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Anisotropic Cracking of Nanocrystal Superlattices Benjamin T. Diroll, Xuedan Ma, Yaoting Wu, and Christopher B. Murray Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03123 • Publication Date (Web): 18 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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Anisotropic Cracking of Nanocrystal Superlattices Benjamin T. Diroll,1† Xuedan Ma,2 Yaoting Wu,1 and Christopher B. Murray1,3 1

Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, PA

19104, United States 2

Center for Nanoscale Materials, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont,

IL 60439, United States 3

Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut

Street, Philadelphia, PA, 19104, United States

ABSTRACT. The synthesis colloidal nanocrystals in non-polar organic solvents has led to exceptional size- and shape-control, enabling the formation of nanocrystal superlattices isostructural to atomic lattices built with nanocrystals rather than atoms. The long aliphatic ligands (e.g. oleic acid) used to achieve this control separate nanocrystals too far in the solidstate for most charge-transporting devices. Solid-state ligand exchange, which brings particles closer together and enhances conductivity, necessitates large changes in the total volume of the solid (compressive stress), which leads to film cracking. In this work, truncate octahedral lead selenide nanocrystals are shown to self-assemble into body-centered cubic superlattices in which the atomic axes of the individual nanocrystals are co-aligned with the crystal axes of the superlattice. Due to this co-alignment, upon ligand exchange of the superlattices, cracking is preferentially observed on superlattice directions. This observation is related to

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differences in the ligand binding to exposed {100} and {111} planes of the PbSe nanocrystal surfaces. This result has implications for binary and more complex structures in which differential reactivity of the constituent elements can lead to disruption of the desired structure. In addition, cracks in PbSe superlattices occur in a semi-regular spacings inversely related to the superlattice domain size and strongly influenced by the presence of twin boundaries, which serve as both emission centers and propagation barriers for fractures. This work shows that defects, similar to behavior in nanotwinned metals, could be used to engineer enhanced mechanical strength and electrical conductivity in NC superlattices.

KEYWORDS. Nanocrystal Superlattice, Body Centered Cubic, Twining, Ligand Exchange, Fracture Monodisperse colloidal nanocrystals (NCs) can be self-assembled into periodic arrays, termed NC superlattices, which resemble crystal structures observed in atomic and molecular solids.1 The structural diversity of NC superlattices is extensive,2 including single-component,1 binary,3 ternary,4,5 and doped lattices,6 liquid crystals,7 and quasicrystals,8,9 employing both quasi-spherical and anisotropic building blocks. These materials are predicted to give rise to controllable band structure and optoelectronic properties10 which are not achieved in bulk materials or isolated NCs. Despite the large diversity of novel materials, examples in which crystallization of NCs into organized lattices enables emergent behavior or improved properties, compared to random amorphous solids, is relatively limited.11–17 Achievements in self-assembly are largely enabled through exquisite control over size18 and shape19 achieved using organic ligands with long alkyl chains, which promote solubility in non-polar organic solvents now ubiquitous in synthetic methods. A longstanding challenge arising from the development of ligand-controlled synthesis of colloidal NCs in organic solvents is that these long alkyl chain


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ligands present a substantial electronic barrier and enforce a larger interparticle distance (~2 nm) than acceptable for efficient charge conduction between NCs in a NC solid. Broadly, two general strategies have been devised to overcome the poor conductivity of NC solids made with aliphatic ligands: solution exchange20 and solid exchange.21,22 In solution exchange, compact ligands typically charged-stabilize NCs against agglomeration and can be deposited as close-packed solids. However, these systems are not yet observed to self-assemble into anything like the structural diversity or quality of superlattices with long organic ligands. In solid exchange, ligands of a pre-cast film are removed by a second processing treatment with a shorter displacing ligand. This displacement step induces large changes in the volume of the solid, leading to densification of the film and the development of cracks.22–24 For example, replacement of 1 nm ligands on 7 nm particles with 0.5 nm ligands yields a ~27 % decrease in the volume of the solid. To overcome this problem, additional NCs may be deposited infill void regions,22,25 but infilling has not been successfully applied to superlattices, which must not only contract globally but also preserve the long-range order of NCs. Despite a small number of examples6,13,24,26,27 in which fracture of superlattice films has been overcome to generate conductive, ordered assemblies, this remains a challenge and devices made of superlattices are in most respects inferior in performance compared with glassy NC solids. In this work, we explore the fracture of self-assembled superlattices of lead selenide (PbSe) upon ligand exchange. The underlying co-alignment of the atomic and superlattice crystal axes achieved in bcc or bct superlattices of PbSe NCs28–32 leads to anistropic mechanical weakness during ligand-exchange and concomitant volume contraction. We use well-understood twin boundary regions to index cracking along directions of the bcc superlattices and find this anisotropic cracking is common to many different ligand exchanges. Within a single NC


