Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms

Structure of a seeded palladium nanoparticle and its dynamics during the hydride phase transformation

Palladium absorbs large volumetric quantities of hydrogen at room temperature and ambient pressure, making the palladium hydride system a promising candidate for hydrogen storage. Here, we use Bragg coherent diffraction imaging to map the strain associated with defects in three dimensions before and during the hydride phase transformation of an individual octahedral palladium nanoparticle, synthesized using a seed-mediated approach. The displacement distribution imaging unveils the location of the seed nanoparticle in the final nanocrystal. By comparing our experimental results with a finite-element model, we verify that the seed nanoparticle causes a characteristic displacement distribution of the larger nanocrystal. During the hydrogen exposure, the hydride phase is predominantly formed on one tip of the octahedra, where there is a high number of lower coordinated Pd atoms. Our experimental and theoretical results provide an unambiguous method for future structure optimization of seed-mediated nanoparticle growth and in the design of palladium-based hydrogen storage systems

Imaging the Phase Transformation in Single Particles of the Lithium Titanate Anode for Lithium-Ion Batteries

Lithium uptake and release in lithium titanate (LTO) anode materials during a discharge and charge cycle is one of the fundamental processes of a lithium-ion battery (LIB), still not fully understood at the microscopic level. During the discharge cycle, LTO undergoes a phase transformation between Li4Ti5O12 and Li7Ti5O12 states within a cubic crystal lattice. To reveal the details of the microscopic mechanism, it is necessary to track the sequence of phase transformations at different discharge/charge states under operating conditions. Here, we use in situ Bragg coherent diffraction imaging (BCDI) and in situ X-ray diffraction (XRD) experiments to examine the lithium insertion-induced materials phase transformation within a single LTO particle and a bulk battery analogue, respectively. BCDI analysis from (111) Bragg peak shows the two-phase transformation manifesting as a distinct image phase modulation within a single LTO nanoparticle occurring in the middle of the discharge region then subsiding toward the end of the discharge cycle. We observe the biggest phase variation at the two-phase stage, indicating the formation of phase domains of 200 nm in size during the discharge process. We also observe a lattice contraction of >0.2% in a single LTO nanoparticle at the (400) Bragg peak measurement, larger than that in the corresponding bulk material. Our observation of this phase transformation at a single-particle level has implications for the understanding of the microscopic/mesoscale picture of the phase transformation in anode and cathode LIBs materials

Structural Explanation of the Dielectric Enhancement of Barium Titanate Nanoparticles Grown under Hydrothermal Conditions

When synthesized under certain conditions, barium titanate (BaTiO3, BTO) nanoparticles are found to have the non-thermodynamic cubic structure at room temperature. These particles also have a several-fold enhanced dielectric constant, sometimes exceeding 6000, and are widely used in thin-layer capacitors. A hydrothermal approach is used to synthesize BTO nanocrystals, which are characterized by a range of methods, including X-ray Rietveld refinement and the Williamson–Hall approach, revealing the presence of significant inhomogeneous strain associated with the cubic phase. However, X-ray pair distribution function measurements clearly show the local structure is lower symmetry than cubic. This apparent inconsistency is resolved by examining 3D Bragg coherent diffraction images of selected nanocrystals, which show the existence of ≈50 nm-sized domains, which are interpreted as tetragonal twins, and yet cause the average crystalline structure to appear cubic. The ability of these twin boundaries to migrate under the influence of electric fields explains the dielectric anomaly for the nanocrystalline phase

Scaling behavior of low-temperature orthorhombic domains in the prototypical high-temperature superconductor La₁.₈₇₅ Ba₀.₁₂₅ CuO₄

Structural symmetry breaking and recovery in condensed-matter systems are closely related to exotic physical properties such as superconductivity (SC), magnetism, spin density waves, and charge density waves (CDWs). The interplay between different order parameters is intricate and often subject to intense debate, as in the case of CDW order and superconductivity. In La₁.₈₇₅ Ba₀.₁₂₅ CuO

Impact of Enhancer of Zeste Homolog 2 on T Helper Cell-Mediated Allergic Rhinitis

Enhancer of zeste homolog 2 (Ezh2) has been shown to play a role in the differentiation of T helper (Th) 1 and 2 cells in mice studies using Ezh2-deficient T cells. However, the results have been inconsistent, and the function of Ezh2 in human Th1 and Th2 cell differentiation and its association with disease remains controversial. We measured the expression of Ezh2 in Th1 and Th2 cells in peripheral blood mononuclear cells after acute challenge with house dust mite using flow cytometry in patients with allergic rhinitis (AR) and controls. The role of Ezh2 was further explored by adding the p38 inhibitor to see if this affected allergen-induced Th1 and Th2 differentiation. The expression of Ezh2 in the Th1 and Th2 cells was significantly lower in the patients than in the controls and was negatively correlated with serum IL-17A levels in the patients. Ex vivo allergen challenge resulted in rapid Th2 cell differentiation, which was negatively associated with the Ezh2 expression in Th2 cells. Inhibiting p38 activity increased the expression of Ezh2 in Th2 cells and reduced the number of differentiated Th2 cells. Our findings suggest that Ezh2 expression is potentially associated with AR development

Anisotropy of antiferromagnetic domains in a spin-orbit Mott insulator

The temperature-dependent behavior of magnetic domains plays an essential role in the magnetic properties of materials, leading to widespread applications. However, experimental methods to access the three-dimensional (3D) magnetic domain structures are very limited, especially for antiferromagnets. Over the past decades, the spin-orbit Mott insulator iridate Formula Presented has attracted particular attention because of its interesting magnetic structure and analogy to superconducting cuprates. Here, we apply resonant x-ray magnetic Bragg coherent diffraction imaging to track the real-space 3D evolution of antiferromagnetic ordering inside a Formula Presented single crystal as a function of temperature, finding that the antiferromagnetic domain shows anisotropic changes. The anisotropy of the domain shape reveals the underlying anisotropy of the antiferromagnetic coupling strength within Formula Presented. These results demonstrate the high potential significance of 3D domain imaging in magnetism research

