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1 Powered by TCPDF ( This is n electronic reprint of the originl rticle. This reprint my differ from the originl in pgintion nd typogrphic detil. Enevoldsen, Georg H.; Foster, Adm; Christensen, Mon C.; Luritsen, Jeppe V.; Besenbcher, Flemming Noncontct tomic force microscopy studies of vcncies nd hydroxyls of TiO2 (110) Published in: PHYSICAL REVIEW B DOI: /PhysRevB Published: 01/01/2007 Document Version Publisher's PDF, lso known s Version of record Plese cite the originl version: Enevoldsen, G. H., Foster, A. S., Christensen, M. C., Luritsen, J. V., & Besenbcher, F. (2007). Noncontct tomic force microscopy studies of vcncies nd hydroxyls of TiO2 (110): Experiments nd tomistic simultions. PHYSICAL REVIEW B, 76(20), [205415]. DOI: /PhysRevB This mteril is protected by copyright nd other intellectul property rights, nd dupliction or sle of ll or prt of ny of the repository collections is not permitted, except tht mteril my be duplicted by you for your reserch use or eductionl purposes in electronic or print form. You must obtin permission for ny other use. Electronic or print copies my not be offered, whether for sle or otherwise to nyone who is not n uthorised user.

2 Noncontct tomic force microscopy studies of vcncies nd hydroxyls of TiO : Experiments nd tomistic simultions Georg H. Enevoldsen, 1 Adm S. Foster, 2 Mon C. Christensen, 1 Jeppe V. Luritsen, 1 nd Flemming Besenbcher 1 1 Interdisciplinry Nnoscience Center (inano) nd Deprtment of Physics nd Astronomy, University of Arhus, DK 8000 Arhus C, Denmrk 2 Lbortory of Physics, Helsinki University of Technology, I Espoo, Finlnd Received 3 July 2007; revised mnuscript received 25 September 2007; published 13 November 2007 From n interply of noncontct tomic force microscopy experiments nd simultions, we present here detiled ccount of tomic-scle contrst encountered in force microscopy of the prototypicl metl-oxide surfce TiO We hve previously shown for this surfce how the tomic-scle tomic force microscopy AFM contrst depends crucilly on the tip-termintion polrity. Here, we extend this finding by lso tking into ccount the influence of the tip-surfce imging distnce s controlled by the scnning prmeters. Atomic-resolution imging is shown to be possible in three distinctly different types of contrst modes corresponding to three different types of tip-pex termintions. In the two predominnt modes, the AFM contrst is found to be dominted principlly by the polrity of the electrosttic interctions between the tip-pex toms nd the O nd Ti surfce sublttices. A negtively presumbly O terminted tip genertes AFM imges in which the positive sublttice Ti nd bridging hydroxyl OH dsorbtes re imged s bright protrusions, wheres positively terminted tip Ti + results in AFM imges with inverted contrst. Experiments show tht the qulittive detils of the imging contrst of the surfce signtures re retined t ll relistic tip-surfce imging distnces for both tips, but detiled comprison of AFM imges recorded t different scnning prmeters with clculted site-specific force-distnce curves illustrtes how the quntittive ppernce my chnge s the surfce is probed t closer distnces. The third observed imging mode, which, however, is obtined quite seldom, reflects tip hving predominntly covlent interction with the surfce toms, since the resulting imging contrst is very close to the rel topogrphic structure of the surfce. We expect tht lso for other surfces with n ionic or semi-ionic chrcter tht the tomic-scle AFM contrst depends strongly on the exct nture of the tip pex in similr wy, nd the present nlysis outlines how ll imging modes cn be included in n tomic-scle nlysis to revel the chemicl identity of defects nd dsorbtes on such surfces. DOI: /PhysRevB PACS number s : Bs, Gh, Mg, Ps I. INTRODUCTION Atomic force microscopy AFM is scnning probe microscopy technique 1 cpble of reveling the tomic structure of surfces nd molecules dsorbed on surfces in rel spce, even under different environmentl conditions. 2 4 As surfce nlyticl tool, the min importnce of AFM derives from the fct tht it cn be pplied to ny surfce, conducting s well s nonconducting, s opposed to the scnning tunneling microscopy 5 STM for which the surfce hs to be conducting. Especilly, when operted in the noncontct mode nc-afm or dynmic AFM under ultrhigh vcuum UHV conditions, 2,3 it hs successfully been demonstrted tht AFM is cpble of producing genuine tomic-resolution imges of single crystl surfces. 6 During the lst decde, tomic resolution of surfces nd single-tom defects hs been reported on number of insulting surfces, 4,7 but in mny cses, the contrst mechnisms responsible for the nc- AFM imges re not fully understood. 8 Recent nc-afm studies combined with simultions bsed on density functionl theory 9 11 hve demonstrted tht the contrst in tomiclly resolved AFM imges of compound surfces should, in generl, be considered s rther complicted convolution between geometricl fetures pertining to the surfce nd chemicl contribution. The tomic-scle AFM contrst is determined by the short-rnge forces which set in when the AFM tip pex is brought in close proximity of the surfce. The short-rnge forces my thus be dominted by covlent or ionic contributions, nd the specific nture of this chemicl interction thus depends intimtely on the surfce nd the structure nd composition of the tip pex. It is generlly ccepted tht typiclly only few toms prticipte in the direct bonding to the surfce, nd experimentl experience hs shown tht most such nnotips re frgile nd my chnge frequently due to mterils exchnge between the surfce nd tip. Due to the very locl nture of the interction, even smll chnges cn hve drmtic effect on the imging contrst, s we hve previously shown for the TiO surfce. 11 In tht pper, it ws demonstrted how chnges in the tomic rrngement of the tip pex resulted in two predominnt types of tom-resolved AFM imges of the TiO 2 surfce, neither of which reveled the true geometricl topogrphy of the surfce or its defect nd dsorbtes. It ws lso demonstrted how the complementry informtion obtined from both types of AFM imges could be combined to construct relistic model of the tip-surfce interction nd, s next step, how the informtion in the AFM imges cn be used to discriminte between nd subsequently chemiclly identify the prevlent surfce defects nd dsorbtes s oxygen vcncies nd hydroxyls on the TiO surfce. As n extension of these studies, we present here thorough nd comprehensive nc-afm study of the TiO surfce /2007/76 20 / The Americn Physicl Society

