Supporting Information

Size: px

Start display at page:

Download "Supporting Information"

Georgiana Garrison
5 years ago
Views:

1 Supporting Information Dynamics and Removal Pathway of Edge Dislocations in Imperfectly Attached PbTe Nanocrystal Pairs; Towards Design Rules for Oriented Attachment Justin C. Ondry,, Matthew R. Hauwiller,, and A. Paul Alivisatos *,,, Department of Chemistry, University of California, Berkeley, California 94720, United States Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States Department of Materials Science and Engineering, University of California, Berkeley, California 94720, United States Kavli Energy NanoScience Institute, Berkeley, California 94720, United States 1

2 Figure S1 analysis of all the possible Burgers vectors and glide planes for b=½<110> edge dislocations for {100} (A) and {110} (B) attachment of rock salt crystals. The right two examples of {110} attachment are very unlikely because they do not involve step edges, instead it would require the shearing of the crystal by a[110]. We did not observe any dislocations like this. 2

3 Figure S2 Overview of the characterization of the initial PbTe nanocrystals. A) low resolution TEM image of the nanocrystals. B) size and size distribution of the PbTe nanocrystals used in this work. C) several HRTEM images of individual PbTe nanocrystals down the <100> zone axis showing the quasi cubic shape mostly terminated with {100} facets. Several of the nanocrystals have step edges which are necessary for imperfect oriented attachment. In addition, some of the particles have significant {110} termination. 3

4 Figure S3 HRTEM of the PbTe nanocrystals after solvent mediated sandwiching between multilayer graphene sheets. Particles show significant attachment on the {100} facets, and to a lesser extent attachment on {110} facets. Figure S4 Additional examples of imperfect oriented attachment. A) HRTEM image of 2 PbTe particles which have imperfectly attached on {100} facets giving rise to a b=½[110] edge dislocation. B) HRTEM image of 2 PbTe particles which have imperfectly attached on {110} facets giving rise to a b=½[110] edge dislocation. 4

5 Figure S5 Method for objectively determining dislocation position. Automated scripts in Gatan Digital Micrograph and ImageJ were used to perform this analysis on each frame automatically. We show an example progression of the analysis for one frame of the imperfect attachment on the {100} facets shown in in Figure 2. The raw data and each step of the analysis for both figure 2 and 3 are available on the DASH repository at First, the movies were drift corrected using a cross correlation method using the raw images as inputs and manually checked and corrected where necessary (Stack Alignment, Dave Mitchell's DigitalMicrograph Scripting Website, The geometric phase analysis (GPA) and all other analysis was performed with the raw but drift corrected unrotated images from our CCD camera to avoid introducing artifacts. Geometric phase analysis was performed using the GPA tool contained in the FRWRtools plugin ( for Gatan Digital Micrograph. The (200) and (020) peaks were used for analysis with a reference lattice with a and b parameters of 3.09Å with a 90 angle between the two, a resolution of 0.7 nm and a smoothing of 0.6 with a symmetric strain matrix. After this analysis, all images were rotated to the same orientation, using a bilinear interpolation in ImageJ, as shown in figure 2 to facilitate comparison. A) Raw HRTEM image of the imperfectly attached particles. B) ε xx map determined by GPA analysis for the imperfectly attached PbTe particles. We note that the ε yy and ε xy strain output from the GPA will produce the same result for dislocation position (within a pixel) however the ε xx map was used for all the samples shown here for consistency. C) The ε xx strain map was overlaid with the HRTEM image of the particles and each frame was manually inspected to ensure erroneous results were avoided. For some frames, an instability in the microscope (sample vibration, CCD readout error, etc.) produced suboptimal images which gave several discontinuities in the strain map within the particle. These frames were carefully inspected and only points where the dislocation resided were retained. D) Discontinuities in the strain map were determined with single pixel accuracy by finding the maximum in the strain map using ImageJ. Finding the minima also produced the same result, only shifted one pixel adjacent. For consistency, we use the maxima for all analysis. E) A mask was applied to 5

6 remove the discontinuities which result from the amorphous background. F) Final position of the dislocation which was imported into matlab for plotting. We note that this analysis picks out the two components of the dislocation resulting from the extra (100) and (010) plane respectively although no effort was made to plot those separately in the graphs shown in figures 2 and 3. Figure S6 Strategy for analyzing the average misorientation angle. The same initial analysis protocols were used as discussed in figure S4. A) Raw HRTEM image of the two particles. B) rotation map from the GPA of a single frame. The colors correspond to rotation of the lattice relative to a reference lattice. Two boxes were drawn that contained the top and bottom particle. The average and standard deviation of the rotation value were calculated for each box and the difference was taken as the misorientation angle between the two crystallites. The standard deviation of the misorientation angle was determined by adding the standard deviation of the rotation value for each domain in quadrature. This error is both a metric for the intrinsic error in the measurement and to variations in the orientation across individual crystallites due to strains imposed by the dislocation. C) the misorientation angle was measured in real space for some frames to validate the GPA determined misorientation angle. 6

