Quantitative nanostructure characterization using atomic pair distribution functions obtained from laboratory electron microscopes

Transcription

1 248 Z. Kristllogr. 2012, 227, / DOI /zkri # y Oldenourg Wissenshftsverlg, Münhen Quntittive nnostruture hrteriztion using tomi pir distriution funtions otined from lortory eletron mirosopes Milind Aeykoon I, Christos D. Mlliks II, Pvol Juhás III, Emil S. Božin I II, IV, Merouri G. Kntzidis I, III nd Simon J. L. Billinge*, I Condensed Mtter Physis nd Mterils Siene Deprtment, Brookhven Ntionl Lortory, P.O. Box 5000, Upton, New York 11973, USA II Deprtment of Chemistry, Northwestern University, 2145 Sheridn Rod, Evnston, IL, 60208, USA III Deprtment of Applied Physis nd Applied Mthemtis, Columi University, 500 West 120th Street, New York, 10027, USA IV Mterils Siene Division, Argonne Ntionle Lortory, Chigo, Illinois 60439, USA Reeived Deemer 17, 2011; epted Ferury 10, 2012 Pir distriution funtion / Eletron diffrtion / Nnomterils / Polyrystlline films Astrt. Quntittively relile tomi pir distriution funtions (PDFs) hve een otined from nnomterils in strightforwrd wy from stndrd lortory trnsmission eletron mirosope (TEM). The pproh looks very promising for mking eletron derived PDFs (epdfs) routine step in the hrteriztion of nnomterils euse of the uiquity of suh TEMs in hemistry nd mterils lortories. No speil tthments suh s energy filters were required on the mirosope. The methodology for otining the epdfs is desried s well s some opportunities nd limittions of the method. 1. Introdution One of the gret hllenges of nnosiene is to otin the quntittive strutures of nnoprtiles [4, 18]. The tomi pir distriution funtion (PDF) method hs reently emerged s powerful tool for doing this [13, 19, 3, 28, 27, 21, 24, 22, 29], ut otining the required high qulity diffrtion dt to High momentum trnsfer with good sttistis generlly requires synhrotron X-ry or splltion neutron dt from ntionl user fility. Here we show tht dt of suffiient qulity for quntittive nlysis of nnoprtile struture using the PDF n e otined from trnsmission eletron mirosopes (TEM) ville t mny reserh institutions. Quntittive struturl models were pplied to PDFs of severl nnoprtile systems showing tht eletron PDFs n e modeled with the powerful emerging modeling tools for studying PDFs in generl [15, 25, 32, 5]. This pproh omplements medium nd high resolution imging methods for studying nnoprtiles in the TEM. The ese of dt olletion nd uiquity of TEMs will mke this n importnt tool in the hrteriztion of nnostrutured mterils. * Correspondene uthor (e-mil: s2896@olumi.edu) A hllenge when using eletrons s proe is tht they stter strongly [11, 9] nd not ording to the wek sttering kinemtil sttering equtions on whih the PDF nlysis is sed [12, 34]. This would pper to rule out eletrons s soure of diffrtion dt for PDFs exept in the ses of very dilute, suh s gs-phse [31], smples. However, kinemtil, or nerly kinemtil, sttering is otined from eletrons when smple volumes re suffiiently smll tht multiple sttering events re not of high proility efore the eletrons exit the smple (typilly few nm of thikness), or when the sttering from the smples is highly inoherent, for exmple the sttering from morphous mterils nd wy from zone xes in rystl [35]. In these ltter ses, there is still signifint multiple sttering, ut it should e is suffiiently inoherent tht it n e treted s kground nd sutrted nd the resulting oherent signl n e treted kinemtilly. This hs een disussed in detil in numer of pulitions [7, 2, 1, 20]. This is used in the rpidly growing field of eletron rystllogrphy [35], nd hs een demonstrted in previous work of eletron diffrtion (ED) from glsses nd morphous mterils [23, 8, 7, 17, 26], though little hs een done in the wy of quntittive modeling in those studies. In these respets, the study of smll nnoprtiles is prtiulrly fvorle. The smples re inherently thin, limited to the dimeter of the nnoprtiles when they re dispersed s su-mono-lyer on holey ron support, nd the struture is typilly less oherent thn from rystls euse of the finite size effets tht signifintly roden Brgg peks nd the often lower symmetries of nnoprtile strutures due to surfe nd ulk relxtions. In ft fortuitously, the sttering is most kinemtil preisely for the smll nnoprtiles (<10 nm) tht re most enefiilly studied using PDF methods [13, 19, 3, 28, 27, 21, 24, 22, 29]. Here we show how to otin PDFs from norml trnsmission eletron mirosope (TEM) found in mny reserh ls. We find tht the resulting eletron PDFs (epdfs) n e modeled to extrt quntittive struturl informtion out the lol struture using PDF refine-

