Ferroelectric STO? Tilt and Astigmatism May Lead to Misleading Displacements at Atomic Resolution

The ellipticity of atomic columns in ADF-STEM data is a helpful indicator of ferroelectric phenomena in perovskite specimens such as STO, a paraelectric, or PZO, an antiferroelectric, during experimental time. Ellipticity may be due to structural displacement in column when the specimen is oriented to zone axis, erroneous displacement when the specimen is mis-tilted away from zone-axis, or probe astigmatism. It is tempting for a microscopist to erroneously ‘correct’ ellipticity from mis-tilt through stigmation. This may preserve artificial displacements, potentially causing STO to appear ferroelectric and PZO appear paraelectric in displacement maps. In this study, the effects of tilt and astigmatism on column ellipticity were measured from multislice simulations of ADF-STEM images, with the aim of establishing acceptable tilts for precise, experimental observations of local polarization. The effects of mis-tilt and astigmatism cannot be resolved in standard ADF-STEM imaging leading to 4D-STEM datasets as an option for future characterization of antiferroelectric PZO. The trained instinct of microscopists working with atomic resolution ADF-STEM is to make atomic columns appear round by simultaneously adjusting astigmatism and defocus. However, column ellipticity E may be a helpful indicator of functional behavior during experimental time. It may reflect true structural displacements or arise from specimen mis-tilts and poor stigmation. Even small mis-tilts (6 mrad) can cause artificial displacements in ABF [1] and ADF [2,3], affecting polarization measurements. This study examines the perovskites SrTiO3 (STO), a paraelectric [4], and PbZrO3 (PZO), an antiferroelectric [5], to illustrate ellipticity from mis-tilt (STO) or structure (PZO). Multislice ADF-STEM simulations of STO and PZO assess tilt and astigmatism effects on ESr or EPb. Aiming to measure erroneous displacements that may be induced by tilt alone, and test if astigmatism applied to minimize ellipticity induced by tilt preserves displacement. Displacement maps from ADF images characterize polarization and ferroelectric behavior [6]. If mis-tilt cannot preserve the expected property, for instance if STO and PZO appear ferroelectric, then an acceptable range of tilts have been established for experiment. All image simulations and processing were performed using the abTEM Python library [7]. Structural models for Pmm STO and Pbam PZO were obtained from the Materials Project database, entries mp-5229 and mp-542903 [8]. Structure models were prepared with the atomic simulation environment Python library [9]. The Atomap Python library obtained all column positions, ellipticities, and displacement maps by 2-D Gaussian fitting [10]. Multislice simulation parameters: all structures had 20nm thickness and 10 frozen phonon configurations; probe energy 200kV, semi-convergence angle 27 mrad, max. scatter 250 mrad. ADF-STEM images were produced from 4D datasets with virtual detector angles 99-208 mrad. Scan frame was 1 unit cell with pixel size 0.23Å. Output images were processed by tiling, interpolation to 0.1Å pixel size, effective dose 1×10⁷ e Å⁻² with Poisson noise, effective source size 0.5Å with Gaussian blur before Gaussian fitting. Series were run with 0-30 mrad probe tilt, 0-50Å astigmatism (C1,2), no other aberrations, or a combination of probe tilt and astigmatism. E is defined in Atomap as the ratio of larger to smaller standard deviations of the 2-D Gaussian function; a circular column has E=0%. Experimental images were obtained on a probe-corrected Nion UltraSTEM200 (200kV, convergence angle 27 mrad, HAADF collection 99-208 mrad) at the CRANN Advanced Microscopy Laboratory, Trinity College Dublin. Specimen was a supported PZO thin film, grown using chemical solution deposition at Georgia Tech, Atlanta, GA, USA, prepared for STEM as a cross-sectional FIB-lamellar specimen at Queen’s University, Belfast, UK. Early results show that ‘correcting’ erroneous Sr column ellipticity due to probe tilt with astigmatism was achievable in simulations. Fig. 1A shows an ADF-STEM image of STO (001) with no tilt or astigmatism, displaying near-perfectly circular Sr columns with ESr of 0.6%, as expected for the paraelectric Pm-3m structure. Figs. 1B and 1C show ESr of ∼7% induced by 15 mrad probe tilt or 13Å astigmatism, respectively. Two series were simulated to measure the effects of astigmatism and tilt on ESr, with results shown in Fig. 1F. Probe tilt had a greater effect, with ellipticity increasing rapidly beyond 15 mrad. Ellipticity responded more gradually to astigmatism, with higher variability at larger values. To determine their relationship, polynomial functions were fitted to the datasets, allowing the ‘correction’ of tilt-induced ellipticity with astigmatism (Figs. 1D, 1E). Using the equations, ESr =15% could result from either 19.66 mrad tilt or 26.73Å astigmatism. Applying these perpendicularly reduced ESr , potentially restoring round Sr columns. This illustrates a scenario relevant for microscope operators. Fig. 2A shows an experimental ADF-STEM image of a PZO thin film in (120) orientation (shown in overlay), aligning to a high-symmetry direction of the pseudocubic cell. Simulated ADF-STEM images reveal pronounced ellipticity in Pb columns due to displacement, indicative of antiferroelectric behavior. In Fig. 2B, a simulation with no tilt or astigmatism gives EPb of 27.63%, increasing to 32.73% with 10 mrad tilt (Fig. 2C) and 35.97% (Fig. 2D). Further simulations will clarify the relationship between probe tilt, astigmatism, and ellipticity as for STO. The results presented here are shown in the preliminary stages, work is ongoing and will quickly produce displacement maps to measure erroneous displacements that may occur from tilt, and to show that these are preserved when balancing astigmatism is applied. In an experimental ADF-STEM image alone column ellipticity being the result of structure, mis-tilt, astigmatism, or some combination is impossible to discern. Indicating that further work characterizing polarization ordering at atomic resolution must include some reciprocal space measurements. Either a CBED pattern acquired at the site of the ADF-STEM frame to acknowledge local tilt conditions, or by moving to pixelated detector for 4D-STEM data [11]. Summary of ADF-STEM results from Pm3¯m STO (001) multislice simulations. Clockwise from top right. A – C: example simulations with no probe tilt or astigmatism, probe tilt of 15 mrad and 13Å astigmatism with Sr column ellipticity ESr inset. D-E: example of using astigmatism to ‘correct’ erroneous ellipticity due to mis-tilt of 19.66mrad, with tilt only in D and tilt and astigmatism in E. F – Result of simulation series with 0-30 mrad probe tilt (orange) and 0-50Å astigmatism (blue) on ESr. The equations for polynomial fitting curves for each series are shown. Summary of ADF-STEM results from Pbam PZO (120) multislice simulations. From left to right. A Experimental ADF-STEM image obtained by author of a (120) oriented PZO thin film, with PZO (120) unit cell overlay. B-D example simulations with no probe tilt or astigmatism, probe tilt of 10 mrad and 10Å Astigmatism with Pb column Ellipticity EPbr inset. F - Early result of simulation series for PZO 0-10 mrad probe tilt (orange) and 0-10Å astigmatism (blue) on EPb.

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