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superlattice domain, superlattice cracking behaves similarly to a film with uniaxial strain, but across the entirety of the film, the density and size of cracking depends strongly on the size of the superlattice domain with propagation limited by twin boundaries. Typical transmission electron microscope images of 7 nm PbSe NCs capped with oleic acid and evaporated on diethylene glycol to form superlattices are shown in Figure 1. The images show the (110) projection of bcc superlattices with typical grain sizes greater than 1 µm2 with some grains of the superlattices reaching above 100 µm2. As PbSe NCs of this size are approximated as truncated octahedra dominated by {111} and {100} faces,28,30–36 self-assembly into the bcc structure maximizes the packing fraction, encoding co-aligned nanocrystals through entropy maximization, although bct structures have been observed in related systems.29,30 The spotted selected area electron diffraction (SAED) pattern (shown inset to Figure 1b and quantified in Supporting Information Figure S1) of the single superlattice domain in Figure 1b, confirms that, similar to earlier reports on IV-VI NC superlattices,14,24,28,31,32,37 the atomic lattices of the PbSe NCs align systematically with respect to the superlattice axes. The unit cell in Figure 1c represents the packing model derived from earlier literature. In this model of a bcc structure, the family of {hkl} atomic planes are co-aligned with the family of {hkl} planes of the superlattice crystal.


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Figure 1. (a,b) (110) projections of bcc superlattice comprised of 7nm PbSe NCs capped with oleic acid. Inset to (b) is the corresponding SAED pattern for the same spot. (c) Unit cell of truncate octahedral PbSe NCs self-assembled into a bcc superlattice. The surface facets of the PbSe NCs are indicated. (d) Low magnification image of PbSe NC superlattice thin film selfassembled on diethylene glycol and dried on to a TEM grid. The contrast variation of the film arises due to twin boundaries in the film. (e) Two twin boundaries of a 7nm PbSe NC superlattice film, labeled according to literature findings.32 (f) Twin boundary and (inset) corresponding SAED pattern of a PbSe NC bcc superlattice. Scale bars are 50 nm (a), 100 nm (b, e, f), and 5 µm (d). Another characteristic of these structures which has also been identified in previous works is the high density of {112} twin planes, which is the expected twinning plane of bcc lattices.32,38 Shown in Figures 1d-1f, twin planes are ubiquitous in the bcc NC superlattice films, apparent at low magnification (Figure 1d) from contrast changes and apparent texture in the film, often leading to herringbone patterns of contrast. Figure 1e shows a pair of twin boundaries at higher magnification with the (112) twin plane and an (011) plane highlighted. A similar image