2 Quntittive nnostruture hrteriztion using tomi pir distriution funtions 249 ment progrms suh s PDFgui [15]. This opens the door to roder pplition of PDF methods for nnostruture hrteriztion sine TEM is lredy routine prt of the nnoprtile hrteriztion proess [33, 36]. With this development, s well s otining low nd high resolution TEM imges of nnoprtiles, quntittive struturl informtion, similr to tht normlly otined from Rietveld refinement [30, 37] in ulk mterils, is lso ville from nnoprtiles with little dditionl effort. This pproh lso omplements high resolution TEM y getting n verge signl from lrge numer of nnoprtiles rther thn giving informtion from smll prt of the smple tht my not e representtive. The ft tht the rel-spe imges nd the diffrtion dt suitle for struturl nlysis n e otined t the sme time nd from the sme region of mteril is lso lrge dvntge, resulting in more omplete informtion for the hrteriztion of the smple. In some ses, the smll quntity of mteril required for epdf, ompred to X-ry nd neutron PDF mesurements (xpdfs nd npdfs, respetively), my lso e mjor dvntge, s well s the ility to study thin films. Theoretil kground The Fourier trnsform of X-ry or neutron powder diffrtion dt yields the PDF, GðrÞ ording to [14] Q GðrÞ ¼ð2=pÞ Ð mx Q½SðQÞ 1Šsin ðqrþ dq ; ð1þ Q min where the struture funtion, SðQÞ, is the properly normlized powder diffrtion intensity nd Q, for elsti sttering, is the mgnitude of the sttering vetor, Q ¼ 4p sin ðqþ=l. [34, 13] The PDF is lso relted to the tomi struture through GðrÞ ¼ 1 P f i ð0þ f j ð0þ Nr ij hf ð0þi 2 ðr r ij Þ 4prr o ; ð2þ where the sum goes over ll pirs of toms i nd j seprted y r ij in the model. The form ftor of tom i is f i ðqþ nd hf ðqþi is the verge over ll toms in the smple. In Eq. (2), the sttering ftors re evluted t Q ¼ 0, whih in the se of X-rys is the tomi numer of the tom. The doule sums re tken over ll toms in the smple. For multiomponent system, SðQÞ n e written in terms of the onentrtions, i, of the toms [34, 13] SðQÞ ¼1 þ IðQÞ P i jf i ðqþj 2 j P i f i ðqþj 2 : ð3þ In the se of eletrons s proe, the equtions re the sme, providing the sttering n e treted kinemtilly [9]; however, the form ftor must e pproprite for eletrons, f e ðqþ, whih is the Fourier trnsform of the eletroni potentil distriution of n tom. Note tht in the eletron diffrtion literture, it is ommon to use s ¼ 2 sin ðþ=l ¼ Q=2p insted of Q for the independent vrile in the sttering. The eletron form ftor, f e ðqþ, is different to, ut losely relted to, the X-ry form ftor of the sme tom, f x ðqþ, whih is the Fourier trnsform of the eletron density. A useful reltionship etween f e ðqþ nd f x ðqþ is [9] f e ðqþ ¼ m ee 2 Z f x ðqþ 2h 2 Q 2 ; ð4þ where m e nd e re the mss nd hrge of the eletron, respetively, h is Plnk s onstnt, nd Z the tomi numer. This eqution does not give definite vlue for f e ðqþ t Q ¼ 0, ut f e (0) n e lulted y extrpoltion or y using f e ð0þ ¼4p 2 me2 3h 2 ðzhr2 e iþ ; ð5þ where hre 2 i is the men squre rdius of the eletroni shell of the tom [9]. Figure 1 shows omprison etween X-ry nd eletron form ftors, f x ðqþ nd f e ðqþ of Au. This form for the eletron form ftor is pproximte nd these pproximtions my introdue dditionl unertinties in resulting tomi displement prmeters (ADPs) otined from modeling resulting PDFs. However, we elieve tht these errors will e smller thn those introdued due to unounted for multiple sttering effets, s disussed lter, nd n proly e negleted, though this is not definitely estlished. In the se of single rystl ED, rule of thum is tht when the rystl thikness is greter thn Å, dt redution must e done sed on the dynmil diffrtion theory whih ssumes the presene of oherent multiple sttering omponents of eletrons [9]. Depending on the energy of the eletrons, this thikness limit my even fll elow these numers in the presene of hevy elements [9], nd in the se of eletron powder diffrtion, the verge thikness of rystllites in the speimen should lso e less thn few hundred Ångströms to void dynmil sttering effets [10]. Coherent multiple sttering hnges the reltive intensities of Brgg peks from the kinemtil struture ftor vlues, redistriutes intensity to the weker peks t higher vlues of Q [8] nd n llow symmetry disllowed peks to pper in the pttern. If G is the elsti men free pth of the eletron, it Fig. 1. A omprison etween normlized (to f (0)) X-ry nd eletron form ftors, f x ðqþ nd f e ðqþ of Au.

