Nucleation and growth of magnetite from solution

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1 Nucleation and growth of magnetite from solution 1. Supplementary Discussion: Primary Particles The observed primary particles are short lived which hampers their structural analysis. In order to further investigate their composition and structure reference experiments were performed and compared with the observations in the very early stages of the reaction. In the first minute of the reaction low-resolution cryotem imaging revealed the existence of gel-like network structures spanning up to a few hundred nanometers, alongside short aggregates of 2 nm particles (Supplementary Figure S 1A). Attempts to image these network structures at higher resolution requiring a higher electron dose failed due of their electronbeam sensitivity (Supplementary Figure S 1B). In contrast, the 2 nm particles did not show any significant deterioration under the same electron dose. Supplementary Figure S 1B shows an area with radiation damage to the network and the ablation of the vitrified ice layer at the applied electron dose. Within this area some material disintegrated (yellow arrow), whereas other electron-beam stable material remained (blue arrow). The latter type, which was indistinguishable from the unstable structures at low magnification, became predominant after 2 min reaction time and was identified as the observed primary particles. NATURE MATERIALS 1

2 Supplementary Figure S 1. Primary particle formation imaged by low-resolution cryo- TEM. (A) Sample after 1 min before and (B) after disintegration by increased electron dose from attempted high-resolution imaging. Yellow arrows indicate unstable precursor phase, blue arrow indicates electron-beam stable material. Scale bars, 100 nm. The primary particle size was determined in cryo-tem from a defocus series taken in 200 nm steps from -800 nm defocus to focus. Micrographs from -600 nm to -200 nm defocus gave enough contrast to determine primary particle sizes. On each image, primary particle size was determined by manual measurement (using the line tool of ImageJ) of 50 primary particles, which were considered not to be covered by other primary particles in the aggregate. Both long and short axes of primary particles were measured. Determined sizes (± standard deviation) were 1.87 ± 0.20 nm, 1.98 ± 0.20 nm and 1.98 ± 0.28 nm for defocus values of nm, -400 nm and -200 nm, respectively (Supplementary Figure S 2A). Fast Fourier Transformation (FFT) analysis of the primary particles did not reveal any sign of crystalinity. We also performed measurements on primary particles attached to crystalline nanoparticles in 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION the range of focus that allowed lattice fringe imaging (Supplementary Figure S 2B). The measured primary particles were only 1.14 ± 0.25 nm large and also for these no signs of crystalinity were observed in the FFT patterns. A nm -400 nm -600 nm B counts 20 counts ,0 0,5 1,0 1,5 2,0 2,5 3,0 size (nm) 0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 size (nm) C Supplementary Figure S 2. Size distribution histograms of (A) free primary particles measured at different defocus values and (B) primary particles attached to magnetite nanoparticle surfaces. (C) Cryo-TEM image of magnetite nanoparticle with attached primary particles and free primary particles imaged after 2 min precipitation (inset). Reference experiments were performed using ferrihydrite, which was synthesized based on a NATURE MATERIALS 3

4 literature procedure 1. Powder X-ray diffraction of freeze dried samples demonstrated that it was 6-line ferrihydrite. Cryo-TEM of a diluted aqueous solution of the material at ph = 6 revealed a hydrogel-like behaviour with concomitant beam sensitivity (Supplementary Figure S 3A and B). The same observation was made for a dispersion in which the ph was raised to ph = 9, the ph of the reaction described in the manuscript. In a second experiment a solution of FeCl 2 was added to the ferrihydrite dispersion, resulting in a solution with a total iron concentration of 16 M (Fe II / Fe III = 0.55) and a ph of 4.5. In this solution, now aggregates of particles with diameters of nm were observed (Supplementary Figure S 3C) that were demonstrated to be amorphous by low dose electron diffraction and had become insensitive to the electron beam. Remarkably, within collection of aggregated nanoparticles we also found a population of well-defined monodisperse 2 nm particles that also were stable under high resolution cryo-tem imaging (Supplementary Figure S 3D). Similar to the reaction described in the manuscript also the present reaction yielded magnetite as the final product (Supplementary Figure S 3E and F). Similar to what was suggested in the literature 2 these results demonstrate that the reaction of Fe(II) with ferrihydrite can lead to primary particles with a precisely defined diameter and enhanced stability compared to ferrihydrite. In analogy with the results described in the manuscript we suggest that also the primary particles consist of an iron (hydr)oxide with a specific Fe II / Fe III ratio that arises from the interaction of Fe II with ferrihydrite. 4 NATURE MATERIALS