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in Figure 1f was also correlated with SAED (inset), revealing the expected bimodal distribution of PbSe atomic lattice orientations from the two superlattice domains. Additional images of the bcc structures and twin planes can be found in the Supporting Information Figures S2 and S3. Twin boundaries are particularly instructive markers to study the transformation of PbSe superlattices upon ligand exchange and permit facile indexing of cracks with respect to the superlattice axes. Several images of superlattice films after ligand exchange are shown in Figure 2. Ligand-exchange is well-understood to reduce the interparticle spacings of NCs in the solid state, which is well-described in earlier works, including lead salt NC superlattices.22,24,39,40 The ligand exchange reaction results in the removal of surface bound oleic acid ligands observed with FT-IR (See Supporting Information Figure S4).41–44 Similar to solid-state ligand exchange of PbS bcc superlattices,24 we confirm by TEM and X-ray diffraction that interparticle ordering is preserved in the superlattices after ligand exchange (See Supporting Information Figures S5 and S6). Although random cracking of the film occurs (e.g. Figure 2a, bottom and left), this appears most commonly near pre-formed voids. More frequently, the films display fracture patterns in which cracks of the film occur systematically between {011} planes orthogonal to the sample plane such as in Figure 2a (top right) and Figures 2b-2f. Further images of cracked films can be found in Supporting Information Figures S7 and S8, including correlated SAED patterns. The herringbone pattern of cracks in Figures 2b-2e arises from the series of twin planes found in the samples as deposited, with cracks stopping at the twin planes. This same cracking pattern was found for several different ligand exchanges used in thin-film NC devices, including commonlyused ligand-exchange reagents ammonium thiocyanate (SCN),41 ethane dithiol (EDT),39 mercaptopropionic acid (MPA),45 acetic and formic acid (AA and FA),44 and Meerwein’s salt (Et3OBF4).42 It is therefore believed to be unrelated to the chemical nature of the ligand exchange


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and, in so far as all exchange reactions induce large volumetric shifts, the size of the displacing ligand.

Figure 2. Transmission electron microscope images of bcc superlattices of 7 nm PbSe ligandexchanged with (a) formic acid, (b) Meerwein’s salt, (c, d) mercaptopropionic acid, (e) ethane dithiol, and (f) acetic acid. Scale bars are (a-c) 5 um, (d) 2 um, (e) 500 nm, and (f) 100 nm. It is important to distinguish the cracking highlighted in this work from earlier studies of NC film cracking, which have shown random cracking (similar to mud cracks) and anisotropic cracking, but the latter only when induced by an applied stimulus.25,46–53 In these examples, crack pattern formation follows naturally from applied stress (most often due to drying), typically nucleating from a top or bottom surface and extending throughout the thickness of the film. Importantly, it is not related to the underlying crystal structure, NC superlattice axes, or grain boundaries. Related experiments at high-pressure have shown that fcc superlattices undergo lattice contractions of up to ~12 % which can be accommodated reversibly without fracture or cracking.54–56 In the present work, however, the consistent appearance of anisotropic cracking suggests that the strain actuated by ligand exchange is both large and preferentially relieved


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through fracture of the weakest bonds of the superlattice crystal—evidently those of {011} planes. In bulk bcc metals, there is no systematic relationship between cracking and twin boundaries,57 which suggests that particular properties of the NCs are responsible for the observed behavior. The structure of IV-VI NC surfaces58 and their coverage with oleic acid ligands33 is understood on a computational basis. Based upon PbS, the {111} planes on the NCs consist of alternating oleate and hydroxide ions (See Figure S9).33 Oleic acid is bound more strongly to the stoichometric {100} planes on the NC surface via dative interactions with lead surface atoms and hydrogen bonding with the chalcogenide surface atoms, but oleate groups are bound even more strongly to the {111} planes, which are entirely lead-terminated after reconstruction.33 As the bcc superlattice structure co-aligns the planes of the NCs and superlattice, different kinetics and thermodynamics of ligand exchange reactions on the {111} and {100} surfaces of the individual PbSe NCs are replicated with translational symmetry within each superlattice domain. The abundance of cracking along directions, suggests that these are the weakest particle-particle bonds in the solid. This conclusion is the same even if the NCs have {110} surfaces and are not simple truncate octahedra. To underline the essential significance of atomic co-alignment with the superlattices axes, we also synthesized fcc superlattices of similarly-sized PbSe NCs, which show substantially lower preferential orientation of the NCs within the lattice.31 Supporting Information Figure S10 shows an fcc film before and after ligand exchange with acetic acid under the same conditions used on bcc superlattices, with no anisotropic cracking observed in the film. This work only captures the films before and after ligand exchange, so discriminating between fracture which arises from different amounts of ligand exchange on the different facets