3 250 M. Aeykoon, C. D. Mlliks, P. Juhás et l. hs een shown tht PDF determined from polyrystlline Pt smple does not ffet the positions of the PDF peks for D/G 5, where D is the prtile size, ut it does ffet the determintion of oordintion numers [2]. Here we show tht model fits my e good, even in the presene of signifint multiple sttering, while refined therml ftors re underestimted, though it is desirle to optimize experimentl onditions suh s to minimize multiple sttering. Inoherent multiple sttering n e oserved in ED ptterns in the form of inresed kground [9] whih does not ffet the reltive intensities of the Brgg peks. This is why, in the se of less oherent struture, dynmil sttering effets re less importnt. In this study, ll the speimens used were nnosized smples: thin films, disrete nnoprtiles, or gglomertes of nnoprtiles. In this se, the hope ws tht multiple sttering would not introdue undue errtions into the kinemtil diffrtion pttern nd relile PDF will result. We found this to e lrgely true with n exeption we disuss elow. 2. Experimentl Nnorystlline thin film, or dispersed nnoprtiulte smples, were distriuted on holey ron grid nd ED dt tken with short mer length, to give the widest Q-rnge, nd reltively lrge em-size (2 5 mm dimeter) on the smple, to otin the est possile powder verge. To improve the powder verge different regions of the smple were illuminted y trnslting the smple under the em. In other respets, the TEM ws used in stndrd onfigurtion using CCD detetor with no energy filtering nd operted t 200 kev (wvelength, l ¼ 0: Å). All seleted re ED experiments were rried out t room temperture on Hithi H KeV trnsmission eletron mirosope equipped with Gtn Orius SC600 CCD Cmer (24 24 mm tive re). Typil exposure time per frme ws round 0.3 s. Formvr oted 300 mesh opper grids (Eletron Mirosopy Sienes) stilized with n evported ron film were used to support the metlli films nd nnoprtiles. Deposition of gold on the ron oted side of the TEM grid ws performed with Denton Vuum DeskIII sputterer gve uniform film. The thikness of the film ws mesured in rel time during the sputtering proess with the id of thikness monitor (Mxtek, In TM-350). Prt of the grid ws msked during the deposition nd this msked re ws used to extrt the diffrtion intensity of the support. No differenes were found in the diffrtion intensity dt of the kground (ron nd polymer films) etween different grids. Deposition on the side of the grid tht ws oted with the polymer gve Au nnoprtiles with wide rnge of sizes up to 100 nm. NCl nnoprtiles were deposited on TEM grid y rdio-frequeny therml evportion method. For omprison, X-ry mesurements on Au nnoprtiles were rried out in the rpid quisition mode (RAPDF) [6] using Perkin Elmer morphous silion 2D detetor t emline X7B t Ntionl Synhrotron Light Soure (NSLS) t Brookhven Ntionl Lortory (BNL). Nnoprtiles in ethnol solution were loded in 1 mm dimeter kpton tue seled t oth ends, nd mounted perpendiulr to the X-ry em. The dt were olleted t room temperture using the X-ry energy of 38 kev (l ¼ 0:3196 Å). The dt were olleted in multiple 4 s exposures for totl olletion time of 5 min. To lirte the onversion from detetor oordintes to sttering ngle, it is neessry to mesure the ED pttern from stndrd of known lttie prmeters. The softwre for reduing the dt to 1D, Fit2D [16] uses this to optimize the effetive smple-detetor distne, find the enter of the Sherrer rings on the detetor, nd orret for errtions suh s ny devition from orthogonlity of the detetor nd the sttered em. Typil stndrds used y the progrm re Al 2 O 3, CeO 2, LB 6, NCl nd Si. However, for the ED experiment it is neessry to hve nno-smple stndrd to otin good powder verge. For this, gold nnoprtiles of dimeter 100 nm were used nd literture vlue of Å for the lttie prmeter. The effetive smple-detetor distne depends on the settings of the mgneti lenses used in the mirosope. We ssumed tht the energy of the eletrons, 200 kev, is well known (resulting in l ¼ 0: Å), though for the most urte results the eletron wvelength should e lirted using stndrd methods. One these lirtion quntities re known, they re fixed nd the sme vlues re used to onvert the smple dt. From this perspetive, it is essentil tht the smple is mesured under identil onditions s the stndrd, inluding mer length nd fous. We found tht even snning round smple to find different viewing re resulted in smll vrition in the position on the detetor of the enter of the resulting diffrtion pttern. It ws thus neessry to run seprte lirtion run on eh diffrtion pttern to determine the enter of the rings, while keeping the mer-length from the Au lirtion. 3. Dt nlysis The 2D ED imges were red nd integrted into 1D powder diffrtion ptterns, fter sutrting properly sled kground mesurement of the empty holy ron grid nd msking the missing em stop region. The dt hve to e further proessed to otin the PDF. Other orretions were pplied to the rw dt to ount for experimentl effets nd properly normlized nd divided y hf e ðqþi 2 [13], resulting in the totl sttering struture funtion, SðQÞ. The kernel of the Fourier trnsform is the redued struture funtion, FðQÞ ¼Q½SðQÞ 1Š. We used home-written progrm, PDFgetE, to rry out these steps. The PDF is then strightforwrdly otined s the Fourier trnsform of FðQÞ ording to Eq. (1), whih is lso rried out in PDFgetE. One the PDFs re otined, they n e modeled using existing PDF modeling progrms. Here we used PDFgui [15].