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6 Supplementary Figure S 3. Cryo-TEM of ferrihydrite at ph=6 (A) before and (B) after exposure to increased electron dose. (C) Ferrihydrite in the presence of Fe(II) (Fe (II)/Fe(III) = 0.55, inset: low-dose diffraction. (D) Monodisperse 2 nm particles present in solution of ferrihydrite with Fe(II). (E) Magnetite and (F) Selcted area electron diffraction of magnetite and its radial intregation (inset). 2. Supplementary Discussion: Model 2.1 Supersaturation The used description for the classical nucleation theory is, where is the free energy, R the radius, the surface energy and the bulk energy. The bulk energy depends on the supersaturation by, where is the volume of single units that assemble the bulk, is the Boltzmann constant and is the temperature. The supersaturation itself is defined as, where is the concentration and is the solubility limit. Thus, the formation of a nucleus can also be described as. (S1) The critical radius is then given by (S2) and the respective thermodynamic energy barrier by. (S3) 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION We defined the free energy for nucleation from primary particles as. Thus, the thermodynamic energy barrier for this case becomes. (S4) Note that this description is therefore equivalent to a change in the saturations of the solution: when we express the primary particles free excess energy density by a term ln, we obtain, which allows us to determine a factor by which the saturation-equivalent changes due to the presence of the primary particles. 2.2 Metastability and Stability Generally, we can discuss the following theoretical situations for f P : 1. : In this case the clusters/primary particles have exactly the same stability as ions in the solution ( ) and therefore we obtain no difference in the energy barriers as from nucleation from ions: and. 2. : In this case the clusters/primary particles are stable with respect to the solution ( ), as a consequence the saturation-equivalent decreases (i.e., ). An example of such a scenario is depicted in Figure 3 of the paper and here in the left column of Supplementary Figure S 4. The boundary (Supplementary Figure S 4A, black dashed line) shifts towards larger and smaller, which means we increase the parameter space in favour of nucleation of phase C NATURE MATERIALS 7

8 instead of phase A (light gray area). For example a system in which and (red dot), a relative primary particle stability (black dashed line) is sufficient to reverse the thermodynamic energy barriers when nucleating from primary particles instead of atoms or molecules in solution. This reversal is depicted in Supplementary Figure S 4B (nucleation from ions) and S 4C (nucleation from primary particles): for the aforementioned set of parameters the thermodynamic barrier of the amorphous phase is lower than the crystalline phase when nucleating from ions in solution ( in S4B). As the consumption of stable primary particles in the nucleation requires energy, the thermodynamic barriers for nucleation from primary particles of both phases increase by the additional dissolution work (green dashed lines). However, as the volume of the consumed primary particle aggregate differs for the formation of nuclei of phases A and C, under the given set of parameters, the thermodynamic barrier for nucleation of the amorphous phase becomes larger than for the crystalline phase ( in S4C). Note that in a special case when, the clusters/primary particle are equally or more stable than the amorphous phase which enables only nucleation of the more stable crystalline phase from them, if such exists. 3. : In this case the clusters/primary particles are metastable with respect to the solution ( ) as a consequence the saturation-equivalent increases (i.e., ). An example of this scenario with the same surface and bulk energy parameters but metastable is depicted in the right column of Supplementary Figure S 4. Here the boundary (Supplementary Figure S 4D, dashed line) shifts 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION towards smaller and larger, which increases the possible parameter space that favours nucleation of phase A over nucleation of phase C. As can be seen in Supplementary Figure S 4E and F, the presence of metastable primary particles in the nucleation pathway leads to a lowering of the thermodynamic barriers due to a release of energy by the consumption of the primary particles; however, in this case the thermodynamic barrier of phase A still remains lower than of phase C. Note that an interesting effect can be observed when the system is in a supersaturated state with respect to the crystalline phase but undersaturated for the amorphous phase. In this case the driving force for the formation of the amorphous bulk phase and the thermodynamic barrier becomes infinite ( ). Therefore, the nucleation of the amorphous phase is not expected ( ). However, when the primary particles are sufficiently metastable, they can enable and favour nucleation of the amorphous phase over nucleation of the crystalline phase ( ). This scenario is depicted in Supplementary Figure S 5 for, (red dot) and a relative primary particle metastability. NATURE MATERIALS 9

