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bind defïŠ! /pgf6{gsave exec 1.0 pgfw [ ] 0.0 setdash -4.50003 -5.00005 moveto 0.49998 0.0 lineto -4.50003 5.00005 lineto pgfstr grestore} bind defòŽ! /pgf7{gsave exec 1.0 pgfw -2.50002 0.0 translate [ ] 0.0 setdash 3.00003 0.0 moveto 3.00003 1.65689 1.65689 3.00003 0.0 3.00003 curveto -1.65689 3.00003 -3.00003 1.65689 -3.00003 0.0 curveto -3.00003 -1.65689 -1.65689 -3.00003 0.0 -3.00003 curveto 1.65689 -3.00003 3.00003 -1.65689 3.00003 0.0 curveto closepath gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath grestore} bind defïß! /pgf8{gsave exec 1.0 pgfw [ ] 0.0 setdash 1.0 0.0 moveto -5.00005 3.00003 lineto -11.00012 0.0 lineto -5.00005 -3.00003 lineto closepath gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath grestore} bind defŸ ó³ ¸ txb¼ESM‘€2.Ž‘$«…T‘ÿzemporal‘€deÙ™væfelopmentŽŸ!‘ï[src:21C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texóÒ+|æ txr»The–³étwæfo›³êgraphene“samples“haÌÌvÙ™e“been˜imaged“ten“and˜twenty“times“respectiÀvšÙ™ely‘ÿY™.‘µUThe“e˜xposure“time‘³êfor“eachŽ¤indiÀvidual–Óimage“is“1s.‘CThe“structural“changes“in“the“graphene“lattice“o•Ù™v“er–Ótime“is‘Òhere“analyzed“by“applying“theŽ¡proposed–3ªmethod›3©to“each˜eÙ™xposure“separately˜and“eÙ™xtracting˜the“estimated“C-C‘3{bond˜lengths.‘4–Section˜2.1“containsŽ¡illustrations–Ðand“descriptions“for“the‘Ðten“eÙ™xposures“of“the“pristine“graphene“sample.‘ ïSection“2.2“contains“similarŽ¡information–€for“the“twenty“eÙ™xposures“of“the“altered“graphene“sample.Ž¡‘ï[src:27C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texThe–$¤hó3ypothesis“of›$£whether“the“material“changes“signi cantly“during˜the“time“of“the“e•Ù™xposures˜haÌÌv“e–$¤been“testedŽ¡using–­Ya›­Zruns“test.‘¡¥The“null“hó3ypothesis˜of“the“aÌÌvÙ™erage“bond˜length“changing“randomly˜o•Ù™v“er–­Ytime“could“not˜be“rejectedŽ¡in–Fneither›Gthe“pristine˜case“(ó,iû txmi¿p‘½æ»=‘½å0¿:»81),‘&˜nor˜in“the“altered˜case“(¿p‘½æ»=‘½å0¿:»83).‘©mThus“there˜is“no˜eÀvidence“for˜a“temporalŽ¡trend–€in“either“case.ŽŸ$ó¨»ÙÙ txiÈ2.1.Ž‘Pristine‘€grÙ™apheneŽŸ‘ï[src:34C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.tex»The–°ten“eÙ™xposures›¯of“the“pristine“graphene“sample˜haÌÌvÙ™e“underÑëgone“the“analysis“described˜in“the“main“teÙ™xt.‘~FigureŽ¡1– contains› the“cumulatiÀvÙ™e“distribÌÌution˜functions“(CDFs)“of˜the“estimated“C-C‘Úbond“lengths“for˜each“eÙ™xposure.‘ù TheŽ¡histograms–ÖTrepresenting“the›ÖUsame“distribÌÌutions“can“be˜seen“in“the“main“teÙ™xt.‘–The“distribÌÌutions˜are“colored“accordingŽ¡to–)their“number“in“the“sequence,–Ti.e.,“the–) rst“ešÙ™xposures“are“dark“blue‘)žand“the“last“e˜xposures“are“bright“green.‘pIt“isŽ¡apparent–€that“the“estimated“distribÌÌutions“are“vÙ™ery“similar‘ÿs3.Ž¡‘ï[src:46C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texThe–ë‡ rst›ë†and“the˜last“eÙ™xposure˜in“the˜sequence“haÌÌvÙ™e˜been“o•Ù™v“erlaid˜the–ë‡estimated˜C-C‘ëkbonds˜in“Figures˜2{3.‘\-TheŽ¡C-C‘˜•bonds–˜›are“colored“according“to“their“length“and“clearly“ešÙ™xhibit“strong‘˜œhomogeneity“o˜v˜er“the“e˜xtent“of“the“image.Ž¡Exposures–€twæfo“through“nine“eÙ™xhibit“similar“structures.Ž¡‘ï[src:50C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texA‘;$runs–;Utest›;Tis“used“to˜test“the˜hó3ypothesis“of˜a“temporal“trend˜in“the˜aÌÌvÙ™erage“C-C›;$bond“length.