7 Figure S7 model of a b=a/2<100> edge dislocation with improper bonding circled. which indicates that this is likely not the true structure. 7

8 Figure S8 Comparison of experimental and simulated HRTEM images for the b=a/2[101] mixed dislocation. A) Experimental HRTEM image of a b=a/2[101] mixed dislocation. B) Simulated HRTEM image of the mixed dislocation structure presented in figure 3E. The mixed dislocation structure was generated using the Atomsk software using anisotropic elasticity. Briefly a 54Å by 60Å by 35Å thick supercell of PbTe was generated, then a b=a/2[101] mixed dislocation was cut from the crystal using anisotropic elasticity theory and elastic constants for bulk PbTe. The Atomsk software displaces the atoms based on strain fields around a dislocation in an infinite crystal. No efforts were made to further relax the structure beyond continuous elastic theory for an infinite crystal. For these reasons, the simulated dislocation structure does not capture the misorientation observed in the experimental imperfectly attached particles. HRTEM images from the mixed dislocation structure were simulated using the multislice method implemented in 8

9 the computem software. 1 The dislocation structure was placed in the center of a 180Å by 180Å by 35 Å supercell surrounded by vacuum. Imaging parameters for the simulated images were set for near Scherzer conditions based on estimated parameters for our Tecnai T20 S-Twin TEM. Simulation parameters are as follows: Accelerating voltage 200keV, C3 Spherical aberration coefficient: 1.2mm, Defocus: -45nm, Defocus: 15nm, Beam convergence angle: 0.3mrad, Objective aperture: 20mrad, transmission function size: 1024 by 1024-pixels and slice thickness: 2Å. All higher order aberrations were set to be zero since our instrument is C3 limited and all higher order aberrations are insignificant compared to C3. Images were simulated at 0K (no atom vibrations). Gaussian noise was added to the simulated image to account for camera noise. The simulated images have improved contrast compared to the experimental images. This increase in contrast is a result of not including atom vibrations in the simulated image and is a well-known artifact in HRTEM image simulation. 2 Further in the simulated images we did not account for the modulation transfer function of our TEM camera which would lead to further blurring of the image. C) and D) Blue and yellow lines are overlaid on the (100) and (010) planes respectively as guides to the eye showing the apparent screw dislocation. 9

10 Figure S9 Additional examples of edge to partial screw conversion during electron beam exposure of imperfectly attached PbTe particles. A) HRTEM (left) and {100} bandpass Fourier filtered (right) image of two particles attached on {110} facets with a pure edge dislocation exemplified by the extra (100) and (010) planes outlined by blue and yellow lines respectively. B) HRTEM image and {100} bandpass Fourier filtered (right) image of the same particles 6 frames later with only an extra (100) plane indicative of conversion to a screw dislocation. C) HRTEM (left) and {100} bandpass Fourier filtered (right) image of two particles attached on {100} facets with a pure edge dislocation exemplified by the extra (100) and (010) planes outlined by blue and yellow lines respectively. B) HRTEM image (left) and {100} bandpass Fourier filtered (right) image of the same particles a single frame later with only an extra (010) plane indicative of conversion to a screw dislocation. We note that in panel D, the top crystallite is rotated off the <001> zone axis as seen by the change of contrast which is consistent with the expected out of plane rotation for a screw dislocation. Figure S10 A) and B) HRTEM images of imperfectly attached PbTe nanocrystals which show dislocations which have partial screw character initially. It is unclear if these dislocations were pure edge dislocations initially and converted to partial screw character during electron beam irradiation while focusing. Further the loss in contrast of the bottom crystal in both cases in indictive of a rotation around the attachment axis. 10

11 Figure S11 (A-D) HRTEM image simulations of a 3.8nm PbTe cuboctahedra with different degrees of rotation around the [100] axis. This shows that a slight tilt of the crystal coming from the screw dislocation can reduce the contrast of the corresponding (010) planes which are perpendicular to the rotation axis. This is consistent with the reduced contrast of the planes perpendicular to the rotation imparted by the screw dislocation seen in figure S10 A and B. (E- H) crystal models used to generate the simulated images. Yellow corresponds to Te and blue corresponds the Pb. Crystal models were cut from a bulk crystal of PbTe using VESTA with {110} cutoff planes 22.59Å from the origin and {111} cutoff planes Å from the origin. The structures were exported as.xyz files from VESTA and imported into matlab where a custom script was used to rotate the particle the specified amount around the given axes. The rotated nanocrystals were placed in a 100Å by 100Å by 100Å supercell. Simulations were performed using the same parameters as used for figure S8. (1) Kirkland, E. J. Advanced Computing in Electron Micoscopy; Second Edi.; Springer, (2) Van Dyck, D.; Lobato, I.; Chen, F. R.; Kisielowski, C. Do You Believe That Atoms Stay in Place When You Observe Them in HREM? Micron 2015, 68,

CHEM-E5225 :Electron Microscopy Imaging II

CHEM-E5225 :Electron Microscopy Imaging II D.B. Williams, C.B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, Springer Science & Business Media, 2009. Z. Luo, A Practical Guide