3 ENEVOLDSEN et l. From lrge dt set consisting of more thn 500 tomresolved imges tken with rnge of different tips, we hve mnged to group ll our tom-resolved imges into three ctegories contrst modes determined by the nture of the tip pex. First, we focus on two distinctly different contrst modes for nc-afm imging of the TiO surfce, corresponding to the two predominnt types of tip-termintion polrities, nmely, positive nd negtive, which enble us to ssign the chemicl identity to ll surfce fetures imged by nc-afm on the TiO surfce. We lso discuss third, but fr less frequent, nc-afm imging mode which, in contrst to the two predominnt imging modes, yields n imge contrst resembling closely the rel topogrphy of the hydroxylted TiO surfce. For ech of the predominnt contrst modes, we explore the prmeters which control the contrst of nc-afm imges, such s the tip-surfce imging distnce mplitude setting, frequency shift set point. The experimentl observtions re then compred to theoreticl clculted spectroscopic curves, nd using this pproch, we cn explin the contrst mechnisms for this surfce. The present study my thus serve s generl reference for AFM studies of the TiO surfce, which hs evolved into the most studied metl-oxide surfce in recent yers. 16,17 The present study lso provides detiled ccount of the dependencies of both the tip polrity nd tip-surfce imging distnce on the ctul nc-afm contrst on metl oxide, nd the results re expected to be of generl pplicbility for AFM imging of ionic or semi-ionic compound mterils nd metl oxides, in prticulr. So fr, limited number of tom-resolved studies hve been reported for ionic mterils, e.g., NCl, 18 nd KBr, 19 or metl oxides such s MgO 001, 20,21 CeO 2 110, 22,23 or Al 2 O , 24 nd in most cses, the imging contrst is ssocited with only one of the sublttice ions when the surfce is probed with nc- AFM in the ttrctive force regime. Finlly, we show tht nc-afm cn directly imge the dynmic process of the splitting of pired hydroxyls on the TiO surfce long the 110 direction nd the diffusing of single hydroxyls long the sme direction, consistent with the findings of the previous STM study. 25 II. METHODS A. Experimentl detils The experimentl setup consists of n ultrhigh vcuum UHV chmber with bse pressure below mbr equipped with n Omicron vrible-temperture AFM/STM. The nc-afm control unit ws enhnced by dding digitl NnoSurf EsyPLL controller unit for improved frequency shift detection. The cntilevers used for the experiments were ll uncoted silicon cntilevers Nnosensors, type NCH with resonnce frequencies in the rnge khz nd spring constnts of 19 N/m. We found tht it ws very useful to use Ar + ion bombrd E 2 kev, fluence cm 2 of the tip both s n initil clening procedure of the tip nd s mens to shrpen up blunt tip. The experimentl setup did not llow for direct grounding of the tip during ion-bombrdment process, but, lthough this my hve reduced the efficiency of the ion-bombrdment process, this did not led to ny permnent chrging of the tip. The imges presented in this pper were ll tken using noncontct AFM nc-afm operted in the frequency modultion mode or dynmic AFM, 26 where the tip-cntilever system is excited t its first mechnicl resonnce frequency to constnt mplitude in close proximity of the surfce. The forces rising between the tip nd the surfce, e.g., vn der Wls vdw, chemicl, nd electrosttic forces, cuse shift in the resonnce frequency of the tip-cntilever system reltive to the free resonnce frequency referred to s frequency shift, or simply df. For the experiments presented here, we probed the TiO surfce in the ttrctive regime, which cused the resonnce frequency to shift down, resulting in negtive frequency shift. All the reported frequency shift vlues re negtive, with lrger vlues mening more negtive vlues. As the tip ws rster scnned cross the surfce, vritions in the frequency shift signl were recorded nd used to generte the nc-afm imges, either s the direct imging signl constnt height imges or, s presented here, s feedbck-loop signl controlling the tip-surfce distnce to mintin preset frequency shift set-point signl constnt frequency shift imges. In this wy, the tip trces the surfce on contour of constnt frequency shift, nd the chnges in tip-surfce distnce, controlled by the feedbckloop, re used s the imging signl, generting topogrphic imge of the surfce. The bis voltge pplied to the surfce reltive to the tip U bis ws monitored regulrly nd djusted to minimize the electrosttic forces rising from the contct potentil difference CPD. 27,28 We found tht the CPD chnged significntly, rnging from vlue of 2 3 V for new tip to V for tip clened with the Ar + ion-bombrdment process described bove. The frequency shift set point t which the optiml tomic resolution could be obtined vried significntly from experiment to experiment. In this pper, we present nc-afm imges tken with wide rnge of different tips, recorded t negtive frequency shift set points rnging from few hertz to few hundred hertz, reflecting the fct tht the mcroscopic shrpness tip-pex rdius of the AFM tip nd therefore the long-rnged vdw forces vried from tip to tip nd from experiment to experiment. 9 Surprisingly, we observed tht the mcroscopic shrpness of the tip did not ffect the qulity of the tomic resolution on flt terrces of the surfce to ny gret extent, nd, to certin degree, reltively blunt tips generlly provided more stble nc-afm imging. Therefore, for constnt frequency shift imges recorded with different tips, the frequency shift set point cnnot generlly be used lone s n indiction for how closely the tip probes the surfce. When compring experimentl nc-afm imges with theoreticlly clculted imges, the vritions in the tip shrpness, s evident from the wide rnge of frequency shift set points, re, however, not problem, since the long-rnged vdw forces cn be ccounted for rther precisely in the theoreticl modeling see next section. We found tht the vrition of the vdw contribution due to the mcroscopic tip shpe did not chnge the qulittive ppernce of the resulting force curves, nd the vritions in the contrst described in this study should therefore be vlid for both shrp nd

