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Distributions of potential and lithium content inside lithium ion batteries highly affects their performance and durability. An increased heterogeneity of the lithium distribution is expected in thick electrodes with high energy densities or cycling at high currents. To optimize electrodes and cells designs, it is crucial to probe lithium concentration gradients across the depth of the electrode, but also to predict their occurrence and magnitude as a function of materials properties. Here, we follow the lithium distribution across a $80~\mu m$ thick porous graphite electrode using a $1~\mu m$ focused synchrotron X-ray beam. The sequential formation of the individual Li$_x$C$_6$ phases during lithium de-insertion is extracted from X-ray diffraction patterns, allowing the quantification of lithium concentration across the electrode thickness. Analyzing the evolution of heterogeneities as a function of time, we recover the striking features we predicted with a porous electrode model, including the succession of homogeneous and heterogeneous distributions of lithium. However, a clear difference is obtained at high stoichiometry, with a much more homogeneous distribution than initially predicted. Revisiting the interplay between transport and kinetic transfers limitations in the porous electrode model, we suggest that the kinetics of lithium (de)-insertion is highly reduced during the LiC$_6$/LiC$_{12}$ phase transition., Comment: 17 pages, including 10 figures + 8 pages of Supplementary Information (total 25 pages)

Complex hierarchical shapes are widely known in biogenic single crystals, but growing of intricate synthetic metal single crystals is still a challenge. Here we report on a simple method for growing intricately shaped single crystals of gold, each consisting of a micron-sized crystal surrounded by a nanoporous structure, while the two parts comprise a single crystal. This is achieved by annealing thin films of gold and germanium to solidify a eutectic composition melt at a hypoeutectic concentration (Au-enriched composition). Transmission electron microscopy and synchrotron submicron scanning diffractometry and imaging confirms that the whole structure was indeed a single crystal. A kinetic model showing how this intricate single-crystal structure can be grown is presented.

Halide perovskites are promising semiconductors for inexpensive, high-performance optoelectronics. Despite a remarkable defect tolerance compared to conventional semiconductors, perovskite thin films still show substantial microscale heterogeneity in key properties such as luminescence efficiency and device performance. This behavior has been attributed to spatial fluctuations in the population of sub-bandgap electronic states that act as trap-mediated non-radiative recombination sites. However, the origin of the variations, trap states and extent of the defect tolerance remains a topic of debate, and a precise understanding is critical to the rational design of defect management strategies. By combining scanning X-ray diffraction beamlines at two different synchrotrons with high-resolution transmission electron microscopy, we reveal levels of heterogeneity on the ten-micrometer scale (super-grains) and even ten-nanometer scale (sub-grain domains). We find that local strain is associated with enhanced defect concentrations, and correlations between the local structure and time-resolved photoluminescence reveal that these strain-related defects are the cause of non-radiative recombination. We reveal a direct connection between defect concentrations and non-radiative losses, as well as complex heterogeneity across multiple length scales, shedding new light on the presence and influence of structural defects in halide perovskites.

Ultrastructural fluctuations at nanoscale are fundamental to assess properties and functionalities of advanced out-of-equilibrium materials. We have taken myelin as a model of supramolecular assembly in out-of-equilibrium living matter. Myelin sheath is a simple stable multi-lamellar structure of high relevance and impact in biomedicine. Although it is known that myelin has a quasi-crystalline ultrastructure there is no information on its fluctuations at nanoscale in different states due to limitations of the available standard techniques. To overcome these limitations, we have used Scanning micro X-ray Diffraction, which is a non-invasive probe of both reciprocal and real space to visualize statistical fluctuations of myelin order of the sciatic nerve of Xenopus Laevis. The results show that the ultrastructure period of the myelin is stabilized by large anti-correlated fluctuations at nanoscale, between hydrophobic and hydrophilic layers. The ratio between the total thickness of hydrophilic and hydrophobic layers defines the conformational parameter, which describes the different states of myelin. Our key result is that myelin in its out-of-equilibrium functional state fluctuates point-to-point between different conformations showing a correlated disorder described by a Levy distribution. As the system approaches the thermodynamic equilibrium in an aged state the disorder loses its correlation degree and the structural fluctuation distribution changes to Gaussian. In a denatured state at low pH, it changes to a completely disordered stage. Our results clarify also the degradation mechanism in biological systems by associating these states with variation of the ultrastructural dynamic fluctuations at nanoscale., Comment: 21 pages, 6 fugures

Crystals in nature often demonstrate curved morphologies rather than classical faceted surfaces. Inspired by biogenic curved single crystals, we demonstrate that gold single crystals exhibiting curved surfaces can be grown with no need of any fabrication steps. These single crystals grow from the confined volume of a droplet of a eutectic composition melt which forms via the dewetting of nanometric thin films. We can control their curvature by controlling the environment in which the process is carried out, including several parameters, such as the contact angle and the curvature of the drops by changing the surface tension of the liquid drop during crystal growth. Here we present an energetic model that explains this phenomenon and predicts why and under what conditions crystals will be forced to grow with the curvature of the micro droplet even though the energetic state of a curved single crystal is very high., Comment: ACS Nano, 2014

Single crystals in nature often demonstrate fascinating intricate porous morphologies rather than classical faceted surfaces. We attempt to grow such crystals, drawing inspiration from biogenic porous single crystals. Here we show that nanoporous single crystals of gold can be grown with no need for any elaborate fabrication steps. These crystals are found to grow following solidification of a eutectic composition melt that forms as a result of the dewetting of nanometric thin films. We also present a kinetic model that shows how this nano-porous single-crystalline structure can be obtained, and which allows the potential size of the porous single crystal to be predicted. Retaining their single crystalline nature is due to the fact that the full crystallization process is faster than the average period between two subsequent nucleation events. Our findings clearly demonstrate that it is possible to form singe crystalline nano porous metal crystals in a controlled manner. INTRODUCTION, Comment: Nature Communication, 2015