10 A Relative Surface Energy A / C 1,0 0,8 0,6 0,4 0,2 G A = G C G A = G C G A < G C D Relative Surface Energy A / C 1,0 0,8 0,6 0,4 0,2 G A = G C G A = G C 0,0 0,0 0,2 0,4 0,6 0,8 1,0 Relative Bulk Energy g A /g C 0,0 0,0 0,2 0,4 0,6 0,8 1,0 Relative Bulk Energy g A /g C B E - 4 / 3 R 3 f P Free Energy G Phase C G C Free Energy G Phase C G C Phase A G P Primary Particle P G A Phase A GP Primary Particle P G A R P - 4 / 3 R 3 f P Radius R R P Radius R C Free Energy G = G + 4 / 3 R 3 f P Phase A Phase C Primary Particle P G C G A - 4 / 3 R 3 f P F Free Energy G = G + 4 / 3 R 3 f P Phase C Primary Particle P Phase A G A G C - 4 / 3 R 3 f P R P Radius R R P Radius R Supplementary Figure S 4. Influence of (A,B,C) stable and (D,E,F) metastable primary particles on nucleation pathways. (A, D) Phase diagrams showing which set of parameters 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION, and favour nucleation of the amorphous phase (gray areas) or crystalline phase (white areas) when nucleating from primary particles. Red dot indicates parameters for the following plots. (B, E) Energy landscapes of nuclei forming from atoms/molecules in solution and (C, F) from primary particles. NATURE MATERIALS 11

12 A Relative Surface Energy A / C 1,0 0,8 0,6 0,4 0,2 0,0 G A = G C G A = G C Relative Bulk Energy g A /g C -0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 B - 4 / 3 R 3 f P Phase A G A 8 Free Energy G Phase C G C G P Primary Particle P R P Radius R C Free Energy G = G + 4 / 3 R 3 f P Phase C G C Primary Particle P Phase A G A - 4 / 3 R 3 f P R P Radius R Supplementary Figure S 5. Influence of metastable primary particles on a nucleation pathway in the case of a solution which is undersaturated with respect to phase A but supersaturated with respect to phase C. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION 3. Supplementary Data Supplementary Figure S 6. TEM images of a growth time series (60 min, 180 min and 360 min) of particles grown at ph = 10 (A - C) and ph = 11 (D - F). Scale bars, 100 nm. SEM images of the same series of particles grown at ph = 9 (G - I). Scale bars, 300 nm. NATURE MATERIALS 13

14 Supplementary Figure S 7. Particle size distributions of magnetite nanoparticles. (A, B) ph = 9, (C, D) ph = 10 and (E, F) ph = 11. Left column shows original distribution, right column distribution normalized with respect to mean diameter indicating self-similarity. 14 NATURE MATERIALS

