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Deciphering chemical order/disorder and material properties at the single-atom level


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 defects1,2,3. Such disruption in periodicity strongly affects material properties and functionality1,2,3. Despite rapid development of quantitative material characterization methods1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, correlating three-dimensional (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 interfaces19,20; but these calculations rely heavily on average atomic models extracted from crystallography. To improve the predictive power of first-principles 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 iron-platinum nanoparticle, and correlate chemical order/disorder and crystal defects with material properties at the single-atom level. We identify rich structural variety with unprecedented 3D detail including atomic composition, grain boundaries, anti-phase boundaries, anti-site 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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Figure 1: 3D determination of atomic coordinates, chemical species and grain structure of an FePt nanoparticle.
Figure 2: 3D identification of grain boundaries and chemical order/disorder.
Figure 3: Observation of anti-site point and swap defects, and statistical analysis of the chemical order/disorder and anti-site density.
Figure 4: Local MAEs between the [100] and [001] directions determined using measured atomic coordinates and species as direct input to DFT.

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We thank J. Shan, J. A. Rodriguez, M. Gallagher-Jones and J. Ma for help with this project. This work was primarily supported by the Office of Basic Energy Sciences of the US DOE (DE-SC0010378). This work was also supported by the Division of Materials Research of the US NSF (DMR-1548924 and DMR-1437263) and DARPA (DARPA-BAA-12-63). The chemical ordering analysis and ADF-STEM imaging with TEAM I were performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, which is supported by the Office of Science, Office of Basic Energy Sciences of the US DOE (DE-AC02-05CH11231). M.E. (DFT calculations) was supported by the US DOE, Office of Science, Basic Energy Sciences, Material Sciences and Engineering Division. DFT calculations by P.K. were conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. This research used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science of the US DOE (DE-AC05-00OR22725).

Author information

Authors and Affiliations



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.

Corresponding author

Correspondence to Jianwei Miao.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks M. Farle and A. Kirkland for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 A representative tomographic tilt series from an FePt nanoparticle.

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 ADF-STEM. 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 × 106 electrons per Å2. Scale bar at top left, 2 nm.

Extended Data Figure 2 Classification of potential atoms and non-atoms.

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 non-atoms (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 non-atoms (d). Careful examination of the 5,889 non-atom 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 re-classify the non-atom category (Methods), producing 23,804 atom candidates (e) and 5,521 non-atoms. 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.

a–c, 3D intensity distribution of the Pt atom (all Pt atoms are assumed to be identical in our model) in the xy (a), yz (b) and xz (c) planes after refining the traced atomic model16 (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 xy (d), yz (e) and xz (f) planes. g, Corresponding line-cuts through the refined (red) and average (green) Pt atoms. h–j, As ac but for the Fe atom. km, Same as df 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.

a, b, Comparison between the experimental (a) and multislice ADF-STEM 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. Poisson-Gaussian noise was then added to the multislice image. c, Line-cut of (a) and (b) along the dashed rectangle in a, showing good agreement between the experimental and multislice images. Note that a slight in-plane rotation was applied to the images to make horizontal line-cuts 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 root-mean-square deviation of 22 pm.

Extended Data Figure 5 Lattice analysis of the measured 3D atomic model.

a–d, Four fcc sub-lattices for the atomic sites of the FePt nanoparticle (Fe, red; Pt, blue). Two of the four sub-lattices in the two large L12 grains swap Fe for Pt atoms and vice versa (a, b), while the other two sub-lattices 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 (‘non-fcc’).

Extended Data Figure 6 Measurements of 3D atomic displacements in the FePt nanoparticle.

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 not49. 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 anti-phase boundaries.

a, By comparing the measured atomic coordinates with an ideal fcc FePt lattice and using a cross-validation (CV) method50, 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 under-fit. The resulting position error was estimated by using all sites to fit a lattice using the minimum-CV number of fitting variables, shown in the lower panel as the displacement (root-mean-square fitting) error. b, 3D atomic positions (Fe, red; Pt, blue) overlaid on the 3D reconstructed intensity for an anti-phase boundary (white dashed lines) between two L12 FePt3 grains. The arrows indicate two anti-site 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.

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 L10 sphere inside cubic L12 grains with different sizes. Red dots are the local MAEs averaged by sliding a 32-atom volume inside the corresponding six supercells. b, MAEs of all sliding 32-atom volumes inside a 1,470-atom supercell as a function of the L10 order parameter difference. The L10 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 32-atom volume. Dots and error bars represent the mean and the standard deviation, with the number of 32-atom 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 iso-surface rendering of the local MAE (top) and L10 order parameter differences (bottom) inside the 1,470-atom supercell. d, Local MAE distribution at an L10 and L12 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 L10 grain in the nanoparticle.

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 Table 1 Residual aberrations in the STEM probe

Supplementary information

Progressive orthoslices along the [010] direction (y-axis), showing the 3D reconstructed intensity from 68 experimental ADF-STEM images.

Each orthoslice integrates the intensity of a 1.86-Å-thick layer and individual Fe and Pt atoms can be clearly distinguished from their intensity contrast. (MP4 2311 kb)

3D visualization of the different phases in the FePt nanoparticle.

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 Pt-rich A1 grain. (MP4 9574 kb)

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Yang, Y., Chen, CC., Scott, M. et al. Deciphering chemical order/disorder and material properties at the single-atom level. Nature 542, 75–79 (2017).

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