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(thermodynamic origin) or different rates (kinetic origin) is challenging from TEM analysis alone. However, two pieces of evidence support a kinetic origin. First, the near complete removal of ligands observed in many cases suggest that differences in the degree of ligand-exchange on the different surfaces are small.39,41,42 (See also Supporting Information Figure S4.) Second, the chemical diversity of ligand-exchange processes in which anisotropic cracking occurs also argues in favor of kinetic discrimination, potentially of the oleic acid/oleate leaving group, as the thermodynamics of each of the displacing ligands on the dominant PbSe NC surfaces is likely to be quite different.

Figure 3. (a) Definition of domain length (Ldomain), from one twin plane to the next, crack-tocrack length (Lcc), and crack width (Wc). Line-cuts of intensity through the microscopy data of a mercaptopropionic acid-exchanged film were taken parallel to the twin planes. (b) Representative line cuts for three different domain lengths. (c) Probability histograms of the crack-to-crack spacing plotted from aggregated data of different domain length ranges. (d) Cartoon view of NC film from the side showing the stress of an arbitrary fragment, which is highest at the middle, until it reaches the cracking threshold (σ*).48 Diagram of sample plane with cracks pinned at twin boundaries, forming lens shapes of fixed aspect ratio such that the ratio of Wc and Ldomain is roughly constant (k). At a larger length scale, two significant features of the cracking observed in ligandexchanged bcc PbSe NC superlattices are that the spacings of fractures are quasi-regular and that


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the density of cracking is proportional to the domain size, specifically the distance between twin boundaries. We explore these effects in quantitative detail for the mercaptopropionic acidexchanged film shown in Figure 2c. Figure 3a defines relevant parameters for quantitative analysis: Ldomain, the shortest distance of a single crystal superlattice from one twin plane to the next; Lcc, the distance between cracks along a line drawn parallel to the twin plane at the midpoint of the domain; and Wc, the crack width. For any given line-cut, the total length is the sum of all Lcc spacings and all Wc spacings. To provide a more robust quantitative analysis of film fracture, more than 40 line-cuts ranging from 3-20 µm in distance, were analyzed. All of the data analyzed here was collected from a region of similar thickness (~100 nm), as judged from the similarity in electron cross section (i.e. imaging contrast under similar conditions). Therefore we do not consider the role of sample thickness, which is the critical parameter in other works on NC film fracture,46–50 and instead study domain size exclusively in the two dimensional sample plane. Figure 3b shows typical line-scans of the collected CCD image intensity for a range of domain length values from 5.9 µm to 0.8 µm. Statistics on the cracking behavior of the film were obtained using an automated analysis to accurately compute the values of Lcc and Wc for each line-cut. Histograms of the inter-crack distance for several ranges of the domain length are shown in Figure 3c, demonstrating both a clear peak probability of Lcc dependent upon Ldomain and an increase in Lcc with Ldomain. The observation of quasi-regular crack spacing within a single superlattice domain is explained by a sheer-lag model similar to nanoscopic films which are uniaxially strained without slip.48,59 Regular crack spacings emerge because the stress on a film is maximized at the center of a given region (Figure 3d), leading to serial cracking at the middle


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of subdivided regions once the fracture threshold is reached, as has been demonstrated with uniaxially-strained NC monolayers.48,60 Although this model has been used to derive physical properties of materials,48,59 in this case the magnitude of applied stress is not known precisely. The TEM images, in effect, capture the sample at a single point in the stress versus strain curve and, critically, we do not capture the onset of fracture. More significantly, the density of fractures varies remarkably across the film, suggesting that the physics derived from uniaxial strain are insufficient by themselves to explain cracking in these films. In previous studies, crack spacing or density has been shown to scale in predicable ways against a single parameter, typically film thickness (for drying-mediated cracking) or applied stress.46–49 The large distribution of inter-crack lengths could therefore be attributed to heterogeneity of strain. However, the microscopic uniformity of the sample and all past work studying ligand exchange processes, which typically proceed rapidly to completion, it is unlikely that ligand exchange proceeds in substantially different ways across the film. We propose an alternative explanation: the differences in cracking density observed in this work are attributed to in-plane boundary conditions presented by the twin planes. For edge dislocations, it is well-known in bulk metals that twin boundaries are both emission sources and propagation boundaries61,62 and something similar appears with the cracks in the superlattice film. The cracks, which are structurally similar to edge dislocations, stop at twin boundaries, which do not slip along the domain edges. Accordingly, many cracks, most clearly in Figure 2b, have a lens-like shape (vesica piscis) defined by the film bending outward along the direction, but pinned to vertex at the twin boundary edges. Within the model presented in Figure 3e, the amount of strain relief which may be conferred by a single film fracture depends on the domain size, because the cracks have a fixed curvature or aspect ratio. Therefore, within this


