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# Self-similar mesocrystals form via interface-driven nucleation and assembly

## Abstract

Crystallization by particle attachment (CPA) is a frequently occurring mechanism of colloidal crystallization that results in hierarchical morphologies1,2,3,4. CPA has been exploited to create nanomaterials with unusual properties4,5,6 and is implicated in the development of complex mineral textures1,7. Oriented attachment7,8—a form of CPA in which particles align along specific crystallographic directions—produces mesocrystals that diffract as single crystals do, although the constituent particles are still discernible2,9. The conventional view of CPA is that nucleation provides a supply of particles that aggregate via Brownian motion biased by attractive interparticle potentials1,9,10,11,12. However, mesocrystals often exhibit regular morphologies and uniform sizes. Although many crystal systems form mesocrystals1,2,3,4,5,6,7,8,9 and individual attachment events have been directly visualized10, how random attachment events lead to well defined, self-similar morphologies remains unknown, as does the role of surface-bound ligands, which are ubiquitous in nanoparticle systems3,9,11. Attempts to understand mesocrystal formation are further complicated in many systems by the presence of precursor nanoparticles with a phase distinct from that of the bulk1,13,14. Some studies propose that such particles convert before attachment15, whereas others attribute conversion to the attachment process itself16 and yet others conclude that transformation occurs after the mesocrystals exceed a characteristic size14,17. Here we investigate mesocrystal formation by iron oxides, which are important colloidal phases in natural environments18,19 and classic examples of systems forming ubiquitous precursor phases and undergoing CPA accompanied by phase transformations15,19,20,21. Combining in situ transmission electron microscopy (TEM) at 80 degrees Celsius with ‘freeze-and-look’ TEM, we tracked the formation of haematite (Hm) mesocrystals in the presence of oxalate (Ox), which is abundant in soils, where iron oxides are common. We find that isolated Hm particles rarely appear, but once formed, interfacial gradients at the Ox-covered surfaces drive Hm particles to nucleate repeatedly about two nanometres from the surfaces, to which they then attach, thereby generating mesocrystals. Comparison to natural and synthetic systems suggests that interface-driven pathways are widespread.

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## Data availability

The data supporting the findings of this study are available from the corresponding authors upon request. Source data are provided with this paper.

## Code availability

The codes used for the findings of this study are available from the corresponding author upon request.

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## Acknowledgements

We thank C. Wang, J. Tao, M. E. McBriarty, E. Ilton and E. Nakouzi for discussions. We thank D. Li, C. Wang and L. Kovarik for TEM support. This material is based on work supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Geosciences Program at Pacific Northwest National Laboratory (PNNL). High-resolution TEM and STEM imaging and DFT simulations were performed in the Environmental and Molecular Sciences Laboratory, a DOE Office of Science User Facility at PNNL sponsored by the Office of Biological and Environmental Research. PNNL is a multiprogramme national laboratory operated for the DOE by Battelle under contract no. DE-AC05–76RL01830.

## Author information

Authors

### Contributions

J.J.D.Y. supervised the project. G.Z. performed the spindle haematite syntheses, regular TEM, reference-grid TEM, and in situ TEM experiments; G.Z. and J.J.D.Y. analysed and discussed the data. M.L.S. performed the simulation; J.S.L. performed the FTIR measurement; G.Z. and M.S. performed the 3D tomography experiment; G.Z. and J.A.S. performed the cryo-TEM experiment; X.H. provided haematite samples for FTIR measurement; B.A.L. calculated the interfacial free energy. B.A.L. and K.M.R. engaged in discussion extensively. All authors wrote the manuscript.

### Corresponding author

Correspondence to James J. De Yoreo.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Stephan E. Wolf and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Characteristics of rhombohedral Hm versus spindle Hm.

a, b, TEM image of rhombohedral Hm, synthesized without adding Ox. c, HRTEM image of the edge of rhombohedral Hm showing a smooth surface with a perfect two-dimensional lattice. Inset, the corresponding FFT. df, TEM image of spindle Hm with a rough surface, synthesized with the addition of Ox, showing that the spindle is comprised of atomically aligned primary particles. Insets in ef, are FFTs of their respective images. g, h, Example of the use of electron diffraction to identify the elongation direction of the spindle. Similarly, an FFT of the HRTEM image (e, inset) was used to identify the elongation direction of the spindle, which is [001]. i, High-resolution STEM image of the edge of the spindle highlighting the continuity of the lattice from particle to particle. Potential nanopores are indicated by the arrow in i.

### Extended Data Fig. 2 Cryo-TEM investigation of the growth of spindle-shaped Hm mesocrystal from Fh at 90 °C.

a, Loose aggregates of Fh after 1 h. b, Hm spindles appear among Fh aggregates after 3 h. c, Spindle Hm after 8 h. d, Schematic of cryo sample preparation and sublimation of the vitrified ice to remove the background from the ice. e, HRTEM of the spindle to confirm the formation of Hm. Inset, FFT.

### Extended Data Fig. 3 TEM imaging of a cross-section of a Hm spindle.

a, Schematic of a spindle consisting of an aggregate of primary particles. b, TEM image of the cross-section through a cut parallel to the yz plane. Inset, FFT of the structure. c, Cross-section of a cut parallel to the xy plane. Inset, FFT of the structure. d, Line profile along the (104) plane in the inset to b. e, Line profile (arbitrary units) along the $$(1\bar{1}\bar{4})$$ plane in the inset to c. The elongation can be used to measure the particle misorientation.

