Pair Distribution Function Obtained from Electron Diffraction: An Advanced Real-Space Structural Characterization Tool

Pair distribution function from electron diffraction (ePDF) is a remarkable technique capable of elucidating the atomic arrangement materials with high spatial resolution, especially those that do not present sharp reflections, such as amorphous and nanoparticles. Higher electron-matter interaction favors use ePDF for have weak Bragg higher amounts diffuse scattering. The analysis treatment reciprocal-space data are nowadays well developed, determining g(r) results. However, efforts should be made to enable improve quantitative analysis. Recent advances proved can reveal local structure details solid frozen liquid materials. Interpretation PDF real-space results requires simulations using structural references or fittings refine structure. We believe will become standard structure-characterization method nanomaterials Atomic-scale determination crucial understanding nanomaterial properties development new technologies. Although pair (PDF) by neutrons X-ray scattering profile has been used study materials, offer advantages characterize clusters, samples, nanomaterials. Electrons power than X-rays, allowing acquirement small sample time-efficient acquisition. Compared synchrotron X-rays sources PDF, availability microscopes worldwide advantageous. Nowadays, rise methodologies specific software analysis, scientific community benefit advanced transmission microscopy (TEM) integrating commonly available TEM analyses—size, distribution, shape, high-resolution visualization—with determination, both bulk surface configurations. Therefore, potential routine characterization tool science. In science, fundamental their applications. Crystalline structures successfully determined traditional techniques (XRD) (ED), which performed in (TEM).1Brandon D. Kaplan W.D. Microstructural Characterization Materials.2nd Edition. John Wiley, 2008Crossref Scopus (196) Google Scholar, 2David W. Shankland K. McCusker L. 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Nanoparticles: strained stiff.Science. 2004; 305: 651-654Crossref (394) instance, illustrate effect Figure 1A shows patterns ZrO2 microcrystals compared mean particle 3 nm. It important point out (HRTEM) image pictured inset confirms nature nanocrystals. This example broadening due size, described Scherrer equation, how non-trivial last decade, based neutron total mature well-established providing information materials.11Egami T. Billinge Underneath Peaks, Structural Analysis Complex Materials.1st Pergamon 2003Google Scholar,12Billinge S.J. Nanoscale order (PDF): there’s plenty room middle.J. Solid State 181: 1695-1700Crossref (109) this Perspective, we analyze review current progress challenges (mainly SAED) obtain i.e., ePDF, an degree disorder. Instead performing extensive published articles literature, provide obtained conventional nanomaterials, liquids. also importance combining theoretical calculations detailed analyses materials' arrangements. strongly functionality TEM, obtaining information. Materials ordering arrangement. At distances, nearest neighbors, dominated chemical bonds well-defined distances angles, originating short-range (SRO).13Egami S.J.L. Peaks: Series, Elsevier Science, 2012Google correlation holds long they exhibit long-range (LRO).13Egami Whereas (LRO) analyses, glasses, liquids challenge. These intermediate between SRO LRO (approximately 1–10 nm), named middle-range (MRO).12Billinge Likewise, sizes below 10 nm, having only few thousand atoms no LRO, up MRO, effects. reciprocal space challenge broaden, signal intensity diminishes, overlap.6Petkov Nanoparticles 20 200 nm usually defined peaks. Perspective will, therefore, generic term when broadly referring nanoparticles dimensions 2 Quantitative (SRO MRO) amorphous, liquids, nanocrystalline require go beyond identification reflections special approach neighbors’ coordination numbers Scholar,14Klug H.P. Alexander X-Ray Procedures: Polycrystalline Amorphous New York1974Google To better understand technique, imagine two-dimensional square (2D crystal) mark central atom lattice, illustrated 1B. 0 K, reference first sphere, where coordinated four neighbors at distance r1=r, next-nearest r2=2r, another r3=2r, eight r4=5r, so on. 1C number (n(r)) found radial r away T=0K. temperatures T>0K, but melting temperature (TM), increases slightly presence thermal vibrations, amplitude frequency displacements increase; however, still same. Under condition, around now 1D, displacement leads (broadened signal) instead exactly value n(r) (discrete peak). simple suitable parameter represent real One way describe correlations all positions via interatomic rij within system, i j being individual atoms. Thus, given density ?(r), known function,11Egami Scholar?(r)=?0g(r)=14?Nr2?i?j?(r?rij),(Equation 1) ?(r?rij) Dirac delta, ?0 material (number per volume, calculated taking inside unit cell divided volume), N Equation 1 r, graph. experimental relative possible. accounts probability finding atom, g(r).11Egami Both ?