedure, Ray was additionally used to assess the agreement between experimental andFD-calculated I(E) curves (i.e., those from reference structures at each FD/TL cycle); thisserved to verify the trend indicated by Rp, that improved account of experimental data wasbeing achieved, irrespective of the tensor I RED approximation and the particular R-factorused. Table 6.2 illustrates this point for model PDOMA in particular, but the sameobservations could be made for the other models. For example, Rp decreased steadilyfrom an initial value of 0.4294 for the first set of FD-calculated curves to 0.3101 by thefourth set, but Ray increased to 0.3161 for the the fifth set. The corresponding Ray valuesare 0.3380, 0.2285, and 0.2397 and show the same trend as R P.Visual analysis (Fig. 6.5) of 15 beams for 12 models requires some care, but itappears to support the R-factor analysis. For model PDO, the correspondence betweenexperimental and calculated I(E) curves appeared best for beam (0.2 1.4), with generallygood agreement for beams (0 1), (0 2), (0.2 0.4), (0.6 0.8), (0.4 0.8), (0.4 1.2), (0.2 1.6),113Table 6.1^Comparison of the level of agreement achieved between calculated andexperimental I(E) curves for the 12 models in Fig. 6.2, with the model giving the overallbest fit in bold. Values listed are for the final FD/TL cycle. Ray for the final referencestructure are included to verify the trend indicated by R p. DISP indicates the level ofconvergence achieved within the context of tensor LEED, as given by the type andmagnitude of maximum displacement in the final cycle. Only one cycle was performed formodel PDOU since the value of DISP is within the range of validity of the tensor LEEDapproximation.Model # cycles I^FD: Rp (Ray)  TL: Rp Vor (eV) DISP (A)PDO 10 0.2429 (0.2061) 0.2323 0.04 Apd = 0.07PDOS 8 0.2874 (0.2196) 0.2514 -3.51 Apd = 0.09PDOMA 6 0.3186 (0.2353) 0.2708 0.76 Apd = 0.17PDOU 1 0.4590 (0.3354) 0.3152 0.16 Apd = 0.11 4F 10 0.3296 (0.3207) 0.3093 -5.83 Apd = 0.084FB 2 0.3502 (0.2800) 0.3306 -4.87 Ao = 0.064FMA 6 0.3505 (0.2869) 0.3283 -5.13 Apd = 0.084B0 3 0.3253 (0.2618) 0.2921 -1.29 Apd = 0.064BU 3 0.3683 (0.2948) 0.3328 -3.43 Dpd = 0.102BU2 3 0.3218 (0.2821) 0.3129 -10.00 Do = 0.042BU1 3 0.3904 (0.3133) 0.3722 -5.22 Apd = 0.052BOU 3 0.3566 (0.3055) 0.3512 -4.68 Dpd = 0.03D11 Atomic coordinatesx^y^z0.0000 1.9916 -2.82891.0450 2.7505 -1.37533.2644 1.3958 -1.32255.3138 2.7433 0.12180.0000 3.5094 0.0784(170224.1258 1.37533677)(19804)0.0000 0.0000.32140.8803 1.3753 2.75050.2515 0.6835 1.38792.8861 0.8870 1.35295.3643 0.0715 2.5961Figure 6.4 Top views showing explicitly TLEED-optimized lateral displacements in the final cycle for two Pd0(001)- reconstruction models(PDO and PDOS), a bridge-site overlayer model (4B0), and a hollow-site overlayer model (4F), with the corresponding I(E) curves in Fig. 6.5.Atomic coordinates are given for model PDO because it is the structure which gives the overall best account of experimental data Some atomsare labelled to correspond to the displacements listed in Table 6.3; also defined are some vertical displacements.Figure 6.4, continued4F4B0PDOSPDO116( 0 1 ) ( 0 2)40 60 80 100 120 140 160 180 200^80 100 120 140 160 180 200^180ENERGY (eV)Figure 6.5 TL-calculated curves for the opttimized structures in Fig. 6.4. R-factor analysisindicates that PDO gives the best agreement with experimental data (Bp= 0.232).(0.8 1.0)(021.01 (0A 1.4)(02 I A)4F100 120 140 180 ISO 200 120 140 100 180 200 120 140 1110 180 200 100 120 140 100 ISO 200ENERGY (eV)(02 0.4)^ (02 OA)40 00 80 100 120 140 100 180 200 40 00 110 100 120 NO 100 100 200Figure 6.5, continuedENERGY (eV)(0211)(0.4 12) (0.411)10212)208200 20 100 120 140 190 180^138(0.4 0.2)40 20 20 100 120 440 180 180 20C 80 80 100 120 140 180 180 in 910(020.2)opPOOP130214204F40 80 80 100 120 140 100 120 2004FFigure 6.5, continued119Table 6.2 Rp and maximum displacement (DISP) for the sequence of FD/TLcalculations done for PDOMA. Note the decrease in agreement, as indicated by a highervalue for Rp, after the fourth cycle; R-values which are lower in the previous cycles maybe unreliable due to the large values of DISP in those cycles. FD values are obtained fromcomparison with experiment of full-dynamical calculated I(E) curves, while TL valuesresult from optimization of each reference structure.Iter. # -->^1 2 3 4 5 6FD : R v 0.3380 0.2678 0.2488 0.2285 0.2397 0.2353FD : Rp 0.4294 0.3547 0.3267 0.3101 0.3161 