15 SUPPLEMENTARY INFORMATION 4. Full Methods Precipitation experiments. Reactions were performed with a commercial titration setup (Metrohm AG, Herisau, Switzerland). The setup was computer-controlled by the software Tiamo 1.0. The setup consists of a dosing device 776 Dosimat with an 806 Exchange Unit (1 ml dosing cylinder, No ) and a titration device 719 Titrino with an 806 Exchange Unit (5 ml dosing cylinder, No ). Microloader tips (Eppendorf, Hamburg, Germany, No ) were used as inlets into the reaction vessel. Reactions were performed in a 50 ml titration vessel with thermostat jacket (No ), which was kept at a constant temperature with a thermostat Lauda M3 (Lauda-Königshofen, Germany). Solutions were stirred at maximum speed ( min -1 ) with a mechanical stirrer 802 Rod Stirrer (No ). The ph was measured using a ph electrode Biotrode (Metrohm, No ). The ph electrode was calibrated using commercial calibration buffers ph = 4.0, 7.0 and 9.0. Iron chloride solutions with a stoichiometric ratio Fe(II) / Fe(III) = 1 / 2 and total iron concentrations of 0.1 M and 1 M of 100 ml were prepared from ferrous chloride tetrahydrate and ferric chloride. Sodium hydroxide solutions were used as supplied. Deionized water and all solutions were initially purged for at least 15 minutes with nitrogen before use. All experiments were performed under nitrogen atmosphere. 10 ml deionized water were initially set to the appropriate ph with NaOH and equilibrated to 25 ± 0.1 C. Magnetite co-precipitation was initiated by addition of the stoichiometric iron solution to the reactor at a rate of 1 µl min -1. The ph of the solution in the reaction vessel was simultaneously kept constant ( ph = ± 0.1 for 0.1 M solution experiments, ph = ± 0.4 for 1 M solution experiments) by addition of sodium hydroxide controlled by the setup. Ferrous chloride tetrahydrate (VWR, No ), ferric chloride (Sigma-Aldrich, No ), standard sodium hydroxide solutions 1 M (Merck, No ) and 0.1 M (Acros NATURE MATERIALS 15

16 Organics, No ) were used as supplied by the manufacturers. Cryo-TEM. Cryo-TEM Cu grids, R2/2 Quantifoil Jena grids (Quantifoil Micro Tools GmbH) were surface plasma treated for 40 seconds using a Cressington 208 carbon coater prior to use. Samples were taken from the reaction mixture at different time points between 1 and 82 min. Then, vitrification was carried out using an automated vitrification robot (FEI Vitrobot Mark III) by plunging in liquid ethane. The entire sample preparation procedure was performed under nitrogen atmosphere and at 100% humidity to prevent oxidation and dryinginduced crystallization, respectively. Vitrified samples were studied on the TU/e CryoTitan (FEI, equipped with a field emission gun (FEG) operating at 300 kv and a post column Gatan Energy Filter (GIF). Images were recorded using a post-gif 2k 2k Gatan CCD camera. The DiffTools package supported by DigitalMicrograph software and crystallography data of magnetite (162349) from the Inorganic Crystal Structure Database were used as an aid to analyse the Fast Fourier Transformations (FFTs) generated from the HR cryo-tem images. XRD. Dried precipitates were investigated at the µ-spot beamline, BESSY II, Berlin. Samples were dried on Kapton thin film and measured in transmission with a 100 µm wide beam of 15 kev (λ = Å). Diffraction data was acquired at a distance of 150 mm on a pixel MarMosaic 225 (Mar USA, Evanston, USA) CCD camera with µm pixel size. Data was analysed with the Fit2D software ( Magnetite nanoparticle size was determined by fitting of the magnetite (311) Bragg peak by Scherrer analysis with a pseudo- 16 NATURE MATERIALS

17 SUPPLEMENTARY INFORMATION Voigt function and instrumental broadening correction 3,4. TEM. Particles were adsorbed from aqueous suspensions to carbon film Cu TEM grids for 15 min. After removal of the liquid with Kimwipe paper, grids were washed with a drop of milli- Q water to remove residual salt precipitates. Imaging was performed on Zeiss EM 912 Omega with 120 kv acceleration voltage. SEM. SEM imaging was performed on a LEO 1550-Gemini microscope. For sample preparation a few µl aqueous suspension were deposited on Al stubs and air-dried. No coating was applied to samples in order to preserve particle sizes. 5. Supplementary References 1 Liu, H., Ma, M., Qin, M., Yang, L. & Wei, Y. Studies on the controllable transformation of ferrihydrite. J. Solid State Chem. 183, , (2010). 2 Tronc, E., Belleville, P., Jolivet, J. P. & Livage, J. Transformation of ferric hydroxid into spinel by Fe(II) adsorption. Langmuir 8, (1992). 3 Paris, O. et al. A new experimental station for simultaneous X-ray microbeam scanning for small- and wide-angle scattering and fluorescence at BESSY II. J. Appl. Cryst. 40, S466-S470 (2007). 4 Fischer, A., Schmitz, M., Aichmayer, B., Fratzl, P. & Faivre, D. Structural purity of magnetite nanoparticles in magnetotactic bacteria. J. R. Soc. Interface 8, (2011). NATURE MATERIALS 17