Evolution of ferroelastic domain walls during phase transitions in barium titanate nanoparticles

In this work, ferroelastic domain walls inside BaTiO3 (BTO) tetragonal nanocrystals are distinguished by Bragg peak position and studied with Bragg coherent x-ray diffraction imaging (BCDI). Convergence-related features of the BCDI method for strongly phased objects are reported. A ferroelastic domain wall inside a BTO crystal has been tracked and imaged across the tetragonal-cubic phase transition and proves to be reversible. The linear relationship of relative displacement between two twin domains with temperature is measured and shows a different slope for heating and cooling, while the tetragonality reproduces well over temperature changes in both directions. An edge dislocation is also observed and found to annihilate when heating the crystal close to the phase transition temperature

Author Correction: Three-dimensional strain imaging of irradiated chromium using multi-reflection Bragg coherent diffraction

The original version of this Article did not correctly credit and cite relevant previous work. The fifth to seventh sentences of the fifth paragraph of the ‘Three-dimensional imaging of the defects’ section previously read: “In our case, BCDI is sensitive to defects such as voids and dislocations through its strain field sensitivity rather than the spatial resolution46. This is illustrated by the relationship between the continuum representation of the crystal, (Formula presented.) , and the diffraction intensity, I(q) in the far field under a perfectly coherent illumination and in the kinematical scattering approximation given by (Formula presented.). Here, r and q are the real and reciprocal space coordinates respectively, (Formula presented.) is the Fourier transform, Q is the measured Bragg peak, and u(r) is the vector displacement field that is a continuum description of how the atoms are displaced from their equilibrium positions47.” The correct version reads: “In our case, BCDI is sensitive to defects such as voids and dislocations through its strain field sensitivity rather than the spatial resolution46. This is demonstrated by the relationship (Formula presented.). whereby (Formula presented.) is the intensity, (Formula presented.) is the mathematical description of the crystal as a continuum, (Formula presented.) denotes the Fourier transformation operator, Q is the Bragg reflection that was measured, and u(r) is the displacement field47.” The final six sentences of the Results section previously read: “Furthermore, underestimating the defect density prevents TEM from accurately determining the corresponding change in properties. For instance, Weiß et al. show a factor of 2 between measured and calculated change in hardness for neutron irradiated EUROFER9771. Meanwhile, Reza et al. report the same discrepancy between Transient Grating Spectroscopy (TGS)-measured and TEM-determined thermal diffusivity for self-ion irradiated tungsten72. It is important to note that when Reza et al. included small defects from molecular dynamics (MD) simulations, the combination of the TEM and MD data matches TGS measurements. This result confirms the theory that point defects play a significant role in the thermal diffusivity of a material and further reinforces the need to accurately characterize small defects in order to evaluate irradiation-induced changes in properties.” This has been replaced with: ““Hirst et al. opined that the underestimated defects density in TEM measurements comes with a corresponding mischaracterization of the materials properties70. This is demonstrated in a study by Weiß et al. who showed that the hardness values obtained from TEM data of neutron irradiated reduced activation ferritic/martensitic steel is significantly smaller than values from tensile testing. This clearly support the notion that underestimation of point defects from TEM analysis which goes into the dispersed barrier hardening model affects the calculated hardness value71. Hence, the difference in the magnitude of swelling between TEM and BCDI estimates is well justified. In a bid to accurately quantify nanoscale defects in irradiated materials, Meslin et al., used multiple characterization techniques which include TEM, Small Angle Neutron Scattering, Positron Annihilation Spectroscopy and Atom Probe Tomography which are sensitive to different types of nanoscale defects. The study clearly demonstrates the strength and complementarities of each technique72. This further support the need to develop multiple characterization techniques that can complements TEM for defects quantification and building predictive tools.” Consequently, Reference 72, which previously read “Reza, A., Yu, H., Mizohata, K. & Hofmann, F. Thermal diffusivity degradation and point defect density in self-ion implanted tungsten. Acta Mater. 193, 270–279 (2020)”, has been replaced by “Meslin, E. et al. Characterization of neutron-irradiated ferritic model alloys and a RPV steel from combined APT, SANS, TEM, and PAS analyses J. Nucl. Mater. 406, 73–83 (2010).” This has been corrected in both the PDF and HTML versions of the Article

Three-dimensional strain imaging of irradiated chromium using multi-reflection Bragg coherent diffraction

Radiation-induced materials degradation is a key concern in limiting the performance of nuclear materials. The formation of nanoscale void and gas bubble superlattices in metals and alloys under radiation environments can effectively mitigate radiation-induced damage, such as swelling and aid the development of next generation radiation tolerant materials. To effectively manage radiation-induced damage via superlattice formation, it is critical to understand the microstructural changes and strain induced by such superlattices. We utilize multi-reflection Bragg coherent diffraction imaging to quantify the full strain tensor induced by void superlattices in iron irradiated chromium substrate. Our approach provides a quantitative estimation of radiation-induced three-dimensional (3D) strain generated at the microscopic level and predicts the number density of defects with a high degree of sensitivity. Such quantitative evaluation of 3D strain in nuclear materials can have a major impact on predicting materials behavior in radiation environments and can revolutionize design of radiation tolerant materials