Nature  Letter
Deciphering chemical order/disorder and material properties at the singleatom level
 Yongsoo Yang^{1}^{, *}
 ChienChun Chen^{1, 2}^{, *}
 M. C. Scott^{1, 3}^{, *}
 Colin Ophus^{3}^{, *}
 Rui Xu^{1}^{, }
 Alan Pryor^{1}^{, }
 Li Wu^{1}^{, }
 Fan Sun^{4}^{, }
 Wolfgang Theis^{5}^{, }
 Jihan Zhou^{1}^{, }
 Markus Eisenbach^{6}^{, }
 Paul R. C. Kent^{7, 8}^{, }
 Renat F. Sabirianov^{9}^{, }
 Hao Zeng^{4}^{, }
 Peter Ercius^{3}^{, }
 Jianwei Miao^{1}^{, }
 Journal name:
 Nature
 Volume:
 542,
 Pages:
 75–79
 Date published:
 DOI:
 doi:10.1038/nature21042
 Received
 Accepted
 Published online
Perfect crystals are rare in nature. Real materials often contain crystal defects and chemical order/disorder such as grain boundaries, dislocations, interfaces, surface reconstructions and point defects^{1, 2, 3}. Such disruption in periodicity strongly affects material properties and functionality^{1, 2, 3}. Despite rapid development of quantitative material characterization methods^{1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}, correlating threedimensional (3D) atomic arrangements of chemical order/disorder and crystal defects with material properties remains a challenge. On a parallel front, quantum mechanics calculations such as density functional theory (DFT) have progressed from the modelling of ideal bulk systems to modelling ‘real’ materials with dopants, dislocations, grain boundaries and interfaces^{19, 20}; but these calculations rely heavily on average atomic models extracted from crystallography. To improve the predictive power of firstprinciples calculations, there is a pressing need to use atomic coordinates of real systems beyond average crystallographic measurements. Here we determine the 3D coordinates of 6,569 iron and 16,627 platinum atoms in an ironplatinum nanoparticle, and correlate chemical order/disorder and crystal defects with material properties at the singleatom level. We identify rich structural variety with unprecedented 3D detail including atomic composition, grain boundaries, antiphase boundaries, antisite point defects and swap defects. We show that the experimentally measured coordinates and chemical species with 22 picometre precision can be used as direct input for DFT calculations of material properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy. This work combines 3D atomic structure determination of crystal defects with DFT calculations, which is expected to advance our understanding of structure–property relationships at the fundamental level.
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At a glance
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Author information
Author footnotes
These authors contributed equally to this work.
 Yongsoo Yang,
 ChienChun Chen,
 M. C. Scott &
 Colin Ophus
Affiliations

Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, California 90095, USA
 Yongsoo Yang,
 ChienChun Chen,
 M. C. Scott,
 Rui Xu,
 Alan Pryor,
 Li Wu,
 Jihan Zhou &
 Jianwei Miao

Department of Physics, National Sun Yatsen University, Kaohsiung 80424, Taiwan
 ChienChun Chen

National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
 M. C. Scott,
 Colin Ophus &
 Peter Ercius

Department of Physics, University at Buffalo, the State University of New York, Buffalo, New York 14260, USA
 Fan Sun &
 Hao Zeng

Nanoscale Physics Research Laboratory, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
 Wolfgang Theis