4 NONCONTACT ATOMIC FORCE MICROSCOPY STUDIES OF blunter tips. An exct quntittive correspondence of the imge corrugtion my esily be obtined for imges obtined with specific tip by fitting the vdw contribution s ws done in, e.g., Ref. 11. The TiO crystl ws initilly clened using severl cycles of Ar + ion bombrdment E 800 ev, fluence cm 2 followed by nneling T 950 K,t 20 min. After initil clening, it ws sufficient with single clening cycle prior to ech experiment to produce clen nd impurity-free surfce suitble for experiments, ll of which were crried out t room temperture. B. Theoreticl clcultions The clcultion of the tip-surfce interctions on the microscopic scle ws performed using sttic tomistic simultions, s implemented in the two-dimensionl periodic codes MARVIN. 29 This simultion technique uses point chrges nd polrizble shells to represent toms nd pir potentils to represent tomic interctions. The rutile TiO surfce ws represented by unit cell which ws thick enough to converge the surfce structure nd lrge enough to void spurious interctions between dsorbtes. We used metl-oxide cluster tip model, nmely, 64-tom MgO cube. Such cluster tip model provides well-defined nnoprobe where the cube cn be oriented to expose either positive Mg 2+ or negtive O 2 electrosttic potentil from the tip pex. 30 The top 20 toms of the tip nd the bottom lyer of the surfce were kept frozen during simultions to represent the bulk, while ll other toms were llowed to fully relx with respect to intertomic forces. The pir potentil prmeters for the TiO surfce nd its interction with wter were tken from Ref. 31, nd these hve been extensively tested ginst both first-principles clcultions nd experimentl dt. The remining prmeters for the tip nd tipsurfce interction were obtined from Ref. 32. We lso considered severl other plusible tip models in the simultions, including some bsed on SiO 2 nd TiO 2, including wter tip-pex contmintion. These other tip models did not chnge the results presented here significntly, which shows tht the MgO tip represents relible nd generl model of n ionic tip due to the dominnce of electrosttics in the imging interctions. Once the models of the tip nd surfce re estblished, we define three-dimensionl grid over the surfce nd clculte the force between tip nd surfce t ech point on this grid. This clcultion provides the microscopic forces between tip nd surfce, but in order to generte imges which cn be compred to experiment, it is importnt to include the longrnge mcroscopic vdw interction between the tip nd surfce. This contribution cts s bckground ttrctive force, which is importnt in terms of reproducing the experimentlly observed frequency chnges, but is independent of the identity of the tip-pex tom nd the surfce tom beneth nd does not ply role in tomic displcements. This mens tht the interctions cn be clculted seprtely nd only combined for the finl stges of modeling. The vdw force is minly determined by the rdius of the mcroscopic prt of the tip nd the Hmker constnt of the system, nd for simplicity, the mcroscopic prt of the tip is represented by cone with sphere t the end into which the nnotip is embedded. 33 Since the originl tip is very likely to consist of oxidized silicon, we fix the Hmker constnt to the vlue for SiO 2 -TiO 2, 34 nd we were then ble to fit the tip-pex rdius to reproduce the experimentlly mesured surfce contour contrst defined s the corrugtion of the Ti 5c reltive to the O 2c rows, C Ti-O t the set point for the constnt frequency chnge. Microscopic nd mcroscopic forces re combined to provide detiled mp of the force cross the surfce. This mp is then used s input in simple model 33 of the cntilever oscilltions using experimentl prmeters to provide the chnge in frequency frequency shift of the cntilever t given tip-surfce imging distnce. These dt cn subsequently be either directly used to produce n imge t constnt height or interpolted to produce topogrphic imge t constnt frequency chnge. Frequency chnge curves df vs distnce re extrcted directly from clculted imges by plotting the frequency chnge s function of distnce t specified lterl position in the imge. III. RESULTS AND DISCUSSION A. Rutile TiO surfce Figure 1 shows typicl lrge-scle nc-afm imge of the rutile TiO surfce recorded t room temperture some time fter preprtion. The imge revels chrcteristic striped pttern consisting of bright prllel rows seprted by 0.65 nm. This pttern reflects the tomic rrngement of the TiO surfce s depicted in the bll models in Figs. 1 b top view nd 1 c side view, where lternting rows of twofold coordinted bridging oxygen toms O 2c nd fivefold coordinted in-plne titnium toms Ti 5c locted long the 001 direction form 1 1 surfce structure with periodicity of nm long the 110 direction. Also visible in Fig. 1 re severl bright protrusions locted in between the bright rows. From the extensive literture vilble on the TiO surfce, 11,35,36 it is well known tht this surfce, when prepred under stndrd UHV conditions, is not perfectly stoichiometric. Oxygen toms re removed from the TiO surfce during the clening cycles, reducing it slightly, nd s result, unoccupied O 2c sites rise, referred to s bridging oxygen vcncies O-vc. 35 These oxygen vcncies re known to be very rective, nd they rect redily with moleculr wter, 37 which is ever present in the residul gs even under extreme UHV pressures, dsorbed on the surfce. The rection cuses the wter molecules to dissocite in the vcncies followed by proton trnsfer to the neighboring O 2c, resulting in the formtion of pired side-by-side hydroxyl groups, referred to s double hydroxyls. 25,36 From the literture, it is lso well known tht these re not stble over time, but through n interction with dditionl wter molecules from the residul gs phse, they split up nd form isolted single hydroxyl groups. 25,38 In recent letter, we showed how O-vc defects nd dsorbtes such s nd cn be distinguished in nc-afm experiments, 11 nd

5 ENEVOLDSEN et l. b ~0.295 nm c [110] ~0.092 nm ~0.152 nm ~0.649 nm FIG. 1. Color online nc-afm imge nm 2 of the TiO surfce. Bll models of the TiO surfce re depicted in b top down nd c side view, respectively. Drk red blls lrge, blck : Twofold coordinted bridging oxygen toms O 2c, formlly O 2. Light red blls lrge, light gry : In-plne threefold coordinted oxygen toms. Drk silver blls smll, drk gry : In-plne fivefold coordinted titnium toms Ti 5c, formlly Ti 4+. Light silver blls smll, light gry : Sixfold coordinted titnium toms. White blls smll, white : Hydrogen toms. Distnces re bsed on Refs. 35, 55, nd 56. we find tht even under extremely good UHV conditions with mesured prtil pressure of H 2 O in the low mbr rnge, the trnsformtion from freshly prepred TiO surfce primrily covered with O-vc to fully hydroxylted surfce occurs within the first 2 h fter preprtion. Additionlly, we find tht the initil coverge of O-vc increses slightly with the number of clening cycles, in ccordnce with Ref. 36, nd for the experiments presented here, it ws estimted to be round 5% per surfce unit cell. The results presented in the following therefore reflect nc-afm imges of the TiO surfce in the hydroxylted stte, where the predominnt surfce defects re. B. Imge mode switching When imging the TiO surfce, primrily two types of nc-afm imging contrst modes were obtined s shown in Figs. 2 nd 3. In both cses, the chrcteristic brightdrk striped pttern ssocited with the 1 1 surfce structure is clerly resolved. However, upon close inspection, the two imges re seen to differ significntly, despite the fct tht they both represent the exct sme surfce. In both imges, the surfce shows smll popultion of defects. In Fig. 2, dditionl bright protrusions pper in between the bright prllel rows, similr to Fig. 1, wheres Fig. 3 shows dditionl drk holes locted in registry with the bright rows. We identify the defects s nd groups s indicted in the imges, in ccordnce with the results we presented in previous work. 11 From the expected position of the nd groups see Fig. 1, it is therefore cler tht the ionic sublttice imged bright differs in the two imges. We thus conclude tht the Ti 5c rows re imged bright in Fig. 2, despite their lower geometric positions, with the OH groups imged s bright protrusion in between the bright Ti 5c rows. Note tht this imge contrst closely resembles the somewht counterintuitive wy the TiO surfce is imged by STM due to electronic effects. 