Crystal Formation Unraveled

August 28, 2020 – How does a crystal begin? Researchers from Ulm, Nottingham, Leeds and AIST in Japan filmed iron, gold and rhenium atoms inside carbon nanotubes as they formed crystal nuclei, atom by atom. In all three metals, the atoms first gathered into a disordered cluster that only later turned crystalline, the long-debated two-step path of nucleation.

Every crystal starts as a handful of atoms that, at some moment, fall into order. That moment decides the structure and size of the crystals that follow, and with them the properties of materials from semiconductors to drugs. Yet it had never been watched atom by atom. Researchers from Ulm University, the Universities of Nottingham and Leeds and the National Institute of Advanced Industrial Science and Technology (AIST) in Japan have now filmed the birth of metal crystals inside carbon nanotubes, with every atom visible.

The team of Kecheng Cao, Johannes Biskupek, Andrei Khlobystov and Ute Kaiser followed three metals: iron, gold and rhenium. Each found its own way to the crystal, but all three took the same detour. The atoms first gathered into a disordered, amorphous cluster, and only this cluster turned into a crystal. Such a two-step path had been postulated in theory and debated for years. The images now show it directly.

One step or two?
The classical nucleation theory describes crystal formation in a single step: atoms, ions or molecules attach one by one to an ordered structure until it is large enough to grow on its own (Fig. 1a)^[1],[2]. Many observations do not fit this picture, and so a two-step nucleation mechanism was proposed (Fig. 1b)^[3]–[5]. In it, an amorphous precursor forms first and is replaced by a crystalline phase only in a second step^[6]–[8]. The precursor may also have to reach a certain size before it can crystallize, as sketched in Fig. 1c^[9],[10].

Testing these ideas is hard because the decisive stage is small and fast. Cryogenic electron microscopy freezes nucleation at discrete moments^[11],[12], and X-ray diffraction^[13], atomic force microscopy^[1],[14] and optical microscopy^[15] are too slow or too coarse for single atoms. Liquid-cell electron microscopy can follow the growth of metal nanocrystals in solution in real time, but the liquid and the cell windows scatter the electrons, and the very first steps stay out of sight. Critical nuclei are thought to contain 100 to 1000 atoms, a size no method could resolve atom by atom, so a conceptually new approach was needed^[16].

Test tubes, an atomic injector and an electron beam
The team used single-walled carbon nanotubes (SWNTs) as test tubes only about 1.5 nm wide^[17]–[19]. The tubes are transparent to electrons, chemically and thermally stable, and their wall serves as a substrate on which a crystal nucleus can form. Inside the tube, the metal atoms cannot escape, and they stay in the field of view of the microscope.

The nanotubes were filled with vapors of metal compounds, which left metal atoms and small clusters inside (recipe in the box). In Ulm, the samples were imaged with an aberration-corrected FEI Titan 80-300 microscope at 80 kV (AC-HRTEM), in time series of up to several minutes. At 80 kV the electrons do not knock carbon atoms out of the tube wall. The electron beam does two jobs at once: it takes the pictures and it transfers small amounts of energy to the metal atoms, much like heating. This energy drives the nucleation.

For iron, the team found an unexpected helper. Ferrocene, the iron compound used for filling, leaves behind mobile clusters of amorphous carbon that carry iron atoms (Fig. 2). These complexes slide along the tube within seconds, because the inner wall of a nanotube is almost frictionless. Electron energy loss maps recorded at AIST with a scanning transmission electron microscope (STEM) at 60 kV confirmed the iron in them. The team called them “atomic injectors”: they deliver iron atoms, one by one, to a growing nucleus.

Iron: from two atoms to a crystal in four stages
The full birth of an iron crystal was recorded in one experiment at a dose rate of 1.4 × 10⁶ electrons per nm² and second (Video 1). It ran through four stages (Fig. 3 and 4).

Diatomic seed (0–13 s): Two iron atoms form a pair on the outside of the tube wall, 0.32 to 0.34 nm apart (Fig. 3). A free Fe₂ molecule would have a bond length of only 0.20 nm. The tube stretches the pair to a distance much closer to that in bulk γ-iron (0.29 nm), and in doing so it weakens the bond from 2.2 eV to 0.8 eV. At 8 s, the right iron atom passes through the wall into the tube, which points to a vacancy defect in the wall at this spot.

Atom delivery (13–50 s): An atomic injector slides along the tube towards the seed and pushes its right atom aside, to 0.43 nm (Fig. 3a–c). This frees space, and at 19 s a third atom moves from the injector into the seed. Within the next 4 s the seed grows into a cluster of about 17 iron atoms, while only one atom remains in the injector. The cluster stays amorphous. Once it has handed over its atoms, the injector moves on along the tube.

