Periodic Reporting for period 4 - 3D-PXM (3D Piezoresponse X-ray Microscopy)
Berichtszeitraum: 2023-07-01 bis 2025-06-30
Electrically polar materials are key to essential technologies, such as those used for digital memory and the generation and storage of energy. However, there’s no methods by which researchers can directly visualize electrical polarization inside the materials themselves. This project sought to remedy this by developing a new type of microscope that used high-energy x-rays to visualize the atomic distortions associated with the polarization. In tandem with its development, this new capability was used to study and 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 therefore benefits society through a variety of means: via improving the understanding of these technologically-critical materials such that they may be further improved in terms of their performance, cost and environmental impact, but also via opening doors to new scientific and technological discoveries through the unique capabilities of the methodologies developed.
From the beginning of the project to its conclusion, the work progressed along two tightly linked tracks: The development of a fundamentally new x-ray microscopy capability, and its application to understanding how microscopic defects control the electrical behaviour of polar materials.
Development of a new x-ray microscopy methodology: A corel achievement of the project is the experimental demonstration of a new coherent x-ray microscopy approach capable of retrieving both the amplitude and phase of high-energy x-ray fields. Using a Fourier ptychographic framework, we showed that this is possible at hard x-ray energies (17 keV), which are essential for probing deep inside bulk materials. Importantly, the method was demonstrated not only for transmitted x-rays, but also for Bragg-diffracted x-rays, allowing crystalline distortions to be mapped directly. In this configuration, the technique provides access to lattice strain and crystal misorientation with spatial resolution exceeding that of current state-of-the-art methods, such as dark-field x-ray microscopy. This represents a significant methodological advance for non-destructive structural imaging.
Instrumentation and optical characterization: The phase-sensitive nature of the new imaging approach also enabled a second, unexpected advance: an unprecedented quantitative characterization of the microscope itself. We were able to directly measure and correct for subtle misalignments in the instrument that would otherwise limit image quality, and to generate spatial maps of aberrations in the x-ray objective lens. These results have been crucial for pushing the instrument towards its ultimate performance limits, with a clear pathway toward ~30 nm spatial resolution. Beyond this specific project, these capabilities provide a powerful diagnostic and optimization tool for advanced x-ray microscopes more generally.
Retrieval of electrical polarization: To convert the measured x-ray phase and amplitude images into maps of electrical polarization, we developed a new theoretical framework based on thermodynamic potentials. While different from the density-functional-theory-based approach originally proposed, this method offers equivalent physical insight while being far more computationally efficient, making it practical for large experimental datasets. This approach provides a direct link between measured atomic-scale distortions and functional electrical properties. The methodology is currently being prepared for publication and represents a key conceptual advance in how polarization can be extracted from experimental data.
Defect mapping and materials discoveries: Alongside the methodological developments, the project delivered major scientific results on defect–property relationships in polar materials. We quantitatively mapped how grain boundaries constrain elastic deformation in antiferroelectric energy-storage materials, and showed how this directly influences domain wall behaviour and polar ordering. This provides the first direct experimental insight into mechanisms that limit the performance of high-power capacitors. Similarly, we also mapped dislocation networks in a nominally non-polar crystal (SrTiO₃) and demonstrated how their charged nature affects the mobility of point defects, revealing the formation of polar defect dipoles. We then developed and demonstrated a new approach for mapping nanoscale disorder across macroscopic samples, overcoming a long-standing limitation in diffraction-based imaging. Finally, close to the end of the project, we obtained experimental evidence that chemical point defects (such as oxygen vacancies) can be directly visualized in diffraction microscopy images. Although still at proof-of-concept stage, this result opens a new pathway toward quantitative, bulk-sensitive defect imaging.
Dissemination and exploitation: The project has resulted in a substantial body of dissemination, including peer-reviewed publications, manuscripts under review, and intellectual property. In total, three new coherent x-ray microscopy techniques were developed—exceeding the original objectives—and a patent has been filed on a broadly applicable phase-retrieval approach that has already shown impact beyond materials science, including in biological imaging and photonics.
Together, these outcomes demonstrate that the project has achieved—and in several respects exceeded—the scientific and technological goals proposed for the project.
Development of a new x-ray microscopy methodology: A corel achievement of the project is the experimental demonstration of a new coherent x-ray microscopy approach capable of retrieving both the amplitude and phase of high-energy x-ray fields. Using a Fourier ptychographic framework, we showed that this is possible at hard x-ray energies (17 keV), which are essential for probing deep inside bulk materials. Importantly, the method was demonstrated not only for transmitted x-rays, but also for Bragg-diffracted x-rays, allowing crystalline distortions to be mapped directly. In this configuration, the technique provides access to lattice strain and crystal misorientation with spatial resolution exceeding that of current state-of-the-art methods, such as dark-field x-ray microscopy. This represents a significant methodological advance for non-destructive structural imaging.