Despite intensive research a physical explanation of high Tc superconductors remains elusive. One reason for this is that these materials have generally a very complex structure making useless theoretical models for a homogeneous system. Little is known on the control of the critical temperature by the space disposition of defects because of lack of suitable experimental probes. X-ray diffraction and neutron scattering experiments used to investigate y oxygen dopants in YBa2Cu3O 6+y lack of spatial resolution. Here we report the spatial imaging of dopants distribution in-homogeneity in YBa2Cu3O6.67 using scanning nano X-ray diffraction. By changing the X-ray beam size from 1 micron to 300 nm of diameter, the lattice inhomogeneity increases. The ordered oxygen puddles size distribution vary between 6-8 nm using 1x1 {\mu}m2 beam, while it is between 5-12 nm with a fat tail using the 300x300 nm2 beam. The increased inhomogeneity at the nanoscale points toward an intrinsic granular complexity., Comment: letter, 4 figures

While it is known that the nature and the arrangement of defects in complex oxides have an impact on the material functionalities little is known on control of superconductivity by oxygen interstitial organization in cuprates. Here we report direct compelling evidence for the control of Tc, by manipulation of the superconducting granular networks of nanoscale puddles, made of ordered oxygen stripes, in a single crystal of YBa2Cu3O6.5+y with average formal hole doping p close to 1/8. Upon thermal treatments we were able to switch from a first network of oxygen defects striped puddles with OVIII modulation (qOVIII(a*)=(h+3/8,k,0) and qOVIII(a*)=(h+5/8,k,0)), to second network characterized by OXVI modulation (qOXVI(a*)=(h+7/16,k,0) and qOXVI(a*)=(h+9/16,k,0)), and finally to a third network with puddles of OV periodicity (qOV(a*)=(4/10,1,0) and qOV(a*)=(6/10,1,0)). We map the microscopic spatial evolution of the out of plane OVIII, OXVI and OV puddles nano-size distribution via scanning micro-diffraction measurements. In particular, we calculated the number of oxygen chains (n) and the charge density (holes concentration p) inside each puddle, analyzing areas of 160x80 {\mu}m2, and recording 12800 diffraction patterns to reconstruct each spatial map. The high spatial inhomogeneity shown by all the reconstructed spatial maps reflects the intrinsic granular structure that characterizes cuprates and iron-chalcogenides, disclosing the presence of several complex networks of coexisting superconducting domains with different lattice modulations, charge density and different gaps like in the proposed multi-gaps scenario called superstripes., Comment: 5 figures

Oxygen chain fragments are known to appear at the insulator to superconductor transition (SIT) in YBa2Cu3O6+y. However the self organization and the size distribution of oxygen chain fragments is not known. Here we contribute to fill this gap, using scanning micro X ray diffraction which is a novel imaging method based on advances in focusing synchrotron radiation beam. This novel approach allows us to probe both real-space and k-space of a high-quality YBa2Cu3O6.33 single crystals with Tc=7K. We report compelling evidence for nanoscale striped puddles, with Ortho-II structure, made of chain fragments in the basal Cu(1) plane with local oxygen concentration 0.5. The size of the Ortho-II puddles spans a range between 2 and 9 nanometers. The real space imaging of Ortho-II puddles granular network shows that superconductivity, at low hole-doping regime, occurs in a network of nanoscale oxygen ordered patches, interspersed with oxygen depleted regions. The manipulation by thermal treatments of the striped Ortho II puddles has been investigated focusing on the spontaneous symmetry breaking near the order to disorder phase transition at 350 K., Comment: 6 pages, 5 Figures

Electronic functionalities in materials from silicon to transition metal oxides are to a large extent controlled by defects and their relative arrangement. Outstanding examples are the oxides of copper, where defect order is correlated with their high superconducting transition temperatures. The oxygen defect order can be highly inhomogeneous, even in "optimal" superconducting samples, which raises the question of the nature of the sample regions where the order does not exist but which nonetheless form the "glue" binding the ordered regions together. Here we use scanning X-ray microdiffraction (with beam 300 nm in diameter) to show that for La2CuO4+y, the "glue" regions contain incommensurate modulated local lattice distortions, whose spatial extent is most pronounced for the best superconducting samples. For an underdoped single crystal with mobile oxygen interstitials in the spacer La2O2+y layers intercalated between the CuO2 layers, the incommensurate modulated local lattice distortions form droplets anticorrelated with the ordered oxygen interstitials, and whose spatial extent is most pronounced for the best superconducting samples. In this simplest of high temperature superconductors, there are therefore not one, but two networks of ordered defects which can be tuned to achieve optimal superconductivity. For a given stoichiometry, the highest transition temperature is obtained when both the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated spots. We speculate that the relationship between material complexity and superconducting transition temperature Tc is actually underpinned by a fundamental relation between Tc and the distribution of ordered defect networks supported by the materials., Comment: 20 pages, 5 figures

It is well known that the microstructures of the transition-metal oxides (refs 1-3), including the high-transition-temperature (high-Tc) copper oxide superconductors (refs 4-7), are complex. This is particularly so when there are oxygen interstitials or vacancies (ref.8), which influence the bulk properties. For example, the oxygen interstitials in the spacer layers separating the superconducting CuO2 planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2) (ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+y) (refs 11-15) that induce enhancements in the transition temperatures with no changes in hole concentrations. It is also known that complex systems often have a scale-invariant structural organization16, but hitherto none had been found in high-Tc materials. Here we report that the ordering of oxygen interstitials in the La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-Tc superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 microns. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature., Comment: 10 pages, 5 figures