4 Quntittive nnostruture hrteriztion using tomi pir distriution funtions Results Tle 1. Refined prmeters for 2.7 nm thik nnoprtiulte Au film, 100 nm dimeter nnoprtiles (NP) from epdfs nd from gold nnoprtile smple from xpdfs. The struture model is the f ulk gold struture, spe-group Fm3m. It ws not possile to mesure the nnoprtile size from the epdfs s we were not le to lirte the intrinsi Q-spe resolution of the ED mesurement llowing us to seprte the instrumentl resolution nd prtile size effets in the epdfs. epdf (film) epdf (NP) xpdf Q mx (Å 1 ) Fit rnge (Å) Cell prmeter (Å) 4.075(3) 4.076(2) 4.058(1) U iso (Å 2 ) 0.033(4) (3) 0.014(1) Dimeter (Å) (9) Q-dmp (Å 1 ) 0.095(5) 0.095(5) 0.047(2) Rw (%) : film thikness mesured during deposition : NP dimeter estimted diretly from the TEM imge Fig. 2. () A TEM imge of the 2.7 nm thik Au film used for ED. () A flse-olor 2D ED pttern olleted on this smple using 200 kev eletrons. Lighter olors indite higher intensity. The drk r ross the middle of the imge is the shdow of the em-stop. () 1D Au eletron powder diffrtion pttern otined y integrting round the rings in 2. The inset shows the high Q region of the ED pttern on n expnded y-sle. The dotted lines re guides to the eye. A low resolution TEM imge of the 2.7 nm thik Au film is shown in Fig. 2. The film is uniform nd fetureless in the imge, ut region t the edge of the film ws seleted for imging so tht the edge of the film gives visul ue to its presene. An ED pttern from position wy from the edge of the film is shown in Fig. 2. We n see series of onentri irles due to the Sherrer powder diffrtion rings in trnsmission geometry. The resulting 1D ED pttern, otined y integrting round the rings in the 2D pttern is shown in Fig. 2. Brod diffuse fetures re oserved tht re onsistent with the nnorystllinity of the smple. Wek fetures re lerly evident up to Q ¼ 12 Å 1 (Fig. 2 inset), ut less pprent eyond tht point. The FðQÞ from the sme dt fter orretion is shown in Fig. 3 nd the resulting epdfs in Fig. 3, with the lulted PDF from model of the gold f struture plotted on top in red. For omprison, in Fig. 3 nd d we show the X-ry derived FðQÞ nd xpdf, respetively. Unfortuntely this is not diret omprison etween identil smples. We were not le to ollet X-ry dt from the sme film s the epdf s it ws too thin to get suffiient signl in the X-ry mesurement. The struture funtions of the eletron nd X-ry dt (Fig. 3 nd, respetively) re lerly highly similr. Fetures in the efðqþ re roder thn the X-ry se ut the fetures re ll reognizle nd hve the orret reltive intensities. Likewise, the e- nd xpdfs (Fig. 3 nd d, respetively) re highly similr, with the fetures in the epdf of the nnosle film eing roder. The qulity of the fits is omprle for oth the epdf nd xpdf urves, with the epdf giving slightly lower (etter) greement ftor. The refined prmeters re presented in Tle 1. The redth of the epdf peks re ommodted in the model y giving gold very lrge ADPs, twie s lrge s those in the X-ry mesured gold nnoprtiles tht re lredy lrge. This indites the presene of signifint tomi sle disorder in the film nd is not oming from the epdf mesurement itself. This is disussed in greter detil elow. These results lerly demonstrte tht quntittively relile epdfs n e otined from nnorystlline mterils in stndrd lortory TEM. The ounting sttistis from the eletron dt ompre fvorly to those from the X-ry mesurements (Fig. 3 nd ), despite the muh shorter mesurement time, suggesting tht epdf determintion ould eome useful generl hrteriztion tool during nnoprtile synthesis. Two effets re lerly evident in the Q-spe dt: low Q-spe resolution nd the rpid diminishing of the mplitude of sttered fetures

