Ferroelectric order in individual nanometrescale crystals Mark J. Polking 1, Myung-Geun Han 2, Amin Yourdkhani 3,4, Valeri Petkov 5, Christian F. Kisielowski 6, Vyacheslav V. Volkov 2, Yimei Zhu 2, Gabriel Caruntu 3,4, A. Paul Alivisatos 7,8 *, and Ramamoorthy Ramesh 1,7 * 1 Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720; 2 Condensed Matter Physics and Materials Sciences Department, Brookhaven National Laboratory, Upton, New York 11973; 3 Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148; 4 Advanced Materials Research Institute, University of New Orleans, New Orleans, Louisiana 70148; 5 Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859; 6 National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California 94720; 7 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720; and 8 Department of Chemistry, University of California, Berkeley, Berkeley, California 94720 *Correspondence should be addressed to: rramesh@berkeley.edu; APAlivisatos@lbl.gov NATURE MATERIALS www.nature.com/naturematerials 1
Figure S1 Transmission electron microscope (TEM) images of GeTe and BaTiO 3 nanocrystals. a, TEM image of 8 nm diameter GeTe nanocrystals. b, TEM image of 15 nm average size BaTiO 3 nanocubes. c, TEM image of 10 nm average diameter BaTiO 3 nanospheres. 2 NATURE MATERIALS www.nature.com/naturematerials
Figure S2 Quantitative analysis of atomic-resolution reconstructed phase images. a, Reconstructed phase image of a GeTe nanocrystal. b,, Reconstructed phase image with peak positions determined by the Gaussian peak fitting function in MacTempas X (Total Resolution, Inc.). c, Reconstructed phase image with the best-fit lattice calculated using a least-squares routine. d, Corresponding map of local polar displacements (vectorr magnitudes given by color scale). NATURE MATERIALS www.nature.com/naturematerials 3
Figure S3 Simulated phase images for 10 nm BaTiO 3 nanocubes. Simulations weree performed with a fixed [001] polarization vector for BaTiO 3 nanocubes tilted by 10 mrad from the exact [010] zone axis (seee Fig. 1b) at different azimuthal (or precession) angles 0-315 around the normal to the image plane. A strong shift off the oxygen columns with respect to the Ba and Ti/O columns can be observed (inset), providing a sensitive indicator of crystal tilt. 4 NATURE MATERIALS www.nature.com/naturematerials
Figure S4 Comparison of experimenta al and simulated holographic phase images. a, Theoretical phase image for a BaTiO 3 nanocrystal with a linear, monodomain polarization state (P s = 25 C/cm 2 and ε r = 60). b, Experimental phase image (3 times amplified) for a BaTiO 3 nanocrystal poled at +3 V. c, Line profiles obtained for the regionss indicated with arrows in a and b. The solid green line represents the calculated phase shift in the electron wave due only to the surface charge (P s ). The solid red line represents the calculated total phase shift due to the surface charge and the mean-inner-potential (17.9 V) of the BaTiO 3 nanocube. Strong, quantitative agreement between the experimental and theoretical phase images can be observed. Piezoresponse Phase (deg.) 250 200 150 100 50-20 -15-10 -5 0 5 10 15 Bias Voltage (V) A 20 PiezoresponseAmplitude (nm) 1.2 0.8 0.6 0.4 0.2 0-20 -15-10 -5 0 5 10 15 20 Bias Voltage (V) B Figure S5 Piezoresponse force microscope measurements of individual 5 nm BaTiO 3 nanocubes. a, Plot of piezoresponse phase vs. applied bias for an individual 5 nm BaTiO 3 nanocube at 25 C. b, Corresponding plot of piezoresponse amplitude vs. applied bias for an individual 5 nm BaTiO 3 nanocube. No hysteresis is evident at room temperature, indicating a disappearance of ferroelectric switching behavior. NATURE MATERIALS www.nature.com/naturematerials 5
Cubes 15 nm 0.8 0.6 0.4 0.2 Cubes 8-9 nm Spheres 10 nm -0.2 0 10 20 30 40 50 Radial Distance (Å) Figure S6 Comparison of atomic pair distribution functions for BaTiO 3 nanocrystals with different morphologies and sizes. Experimental atomic pair distribution functions of BaTiO 3 nanocubes and nanospheres (symbols) are compared with model ones (blue lines) featuring a tetragonal, polar phase. The residual differences (data minus model) are shown in red. A closer match with the tetragonal model is observed for cubes than for spheres of similar size, indicating reduced structural disorder in cubic particles. A still closer match is apparent for the larger (15 nm) cubes. 6 NATURE MATERIALS www.nature.com/naturematerials
2.0 1.5 0.5-0.5 Experimental data Cubic Model Rhombohedral Model 20 Å - 0 5 10 15 20 2.0 Experimental Data 1.5 Cubic Model Rhombohedral Model 0.5-0.5 35 Å - 0 5 10 15 20 25 30 35 2.0 Experimental Data Cubic Model 1.5 Rhombohedral Model 0.5 50 Å -0.5-0 5 10 15 20 25 30 35 40 45 50 Radial Distance (Å) Figure S7 Comparison of atomic pair distribution functions for 8 nm GeTe nanocrystals at different length scales. The experimental atomic PDFs for GeTe (symbols) are compared with model PDFs featuring cubic (blue lines) and rhombohedral (red lines) structures for length scales of 20, 35, and 50 Å. The rhombohedral model with polar distortions yields a superior fit at shorter length scales, but the quality of the fit becomes comparable for both models at longer length scales. NATURE MATERIALS www.nature.com/naturematerials 7