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model, ligand exchange represents roughly equivalent stress applied to all domains, but the similar aspect ratio of the lens-shaped cracks means that superlattices with larger Ldomain will have cracks that are less numerous in number but have larger 〈Wc〉 to accommodate a fixed amount of strain.

Figure 4. (a) Average Lcc and Wc spacings as a function of domain length for an MPAexchanged PbSe superlattice film. (b) Fractional length of crack and film sections (compared to total length) as a function of Ldomain. The detailed analysis of single-domain data in Figure 4 supports both major aspects of this model. The average value of the crack-to-crack spacing (〈Lcc〉) and crack width (〈Wc〉) for each of the line scans is plotted versus Ldomain in Figure 4a. Both average spacings increase in a similar, non-linear manner with the domain length. The non-linear response at large Ldomain may reflect non-linear mechanical response, but could also reflect relaxation or partial breaking of the boundary conditions of the model (e.g. slip on twin planes or cracking across planes). The plot in


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Figure 4b confirms that Lcc and Wc rise in tandem with the domain length, occupying a roughly fixed proportion (25 % ± 3%) of the length of each of the line-cuts, which indicates both a uniform transformation of the film in all domains and a similar average aspect ratio or shape to cracks in superlattices of many different sizes. Consistent with the model in which cracks are pinned at twin boundaries and therefore have defined aspect ratios, smaller domains exhibited more, but smaller, cracks than large domains and all superlattice domains showed similar amounts of contraction along the directions. In conclusion, we have demonstrated that the formation of PbSe NC superlattices of a bcc structure undergo anisotropic fracture upon ligand exchange. Cracking patterns are systematically related to the lattice directions of the superlattice and the crystal axes of the NCs. Although in this system, co-alignment of superlattice and atomic axes is what enables anisotropic fracture, any structural anisotropy may encode similar results. Microscopically, facet-dependent ligand reactions strain stronger and weaker interparticle bonds, which leads to systematical fracture in directions under the large compressive strains of ligand exchange. This underlines the significance of facet-specific surface chemistry and its relationship to ligand exchange. Multi-component solids may present particularly significant challenges for preserving the structural integrity of the solid if the components display different susceptibility to ligand exchange. The cracking patterns within single NC superlattice domains exhibit quasi-regular spacings observed in uniaxially stressed systems described by a shear-lag model; comparing domains, the density of cracking is strongly size-dependent, which we have attributed to the additional in-plane constraints of non-slip twin boundaries, which disrupt the propagation of cracks through the film. This work provides insight that, similar to the improved mechanical and


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electrical properties of nano-twinned metals,63,64 twinning defects may improve the mechanical properties and better preserve charge percolation networks in NC superlattices. ASSOCIATED CONTENT Supporting information available: supporting methods and additional experimental data.

AUTHOR INFORMATION Corresponding Author *[email protected] Present Addresses †

Center for Nanoscale Materials, Argonne National Laboratory

ACKNOWLEDGMENT The authors would like to thank Xiao-Min Lin, Dmitri V. Talapin, Heinrich M. Jaeger, and Matthew E. Sykes for helpful discussions of these results. This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357. This research used resources of the National Synchrotron Light Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-AC0298CH10886. C.B.M. acknowledges support from the Richard Perry University Professorship. REFERENCES


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