36 Oppositely in Fig. 3, the O 2c rows re imged bright with both nd groups imged s drk holes in registry with the O 2c rows. The fct tht the TiO surfce cn be imged in two such complementry contrst modes s shown in Figs. 2 nd 3 cn be trced bck to the electrosttic polrity of the imging tip pex. A negtively terminted tip, i.e., n nion e.g., O, genertes n imge where the Ti 5c rows re imged bright nd the O 2c rows imged drk, wheres positively terminted tip, i.e., ction e.g., Ti + genertes n imge with drk Ti 5c nd bright O 2c rows. The physicl reson for these two complementry contrst modes cn be explined from the simple picture of dditionl electrosttic forces rising between the chrged tip-pex tom nd the surfce ions. A positively chrged tip gives rise to n dditionl ttrctive interction with the negtively chrged oxygen nions in the surfce, cusing lrger negtive frequency shift, nd the O 2c rows will thus pper bright. The nd re polrized entities exposing the positive hydrogen proton of the hydroxyl to the AFM tip, nd the O-vc re less negtive thn the O 2c rows, which gives them the sme type of contrst s the positive Ti 5c toms, in this cse, drk reltive to the bright O 2c rows. Conversely, if the polrity of the tip-pex tom is switched from positive to negtive, so is the resulting contrst of ll species, explining the chrcteristic inverse reltionship of the two contrst modes shown in the imges in Figs. 2 nd 3. From our experimentl results, we find tht it is possible to induce the chnge between the contrst modes by gently touching the surfce with the tip, thereby rerrnging nd/or chnging the tip-pex toms so tht the polrity of the outermost tip tom is switched from positive to negtive ion or vice vers. Figure 4 is unique since it depicts n tomiclly resolved nc-afm imge of the hydroxylted TiO surfce recorded t close tip-surfce distnce, which induced sudden tip chnge, resulting in both of the bove described

6 NONCONTACT ATOMIC FORCE MICROSCOPY STUDIES OF fr from the surfce close to the surfce b c Height (nm) H Ti- ~85 pm C Ti-O ~60 pm Dist (nm) [-110} d Height (nm) H Ti- ~-30 pm C Ti-O ~130 pm Dist (nm) FIG. 2. Color online nd b Constnt frequency shift nc-afm imges of the TiO surfce is cutout of Fig. 2 of Ref. 11. In both imges, the Ti 5c rows re imged s bright prllel lines with imged s bright protrusions locted in-between. c nd d Cross-section grphs tken long the white solid lines in the 110 direction in nd b, respectively. Imging prmeters IPs for for b re df= 45 Hz 95 Hz, Ampl p-p 25 nm 25 nm, U bis =0.93 V 0.76 V, nd size=7 7 nm nm 2. imging modes being resolved within the sme imge. The imge contrst of the bottom prt of the imge in Fig. 4 is the sme s tht of the imge in Fig. 3, where drk holes ssocited with groups re imged scttered long nd in registry with the bright O 2c rows, wheres the imge contrst of the upper prt is the sme s tht of the imge in Fig. 2, with bright protrusions lso ssocited with groups re imged lying in between the bright Ti 5c rows. At the point indicted by the lower horizontl white dshed line, the tip probbly cme in close contct with the surfce, cusing the toms forming the tip pex to rerrnge, resulting in semiunstble tip. This event produced fussy contrst for short period few line scns, but reltively quickly the tip-pex stbilized, nd good imging contrst ws recovered. The grph in the left in Fig. 4 shows crosssectionl scn of the nc-afm imge, prllel to the slow scn direction indicted by the verticl white solid line. It is cler tht the chnge in imging contrst is ssocited with tip-jump, where the feedbck loop instntly retrcts the tip, cused by n ltertion of the outermost tip toms. The chnge in height is, however, reltively smll, only 110 pm, indicting tht the chnge in the tip-pex conformtion tkes plce on the single-tom level, nd most likely, single oxygen nion hs been picked up from the surfce nd dded to the tip pex, cusing the tip jump nd switching the polrity of the tip-pex tom from positive to negtive. After the tip chnge, the imging tom on the tip pex is no longer the sme, nd hence the imging site on the tip is no longer the sme. This chnge is lso evident in the imge in Fig. 4, s the bright O 2c rows in the lower prt of the imge do not lign with the drk O 2c rows in the upper prt. In the following, the imging contrst modes in the lower nd upper prts of the imge in Fig. 4 will be referred to s hole mode nd protrusion mode, respectively, referring to the contrst with which the re imged. For both the protrusion mode nd hole mode, we observed vritions in contrst corrugtion. We find tht the corrugtion between the Ti 5c nd O 2c rows C Ti-O, nd lso the reltive height or depth of O-vc,, nd, my vry significntly depending on the nc-afm scnning prmeters nd on the stte of the tip. These dependencies my significntly complicte the interprettion of the AFM imges nd led to confusion bout the stte of the surfce nd the prevlent types of defects or dsorbtes, 39 nd in the following, we will therefore provide detiled nd thorough nlysis of both scenrios

7 ENEVOLDSEN et l. fr from the surfce close to the surfce b c Height [nm] C Ti-O ~70 pm H Ti- ~0 pm 0.05 H Ti- ~-30 pm Dist [nm] C Ti-O ~70 pm d Height [nm] C Ti-O ~50 pm H Ti- ~30 pm Dist [nm] FIG. 3. Color online nd b Constnt frequency shift nc-afm imges of the TiO surfce. In both imges, the O 2c rows re imged s bright prllel rows, with nd only imged s drk holes in registry with these bright rows. c nd d Cross-section grphs tken long the white solid lines in the 110 direction in nd b, respectively. IPs for for b re df= 34 Hz 27 Hz, Ampl p-p 20 nm 20 nm, U bis =0.95 V 2.18 V, nd size=7 7 nm nm 2. C. Negtively terminted tip (protrusion mode) Figures 2 nd 2 b show two tom-resolved AFM imges recorded with negtively terminted tip in the protrusion mode t lrge nd smll tip-surfce imging distnces, respectively. In both imges, we identify the bright rows s the Ti 5c rows, the drk rows in between s the O 2c rows, nd the bright protrusions lying in between the bright rows s. The two imges re, however, mrkedly different on more quntittive