National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
 Markus Eisenbach

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
 Paul R. C. Kent

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
 Paul R. C. Kent

Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182, USA
 Renat F. Sabirianov
Contributions
J.M. directed the project; F.S. and H.Z. prepared the samples; M.C.S., W.T., P.E. and J.M. discussed and/or acquired the data; Y.Y., C.C.C., R.X., A.P.J., L.W., J.Z. and J.M. conducted the image reconstruction and atom tracing; C.O., Y.Y., H.Z., P.E., W.T., R.F.S., M.C.S. and J.M. analysed and interpreted the results; M.E., P.R.C.K., R.F.S., Y.Y., H.Z., C.O., W.T. and J.M. discussed and performed the DFT calculations; J.M., Y.Y., H.Z., P.E., C.O., W.T., M.E., P.R.C.K., R.F.S. wrote the manuscript.
Competing financial interests
The authors declare no competing financial interests.
Reviewer Information Nature thanks M. Farle and A. Kirkland for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Figures
 Extended Data Figure 1: A representative tomographic tilt series from an FePt nanoparticle. (793 KB)
The 68 projection images with a tilt range from −65.6° to +64.0° (shown at top right of each panel) were measured using an ADFSTEM. Careful examination of images taken before and after the tilt series indicates the consistency of the structure throughout the experiment. The total electron dose of the tilt series is 4.8 × 10^{6} electrons per Å^{2}. Scale bar at top left, 2 nm.
 Extended Data Figure 2: Classification of potential atoms and nonatoms. (168 KB)
a, Histogram of the identified local intensity peaks, each of which should belong to one of three categories: potential Pt atoms, potential Fe atoms and potential nonatoms (intensity too weak to be an atom). An unbiased atom classification method was developed to separate these peaks (Methods), resulting in 9,519 Fe (b) and 13,917 Pt (c) atom candidates and 5,889 nonatoms (d). Careful examination of the 5,889 nonatom peaks identified in (d) suggested that some potential atoms might be incorrectly classified into this category. To mitigate this problem, a less aggressive method was implemented to reclassify the nonatom category (Methods), producing 23,804 atom candidates (e) and 5,521 nonatoms. Using the same unbiased atom classification method, we classified 23,804 atom candidates into 9,588 Fe (f) and 14,216 Pt (g) atom candidates.
 Extended Data Figure 3: 3D profile of Pt and Fe atoms obtained from experimental data. (244 KB)
a–c, 3D intensity distribution of the Pt atom (all Pt atoms are assumed to be identical in our model) in the x–y (a), y–z (b) and x–z (c) planes after refining the traced atomic model^{16} (Methods), where red, yellow and blue represent high, medium and low intensity, respectively. d–f, 3D intensity distribution of the average Pt atom of the reconstruction in the x–y (d), y–z (e) and x–z (f) planes. g, Corresponding linecuts through the refined (red) and average (green) Pt atoms. h–j, As a–c but for the Fe atom. k–m, Same as d–f but for the average Fe atom. n, Same as g but for the Fe atoms (pixel size = 0.3725 Å). The slight intensity elongation in d, f, k and m is due to the missing wedge problem.
 Extended Data Figure 4: Validating the measured atomic model using multislice STEM simulations. (589 KB)
a, b, Comparison between the experimental (a) and multislice ADFSTEM simulation (b) images at 0° tilt. The multislice image was convolved with a Gaussian function to account for the source size and other incoherent effects. PoissonGaussian noise was then added to the multislice image. c, Linecut of (a) and (b) along the dashed rectangle in a, showing good agreement between the experimental and multislice images. Note that a slight inplane rotation was applied to the images to make horizontal linecuts for a quantitative comparison. d, Histogram of the difference (deviation) in atomic positions between the experimental atomic model and that obtained from 68 multislice images. 99.0% of the atoms were correctly identified with a rootmeansquare deviation of 22 pm.
 Extended Data Figure 5: Lattice analysis of the measured 3D atomic model. (945 KB)
a–d, Four fcc sublattices for the atomic sites of the FePt nanoparticle (Fe, red; Pt, blue). Two of the four sublattices in the two large L1_{2} grains swap Fe for Pt atoms and vice versa (a, b), while the other two sublattices share the same sites of Pt atoms (c, d). The vertical [001] direction is exaggerated to separate the planes. Approximately 3.4% of the atomic sites (open squares) located on the two surfaces of the nanoparticle along the missing wedge (horizontal) direction were removed from the analysis because their location deviated slightly from the fcc lattice (‘nonfcc’).
 Extended Data Figure 6: Measurements of 3D atomic displacements in the FePt nanoparticle. (1,762 KB)
a–c, Atomic displacements along the [100] (a), [010] (b) and [001] (c) directions, determined by quantitatively comparing the measured atomic coordinates with an ideal fcc lattice. d, 3D atomic displacements in the nanoparticle. The displacement fields indicate that the FePt nanoparticle does not contain substantial strain; the only small strain is observed at the interface between the nanoparticle and the substrate. The black lines in the images show the grain boundaries, indicating that the grain boundaries were not caused by the strain. e–h, {100} facets of the FePt nanoparticle (black arrows) that are dominated by Pt atoms. i–l, {111} facets of the FePt nanoparticle (white arrows) that are less dominated by Pt atoms. This experimental observation confirms previous Monte Carlo simulations, which suggested that when there are excess Pt atoms in the fcc cuboctahedral FePt nanoparticle, the {100} facets are more occupied by Pt atoms, while the {111} facets are not^{49}. The aggregation of the Fe atoms on two opposite surfaces of the nanoparticle is due to the missing wedge problem.
 Extended Data Figure 7: 3D precision estimation for atomic coordinate measurements and 3D identification of antiphase boundaries. (792 KB)
a, By comparing the measured atomic coordinates with an ideal fcc FePt lattice and using a crossvalidation (CV) method^{50}, we estimated an average 3D precision of 21.6 pm for all the atoms, which agrees well with the multislice result (22 pm). The CV score was computed by using half of the randomly selected atomic sites to fit the lattice and then measuring the fitting error of the remaining half of the atomic sites. The results of this error metric are shown in the upper panel as a function of the number of variables used to fit the lattice. This value reaches a minimum where the lattice fitting function is neither over nor underfit. The resulting position error was estimated by using all sites to fit a lattice using the minimumCV number of fitting variables, shown in the lower panel as the displacement (rootmeansquare fitting) error. b, 3D atomic positions (Fe, red; Pt, blue) overlaid on the 3D reconstructed intensity for an antiphase boundary (white dashed lines) between two L1_{2} FePt_{3} grains. The arrows indicate two antisite point defects. The background colours of red, yellow and blue correspond to high, medium and low intensity, respectively.
 Extended Data Figure 8: Local MAEs between the [010] and [001] directions determined by using measured atomic coordinates and species as direct input to DFT. (619 KB)
a, Black squares represent the MAEs calculated from six nested cubic volumes of 32, 108, 256, 500, 864 and 1,372 atoms (‘full supercell calculation’). Blue curve shows the results of fitting a L1_{0} sphere inside cubic L1_{2} grains with different sizes. Red dots are the local MAEs averaged by sliding a 32atom volume inside the corresponding six supercells. b, MAEs of all sliding 32atom volumes inside a 1,470atom supercell as a function of the L1_{0} order parameter difference. The L1_{0} order parameter difference was obtained by subtracting the SROP along the [010] direction from that along the [001] direction, and the SROP was computed from each 32atom volume. Dots and error bars represent the mean and the standard deviation, with the number of 32atom volumes n = 6, 18, 28, 76, 134, 461, 243, 183, 107, 121, 49 and 26 (from left to right). Negative MAE values indicate that their local magnetic easy axis is along the [010] instead of the [001] direction. c, 3D isosurface rendering of the local MAE (top) and L1_{0} order parameter differences (bottom) inside the 1,470atom supercell. d, Local MAE distribution at an L1_{0} and L1_{2} grain boundary, interpolated from the sliding local volume calculations and overlaid with measured atomic positions.
 Extended Data Figure 9: Spin and orbital magnetic moments of the atoms in the largest L1_{0} grain in the nanoparticle. (187 KB)
a, b, Histogram of the spin (a) and orbital (b) magnetic moments of the Fe atoms. c, d, Histogram of the spin (c) and orbital (d) magnetic moments of the Pt atoms. e, Spin magnetic moment of the Fe atoms as a function of the Fe coordination number. The circles and error bars represent the mean and the standard deviation, with the number of Fe atoms n = 10, 15, 8 and 8 (from left to right).
Extended Data Tables
Supplementary information
Video
 Video 1: Progressive orthoslices along the [010] direction (yaxis), showing the 3D reconstructed intensity from 68 experimental ADFSTEM images. (2.25 MB, Download)
 Each orthoslice integrates the intensity of a 1.86Åthick layer and individual Fe and Pt atoms can be clearly distinguished from their intensity contrast.
 Video 2: 3D visualization of the different phases in the FePt nanoparticle. (9.34 MB, Download)
 The nanoparticle consists of two large L12 FePt3 grains and seven smaller grains located between them, including three L12 FePt3 grains, three L10 FePt grains and a Ptrich A1 grain.
Additional data