5 252 M. Aeykoon, C. D. Mlliks, P. Juhás et l. d Fig. 3. () Redued struture funtion, FðQÞ, of Au otined from the integrted ED pttern in Fig. 2(), () An FðQÞ of Au nnoprtiles lulted from n XRD pttern olleted t X7B t the NSLS. () Au ulk struture model fit to the resulting epdf from 3(). (d) Au ulk struture model fit to the resulting xpdf from 3(). Oserved nd lulted PDFs re presented with lue irles nd solid red line, respetively. The differene etween oserved nd lulted is offset elow (green solid lines). In oth ses Q mx ¼ 15:25 Å. Fig. 4. () A TEM imge of 100 nm Au nnoprtiles used for ED. Blk dots re the nnoprtiles on the grid nd the lrge white res re the holes in the grid. () A kground sutrted ED imge, olleted from the sme region of the smple using 200 kev eletrons. () The 1D ED pttern otined y integrting round the rings in 4(). The inset shows mgnified region of the integrted ED pttern s indited y the dotted lines. with inresed Q. The ltter is likely to reflet rel differenes in the smples, with the rnge of struturl oherene eing lower in the gold film thn the gold nnoprtiles used in the X-ry experiment. The lower Q-spe resolution ould e either smple or mesurement effet ut this nnot e disentngled without hving well hrterized, kinemtilly sttering, nnoprtile stndrd for ED, whih doesn t urrently exist. The sputtered gold film hs n f gold struture, like the ulk, ut with signifintly more disorder nd nnometer rnge for the struturl oherene. The ED dt were tken with stndrd CCD mer nd no filtering of inelstilly sttered eletrons. This is the most strightforwrd protool for dt olletion s it is the stndrd setup in most lortory TEMs. It is expeted to result in lower qulity PDFs thn those mesured with energy filtered eletrons euse of the higher kgrounds due to inelstilly sttered eletrons [8]. ED dt olleted with n imge plte detetor re lso expeted to e higher qulity due to the low intrinsi detetor noise nd etter dynmi rnge of tht detetor tehnology. Thus, the resulting PDF shown in Fig. 3 represents the seline of wht is possile without speilized instrumenttion. The resulting FðQÞ shows exellent signl to noise up to the mximum essile Q-rnge of 17 Å 1, s evident in Fig. 3. To explore the size limits for Au NPs to stter kinemtilly, we olleted dt from lrger, 100 nm Au nno-

6 Quntittive nnostruture hrteriztion using tomi pir distriution funtions 253 prtiles, nd the results re lso given in Tle 1 nd Figs 4 nd 5. Compring the integrted 1D diffrtion ptterns of the lrge NPs nd the thin Au film, Figs. 4 nd 2, respetively, we see similr fetures, ut in the se of the NPs, the mplitudes of the sttered intensities extend to muh higher Q vlues, s if there is muh smller Deye-Wller ftor for the dt. This n e lerly oserved y ompring the efðqþ of the lrge nnoprtiles in Fig. 5 with those from X-ry diffrtion dt, xfðqþ in Fig. 5. The enhnement in the high-q fetures is lrge nd is lmost ertinly due to signifint oherent multiple sttering in this smple. The resulting epdf from the NPs hs peks tht re orrespondingly shrp ompred to the gold thin film the xpdfs of gold NPs. Regrdless of the presene of signifint multiple sttering, model ws refined ginst the epdf of the 100 nm Au nnoprtiles to see the extent tht the refined struturl model prmeters re ffeted. The struture refinement gve fits tht were slightly worse ut omprle in qulity to the xpdf fits (see Tle 1), R w ¼ 0:24. The refined vlues were similr lso, exept for muh smller tomi displement prmeters (ADPs), due to the rtifiilly shrpened PDF peks. It is somewht remrkle tht, in this se, the dynmil sttering produes fetures in the FðQÞ with pproximtely the orret reltive mplitude, ut extending to muh higher-q. Not only re the PDF peks in the right position [2], ut hve the right reltive mplitudes. Gold my e speil se euse the struture ftors re ll either ones or zero s. This lerly shows tht for strong stterer suh s Au, 100 nm nnoprtiles lredy give signifint dynmi- d Fig. 5. () The redued struture funtion, FðQÞ, of Au lulted from the integrted ED pttern in Fig. 4(), () An FðQÞ generted from n integrted Au NP XRD pttern from 2D dt set olleted t X7B t the NSLS. () Au ulk struture model fit to the resulting epdf from 5(). (d) Au ulk struture model fit to the resulting xpdf from 5(). Oserved nd lulted PDFs re presented with lue irles nd solid red lines, respetively. The differene etween oserved nd lulted is offset elow (green solid lines). Fig. 6. () A TEM imge of the NCl film used for ED. () A flseolor 2D ED imge olleted from this smple using 200 kev eletrons. Lighter olors indite higher intensity. The lk r ross the middle of the imge is the shdow of the em-stop. () The 1D ED pttern otined y integrting round the rings in 6(). The inset shows the high Q region of the ED pttern on n expnded y-sle. The dotted lines re guides to the eye.