(r) structure: former directly latter Fourier transform factor (reciprocal Q-space data). Q magnitude wave vector (Q=4?sin(?)/?), 2? angle incident scattered radiation (X-rays) particles (neutrons electrons), ? wavelength particles.11Egami structure, without translational periodicity, g(r), gives measurement spherical shell thickness r. An calculation demands highest (Qmax). requirement achieved neutrons, (> 30 Å?1). may laboratory sealed tubes Mo (17 keV, Qmax ? 17 Å?1) Ag (22 anodes.15Thomae S.L.J. Prinz N. Hartmann Teck Correll Zobel Pushing quality experiments.Rev. Scientific Instr. 90: 043905Crossref (16) Scholar,16Petkov energy Cu anode (8 8 too low calculations. High easily experiment commercial microscope (80–300 kV).17Gorelik Neder R. Terban M.W. Lee Z. Mu X. Jung Jacob Kaiser Towards function.Acta Section 75: 532-549Crossref (17) Hence, same experiments. electrons much stronger matter, resulting signal, shorter-time collection, smaller required amounts. Consequently, even (micrograms nanograms) enough produce specialized equipment, means good-quality analysis.17Gorelik Another advantage possibility achieving resolution. nanobeam (NBED) spot obtained, making materials.18Hirotsu Y. Ishimaru Ohkubo Hanada Sugiyama Application nano-diffraction materials.J. Electron Microsc. 2001; 50: 435-442Crossref (39) With advent aberration-corrected (Cs-corrected) NBED coherent beam diameter achieved, thus direct observation (SRO) materials.19Hirata Guan Fujita Hirotsu Inoue Yavari Sakurai Chen Direct metallic glass.Nat. Mater. 2011; 10: 2833Crossref (390) Disadvantages come mostly inelastic multiple (dynamical regime), affects acquisition I(Q). Inelastic contributes primarily background data, effects minimized approaches acquiring loss spectroscopy (EELS) detector, filter contribution I(Q).17Gorelik Furthermore, modifies (especially angles) kinematic negligible if free path greater nanomaterials.17Gorelik precession (PED) deconvolution reduce dynamical scattering;20Hoque M.M. Vergara Das P.P. Santiago Kumara Whetten R.L. Dass Ponce ligand-protected under diffraction.J. 123: 19894-19902Crossref (9) Scholar,21Mu Neelamraju Sigle Koch C.T. Totò Schön J.C. Bach Fischer Jansen van Aken P.A. amorphous-to-crystalline transformation MgF2.J. 46: 1105-1116Crossref (22) PED further studies done regarding any case, almost mandatory work samples optimal conditions minimize damage, inelasticity, adequate comparable sources.20Hoque high-Q region, sensitivity lower, signal-to-noise ratio poor higher-order amount lower X-rays.22Zheng J.-C. Zhu Wu Davenport J.W. On x-ray factors valence charge distributions.J. 2005; 38: 648-656Crossref (25) As suggested Mott (fel(s)) related (fx(s)) fel(s) ? (1/s2)/[Z?fx(s)], s (s=2sin(?)/?=Q/2?) Z number. inversely proportional s, indicating decreases faster 2A comparison fel fx carbon, showing fast decay 2B fel2, observed intensity, I?|f|2. By defining drop (?), instance Å?1 (?20), 99.027% maximum Å?1, while ?20 99.958%. practice, high-order small, therefore accumulation times could collect probabilities samples. resolution depends upon S(Q) Qmax; technically, reasonable (Q>18 Å?1).24Skinner L.B. Schlesinger Pettersson L.G. Nilsson Benmore C.J. Benchmark oxygen-oxygen pair-distribution ambient water measurements wide Q-range.J. 138: 074506Crossref (281) hinder good results, literature shown trustworthy samples.25Souza Junior J.B. Schleder G.R. Colombari F.M. de Farias M.A. Bettini J. Heel Portugal R.V. Fazzio Leite E.R. cryogenic microscopy: revealing glassy structure.J. Lett. 2020; 1564-1569Crossref (10) 2C carbon (carbon black nanoparticles) log(I) highlight low-intensity oscillations until 16 Carbon one lightest atoms, other was chosen Different data. colleagues21Mu showed different angular ranges (Q regions) help image. collection regions restricted frame omega-type filter. collecting camera lengths (magnifications) pixel binning regions, increasing counting. powerful here referred case function, just function. Detailed about elsewhere.11Egami section focus acquired change researchers deal problems. fulfill this, succinct description scheme sequence processes discussed hereafter ePDF. A SAED possible, typically decreasing length. besides, lead problems position.24Skinner azimuthal integration centered precisely generates 2D SAED, Gatan Digital Micrograph (GMS) including Difftools26Mitchell Difftools: tools digital micrograph.Microsc. Res. Tech. 71: 588-593Crossref (182) script DAWN27Filik Ashton A.W. Chang P.C.Y. Chater Day Drakopoulos Gerring Hart Magdysyuk O.V. Michalik et al.Processing small-angle DAWN 2.J. 2017; 959-966Crossref (218) used. If needed, digitally correcting nonscattering imperfections stopper, shadows, circularity performed. Typically, gold aluminum calibrate I(Q) dimensions. thin support film subtracted result.17Gorelik does affect positions, extra misinterpretation convolution intensities, interfering final Once reduced F(Q)=Q[S(Q)?1] adjusting proper profile. some cases, modified account