0.3186TL : Rp 0.3036 0.2727 0.2615 0.2551 0.2484 0.2709DISP (A) Do = 0.32 Apd = 0.21 Apd = 0.25 Apd = 0.24 Ao = 0.27 Apd = 0.17Table 6.3^Some optimized structural parameters for model PDO; CM is center-of-mass spacing. Other parameters are defined in Fig. 6.4.Vertical (A) Lateral (A) CM spacing (A) Bond length (A)D11 0.1001 Ao +0.0133 d12 2.2318 O-Pdh 1.7102D 11 ' 0.3428 Ao' +0.1060 d23 2.2018 O-Pdbh 1.6525Dht 0.2782 d34 1.9851 O-Pdbt 1.9449D22 0.3783 02b +0.0566 0 -Pdt 1.5984D22' 0.4816 Am -0.4888D33 0.0505 03 -0.1702D33 ' 0.0429 03' +0.1220120and (0.8 1.4). Although relative peak intensities were not closely reproduced for the lastbeam, the more important peak positions seemed to match those of the experimentalcurve. The double peak between 40 and 60 eV of beam (0.4 0.8) emerged for no modelother than the fully optimized PDO model; even after many refinements in theconventional LEED analysis (see Section 6.4.3), only a single peak could be obtained inthis range for PDO. Both R-factor and visual analyses indicate poor agreement for beams(0.2 0.6) and (0.6 1.8), the latter extending only over a short energy range of 50 eV, whilethe former covers a 160 eV range with many structures in the experimental I(E) curve tomatch. The calculated I(E) curve for beam (0.2 0.6) also contains a number of peaks butis less complex than the experimental curves, and the peaks do not line up with those ofthe experiment. Nevertheless, considering the unusually large data base of 15 beams, 12of which are fractional order beams, and that a reasonably good level of correspondencehas been reached for many of the beams for a relatively complex surface structure, modelPDO most likely resembles closely the actual structure of the Pd(100)-(V52(q5)R27°-0surface. This model will, therefore, be discussed further in relation to structural chemicalprinciples.In PDO, coincidence with the Pd(100) lattice requires a slight expansion of thePdO(001) overlayer; Pd-Pd distance in the plane of the unrelaxed overlayer is 3.075 A,whereas that in bulk PdO is 3.043 A. In addition, registry with respect to the Pd(100)substrate is such that Pd atoms from the oxide layer are placed on three very different"adsoption" sites: one atom per unit mesh sits on-top, two on bridge, and one on hollowsites. As a result, significant expansion of the first-to-second interlayer spacing and/orrumpling of the top metal layers would be expected since the hard-sphere stackingdistance of hollow-site atoms is 1.94 A above the Pd(100) surface while that of on-topatoms is 2.75 A. Both types of relaxations are observed for the final TL-optimizedgeometry of PDO (Table 6.3). Rumplings of magnitude 0.28 A in the oxide layer and1210.48 A in the topmost Pd(100) layer give an effective difference in height of 0.76 Abetween on-top and hollow-site Pd atoms, which is close to the expected difference of0.81 A. The center-of-mass distances indicate a large expansion in the first threeinterlayer spacings, but these values are deceptive in that they do not account for thesubstantial lateral displacement of Pd atoms, often resulting in a contracted Pd-Pd bonddistance. Consider, for example, the top two Pd(100) layers, where a second-to-thirdcenter-of-mass spacing of 2.20 A implies a 13% expansion relative to the bulk distance of1.94 A. Lateral displacements actually lead to a minimum distance of 2.70 A between Pd-Pd nearest neighbours in the second and third layers, corresponding to a 2% contraction,while expansion of the remaining Pd-Pd bond distances (between second and third layers)was typically less than 7%. In addition, Pd atoms tend to be laterally displaced alongdirections which minimized corrugation in the top metal layers: two atoms in the topmostPd(100) layer are displaced (A2h) toward the hollow-site atom, while two are displaced(02h) toward bridge-site atoms lying along the string containing on-top atoms (Fig. 6.4).The effect is to increase the height of the lower Pd atoms within the oxide layer and thusreduce the height difference between higher and lower Pd atoms. A balance is thusachieved between the drive toward maintaining an ideally flat PdO(001) surface and theneed to optimize the total bonding at the surface, in particular, to maximize Pd-Pdbonding (without rumpling, Pdh atoms would sit too high above the surface to bond to Pdatoms in the layer below).Oxygen displacements also appear chemically reasonable in that shorter bondlengths (i.e., stronger bonding) are observed for those Pd atoms which have fewer Pdnearest neighbours. For example, 0 atoms are displaced toward on-top Pd atoms (Pd t),which have only one Pd-Pd bond (to the layer below). The resulting bond length bo_pdtequals 1.60 A, whereas bo_pdbt equals 1.94 A for the bond to bridge-site atoms which havetwo Pd nearest neighbours. Similarly, bo_pdh equals 1.71 A and bo_pdbh equals 1.65 A for122bonds to hollow- and bridge-site Pd atoms, respectively, along the other string. Theaverage 0-Pd surface bond length of 1.73 A is close to the predicted value of 1.76 A for2-coordinate oxygen.6.4.3 Comparison with other modelsAn oxide-reconstruction model of the Pd(100)-(15x .V5)R27°-0 surface does notagree with the distorted hollow-site model of Simmons et a/. 142 However, structuralfeatures of the latter model appear chemically implausible, based on the structure of PdO(Fig. 6.1) as well as the general behaviour of oxygen chemisorbed on metal surfaces. Thedriving force for adsorbate-induced reconstructions is presumably to optimize totalbonding at the surface, often in terms of maximizing the coordination number (CN) of theadsorbed atom. While oxygen chemisorbed in a hollow site (CN=4) may be morefavourable than on a reconstructed oxide layer (CN=2), the large lateral displacement(0.688 A) of 0 atoms suggested in the HREELS study lead to an effective oxygencoordination of one. The shortest 0-Pd bond length of 1.576 A is close to the predictedvalue of 1.504 A for 0 bonding to one Pd atom, essentially forming an 0-Pd double bond,and the largest value of 3.138 A is too long for a meaningful bond to exist. The remainingtwo bond lengths of 2.460 and 2.504 A are also longer than that (2.024 A) 145 reported forbulk PdO, where 0 bonds to four Pd atoms. Allowing an oxygen coordination of threeand averaging the first three values give an 0-Pd bond length of 2.18 A, which is stillrather long compared to the predicted value of 1.91 A (for CN=3). Interestingly, the TL-optimized 4F model in the present study also indicated the formation of an unrealisticallyshort 0-Pd bond (1.40 A), but the longest value is only 2.49 A, giving an average of 1.99A for 4-coordinate oxygen. The 4F model was not favoured by TLEED, however: R p =0.3093 for the optimal geometry, and this is significantly higher than that obtained forPDO (RP = 0.2323).123The (A/5xJ5)R27° structure has also been observed for oxygen chemisorption onMo(100), and a recent X-ray scattering study 146 determined its structure to be a missing-atom reconstruction similar to model 4FMA, but Table 6.1 shows clearly that this cannotbe the correct structure of the Pd(100)-(45x45)R27°-0 surface. It is not surprising,however, that oxygen induces two different reconstructions, both exhibiting the samediffraction pattern, on Pd(100) and Mo(100). First, palladium is an fcc metal, whilemolybdenum is bcc, so that Mo(100) is a much less densely packed surface than Pd(100).0 atoms are still 4-coordinate in model 4FMA, whereas they are 3-coordinate on thereconstructed Mo(100) surface. Furthermore, molybdenum has a large range of oxidestoichiometry and structures, unlike palladium which exists in the bulk just aspd0 . 145,147,148The preliminary conventional LEED analysis also supported PDO-type model,although structural features were not sufficiently refined to allow significant distinctionbetween PDO- and 4F-type models. After 14 full-dynamical calculations to vary atomicpositions within the top two Pd layers of PDO, R p only decreased to 0.3609 from an initialvalue of 0.4084. The situation was even worse for 4F: R p dropped to 0.3771 from 0.4368only after 40 FD calculations. These values can be compared to those in Table 6.1, wherea maximum of 10 FD calculations was performed for any particular model, yet TLEEDoptimization clearly indicated PDO as the model giving the best account of experimentaldata and hence the model which most likely identifies the essential features of the(A/5x -V5)R27° surface structure.6.5 SummaryThe present tensor LEED I(E) analysis favours an oxide-reconstruction model(PDO in Fig. 6.4 and Table 6.3) for the Pd(100)-(A/5xJ5)R27°-0 surface structure: aPdO(001) overlayer is stacked onto the Pd(100) surface such that significant rumpling is124induced in both the oxide and topmost Pd(100) layers. An average O-Pd bond length of1.73 A agrees closely with predicted value for 2-coordinate oxygen, and