### Extended Data Fig. 4 Further examples of applying reference TEM grids to follow the Hm growth on Fh as protruding half-spindles pointing towards the solution.

a, Initial Fh aggregates. b, TEM image showing half-spindles of Hm growing on the original Fh aggregates. Shrinkage of the Fh aggregates from 787 nm to 713 nm is indicated. Arrows highlight the Hm growth over the Fh. c, d, Multiple examples of half-spindle Hm. e, HRTEM showing a half-spindle Hm mesocrystal, the initial Fh, and the boundary between the two. Upon examination of over 30 half-spindles, all were found to point away from the Fh and into the solution. Inset, FFT of the Hm. Note that only Hm spindles on the edges of the Fh aggregates can be used to determine whether or not the spindles point towards the solution, owing to the two-dimensional projection in TEM.

### Extended Data Fig. 5 TEM imaging of Hm spindles grown over rhombohedral Hm seeds.

a, d, Rhombohedral Hm particles with a smooth surface are used as seeds. b, e, Primary Hm particles that have grown over the seeds after 2 h. Inset of e, FFT showing that the seed and the primary particles are crystallographically aligned. c, f, Formation of spindle Hm after 5 h with the rhombohedral Hm seeds still seen inside the spindles. The yellow dashed lines mark the boundaries of the rhombohedral seeds.

### Extended Data Fig. 6 TEM imaging of the growth of rhombohedral Hm over spindle Hm seeds.

This is the inverse process to that shown in Extended Data Fig. 5. a, TEM image of spindle Hm seed. b, c, Growth of Hm over the spindle-shaped seeds in a solution without Ox to direct growth to a classical ion-by-ion process. Inset, electron diffraction pattern from the particle, showing its monocrystalline nature. d, Schematic of the rhombohedral Hm growth over the spindle Hm seed.

### Extended Data Fig. 7 Sequential STEM images of the dissolution of Fh and nucleation of new Hm particles close to the Hm seed/solution interface.

Hm seed particles appear and diffuse within the field of view as denoted by the numbers. Fh aggregates are easily resolved in the STEM mode. The white arrows indicate newly formed Hm particles close to the Hm seeds.

### Extended Data Fig. 8 Post-mortem analyses of products after disassembly of the liquid-cell chips.

The liquid-cell chamber was aged at 80 °C for 5 h in the TEM. a, STEM image of spindle Hm with clear porous structure. b, c, STEM and energy-dispersive X-ray spectroscopy mapping of the spindles in a, showing the oxygen and iron distributions only. d, TEM image of spindle Hm at low magnification showing uniform distribution of spindle Hm on the SiN window. e, Corresponding selected area diffraction from spindles in d highlighting two diffraction rings of Hm from (012) and Hm (104) planes with an interplane distance of 0.37 nm and 0.27 nm, respectively.

### Extended Data Fig. 9 Analysis of the gap size between a Hm seed and a nucleus and its elimination over time during in situ TEM.

The gap is defined as the distance between the edge of the seed and the edge of the new particle. a, TEM image of a spheroidal nucleus that occurs close to the seed surface indicated by the arrow. b, TEM image of the nucleus attaching to the seed particle over time. c, Line profile along the red dashed line in a, measuring the gap size between the nucleus and the seed. The grey value unit is arbitrary. d, Line profile along the red dashed line in b, demonstrating elimination of the gap over time.

### Extended Data Fig. 10 Further examples of the measurement of the gap size between a seed particle and a nucleus.

a, c, TEM image of a spheroidal nucleus that occurs close to the seed surface (a), and its line profile (c) demonstrating the existence of the gap at 23 s of Fig. 3. b, d, TEM image (b) of another case of the gap measurement between the spheroidal nucleus and the seed particle, and the corresponding line profile (d). The overall contrast change could come from a change in focus during the in situ experiment. Line profile units are arbitrary.

## Supplementary information

### Supplementary Information

Supplementary Figures 1–7 and Supplementary Tables 1–2 are in this Supplementary Information file, together with oxalate adsorption kinetics, particle–particle interaction calculation, and accuracy of the simulation.

### Video 1

Tilt series of a spindle-shaped Hm mesocrystal over a range of ±65 degrees, at 2° increments collected in STEM mode.

### Video 2

Hm nucleation close to the Hm seeds and formation of Hm mesocrystal collected in the TEM mode. Fh is difficult to see in the TEM mode due to the low contrast. Playback speed is 2× the original speed. Beam current is 0.7 nA. The dose rate is 2.3 e/Å2/s.

### Video 3

Hm nucleation close to the Hm seeds and formation of Hm mesocrystal collected in the STEM mode. A mixture of Hm seeds and Fh is present initially and the Hm is covered with Fh. See the methods for dose details. Beam current is 0.53 nA. The dose rate is 11.4 e/Å2/s.

### Video 4

Another example of Hm nucleation close to the Hm seeds and formation of Hm mesocrystals collected in the TEM mode. Fh is difficult to see due to the low contrast in TEM mode. Playback speed is 2× the original speed. Scale bar is 20 nm. The dose rate is 6.5 e/Å2/s.

### Video 5

Another example of Hm nucleation close to the Hm seeds followed by attachment to the seeds collected in TEM mode. Playback speed is 2X the original speed. The dose rate is 16.7 e/Å2/s.

### Video 6

TEM observations of Hm nucleation close to Hm seeds and growing Hm spindles followed by attachment to advance the growth of the spindles over a time span of 15 minutes. The electron beam was blocked for most of time course of the experiment, with beam exposure only occurring for collection of short image series in the middle of the experiment. The dose rate is 155 e/Å2/s.

### Video 7

Highlight of TEM observation of near-surface Hm nucleation and attachment taken from the middle portion of video 6.

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Zhu, G., Sushko, M.L., Loring, J.S. et al. Self-similar mesocrystals form via interface-driven nucleation and assembly. Nature 590, 416–422 (2021). https://doi.org/10.1038/s41586-021-03300-0

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