level. Both C Ti-O nd the height of the reltive to the Ti 5c rows H Ti- differ in the two imges. The solid white lines in Figs. 2 nd 2 b re represented s cross sections in Figs. 2 c nd 2 d, respectively, nd from these grphs, C Ti-O is mesured to be 60 pm t lrge tip distnce nd incresing to 130 pm t close tip distnce. The corresponding vlues for H Ti- re mesured to be 85 nd 30 pm, respectively. This finding implies tht even though the polrity of the imging tip-pex tom is identicl in the two imges, there is significnt difference of nerly fctor of 2 in C Ti-O, nd H Ti- even chnges sign. To nlyze further how the imge contrst vries s function of tip-surfce imging distnce, we hve clculted spectroscopic df vs distnce curves. The grph in Fig. 5 shows set of five df vs distnce curves for the negtively 0.20 ~110 pm Height [nm] Dist [nm] fst scn direction TIP-CHANGE FIG. 4. Color online Atomiclly resolved constnt frequency shift nc-afm imge of the TiO surfce, recorded 4 h nd 12 min fter preprtion. White dshed circles nd dotted lines indicte the position of, O 2c, nd Ti 5c rows, s indicted. The imge hs been corrected by line-by-line first order polynomil fit long the fst scn direction for better color contrst. To the left is cross section tken long the solid white verticl line of the rw-dt imge. IP: df= 306 Hz, Ampl p-p 20 nm, U bis = 0.23 V, nd size=9 9 nm 2. hole-mode contrst semi-unstble tip protrusion-mode contrst slow scn direction

8 NONCONTACT ATOMIC FORCE MICROSCOPY STUDIES OF low lrge Frequency shift [rb units] drkest / lowest brightest / highest II I brightest / highest I Norml-Regime IICrossover-Regime drkest / lowest O-vc drkest/ lowest O-vc O-vc brightest/ highest b Tip-surfce distnce [nm] 0.5 constnt df imges c rows rows lrger df set-point I II FIG. 5. Color online Grph with five df vs distnce curves used for identifying the imging contrst of the different species on the surfce s function of tip-surfce seprtion distnce. The zero-point for the x xis is the relxed position of the O 2c toms. The verticl guidelines t x 0.25 nm nd x 0.45 nm hve been rotted nd re depicted on the right showing the reltive cross points for the different curves. b nd c Simulted constnt frequency shift imges of four equidistntly plced long every second O 2c rows. c ws simulted t lrger more negtive frequency shift set point thn b. Imge size= nm 2 terminted tip clculted over the prevlent sites on the surfce. For completeness, we consider both the O 2c nd Ti 5c sublttices s well s O-vc nd 40 sites. The force curves were clculted using stndrd vdw contribution from the mcroscopic tip shpe s discussed in Sec. II. The reltive positions of the force curves were not ffected by chnges in the vdw contribution, nd the qulittive behvior described by the df vs distnce curves is therefore generlly vlid for ny type of mcroscopic tip shpe. The key to understnd the df vs distnce grph in Fig. 5 is to interpret it in constnt height picture. It should be noted tht the experiments presented here were not crried out in the constnt height mode, but the contrst in constnt height imges nd constnt frequency shift imges, s recorded here, re qulittively similr when imging flt surfces. 7 We cn thus nlyze the df vs distnce grphs within constnt height model, in which tips with different vdw contributions shrpness re esier to compre, nd directly compre such df vs distnce grphs qulittively with the results from our experimentl nc-afm imges. The imge contrst, for given tip-surfce imging distnce, cn be estimted by compring the reltive cross points between verticl guideline s shown twice in Fig. 5 nd the site-specific df curves. The inserted verticl guidelines t 0.45 nd 0.25 nm reflect the two imges in Figs. 2 nd 2 b, corresponding to lrge nd smll tip-surfce imging distnces, respectively. For clrity, the sections hve been rotted nd depicted in the right to better illustrte the reltive positions of the crossing points of the five site-specific df curves. At the lrge tip-surfce imging distnce of 0.45 nm, the different chemicl fetures on the TiO surfce would be imged:,, Ti 5c, O-vc, O 2c, in order of decresing brightness or equivlently decresing height. This brightness or height ordering of the different species grees perfectly with the detiled nlysis in our previous study, 11 s well s with the imge nd corresponding cross sections depicted in Figs. 2 nd 2 c, respectively. We will therefore subsequently refer to the tip-surfce imging distnce rnge where this ordering occurs s the norml regime. To verify the direct comprison between the constnt height nlysis of the df vs distnce grph nd our experimentl constnt frequency shift imges, we simulted constnt frequency shift imge see Sec. II in the norml regime, which is shown in Fig. 5 b. The contrst of the simulted imge mtches the nlysis presented bove, with the being significntly brighter thn the Ti 5c row, which is imged bright reltive to the drk O 2c rows. At shorter tip-surfce imging distnce of 0.25 nm, the order of df curves crossing the verticl guideline chnges. Now, the Ti 5c rows re imged with the brightest intensity e.g., highest, followed by,, O-vc, nd O 2c in order of decresing height, with the nd being imged only slightly lower thn the Ti 5c rows. Also, the C Ti-O would be much lrger s compred with the situ

9 ENEVOLDSEN et l. tion for the lrger tip-surfce imging distnce. This brightness or height ordering is in excellent greement with the experimentl smll tip-surfce distnce imge nd crosssection grph shown in Figs. 2 b nd 2 d, respectively. In the following, we refer to the tip-surfce imging distnce rnge, where the contrsts for nd nd Ti 5c re comprble, s the crossover regime. In Fig. 5 c, simulted constnt frequency shift imge in the crossover regime is depicted, nd the qulittive greement with the experimentl nc-afm results is evident. The contrsts for the nd the Ti 5c re now comprble, with the being only slightly brighter thn the Ti 5c, nd the contrst difference between the Ti 5c nd the O 2c rows is significntly lrger, s compred with the simulted norml regime imge in Fig. 5 b. Also, if we compre the two simulted imges in Figs. 5 b nd 5 c, it is evident tht the pprent width of the Ti 5c rows is lrger for the crossover-regime imge. This difference is not directly visible from the df vs distnce curves in Fig. 5, but it mtches perfectly with the results from the experimentl imges in Figs. 2 nd 2 b. The two imges in Figs. 2 nd 2 b nd the df vs distnce grph in Fig. 5 indicte tht for the protrusion mode the C Ti-O nd the H Ti- re coupled, in the sense tht lrger C Ti-O is coupled to smller or more negtive H Ti-. This point will be nlyzed in more detil below. It is somewht unexpected tht the Ti 5c rows cn be imged higher thn the nd groups even though the Ti 5c toms geometriclly reside pproximtely 0.23 nm lower see Fig. 1 d. This point, however, simply underlines the fct tht both the tip-surfce imging distnce, the chemicl identity of the surfce toms, tip, nd surfce relxtion nd, prticulrly for compound oxide surfces such s TiO 2, the electrosttic polrity of the surfce toms re ll importnt prmeters in determining the resulting nc-afm imging contrst. 