structural detailsof the optimized model PDO appear chemically reasonable in that a balance is maintainedbetween adsorbate-metal and metal-metal bonding. This model can also explain why theformation of the (45x45)R27° surface is an activated process, requiring 0 chemisorptionat an elevated temperature: the Pd atom density in the oxide layer is 4/5 that of the cleansurface, so that mass transport is involved during the creation of such a surface. Similarly,the p(5x5) surface is only formed at a high surface temperature and most likelycorresponds to a Pd0(110) overlayer as suggested by Orent and Bader.137Chapter 7 : Concluding remarks^1257.1 Further work on Ni(111)The better level of agreement achieved for the Ni(111)-(2x2)-0 surface structurecompared with the corresponding sulfur systemm 3 suggests the need to reanalyze theNi(111)-(2x2)-S surface, perhaps by incorporating hydrogen into the bulk. Tensor LEEDcan be used to explore a larger volume of parameter space in the S/Ni system than waspossible with conventional LEED. In addition, the well-established 0/Ni surfacestructure, with both vertical and lateral relaxations in the close-packed Ni(111) surface,can serve as a further test of the ability of the TLEED method for reproducing FD results.7.2 Further work on Cu(110)-(2x3)-NThis system has perhaps demonstrated most clearly the limitations of the LEEDtechnique, as determined by the R-factor analysis. The same R-values (Ray = 1/2 (RAJ +RP) 0.19) were obtained for two very different reconstruction models of the Cu(110)-(2x3)-N surface: one has alternating <001>-missing rows, while the other is a highlycorrugated pseudo-(100)-c(2x2)-N overlayer (100G in Fig. 5.8). The (100)-reconstruction model, however, appears to be more consistent with results from many ofthe techniques that have been applied to study this surface. In particular, recentlyavailable STM images suggest a high- and a low-N-coverage (2x3) surface, which can beexplained in terms of the adsorption of N preferentially on 5-coordinate sites (as opposedto 4-coordinate sites) on a (100)-reconstructed surface. Since all LEED calculations ofthe (100)-type models have been based on the high coverage structure (with four N atomsper (2x3) unit mesh), one possibility for improving the agreement between experimentaland calculated I(E) curves for model 100G is to start a new series of tensor LEED126calculations based on a low-coverage (100) structure, with N atoms occupying only 5-coordinate sites. A better approach would be to combine in various proportions thediffracted intensities from the low- and high-coverage calculations to account for the notwell-defined experimental coverage. In addition, a new series of experiments should becarried out to measure the evolution of the I(E) curves with N dosage, to cover a muchwider range than was done in the current study; the nitrogen coverage should bedetermined as well on a more absolute scale, using, for example, the nuclear reactionanalysis technique. A LEED analysis of the Ni(110)-(2x3)-N surface may also provideinsight into the surface structure of both systems. Interestingly, while bulk Cu 3N exists,the corresponding nickel compound is not well known, yet chemisorbed nitrogen induces a(2x3) reconstruction not only on the (110), but also on the (210) surfaces of both thesemetals.7.3 Further work on Pd(100)-05)N5)R27°-0The current tensor LEED analysis of the high coverage 0/Pd(100) system hasidentified some key features of the Pd(100)-(15,015)R27°-0 surface structure: a singlesurface oxide overlayer is formed, which is stacked onto the Pd(100) substrate such thatsignificant rumpling is induced in both the oxide and the top two Pd(100) layers. Theoverall level of correspondence between experimental and calculated I(E) curves is bestfor this type of model, but some discrepancies remain, e.g., for beam (0.2 0.6). R-factoranalysis indicates that the next most likely model of the (/5xV5)R27° surface is also anoxide reconstruction, which differs from the first type mainly in its registry with respect tothe Pd(100) surface. Visual comparison of I(E) curves suggests that including somefeatures of the shifted oxide model into the favoured oxide model may help improve127agreement with experimental data. New calculations could thus be undertaken to combinefeatures from both model types, and additional R-factors can be used during theoptimization procedure (as discussed below).7.4 