‘K—A˜runs‘;Ttest“testsŽ¡if–ìëthe›ìêsequence“of“aÌÌvÙ™erage˜bond“lengths˜being“abo•Ù™v“e–ìëor˜beloÀw“the“o•Ù™v“erall˜aÌÌv“erage–ìëcan“be˜rejected“to˜be“random.‘`YAsŽ¡mentioned›Tabo•Ù™v“e,‘\åthe˜hó3ypothesis˜of‘Trandom˜ordering˜of˜the˜aÌÌv“erage˜C-C‘Tbond˜lengths‘Tcould˜not˜be˜rejected˜accordingŽ¡to–€a“runs“test“(¿p–Ç»=“0¿:»71).‘™Thus,–€as“eÙ™xpected“from“these“visualizations,“there“is“no“eÀvidence“of“a“temporal“trend.ŽŽŸ‘ø{äïcolor push gray 0’ç€1Ž’Ôï color popŽŽŒ‹* §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ z ÿc2Õ‘ø{ä þËšWïcolor push gray 0 4e©ŸÎBï[src:41C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texïTPSfile="esmPristine/temporal_colored_cdf.eps" llx=0 lly=-1 urx=655 ury=361 rwi=4662 ŽŽŸï[src:42C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texó/Ò+|æ txrÚFigure–Î1:‘aïA‘ÎcumulatiÌÍváGe›Îdistrib× ution“function˜(cdf)“for˜each“eáGxposure.‘j@The˜color“scale“is˜such“that˜the“ rst˜eáGxposure“is“dark˜blue“and˜the“last˜is“brightŽŸgreen.ŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻2Ž’Ôï color popŽŽŒ‹  §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÂÕ.‘ø{ä þ U¤ïcolor push gray 0 óª\ŸáB‘áÄï[src:66C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ïePSfile="esmPristine/Graphene_L1_Stelle3_0011_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=516 rwi=4662 Ž’Ôï color popŽŽŽŽ‘X9Ÿý§Çï^PSfile="esmPristine/Graphene_L1_Stelle3_0011_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘s¥ãïcolor push gray 0ÚFigure–2:›záExposure“number“1.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻3Ž’Ôï color popŽŽŒ‹"Ì §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÂÕ.‘ø{ä þ U¤ïcolor push gray 0 óª\ŸáB‘áÄï[src:75C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ïePSfile="esmPristine/Graphene_L1_Stelle3_0020_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=516 rwi=4662 Ž’Ôï color popŽŽŽŽ‘X9Ÿý§Çï^PSfile="esmPristine/Graphene_L1_Stelle3_0020_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘q¥ãïcolor push gray 0ÚFigure–3:›záExposure“number“10.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻4Ž’Ôï color popŽŽŒ‹%‰ §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ z ýœ‘ø{äÈ2.2.Ž‘ {äAlter¡Ged‘€grÙ™apheneŽŸ‘{äï[src:82C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.tex»The–®twenty“ešÙ™xposures“of“the“altered“graphene“sample‘¯haÌÌv˜e“underÑëgone“the“analysis“described“in“the“main“te˜xt.Ž¤‘ø{äFigure–«4›«contains“the˜cumulatiÀvÙ™e“distribÌÌution˜functions“(CDFs)˜for“each˜of“the˜twenty“eÙ™xposures.‘šÎInspecting˜thisŽ¡‘ø{ä gure,‘7there–$Àis“certainly“some“všÀariation“between“the“eÙ™xposures'‘$ÁdistribÌÌutions.‘û.As“mentioned“pre˜viously‘ÿY™,‘7the“hó3ypothesisŽ¡‘ø{äof–a“random“order“of›the“aÌÌvÙ™erage“C-C‘Ýbond“lengths˜could“not“be“rejected“(¿p‘Õ|»=‘Õ{0¿:»96),‘6„i.e.,‘6ƒthere˜is“no“eÀvidence“of“aŽ¡‘ø{ätemporal‘€trend.Ž¡‘{äï[src:85C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texThe–òvÀariation“in“the“estimates“can“be‘óinspected“in“Figures“5{8,›Gîwhere“the“ rst,‘Gïeighth,˜fourteenth“and“twentiethŽ¡‘ø{äešÙ™xposures–D{are“o˜v˜erlaid“the‘Dzestimated“structures“as“e˜xamples.‘ÂIt“is“seen“that›Dzthe“areas“to“the“left“and“the˜right“of“the“holeŽ¡‘ø{äare–¾ estimated›¾¡relatiÀvÙ™ely“consistent,‘ÎIwhile“the˜areas“abo•Ù™v“e˜and–¾ beloÀw˜the“hole˜change“in˜appearance“from˜eÙ™xposure“toŽ¡‘ø{äeÙ™xposure.‘ÜÍThis–flocal›gchange“is˜only“eÀvident˜in“the˜o•Ù™v“erlay–fimage˜and“not˜in“the˜distribÌÌution.