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Abstract:
This talk details a methodology using X-ray diffraction (XRD) to quantify the contribution of domain wall motion to the macroscopic properties (primarily strain and piezoelectric coefficients) of polycrystalline ferroelectric materials. The speaker introduces quantitative metrics derived from XRD peak intensities, specifically the domain switching fraction (Ada) and its equivalent representation as multiples of a random distribution (mrd), moving beyond simple intensity ratios. The core of the presentation revolves around an equation that connects these microscopic, orientation-dependent switching metrics (obtained from pole figures) with the material's intrinsic lattice strain to calculate the extrinsic contribution to macroscopic strain. This approach is demonstrated across various materials (PZT, lead-free BZT-BCT, NBT-BT, thin films) and phenomena, including high-field polling, weak-field piezoelectric response (d33), grain size effects, and irreversible de-aging effects during AC cycling. The talk emphasizes the importance of texture analysis and orientation averaging in polycrystalline samples and presents both synchrotron and lab-based XRD experimental results validating the method's utility in directly measuring extrinsic contributions.
Quantifying Domain Wall Contributions Using X-rays
0:00:15 Introduction & Motivation: The talk focuses on using X-ray diffraction to quantify domain wall contributions to the properties of polycrystalline ferroelectrics. It targets those with basic XRD knowledge.
0:01:08 The "Rabbit Hole": Introduces three key equations: two to calculate domain wall motion metrics (Ada - switching fraction, mrd - multiples of random distribution) from XRD, and one to link these to macroscopic strain.
0:02:22 Domain Wall Contributions: Explains the difference between intrinsic (lattice) and extrinsic (domain wall motion) contributions to piezoelectricity, noting extrinsic effects can dominate (60-70%). Highlights the need for direct experimental evidence.
0:04:41 XRD for Characterization: Shows how XRD peak intensities (e.g., 002 vs 200 in tetragonal) change with applied electric fields (polling, cycling), reflecting domain reorientation.
0:05:44 Need for Quantification: Simple intensity ratios aren't sufficient. Introduces historical context (Berlincourt 1957) and the speaker's unified description linking switching fraction (Ada) and texture (mrd).
0:09:27 Key Equations (1 & 2): Presents the equations to calculate Ada and mrd from the intensities of specific XRD peaks (e.g., 002 and 200) relative to an unpoled state. Shows they are linearly related.
0:10:28 Interpreting Ada and mrd: Explains the physical meaning: Ada=0 (mrd=1) for random, up to Ada=67% (mrd=3 for 002) for fully saturated tetragonal switching parallel to the field.
0:12:14 Examples (High Field): Demonstrates the method on lead-free BZT-BCT (showing mrd/Ada vs. field), grain size effects in BaTiO3 (maximum switching at intermediate size), and PZT thin films (declamping/porosity increase switching).
0:16:53 Example (Frequency Dependence): Shows application to rhombohedral BiFeO3, tracking mrd of the 111 pole (f111) under sinusoidal fields to show decreasing domain wall contribution with frequency.
0:18:35 Importance of Orientation (Texture): Emphasizes that in polycrystals, measurements are needed across different sample orientations (pole figures or Orientation Distribution Functions - ODF).
0:20:20 Intensity Conservation: A key point: the sum of intensities from switching-related peaks (e.g., 002+200) is conserved in all directions, simplifying analysis to pole figures rather than full ODFs.
0:21:29 Pole Figure Measurements: Shows experimental pole figures (mrd or Ada vs. angle to the field) obtained from fitting XRD data collected at different angles, often using synchrotron sources and 2D detectors.
0:24:40 Saturated Switching Model: Introduces a theoretical model calculating the maximum possible texture (mrd vs. angle) if all domains switch optimally, providing a benchmark.
0:27:27 Connecting Microscopic to Macroscopic (Strain): Strain depends on lattice distortion (spontaneous strain) and the extent/orientation of domain switching (Ada/mrd). Introduces averaging over orientation space.
0:30:11 Key Equation (3): Presents the integral equation (and simplified discrete forms) to calculate macroscopic strain by integrating the product of the orientation-dependent switching (Ada or mrd from pole figure) and the projected single-crystal strain over all orientations. Spreadsheet available.
0:33:31 Examples (Polling Strain): Shows calculated strain from switching (using Eq. 3 and measured pole figures) matches measured polling strain in tetragonal PZT and BZT-BCT.
0:35:06 Example (Phase Transition): Applies the method to NBT-BT, separating strain contributions from field-induced phase transitions vs. domain alignment within the induced phase.
0:36:05 Extension to Weak Fields (d33): The same approach can measure tiny changes in Ada/mrd under small AC fields, quantifying the extrinsic contribution to the piezoelectric coefficient (d33).
0:38:03 Example (PZT d33): Calculates ~50% extrinsic contribution to d33 in tetragonal PZT near the MPB. Rayleigh analysis further separates linear/nonlinear extrinsic parts.
0:39:56 Additional Point (Textured Ceramics): Method can be applied to initially textured ceramics, separating processing texture from field-induced switching texture.
0:41:41 Additional Point (De-aging): Monitors both the change in switching (Delta Ada) and the average switching state (Ada) during AC cycling, revealing irreversible de-poling (de-aging), analogous to the Bauschinger effect in metals.
0:45:42 Additional Point (Polarization/Permittivity): Briefly mentions the extension of these concepts to calculate domain contributions to polarization and dielectric permittivity.
0:46:30 Lab-Based Implementation: Showcases an in-situ XRD stage for lab diffractometers, allowing similar experiments (applying fields, varying temperature) without synchrotron access.
0:47:25 Acknowledgements: Thanks students, collaborators, and funding agencies.