7 254 M. Aeykoon, C. D. Mlliks, P. Juhás et l. Tle 2. Refined prmeters for nnoprtiulte NCl from epdfs nd for ulk powder of NCl from the xpdf. The struture model is the f rok-slt struture, spe-group Fm3m. It ws not possile to mesure the nnoprtile size from the epdfs s we were not le to lirte the intrinsi Q-spe resolution of the ED mesurement llowing us to seprte the instrumentl resolution nd prtile size effets in the epdfs. epdf xpdf Q mx (Å 1 ) Fit rnge (Å) Cell prmeter (Å) 5.62(2) 5.63(1) U iso N(Å 2 ) 0.007(5) 0.027(1) U iso Cl(Å 2 ) 0.004(4) 0.016(1) Q-dmp (Å 1 ) 0.095(5) 0.06(1) R w % 33 6 l effets. The resulting PDFs give useful semi-quntittive nd qulittive informtion ut the refined therml prmeters re not relile. Indeed, the effet of the multiple sttering to inrese the rel-spe resolution y oosting the intensities of the high-q peks mkes the PDF peks shrper with the result tht ond-lengths n e extrted with greter preision from the epdf dtin this se. When urte PDF pek positions rther thn quntittive pek intensities re desired, this ould e signifint dvntge of the epdf method, for exmple, when looking for smll pek splittings, or resolving pek overlps, to id in struture solution. A less trivil struture ftor is otined from inry ompounds suh s the NCl studied here. The TEM imge of the smple in Fig. 6 shows tht it onsists of nnosle rystllites, some of whih hve ui hit nd otherstht hve no prtiulr morphology. The orresponding ED pttern in Fig. 6 shows ler nd firly uniform rings, with some spottiness from n imperfet powder verge, whih my ontriute to the oserved disrepnies in the rok-slt model fit to the epdf. Figure 6 shows the integrted ED pttern. The FðQÞ nd the resulting epdf otined from this dt set is shown in Figs. 7 nd, respetively. For omprison, n xfðqþ nd n xpdf otined from ulk rystlline NCl smple re lso shown in Fig. 7 nd d. The rok-slt struture model fits to the PDFs re shown in Fig. 7 nd d nd the results re presented in Tle 2. The e- nd xpdfs re qulittively highly similr, with ll fetures in the xpdf esily reognizle in the epdf. Notly, the reltive intensities of djent peks re similr etween the e- nd xpdfs. Peks in the epdf die out in mplitude with inresing r more quikly, due to the roder fetures in the ED pttern. The overll qulity of the fit to the epdf is worse thn the xpdf of ulk NCl. Refined lttie onstnts gree well within the experimentl unertinty. The epdf refined therml prmeters re muh smller thn those otined from the X-ry dt. This is unlikely to e rel effet s oth the X-ry nd eletron dt were mesured t room temperture, nd it is rther implusile tht the nnoprtiulte smples hve less stti struturl disorder thn ulk NCl. We therefore ssume tht this is the effet of multiple sttering in the dt, similr to tht oserved for lrge Au NPs. Clerly, ADPs refined from epdfs present lower ound on tul smple ADPs. They re urte in the se where multiple sttering is negligile, ut underestimte the therml motions nd stti disorder in the presene of multiple sttering. Fig. 7. () The redued struture funtion, FðQÞ, of NCl otined from the integrted ED pttern in Fig. 6(). () AnFðQÞ of NCl lulted from n X-ry dt set. () NCl ulk struture model fit to the resulting epdf from 7(). (d) NCl ulk struture model fit to the resulting xpdf from 7(). Oserved nd lulted PDFs re presented with lue irles nd solid red lines, respetively. The differene etween oserved nd lulted is offset elow (green solid lines). In oth ses Q mx ¼ 13:6 Å. d 5. Disussion nd onlusions The Au nd NCl exmples estlish tht quntittively, or semi-quntittively, relile PDFs n e otined from nnomterils using eletron diffrtion dt otined on stndrd lortory TEM, without the use of filtering. Beuse of the ese nd speed of olleting suh dt nd the uiquity of suh instruments in hemistry nd mterils lortories, if the rriers to dt proessing ould e overome mking the whole proess strightforwrd, this