Critique of the LEED analysisFundamental to understanding surface reactions is knowing the surface structure,as for example, how the structure of a catalyst affects the rate of reaction. Since mostsystems of practical interest are too complicated for detailed structural analysis, theapproach of surface science is to start with simple systems such as clean, single-crystal(metal) surfaces, on which gases are adsorbed in a controlled manner under UHV.Information gained from the three chemisorption systems investigated in this thesis havethus contributed to our basic knowledge of surface structures, in particular of adsorbate-induced reconstruction of metal surfaces. In addition, this work has provided some insightinto the power as well as the limitations of LEED as a surface structural technique. For asimple system such as that formed by the chemisorption of oxygen onto the Ni(111)surface to form Ni(111)-(2x2)-0, the trial-and-error procedure of the conventional LEEDmethod can locate with some certainty fine structural details such as small lateral andvertical displacements of the local metallic structure, provided that a sufficientlyexhaustive search has been done in parameter space. Analysis of the more complicatedsurfaces of Cu(110)-(2x3)-N and Pd(100)-(/5x\15)R27°-0 was hampered both by thenumerous models and by the large number of parameters within each model that need beconsidered. Evidence from the N/Cu study clearly shows the limitation of the traditionalmethod of LEED crystallography, but even the newly developed tensor LEED/directedsearch method (TLEED) has problems which should be addressed. One of these problems128is the lack of "chemical sensibility" of the directed search method: the search for anoptimal geometry is based solely on R-factors, but care is always needed in assessingwhether the R-factor used is a reliable measure of the agreement between experimentaland calculated I(E) curves. Figure 7.1 illustrates using two beams from the N/Cu analysiswhere, in the absence of redeeming corrections from the other beams, R-factor analysiswould clearly fail. For beam (4/3 1/2), visual analysis suggests little difference in the levelof correspondence with experiment for the two calculated curves: of the six peaks andvalleys to be matched in the experimental curve, FD matches only the one peak near 70eV, and TL matches that in addition to the valley at 97 eV; the I(E) profiles are similarbetween FD and TL over much of the energy range. Yet, the Pendry R p value issignificantly higher for one curve (0.5639 for FD) than for the other (0.3493 for TL).Visual comparison of beam (5/3 1), on the other hand, indicates that the level ofagreement should be much better for the FD curve than for the TL curve, the latter havingno peak between 110 and 120 eV (although the TL curve appears to match the minimumat 130 eV better than the FD curve) and an intensity scale which is 10 times that of theexperiment; nevertheless, compared with the numerical difference seen for the (4/3 1/2)beam, somewhat comparable Ltp values were obtained for the (5/3 1) curves (0.2943 and0.3406, respectively, for FD and TL). These observations are not limited to the Pendry R-factor; of the other nine R-factors summarized by Van Hove and Koestner, 44 all gavesimilar numerical analysis of beam (4/3 1/2), and only three (ROS, R1, R2; see Ref. 44)gave R-values which were consistent with visual analysis of beam (5/3 1). The observedR-values could be explained as follows:(1)^For beam (4/3 1/2), the minimum at 97 eV in the FD curve falls almost exactly atthe maximum in the experimental curves. As a result, in the range 80 to 100 eV,To'C/1^1^1^1^1I^-I /I^/jI/\^\^/I^\^I ^0.5639 I \ /^0.34930.3406^\0.2943—*///x0.17'if129exp^FD^TL (4/3 1/2)^ (5/3 1 )50^60^70^80^90 100 110 100 110 120 130 140 150ENERGY (eV)Figure 7.1 Comparison of two sets of calculated I(E) curves with those fromthe N/Cu experiment. R F. values are given to illustrate the failure of R-factoranalysis for these two beams.130the FD and experimental I(E) curves have exactly opposite slopes. Consequently,R is much higher for the FD curve than for the TL curve.