Extended Data Figure 1: A representative tomographic tilt series from an FePt nanoparticle.Hover over figure to zoom

Extended Data Figure 2: Classification of potential atoms and nonatoms.Hover over figure to zoom

Extended Data Figure 3: 3D profile of Pt and Fe atoms obtained from experimental data.Hover over figure to zoom

Extended Data Figure 4: Validating the measured atomic model using multislice STEM simulations.Hover over figure to zoom

Extended Data Figure 5: Lattice analysis of the measured 3D atomic model.Hover over figure to zoom

Extended Data Figure 6: Measurements of 3D atomic displacements in the FePt nanoparticle.Hover over figure to zoom

Extended Data Figure 7: 3D precision estimation for atomic coordinate measurements and 3D identification of antiphase boundaries.Hover over figure to zoom

Extended Data Figure 8: Local MAEs between the [010] and [001] directions determined by using measured atomic coordinates and species as direct input to DFT.Hover over figure to zoom

Extended Data Figure 9: Spin and orbital magnetic moments of the atoms in the largest L1_{0} grain in the nanoparticle.Hover over figure to zoom

Video 1: Progressive orthoslices along the [010] direction (yaxis), showing the 3D reconstructed intensity from 68 experimental ADFSTEM images.

Video 2: 3D visualization of the different phases in the FePt nanoparticle.

Extended Data Table 1: Residual aberrations in the STEM probeHover over figure to zoom