Instrumentation and optical characterization: The phase-sensitive nature of the new imaging approach also enabled a second, unexpected advance: an unprecedented quantitative characterization of the microscope itself. We were able to directly measure and correct for subtle misalignments in the instrument that would otherwise limit image quality, and to generate spatial maps of aberrations in the x-ray objective lens. These results have been crucial for pushing the instrument towards its ultimate performance limits, with a clear pathway toward ~30 nm spatial resolution. Beyond this specific project, these capabilities provide a powerful diagnostic and optimization tool for advanced x-ray microscopes more generally.
Retrieval of electrical polarization: To convert the measured x-ray phase and amplitude images into maps of electrical polarization, we developed a new theoretical framework based on thermodynamic potentials. While different from the density-functional-theory-based approach originally proposed, this method offers equivalent physical insight while being far more computationally efficient, making it practical for large experimental datasets. This approach provides a direct link between measured atomic-scale distortions and functional electrical properties. The methodology is currently being prepared for publication and represents a key conceptual advance in how polarization can be extracted from experimental data.
Defect mapping and materials discoveries: Alongside the methodological developments, the project delivered major scientific results on defect–property relationships in polar materials. We quantitatively mapped how grain boundaries constrain elastic deformation in antiferroelectric energy-storage materials, and showed how this directly influences domain wall behaviour and polar ordering. This provides the first direct experimental insight into mechanisms that limit the performance of high-power capacitors. Similarly, we also mapped dislocation networks in a nominally non-polar crystal (SrTiO₃) and demonstrated how their charged nature affects the mobility of point defects, revealing the formation of polar defect dipoles. We then developed and demonstrated a new approach for mapping nanoscale disorder across macroscopic samples, overcoming a long-standing limitation in diffraction-based imaging. Finally, close to the end of the project, we obtained experimental evidence that chemical point defects (such as oxygen vacancies) can be directly visualized in diffraction microscopy images. Although still at proof-of-concept stage, this result opens a new pathway toward quantitative, bulk-sensitive defect imaging.
Dissemination and exploitation: The project has resulted in a substantial body of dissemination, including peer-reviewed publications, manuscripts under review, and intellectual property. In total, three new coherent x-ray microscopy techniques were developed—exceeding the original objectives—and a patent has been filed on a broadly applicable phase-retrieval approach that has already shown impact beyond materials science, including in biological imaging and photonics.
Together, these outcomes demonstrate that the project has achieved—and in several respects exceeded—the scientific and technological goals proposed for the project.
The project has advanced the state of the art in x-ray microscopy in a fundamental way. Prior to this work, there was no experimental method capable of directly visualizing electrical polarization inside bulk materials with nanometre-scale resolution. This project has established the essential building blocks of such a capability: phase-sensitive hard x-ray imaging, quantitative instrument correction, and a physically grounded route to extracting polarization from experimental data.
By the end of the project, the major methodological components proposed at the outset have been successfully developed. What remains is their full integration into a unified, optimized microscope. This final integration—combining advanced ptychographic reconstruction algorithms, improved optics and alignment strategies, and polarization-retrieval theory—will require further refinement, but no longer represents a conceptual barrier. The expected near-term outcomes include publications detailing the optical and instrumental advances, the polarization-determination framework, and several high-impact studies applying the method to defect-driven phenomena such as oxygen vacancy distributions, antiferroelectric–ferroelectric phase transformations, and domain-wall dynamics.
More broadly, the work lays the foundation for an entirely new way of studying insulating and polar materials. By enabling direct, non-destructive visualization of how atomic-scale defects control macroscopic electrical functionality deep inside real materials, the project opens new possibilities not only for energy and memory technologies, but for materials science as a whole.
By the end of the project, the major methodological components proposed at the outset have been successfully developed. What remains is their full integration into a unified, optimized microscope. This final integration—combining advanced ptychographic reconstruction algorithms, improved optics and alignment strategies, and polarization-retrieval theory—will require further refinement, but no longer represents a conceptual barrier. The expected near-term outcomes include publications detailing the optical and instrumental advances, the polarization-determination framework, and several high-impact studies applying the method to defect-driven phenomena such as oxygen vacancy distributions, antiferroelectric–ferroelectric phase transformations, and domain-wall dynamics.
More broadly, the work lays the foundation for an entirely new way of studying insulating and polar materials. By enabling direct, non-destructive visualization of how atomic-scale defects control macroscopic electrical functionality deep inside real materials, the project opens new possibilities not only for energy and memory technologies, but for materials science as a whole.