(2)^For beam (5/3 1), the slope between experimental and both calculated curves aresimilar over much of the energy range of interest. Thus, despite the visuallydifferent calculated curves, similar R-values are obtained (for FD and TL).It could be argued that the R-factor comparisons in Fig. 7.1 show sufficiently pooroverall agreement to indicate an incorrect structure; thus, for a given change in geometry(e.g., from FD to TL), it is not critical that changes in individual beam R-values be on thesame quantitative scale (e.g., a substantial decrease in R-value for beam (4/3 1/2), but onlya small increase for beam (5/3 1)). R-values should, in practice, however, indicatequantitatively and consistently changes which give better and worse agreement, sincetensor LEED must follow trends in total R-factors and structural analysis of a completelyunknown and challenging surface inevitably starts from a position of poor agreement.Nevertherless, R-factors must remain the primary tools to quantify the level ofcorrespondence between experiment and calculations in any LEED structural search:visual comparison of I(E) curves for many beams and many models (e.g., for 0/Pd) isdifficult, if not impossible, and lacks objectivity. But, as seen above, a numerical R-factoris "objective" only in its own limited context, and it may not always mimic trends seen bythe human eye.The goal is thus to improve the reliability of R-factors, a measure of which wasdone by Van Hove and Koestner 44 through a series of extensive tests. These authorsshowed that the ten R-factors tested exhibited differing sensitivity to different featuressuch as relative peak heights, widths and positions. Furthermore, in the neighborhood ofthe correct geometry, minima will generally coincide for (1) different R-factors averaged131over all beams, (2) different beams averaged over R-factors, and (3) different energyranges taken from the same beam. These points can be checked in a conventional LEEDanalysis, but point (1) is probably most often used as it is the overall agreement betweenexperimental and calculated I(E) curves which ultimately determines the best structuralmodel of the surface under investigation. With tensor LEED, separate searches could beperformed, each using a different R-factor, and coincidence of structural details could inprinciple be used to measure reliability. When only one R-factor is used in an analysis,that proposed by Pendry54 is often used for its sensitivity to peak positions (which can bemore easily reproduced than, for example, relative peak heights), for its mathematical basis(which should give an upper limit of unity when comparing completely uncorrelatedcurves), and for its apparent physical basis (which measures in terms of Voi the effect ofinelastic scattering on peak widths). In addition, R p can be calculated much more quicklythan, for example, RivizT (by about a factor of ten). One approach then is to use R p toexplore parameter space on a course scale, to match peak positions first; fine-tuning ofstructural details can be done by including other R-factors which emphasizes otherfeatures of I(E) curves. This procedure has generally been used for the work in this thesis.As there is no generally accepted "best" R-factor, it remains essential even withTLEED to continue to make visual inspections of I(E) curves to ensure consistencybetween lower R-values and improved correspondence with experimental data (asdiscussed in Section 5.5.4). In addition, there should be a check regarding the chemicalreasonableness of a particular geometry; ultimately, surface structural models should showbroad agreement with bond length-bond order predictions based on well-established bulkstructures. These checks are especially important in cases where R-factors apparentlycannot distinguish between two very different model types (e.g., missing-row and (100)-reconstruction for N on Cu(110)), yet even more similar model types have been132unambiguously differentiated in other cases (e.g., the 3f and 3h sites for 0 on Ni(111)).For both the Cu(110)-(2x3)-N and Pd(100)-(A/5xA15)R27°-0 surfaces, the discrepanciesbetween experimental and calculated I(E) curves which remain suggest that, although theessential elements of the surface structure have been established, further refinements areneeded.Even with its limitations, LEED is still by far the most developed surfacecrystallographic technique. Many other techniques give only broad structural features,whereas LEED can determine structural details such as bond lengths and surfacerelaxations to within 0.03 A, if a high level of correspondence has been reached betweencalculations and experiment (e.g., for 0/Ni). 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