41 It should be noted tht for the simulted imges, we could not probe the full tip-surfce distnce rnge of the crossover region in Fig. 5 nd rech the point where the Ti 5c rows re imged s the brightest in imges. This difficulty is due to the onset of shrp jump in the force curve over the Ti 5c site, which prevents stble numericl solution of the cntilever dynmics. This jump is very dependent on the exct structurl configurtion nd chemistry of the tip pex, 42 which re unknown in the experiments, nd my be considered technicl limittion of the simultions. It should lso be noted tht the reltively high density of defects in the constnt frequency shift simulted imges mkes n bsolute comprison of contrst between defects nd idel surfce sites, e.g., H Ti-, somewht difficult, s there is risk of significnt degree of cross-tlk. The simulted imges presented here re only ment s supporting mteril for the df vs distnce grph, which holds the rel physicl informtion. Absolute contrst or height should be mesured with respect to surfce sites fr from the OH group. 11 D. Positively terminted tip (hole mode) Figures 3 nd 3 b depict two imges of the TiO surfce recorded with positively terminted tip in the holemode contrst t lrge nd smll tip-surfce imging distnces, respectively. It is noted tht the frequency shift set point t which the two imges were recorded is lmost equl, perhps even suggesting tht Fig. 3 b ws recorded closer to the surfce thn Fig. 3. The imges were, however, recorded with different tips, nd direct comprison of the frequency shift set points is therefore mbiguous, wheres the nlysis presented in the following justifies the bove clssifiction. In both cses, the contrst is now inverted compred to Figs. 2 nd 2 b nd we now identify the bright nd drk rows s the O 2c nd the Ti 5c rows, respectively, nd the species visible s drk holes in registry with the bright O 2c rows re identified s nd s illustrted in the imges. Agin there is significnt difference in the reltive levels of contrst ssocited with the sublttices nd surfce species depending on the minimum tip-surfce imging distnce. In Fig. 3, the nd re imged s well-defined drk holes in registry with the bright O 2c rows. The cross sections shown in Fig. 3 c, indicted by the two white solid lines, revel tht the depth ssocited with the is noticebly lrger s compred with the depth of. The C Ti-O is mesured to be 70 pm, nd the height of the nd defects mesured reltive to the drk Ti 5c rows is found to be 0 nd 30 pm, respectively. The imge in Fig. 3 b is striking in the sense tht the surfce now my seem defect- nd dsorbte-free, i.e., reflecting perfectly stoichiometric TiO surfce, but this is not the cse. The surfce is in the sme chemicl stte s the imges in Fig. 3, nd creful nlysis of the corresponding cross-section grph, shown in Fig. 3 d, indeed revels shllow pit locted in one of the bright O 2c rows representtive of. The C Ti-O nd H Ti- re mesured to be 50 nd 30 pm, respectively. The imge in Fig. 3 b shows tht the cn pper with roughly the sme height s the O 2c rows t smll tip-surfce imging distnces, which effectively mkes them invisible, nd one might erroneously be left with the impression tht the surfce is defect-free. We hve often recorded imges t firly long time fter the initil surfce preprtion, which often only depict bright prllel rows with no dditionl species present on the surfce, which gin might indicte perfectly stoichiometric surfce. The only wy of chieving such surfce stte from the initilly prepred surfce is by hydroxylting ll O-vc, nd then stimulting the desorption of the hydrogen dtoms from the remining hydroxyl groups, e.g., by pplying lrge bis voltge 3 V s demonstrted in previous STM experiments. 13,43 We lwys use moderte bis voltges in the rnge ±1 V, so this effect cnnot ccount for our pprent stoichiometric surfces. The grph in Fig. 6 presents the clculted df vs distnce curves for O 2c, Ti 5c, O-vc,, nd 40 sites for positively terminted tip. Agin, the verticl guideline t 0.45 nm represents the lrge tip-surfce imging distnce, nd it is seen tht the O 2c rows re imged s the highest followed by the O vc, Ti 5c,, nd in order of decresing height, with the Ti 5c nd the being imged t lmost the sme height. This finding is in perfect greement with the experimentl observtions in Fig

10 NONCONTACT ATOMIC FORCE MICROSCOPY STUDIES OF low lrge Frequency shift [rb units] O-vc drkest / lowest brightest/ highest b 0.2 I Norml-Regime II Crossover-Regime II drkest / lowest Tip-surfce distnce [nm] drkest / I lowest brightest / highest O-vc constnt df imges O-vc c rows O-vc rows brightest / highest I lrger df set-point II FIG. 6. Color online Grph with five df vs distnce curves used for identifying the imging contrst of the different species on the surfce s function of tip-surfce seprtion distnce. The zero-point for the x xis is the relxed position of the O 2c toms. The verticl guidelines t x 0.21 nm nd x 0.45 nm hve been rotted nd re depicted on the right, showing the reltive cross points for the different curves. b nd c Simulted constnt frequency shift imges of four equidistntly plced long every second O 2c rows. c ws simulted t lrger more negtive frequency shift set point thn b. Imge size= nm 2 3, nd the imging regime where this ordering is vlid is lbeled the norml regime. The simulted constnt frequency shift imge in the norml regime shows bright O 2c rows reltive to the drk Ti 5c rows with the imged s well-defined drk holes with the sme contrst s the Ti 5c rows, confirming the greement between the theoreticlly df vs distnce curves nd experimentl imges. At closer tipsurfce distnce corresponding to the verticl guideline t 0.21 nm in Fig. 6, the sitution is mrkedly different. Now, the groups re imged s the highest, followed by O 2c,, Ti 5c, nd O-vc in order of decresing height. The predicted height of the s being in between tht of the Ti 5c nd tht of the O 2c rows mtches nicely with the mesured C Ti-O nd H Ti- for the smll tip-surfce distnce s indicted in Fig. 3 d, nd this imging regime is lbeled the crossover regime. In Fig. 6 c, the simulted imge in the crossover regime is shown, nd the signture of the hs wekened noticebly. The contrst of the is now slightly brighter compred with the drk Ti 5c rows, nd the width long the 001 direction hs been reduced, which is gin in qulittive greement with the experimentl findings. At very smll tip-surfce imging distnces, the positively terminted tip cuses