Periodic Reporting for period 2 - 3D-PXM (3D Piezoresponse X-ray Microscopy)
Reporting period: 2020-07-01 to 2021-12-31
Electrically polar materials are key to numerous essential technologies, such as energy storage, energy generation, and digital memory. However, there’s no methods by which researchers can directly visualize electrical polarization inside the materials themselves. This project seeks to remedy this by developing a new type of microscope that uses high-energy x-rays to visualize the atomic distortions associated with the polarization. This new capability will then be used to understand how microscopic defects influence the electrical functionality of polar materials, with a view to engineering new, higher-performance materials in the future.
The project has made substantial progress towards achieving its goals:
1. Proof of principle for the microscopy technique. We’ve demonstrated that the optical phase and amplitude of the x-ray field can be de-convoluted at hard x-ray energies (17 keV) using a Fourier Ptychographic approach. Moreover, we show this works for both the transmitted and Bragg-diffracted x-ray field. In the latter case, we are able to derive the lattice strain and misorientation of crystalline materials with better spatial resolution than the start-of-the-art technique our approach derives from (dark-field x-ray microscopy).
2. Characterization of optics and instrumentation. Our aforementioned implementation of the Fourier Ptychographic approach for de-convoluting the amplitude and phase of the x-ray field has enabled us to quantitatively characterize the imaging instrumentation and optics in unprecedented detail. Specifically, we’ve successfully measured the misalignments in the instrument that give rise to reconstruction errors in the image-forming algorithm, and have made spatial maps of the aberrations in the x-ray objective lens we use. This information is proving crucial in developing the instrumentation to reach its full potential (30 nm spatial resolution).
3. Polarization retrieval method. To determine the electrical polarization from the optical phase and amplitude distribution in the images, we’ve developed a new approach based on thermodynamic potentials. This differs from the DFT-based method described in the initial proposal, but is equal in terms of capability and is much more efficient from a computational standpoint. The description of this approach is currently being prepared for publication.
4. Quantitative defect mapping. At the same time as developing the imaging methods, we’ve also pioneered a new approach for mapping the location and quantity of chemical defects, such as oxygen vacancies. At present, we have experiment proof-of-concept, which is currently under review, and have made significant progress towards building the theoretical framework necessary to correlate the diffraction signal we measure to the defect density in the material.
1. Proof of principle for the microscopy technique. We’ve demonstrated that the optical phase and amplitude of the x-ray field can be de-convoluted at hard x-ray energies (17 keV) using a Fourier Ptychographic approach. Moreover, we show this works for both the transmitted and Bragg-diffracted x-ray field. In the latter case, we are able to derive the lattice strain and misorientation of crystalline materials with better spatial resolution than the start-of-the-art technique our approach derives from (dark-field x-ray microscopy).
2. Characterization of optics and instrumentation. Our aforementioned implementation of the Fourier Ptychographic approach for de-convoluting the amplitude and phase of the x-ray field has enabled us to quantitatively characterize the imaging instrumentation and optics in unprecedented detail. Specifically, we’ve successfully measured the misalignments in the instrument that give rise to reconstruction errors in the image-forming algorithm, and have made spatial maps of the aberrations in the x-ray objective lens we use. This information is proving crucial in developing the instrumentation to reach its full potential (30 nm spatial resolution).
3. Polarization retrieval method. To determine the electrical polarization from the optical phase and amplitude distribution in the images, we’ve developed a new approach based on thermodynamic potentials. This differs from the DFT-based method described in the initial proposal, but is equal in terms of capability and is much more efficient from a computational standpoint. The description of this approach is currently being prepared for publication.
4. Quantitative defect mapping. At the same time as developing the imaging methods, we’ve also pioneered a new approach for mapping the location and quantity of chemical defects, such as oxygen vacancies. At present, we have experiment proof-of-concept, which is currently under review, and have made significant progress towards building the theoretical framework necessary to correlate the diffraction signal we measure to the defect density in the material.
The major aspects of the novel methodology described in the proposal are now developed. What remains is essentially to combine our new ptychographic algorithm, our improvements to the instrumentation and optics, and our scheme for relating the imaging signal to the electrical polarization. This will still require considerable work to fine-tune, but will ultimately set the stage for using this breakthrough new method to carry out unprecedented investigations into the defect-scale structure-property relationships in polar materials. Specifically, we expect publications concerning the optical improvements we are developing, the polarization-determination algorithm, as well as multiple papers concerning the application of the method to oxygen vacancy mapping, antiferroelectric-ferroelectric phase transformations, and high-speed domain wall mobility in ferroelectrics materials. These will be just the tip of the iceberg, however; ultimately we hope the capabilities developed here will facilitate an entirely new approach for characterizing insulating and polar materials in general.