Metastable amorphous state (50–197 s): For 147 s the cluster keeps rearranging. Its atoms shuttle between the inner and outer surface of the tube, and their distances and neighbors change all the time (Fig. 4a).

Ordered crystallite (from 197 s): Suddenly the atoms line up at equal distances that match the (111) plane of γ-iron. From now on, further growth follows this ordered core. Fourier transforms of the images measure how the order appears over time (Fig. 4b, c).

The amorphous stage is the key result. A pair of iron atoms can still fall apart again, and clusters of about 10 atoms neither fall apart nor crystallize. The 17-atom cluster, in contrast, stayed amorphous for more than 142 s before it ordered. A metastable amorphous precursor is therefore necessary for iron to nucleate, and the process follows the two-step mechanism^[8], as detailed in the box.

Gold: order inside an amorphous cluster
For gold, the starting point was a larger amorphous cluster already sitting in the tube (Fig. 5). Some of its atoms diffused into a neighboring carbon structure (violet arrow in Fig. 5a). For the first 16 s under the beam, the cluster was extremely dynamic and showed no order. At 17 s, a crystallite less than 1 nm across appeared inside it, confirmed by its Fourier transform (Fig. 5b). It dissolved within 5 s and reappeared at 23 s.

Once it reached about 1 nm, it stayed, with a well-ordered (111) face of gold. From there, the order spread through the whole cluster over the next 348 s, until the crystallite was about 2 nm long and 1 nm wide at 370 s. In between, it rotated or transformed and showed other orientations, and from 331 s on it returned to the original (111) face. The intensity of the gold reflections in the Fourier transforms jumps when the cluster crystallizes (Fig. 5c), so gold, too, forms its crystal out of an amorphous precursor (Fig. 5d).

The energy for this step comes from the beam. An 80 keV electron can transfer at most 0.96 eV to a gold atom. Earlier work had shown that such energy transfer can affect, melt and even evaporate metal nanocrystals^[22]. Here it was just enough for the cluster to overcome the barrier between the amorphous and the crystalline state. The smallest gold crystallite seen had a radius of only about 0.45 nm, much smaller than the 2 nm nuclei observed for gold in the solution of a liquid cell^[20].

Rhenium: two clusters merge
More atoms make it easier to overcome the energy barrier, so clusters that merge can speed up nucleation. Classical theory usually ignores this route. With rhenium, the team watched it happen (Fig. 6). At the start, two amorphous rhenium clusters of about 10 atoms each sat in the tube. The left one was mobile and moved along the tube. The right one was bound to the wall and partly covered by a carbon shell, which served as the substrate for nucleation.

At 135 s, the left cluster attached to the carbon shell of the right one. At 151 s and 177 s, the two touched briefly through a single rhenium atom, and between 183 s and 185 s they merged completely. The new cluster of about 20 atoms was above the critical size. It stayed amorphous at first and reorganized until, at 308 s, a crystallite with clear lattice planes appeared. For another 124 s it kept restructuring while remaining crystalline (Fig. 6b, c). Rhenium thus follows the same two-step path as iron and gold, except that it reaches the critical size by coalescence.

What it opens up
All three metals crystallized through a metastable amorphous precursor, at room temperature and under the electron beam. The size of this precursor decides whether a crystal forms: for all three metals the critical size is below 2 nm, and for iron and rhenium it lies between 10 and 20 atoms. What differed was how the cluster got there: by collecting single atoms (iron), by ordering an existing amorphous cluster (gold) or by the coalescence of two small clusters (rhenium).

The combination of a nanotube as substrate and delivery channel, and the electron beam as both energy source and camera, opens up a size range below one nanometer that no other method reaches. The results matter for iron, gold and rhenium in carbon-rich environments found in industry, such as Fischer–Tropsch catalysis, the growth of graphene by chemical vapor deposition and steelmaking. Ute Kaiser said: “By successfully recording this process, we hope that in action we will shed light on the fundamental phenomenon of nucleation and crystal growth for the three metals examined and enable a more controlled design of materials in the future.”

Resource:
Cao, K., Biskupek, J., Stoppiello, C. T., McSweeney, R. L., Chamberlain, T. W., Liu, Z., Suenaga, K., Skowron, S. T., Besley, E., Khlobystov, A. N., Kaiser, U. (2020).
Atomic mechanism of metal crystal nucleus formation in a single-walled carbon nanotube.
Nat. Chem. 12(10), 921–928.
https://doi.org/10.1038/s41557-020-0538-9

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