significnt displcement of the hydrogen proton in the OH group wy from the tip, reducing the screening of the underlying bridging oxygen toms, nd the overll interction is convolution between the electrostticlly positive tip pex, positive hydrogen, nd the exposed negtive oxygen ion. For certin tips nd tipsurfce distnces, we expect this convolution to result in the interction over O 2c nd over being similr, nd the signture of the my vnish explining the pprent stoichiometric imges seen in the experiment. It is furthermore noted from the df vs distnce curves in Fig. 6 tht since the Ti 5c nd the O 2c curves run lmost prllel, the C Ti-O should remin lmost constnt independent of the tip-surfce distnces, which is in greement with the experimentlly mesured vlues for C Ti-O s obtined from the imges in Figs. 3 nd 3 b. Also, the pprent increse in width of the drk Ti 5c rows with decresing imging distnce, s evident from the experimentl imges in Figs. 3 nd 3 b, is in good ccordnce with the simulted imges in Figs. 6 b nd 6 c. E. Covlent tip (neutrl mode) We hve lso imged the surfce in third but rther rre mode shown in Fig. 7, which does not fit into the models discussed bove, explining the contrst by n electrostticlly chrged positive or negtive tom terminting the AFM tip. Insted, the surfce ppers in the nc-afm imges s one would expect from the geometry of the hydroxylted TiO surfce see Figs. 1 b 1 d. The O 2c rows re imged bright reltive to the drk Ti 5c rows, with even brighter protrusions lying directly on top of the bright O 2c rows, reflecting the position of the hydrogen toms belonging to the groups. The C Ti-O nd the height of the

11 ENEVOLDSEN et l. b Height [nm] cheight [nm] 0.10 H O- ~25 pm ~25 pm C Ti-O ~40 pm Dist [nm] FIG. 7. Color online Constnt frequency shift nc-afm imge of the TiO surfce, recorded 6 h nd 34 min fter preprtion. The bright prllel lines re the O 2c rows nd the bright protrusions on top of the bright rows re. b nd c Cross sections tken long the two white solid lines in the 110 direction in. The lrge white dotted circle indictes chrge ptch imged slightly higher thn the unperturbed surfce. IP: df= 53 Hz, Ampl p-p 25 nm, U bis =0.95 V, nd size=15 15 nm 2. reltive to the bright O 2c rows re mesured to be 40 nd 25 pm, respectively. A similr imge contrst ws previously reported by Fukui et l. in Ref. 4. We explin this finding in terms of n electrostticlly neutrl nd wekly intercting tip pex, nd possible tip termintion could be tht of pure silicon tip. A silicon tip is generlly considered to bind covlently to most surfces, nd such silicon tip hs theoreticlly been shown to produce bright contrst on the O 2c rows reltive to the drk Ti 5c rows. 44 However, there hve so fr been no published results of the imging of group with silicon tip, nd simulting nc-afm imge of this mode is beyond the scope of this work. In first-principles simultions of the interction of silicon tip with the MgO surfce, 45 we found the interction with the dsorbed hydrogen to be stronger thn with surfce oxygen nd the interction with mgnesium to be much weker. This finding further supports the rgument tht silicon tip is the source of the neutrl-mode imges. The bright, rther lrge re in the center of the imge in Fig. 7, indicted by the dshed circle, is likely to be of the sme origin s similr fetures visible in STM experiments, 46 nmely, chrged subsurfce impurities, which leds to chnges in the locl electronic structure. It is evident from STM imges of the TiO surfce, both from our experience nd tht of others, 38,47 tht hydroxyls nd O-vc re repelled by these chrge ptches or subsurfce impurities which lso seems to be the cse for the imge presented in Fig. 7. It my seem unlikely tht the imge in Fig. 7 hs been recorded with n electrostticlly neutrl tip, since it detects the chrged subsurfce impurities producing lrge re of brighter contrst. The cross-section grph in Fig. 7 c indictes tht the bright re is imged 25 pm higher reltive to the unperturbed surfce. This observtion cn be explined by the fct tht since the locl electronic structure is ltered by the subsurfce impurities, so is the locl surfce potentil or locl work function. This lterntion leds to n uncompensted chnge in the contct potentil difference between the surfce nd the tip, resulting in n dditionl ttrctive contribution to the force, positive contribution to the force grdient, nd ultimtely n incresed negtive frequency shift, cusing the re to be imged slightly higher. 48,49 F. Sttisticl nlysis of different tip termintions nd imging modes It is interesting to nlyze the probbility of certin type of tip ppering, since the mnufcturing of nnotip suitble for tomic resolution, either by ccidentl or controlled contct of n AFM tip with the surfce being imged, must be considered s the outcome of stochstic process. The possibilities re numerous when tking into ccount the detiled structure nd composition of the resulting nnotip, but our experiments clerly show tht tomic resolution on TiO surfce comes only in the three generic ctegories nlyzed bove. Bsed on very lrge sttisticl dt set consisting of more thn 500 tom-resolved imges, we generlly observed the electrosttic tip termintions positive or negtive to be by fr the most dominnt, ccounting for more thn 95% of the totl tomic-resolved imges, split lmost eqully between the positively tip-terminted protrusion mode nd the negtively tip-terminted hole mode. The remining of less thn 5% is identified s neutrl-mode imges most likely recorded with pure silicon tip. This strong sttisticl bis towrd the electrostticlly terminted tips must reflect the sttisticl process of fbricting shrp nnotip in situ by gently touching the surfce with the tip. Intuitively, it mkes sense tht the tip is more likely to pick up or drop some TiO x mteril or rerrnge polr mteril lredy present on the tip, compred with the event for the tip to drop ll polr mteril including the ntive SiO x lyer present on new tips, exposing pure Si tip. Imges recorded