8 Quntittive nnostruture hrteriztion using tomi pir distriution funtions 255 ould eome rodly pplile stndrd nd useful hrteriztion method for nnoprtiles nd thin films. This work lso explores the experimentl prmeters for otining good dt for relile epdfs from nnomterils. Priniplly, smples should e thin enough or, for the se of nnoprtiles, hve suffiiently smll dimeter. Wht this dimeter is depends on the verge tomi numer of the smple. For Au, 100 nm dimeter NPs gve signifint oherent multiple sttering, 2.7 nm thik films did not. For ll mterils we expet tht 10 nm nd smller prtiles will stter kinemtilly; nd these re preisely in the size-rnge of nnoprtiles tht enefit the most from PDF nlysis [22]. Otining good powder verge is lso very importnt prt of powder diffrtion regrdless of the proing tehnique, XRD, ND or ED. This n e esily hieved y using lrge smple volume in ND nd spinning the smple in XRD. However, in ED, oth of these methods eome diffiult due to the limittions of the onfigurtion nd reful smple preprtion in this regrd is very helpful. Agin, for the prtiulr pplition in nnoprtile struture hrteriztion, the smll size of the prtiles mens tht etter powder verges n e otined even from smll smple volumes. However, the qulity of the powder verge should e heked y visul inspetion of the ED imges from the CCD, whih is redily done s is evident in the figures in this pper. The powder verge n e improved y inresing the em-spot size on the smple nd lso y tking multiple imges from different regions of the smple nd verging them. It is lso importnt tht smples e free of texture for PDF nlysis in the urrent implementtion. This my e prtiulrly relevnt in the se of polyrystlline thin films tht re prone to texture, though less so for nnosle nd morphous films nd mono (or few) lyer overges of nnoprtiles on surfe. The rw dt on the 2D detetor should e refully ssessed for the effets of texture. Texture in the plne of the film n e serhed for y looking for systemti intensity vritions round the diffrtion rings on the detetor. Perpendiulr texture ould e ssessed y tking diffrtion ptterns of the film with it tilted t different ngles with respet to the em nd ompring the resulting ring intensities. For highly textured film 2D rther thn 3D PDF trnsform my e more pproprite. In the future we pln to develop nd mke ville softwre for heking for texture nd where possile orreting for it. The mximum ttinle Q mx is determined y the opertionl energy, mer length, dimensions of the detetor nd the dimeter of the mirosope, ut in generl should e mximized. Our eletron mirosope onfigurtion equipped with CCD mer limited Q mx to ð17 18Þ Å. The dvntge of using higher Q mx is the etter rel spe resolution tht results in the epdf. However, stndrd mirosope onfigurtions nturlly give suffiiently high Q mx vlues for most pplitions. Thus there seems to e no impediment to the use of ED from stndrd lortory eletron mirosopes for quntittive nnoprtile struturl hrteriztion using the PDF. Aknowledgements. We would like to knowledge helpful disussions with Mihel Thorpe. We lso thnk Jon Hnson for llowing ess to the X7B emline t NSLS, whih is supported y DOE- BES under ontrt No DE-AC02-98CH Work in the Billinge group ws supported y DOE-BES through ount DE-AC02-98CH Work in the Kntzidis group ws supported y NSF through grnt DMR Referenes [1] Ankele, J.; Myer, J.; Lmprter, P.; Stee, S.: Quntittive eletron diffrtion dt of mrophous mterils. Z. Nturforsh. A 60A (2005) [2] Anstis, G. R.; Liu, Z.; Lke, M.: Investigtion of morphous mterils y eletorn diffrtion: the effets of multiple sttering. Ultrmirosopy 26 (1988) [3] Billinge, S. J. L.: Nnosle struturl order from the tomi pir distriution funtion (PDF): There s plenty of room in the middle. J. Solid Stte Chem. 181 (2008) [4] Billinge, S. J. L.; Levin, I.: The prolem with determining tomi struture t the nnosle. Siene 316 (2007) [5] Cervellino, A.; Ginnini, C.; Guglirdi, A.: DEBUSSY: Deye user system for nnorystlline mterils. J. Appl. Crystllogr. 43 (2010) [6] Chups, P. J.; Qiu, X.; Hnson, J. C.; Lee, P. L.; Grey, C. P.; Billinge, S. J. L.: Rpid quisition pir distriution funtion nlysis (RA-PDF). J. Appl. Crystllogr. 