‘ÜÌFigures˜6“and˜7“shoÀwŽ¡‘ø{äareas,‘ÝÎwhere–—Ùthe“method“fæfails›—Øto“con dently“estimate“anÙ™y˜structure“in“vÙ™ery“loÀw˜contrast“reÙ™gions.‘a#These“structuralŽ¡‘ø{ächanges–2and“the“loss›2in“contrast“in“some“areas“can“be˜correlated“to“a“beam“induced“e ect“as˜described“in“the“mainŽ¡‘ø{ämanuscript.‘$The–ƒ¢reduced›ƒ£contrast“can“originate“from“an“o set“in“height,‘„‹which“results“in“a“change“in˜focus.‘$This“lackŽ¡‘ø{äof–€estimated“structure“in“some“areas“also“adds“to“the“observÙ™ed“vÀariation.ŽŽŸ‘ø{äïcolor push gray 0’ç€5Ž’Ôï color popŽŽŒ‹(G §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ z ÿc2Õ‘ø{ä þËšWïcolor push gray 0 4e©ŸÎBï[src:96C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texïPPSfile="esmHole/temporal_colored_cdf.eps" llx=0 lly=-1 urx=655 ury=361 rwi=4662 ŽŽŸï[src:97C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÚFigure–Î4:‘aïA‘ÎcumulatiÌÍváGe›Îdistrib× ution“function˜(cdf)“for˜each“eáGxposure.‘j@The˜color“scale“is˜such“that˜the“ rst˜eáGxposure“is“dark˜blue“and˜the“last˜is“brightŽŸgreen.ŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻6Ž’Ôï color popŽŽŒ‹0w §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÀ–‘ø{ä þðÔïcolor push gray 0 î,ŸáBï\src:113C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ï_PSfile="esmHole/Graphenea_620000X_0065_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=512 rwi=4662 Ž’Ôï color popŽŽŽŽ‘W Ÿý¨öïXPSfile="esmHole/Graphenea_620000X_0065_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘s¥ãïcolor push gray 0ÚFigure–5:›záExposure“number“1.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻7Ž’Ôï color popŽŽŒ‹3+ §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÀ–‘ø{ä þðÔïcolor push gray 0 î,ŸáBï\src:120C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ï_PSfile="esmHole/Graphenea_620000X_0072_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=514 rwi=4662 Ž’Ôï color popŽŽŽŽ‘W Ÿý¨öïXPSfile="esmHole/Graphenea_620000X_0072_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘s¥ãïcolor push gray 0ÚFigure–6:›záExposure“number“8.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻8Ž’Ôï color popŽŽŒ‹ 5Û §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÀ–‘ø{ä þðÔïcolor push gray 0 î,ŸáBï\src:129C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ï_PSfile="esmHole/Graphenea_620000X_0078_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=514 rwi=4662 Ž’Ôï color popŽŽŽŽ‘W Ÿý¨öïXPSfile="esmHole/Graphenea_620000X_0078_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘q¥ãïcolor push gray 0ÚFigure–7:›záExposure“number“14.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’瀻9Ž’Ôï color popŽŽŒ‹ 8‹ §@á ýt‘ø{äïcolor push gray 0’Ôï color popŽŽ zŸÀ–‘ø{ä þðÔïcolor push gray 0 î,ŸáBï\src:136C:/dtu/phd/projects/graphene/article_patternrecognition/supplementary/esmtemporal.texÿïcolor push gray 0ï_PSfile="esmHole/Graphenea_620000X_0084_coloredbonds.eps" llx=0 lly=-1 urx=516 ury=514 rwi=4662 Ž’Ôï color popŽŽŽŽ‘W Ÿý¨öïXPSfile="esmHole/Graphenea_620000X_0084_colorbar.eps" llx=0 lly=0 urx=74 ury=282 rwi=425 ŽŽŽŽŽŽŸ‘q¥ãïcolor push gray 0ÚFigure–8:›záExposure“number“20.˜C-C“bonds“are“colored“according“to“length.ï color popŽŽŽï color popŽŽŸ‘ø{äïcolor push gray 0’å»10Ž’Ôï color popŽŽŒø;<ƒ’À;è§y3Ì{ä ó/Ò+|æ txró¨»ÙÙ txió,iû txmió³ ¸ txbóÒ+|æ txrù=îßßßßßßß