12 NONCONTACT ATOMIC FORCE MICROSCOPY STUDIES OF Corr. (nm) c Corr. (nm) Protrusion mode / Negtively terminted tip Height [nm] Hole mode / Positively terminted tip Height (nm) - Corrugtion (nm) b Crossover-Regime Norml-Regime Height (nm) Crossover-Regime Corrugtion (nm)d 100% invisible Norml-Regime Height (nm) 0.1 FIG. 8. Color online nd c Sttisticl nlysis 3D Gussin histogrms of corresponding Ti 5c -O 2c corrugtions nd Ti 5c - heights for the protrusion- nd hole-mode imges, respectively. On the sides of the 3D plot xz plne for y=0.25 nd yz plne for x=0.15, drwn re normlized curves representing integrls long constnt x nd y vlues, indicting the reltive bundnce of n independently mesured prmeter. b nd d re contour plots of nd c, respectively. Imging regimes re indicted by dshed circles. In d, solid blck line indicting where would hve exctly the sme contrst s O 2c mking them invisible hs been dded. with hydrogen Si-H or hydroxyl Si-OH terminted tip were tested theoreticlly nd gve lmost no nc-afm contrst, nd this could then ccount for the experimentl observtions not shown where smll tip chnge resulted in significnt deteriortion or complete loss of the tomic contrst. To nlyze the imging prmeter spce ssocited with different levels of contrsts ttinble within ech of the two predominting imging modes in more detil, we mde thorough sttisticl nlysis of corresponding C Ti-O nd H Ti- vlues mesured from very lrge set of 373 experimentl nc-afm imges. It is evident from the df vs distnce curves in Figs. 5 nd 6 tht C Ti-O nd H Ti- re intimtely linked throughout the imging distnce rnge, in unique wy depending on the contrst mode. The nlysis presented here verifies tht we re, in fct, ble to probe the entire imging distnce rnge, reveling lso the dominting level of imge contrst of both linked C Ti-O nd H Ti-, but lso independently mesured C Ti-O nd H Ti- vlues, within ech of the imging modes. Figures 8 nd 8 c re three-dimensionl 3D Gussin histogrms, where ech point in the xy plne is given the following z vlue: ll i exp x height i 2 k x 2 y corr i 2 2, k y where height nd corr re rrys contining the experimentlly mesured nd corresponding C Ti-O nd H Ti- vlues, respectively. The decy constnts k x nd k y re tken to be the pproximte uncertinties for the experimentlly mesured vlues, nd in this cse, both constnts were set to nm. This wy of producing sttisticl histogrms is superior to the more common bin-type histogrms, 50 s the shpe of these ltter ones nd, therefore, the conclusions drwn from them often depend criticlly on the chosen bin sizes nd bin positions. For the histogrm discussed here, there re no djustble prmeters, s the decy constnt is intuitively set to the mesurement uncertinty. In this wy, ech mesurement point is given s weighted distribution, rther thn delt-function-like pek. On the sides of the 3D plots in Figs. 8 nd 8 c, two curves re depicted. They indicte the vlue of integrls long constnt x nd y vlues, nd the curves re then subsequently scled to mtch the mximum z vlue of the corresponding 3D plot for better presenttion. As such, the curves represent the reltive dis

13 ENEVOLDSEN et l. tribution of independently mesured C Ti-O nd H Ti-, respectively, nd the most bundnt vlue is indicted on the grphs. It is evident from these distribution curves tht the ttinble vlues for both C Ti-O nd H Ti- re spred out over much wider rnge for the protrusion-mode imges compred with the hole-mode imges. The grphs in Figs. 8 b nd 8 d re contour plots of the 3D Gussin histogrms in Figs. 8 nd 8 c, respectively, nd here gin the difference in mesurble vlues is evident. This pprent difference in ttinble C Ti-O nd H Ti-, between the protrusion-mode nd the hole-mode imges, is in perfect ccordnce with the df vs distnce curves in the grphs in Figs. 4 nd 6. For the protrusion-mode grph negtively terminted tip, Fig. 4, the curves for the O 2c nd Ti 5c diverge from ech other s the tip-surfce distnce is decresed, indicting tht in constnt frequency shift mesurement, the C Ti-O would increse with n incresing df set point. Also, the verticl distnce between the Ti 5c nd curves vries significntly over the tip-surfce distnce rnge. For the hole-mode grph positively terminted tip, Fig. 6, the sitution is different. Here, the Ti 5c, O 2c, nd curves run much more prllel, indicting tht the reltive mesurble height difference between these species will vry significntly less with the tip-surfce imging distnce. If we nlyze the contour plot for the protrusion-mode mesurements in Fig. 8 b in more detil, we find tht the connection between C Ti-O nd H Ti-, s previously rgued for, is very cler: n increse in C Ti-O is coupled to decrese or negtive increse in H Ti-. The lrge pek in the center of the contour plot, where H Ti- is modertely positive nd the C Ti-O is reltively low, corresponding to the norml regime in the grph in Fig. 5 nd the imge in Fig. 2, sttisticlly domintes the grph nd is s such the most probble wy of imging the TiO surfce. The pek in the top-left corner corresponds to the crossover regime in Fig. 5, where C Ti-O is huge nd H Ti- becomes more nd more negtive, mtching the imge in Fig. 2 b. The pek in the bottom-right corner of the contour plot in Fig. 8 b, where H Ti- is reltively lrge nd C Ti-O is very low nd lmost vnishing, does not seem to fit nywhere on the df vs distnce grph in Fig. 5. We tenttively explin these experimentl dt s imges tken with n tomiclly blunt tip contining mixture of both nion nd ction pex toms, perhps TiO 2 nnocluster sitting in registry with the surfce ions, so tht the Ti 5c -O 2c geometric corrugtion is lmost exctly cnceled out by the electrosttic interctions between the ions in the tip nd surfce. It hs previously been shown how the exct rrngement of the ions in the tip pex reltive to the surfce ions cn hve lrge influence on the imging contrst. 51,52 For the sitution depicted here, it could destroy the tomic resolution on the idel stoichiometric surfce, leving only the ppernce of point defects, such s oxygen vcncies nd hydroxyls tht would brek the tip-surfce symmetry, to be visible. The contour plot for the hole-mode imges in Fig. 8 d is more difficult to divide into norml regime nd crossover regime since C Ti-O nd H Ti- vry significntly less. A solid blck line hs been dded in Fig. 8 d, lbeled 100% invisible, indicting tht for mesurement points directly on top of this line, the would be completely invisible nd therefore immesurble. The two regimes re indicted in the plot, with the norml regime ssigned to the centrl nd sttisticlly dominting region with H Ti- 0, nd the crossover regime ssigned to the region with comprble H Ti- nd C Ti-O, close to the 100% invisible line. G. Splitting of nd dynmics of groups revisited by noncontct tomic force microscopy The dynmic splitting of originlly formed by the dissocition of wter molecules t O-vc sites into two locted on seprte O 2c rows hs been extensively studied by STM, 25 but the process hs not erlier been investigted Before II I I II After b II FIG. 9. Color online nd b Constnt frequency shift nc-afm imges of the TiO surfce, recorded directly fter ech other t 1 h nd 5 min nd 1 h nd 12 min fter preprtion, respectively. The bright lines long the 001 direction re the Ti 5c rows nd the bright protrusions lying in between these bright rows re identified s nd. Two white squres lbeled I nd II re indicted in nd b, shown s zoom ins I bii. The white dotted circles nd rrows indicte where the resided in the previous imge nd where it hs moved to. IPs for for b re df= 45 Hz 55 Hz, Ampl p-p 25 nm 25 nm, U bis =0.93 V 0.93 V, nd size=10 10 nm nm 2. I bi bii