36 (2003) [7] Cokyne, D. J. H.: The study of nnovolumes of morphous mterils using eletron sttering. Annu. Rev. Mter. Res. 37 (2007) [8] Cokyne, D. J. H.; MKenzie, D. R.: Eletron diffrtion nlysis of polyrystlline nd morphous thin films. At Crystllogr. A 44(6) (Nov 1988) [9] Cowley, J. M.: Eletron Diffrtion Tehniques, 1st ed., vol. 1. Oxford University Press, [10] Cowley, J. M.: Diffrtion Physis, 3rd ed. Elsevier, Amsterdm, [11] Cowley, J. M.: Applitions of eletron nnodiffrtion. Miron 35 (2004) [12] Deye, P.: Dispersion of Röntgen rys. Annlen der Physik (Berlin, Germny) 46 (1915) [13] Egmi, T.; Billinge, S. J. L.: Underneth the Brgg peks: struturl nlysis of omplex mterils. Pergmon Press, Elsevier, Oxford, Englnd, [14] Frrow, C. L.; Billinge, S. J. L.: Reltionship etween the tomi pir distriution funtion nd smll ngle sttering: implitions for modeling of nnoprtiles. At Crystllogr. A 65(3) (2009) [15] Frrow, C. L.; Juhás, P.; Liu, J.; Bryndin, D.; Božin, E. S.; Bloh, J.; Proffen, T.; Billinge, S. J. L.: PDFfit2 nd PDFgui: Computer progrms for studying nnostruture in rystls. J. Phys: Condens. Mt. 19 (2007) [16] Hmmersley, A. P.; Svenson, S. O.; Hnflnd, M.; Husermn, D.: Two-dimensionl detetor softwre: from rel detetor to idelised imge or two-thet sn. High Pressure Res. 14 (1996) [17] Hirotsu, Y.; Ohkuo, T.; Be, I.-T.; Ishimru, M.: Eletron diffrtion struture nlysis for morphous mterils. Mter. Chem. Phys. 81 (2003) [18] Jdzinsky, P. D.; Clero, G.; Akerson, C. J.; Bushnell, D. A.; Kornerg, R. D.: Struture of thiol monolyer-proteted gold nnoprtile t 1.1 A resolution. Siene 318(5849) (2007) [19] Juhás, P.; Cher, D. M.; Duxury, P. M.; Punh, W. F.; Billinge, S. J. L.: A initio determintion of solid-stte nnostruture. Nture 440(7084) (2006), [20] Krle, J.: Struture determintion of gseous nd morphous sustnes y diffrtion methods: philosophil onepts nd their implementtion ( review). Pro. Ntl. Ad. Si. USA 74 (1977) [21] Kodm, K.; Iikuo, S.; Tguhi, T.; Shmoto, S.: Finite size effets of nnoprtiles on the tomi pir distriution funtions. At Crystllogr. A 62 (2006) [22] Msdeh, A. S.; Božin, E. S.; Frrow, C. L.; Pgli, G.; Juhás, P.; Krkmkr, A.; Kntzidis, M. G.; Billinge, S. J. L.: Quntittive size-dependent struture nd strin determintion of CdSe

9 256 M. Aeykoon, C. D. Mlliks, P. Juhás et l. nnoprtiles using tomi pir distriution funtion nlysis. Phys. Rev. B 76 (2007) [23] Moss, S. C.; Grzyk, J. F.: Evidene of voids within the sdeposited struture of glssy silion. Phys. Rev. Lett. 23 (1969) [24] Neder, R. B.; Korsunskiy, V. I.; Chory, C.; Müller, G.; Hofmnn, A.; Demski, S.; Grf, C.; Rühl, E.: Struturl hrteriztion of II VI semiondutor nnoprtiles. Phys. Sttus Solidi C 4(9) (2007) [25] Neder, R. B.; Proffen, T.: Diffuse Sttering nd Defet Struture Simultions A ook ook using the progrm DISCUS. Oxford University Press, Oxford, [26] Nörenerg, H.; Säverin, R.; Hoppe, U.; Holzhüter, G.: Estimtion of rdil distriution funtions in eletron diffrtion experiments: physil, mthemtil nd numeril spets. J. Appl. Crystllogr. 32 (1999) [27] Pge, K.; Proffen, T.; Terrones, H.; Terrones, M.; Lee, L.; Yng, Y.; Stemmer, S.; Seshdri, R.; Cheethm, A. K.: Diret oservtion of the struture of gold nnoprtiles y totl sttering powder neutron diffrtion. Chem. Phys. Lett. 393 (2004) [28] Petkov, V.; Gteshki, M.; Niedererger, M.; Ren, Y.: Atomisle struture of nnorystlline B x Sr 1 x TiO 3 (x ¼ 1, 0:5, 0) y X-ry diffrtion nd the tomi pir distriution funtion tehnique. Chem. Mter. 18 (2006) 814. [29] Petkov, V.; Oht, T.; Hou, Y.; Ren, Y.: Atomi-sle struture of nnorystls y high-energy X-ry diffrtion nd tomi pir distriution funtion nlysis: Study of Fe x Pd 100 x (x ¼ 0; 26, 28, 48) nnoprtiles. J. Phys. Chem. C 111(2) (2007) [30] Rietveld, H. M.: A profile refinement method for nuler nd mgneti strutures. J. Appl. Crystllogr. 2 (1969), [31] Shooss, D.; Blom, M. N.; Prks, J. H.; von Issendorff, B.; Herlnd, H.; Kppes, M. M.: The strutures of Ag þ 55 nd Ag 55 : Trpped ion eletron diffrtion nd density funtionl theory. Nno Lett. 5 (2005) [32] Tuker, M. G.; Keen, D. A.; Dove, M. T.; Goodwin, A. L.; Hui, Q.: RMCProfile: reverse Monte Crlo for polyrystlline mterils. J. Phys.: Condens. Mt. 19 (2007) [33] Wng, Z. L.: Trnsmission eletron mirosopy of shpe-ontrolled nnorystls nd their ssemlies. J. Phys. Chem. B 104(6) (2000) [34] Wrren, B. E.: X-ry Diffrtion. Dover, New York, [35] Weirih, T. E.; Láár, J. L.; Zuo, X.; Eds.: Eletron Crystllogrphy: Novel pprohes for struture determintion of nnosized mterils, Springer Amsterdm, [36] Won, J. H.; Sto, K.; Ishimru, M.; Hirotsu, Y.: Trnsmission eletron mirosopy study on FeSi 2 nnoprtiles synthesized y eletron-em evportion. J. Appl. Phys. 100 (July 2006) [37] Young, R. A.: The Rietveld Method, vol. 5 of Interntionl Union of Crystllogrphy Monogrphs on Crystllogrphy. Oxford University Press, Oxford, 1993.