How a New Angle on the Imaging of Nanoscale Metamaterials Resulted in the Discovery of a Novel Crystal Structure

[Top left] Wiel Evers, [top right] Daniel Vanmaekelbergh, [bottom] Mark Boneschanscher

Authors:
M.P. Boneschanscher¹, W.H. Evers² and D. Vanmaekelbergh¹

Affiliation:
¹Condensed Matter and Interfaces, Debye Institute for Nanomaterials Science, Utrecht University, Netherlands.
²Opto-electronic Materials, Delft University of Technology, Netherlands.

In the field of nanotechnology, we are concerned with materials that are larger than atoms, but significantly smaller than what we call ‘bulk’ materials. As the name indicates these nanoparticles have at least one dimension in the nanometre regime. Interestingly, materials within this size regime have physical properties that are not only determined by its chemical constituents (which atoms make up the structure?) but also by their size and shape. The classical rules of physics are not applicable anymore. Instead quantum mechanics dictates how size, shape and chemical composition influence the materials’ properties like adsorption, emission, conduction and magnetism [1].

It is nice that we can design materials at the nanometre scale to have certain desired properties, but in the end we would of course like to use these materials in devices. The trick is to assemble the nanoscale materials in such a way that the engineered material properties due to the nanometre scale of the building blocks are maintained. This process has very aptly been compared to the assembly of LEGO bricks into a LEGO building: the building bricks are still identifiable within the superstructure [2]. The way this assembly is commonly achieved is by means of self-assembly: a suspension containing the nanoparticles is dried under specific circumstances, in order to let the nanoscale building blocks crystallize into a superstructure (see Figure 1). In this superstructure the properties of the nanoscale building blocks are maintained. Moreover, different building blocks can be combined into one superstructure giving rise to synergetic properties [3].

Figure 1: Formation of the nanoparticle superstructures. a, Schematic of the evaporation process during which the nanoparticle superstructures form. b, TEM image of the resulting superstructure. Even though this is a transmission image of a 3D superstructure, the different building blocks (nanoparticles) are still visible.

Since the material properties depend on the way that they can couple to each other in the superstructure, it is of major importance that the exact crystal structure of the superstructure is known. Fully resolving these superstructures however is not an easy task. The usual way this is done in the field is the comparison of transmission electron microscopy (TEM) images (2D projection information) to crystal structures known from the atomic world. This approach has a number of drawbacks, since all information along the 3rd dimension (along the electron beam) is lost. We have addressed this issue before, when we used electron tomography to study superstructures and their defects [4].

In the latest edition of Nano Letters we describe how we have used this technique once more to study a superstructure with a crystal structure not observed in nature before [5]. But let us first have a look into electron tomography. As stated before, TEM creates 2D projection images of our 3D superstructure. Using electron tomography we take multiple TEM images while rotating our sample under the electron beam. In this way we create a tilt series, e.g. a series of transmission images at different angles. Movies of these tilt series can be found here (files si_002 to si_004 are tilt series on different samples). If we now combine all transmission images along the angles under which they were obtained we can reconstruct a 3D image of our superstructure. Movies where we slice through the 3D image can be found here (files si_005 to si_007 are the 3D images corresponding to the tilt series si_002 to si_004). After this it is a question of (rather difficult) computer-aided image analysis to extract the exact coordinates of the nanomaterials making up the superstructure. See Figure 2 for an overview of this process.

Figure 2: Electron tomography process. a, transmission images at different angles are taken and combined into a tilt series. b, after back projection of these transmission images along their respective angles a 3D image reconstruction is acquired, which can then be used for computer-aided image analysis. c, the final crystal structure of the nanoparticle superstructure as extracted from the 3D reconstructed image.

Our particular interest in the structure presented in this work was raised due to the formation process behind these structures. We established in earlier work that in most cases the formation of nanoparticle superstructures can be modelled using hard spheres [6]. This hard sphere model worked very well in predicting the crystal structures of the nanoparticle superstructures formed by a combination of two differently sized nanoparticles. However, there is a certain window of size ratios between the two different nanoparticles where the hard sphere model does not predict any superstructures at all. Therefore we were quite surprised to find that actually quite some different superstructures formed when we combined nanoparticles with just such a size ratio. That is, we did observe quite some different TEM images of what appeared to be different superstructures. The TEM patterns could not be attributed to any projection of a known crystal structure.

Figure 3: Three totally different TEM pictures originating from one and the same crystal structure. a, the [PbSe]₆[CdSe]₁₉ structure imaged along the [0001] direction. b, another crystallite where there is a planar stacking fault. Half of the TEM contrast is caused by the one orientation, the other half by the other orientation. c, yet another crystallite where the crystal growth appeared with the [0001] direction tilted 43^o with respect to the TEM grid.

Therefore we took 3 of such superstructures and performed tomography on them. The TEM images of these 3 structures all appeared to be very different (Figure 3). However, using electron tomography we resolved all three and found that they, in fact, resemble the same crystal structure. This however was a crystal structure not observed in nature before, nor in any artificial crystal structure (although we found an alloy having a similar – but not the same – crystal structure). Its unit cell is made up by 6 PbSe nanocrystals and 19 CdSe nanocrystals, and has a hexagonal symmetry (no. 178 P6m2). The different TEM pictures that we observed appeared to be caused by different orientations of that particular crystal structure and by one structure with a planar defect (Figure 3). This is once more a warning to the field that what you see in TEM is not always what you get.

Finally this discovery will have some implications in the field. First, the structure itself is built from a kagomé lattice, a type of symmetry that is of high interest in the field of condensed matter for its curious spin properties. Secondly the fact that this crystal structure is found in a size regime where no crystal structure was expected implies that either the hard-sphere model is not always valid for nanoparticles, or that this particular crystal structure is overlooked in the hard sphere modelling community. And finally, we hope to have set a new standard in the research to these nanocrystal superstructures: the use of electron tomography to fully resolve structures of interest.

References:
[1] Celso de Mello Donegá, "Synthesis and properties of colloidal heteronanocrystals", Chemical Society Reviews, 40, 1512-1546 (2011). Abstract.
[2] Dmitri V. Talapin, "Is it possible to form much larger ordered nanocrystal assemblies and to transfer them to different substrates?" ACS Nano 2, 1097-1100 (2008). Abstract.
[3] D. Vanmaekelbergh, "Self-assembly of colloidal nanocrystals as route to novel classes of nanostructured materials". Nano Today 6, 419-437 (2011). Abstract.
[4] Heiner Friedrich, Cedric J. Gommes, Karin Overgaag, Johannes D. Meeldijk, Wiel H. Evers, Bart de Nijs, Mark P. Boneschanscher, Petra E. de Jongh, Arie J. Verkleij, Krijn P. de Jong, Alfons van Blaaderen and Daniel Vanmaekelbergh, "Quantitative Structural Analysis of Binary Nanocrystal, Superlattices by Electron Tomography". Nano Letters, 9, 2719-2724 (2009). Abstract.
[5] Mark P. Boneschanscher, Wiel H. Evers, Weikai Qi, Johannes D. Meeldijk, Marjolein Dijkstra, and Daniel Vanmaekelbergh, "Electron Tomography Resolves a Novel Crystal Structure in a Binary Nanocrystal Superlattice". Nano Letters, 13, 1312-1316 (2013). Abstract.
[6] Wiel H. Evers, Bart De Nijs, Laura Filion, Sonja Castillo, Marjolein Dijkstra and Daniel Vanmaekelbergh, "Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices". Nano Letters, 10, 4235-4241 (2010). Abstract.