We show that the combination of X-ray scattering with a nanofocused beam and X-ray cross correlation analysis is an efficient means for the full structural characterization of mesocrystalline nanoparticle assemblies with a single experiment. We analyze several hundred diffraction patterns of individual sample locations, i.e. individual grains, to obtain a meaningful statistical distribution of the superlattice and atomic lattice ordering. Simultaneous small-and wide-angle X-ray scattering of the same sample location allows us to determine the structure and orientation of the superlattice as well as the angular correlation of the first two Bragg peaks of the atomic lattices, their orientation with respect to the superlattice, and the average orientational misfit due to local structural disorder. This experiment is particularly advantageous for synthetic mesocrystals made by the simultaneous self-assembly of colloidal nanocrystals and surfacefunctionalization with conductive ligands. While the structural characterization of such materials has been challenging so far, the present method now allows correlating mesocrystalline structure with optoelectronic properties. Mesocrystals (MC) are three-dimensional arrays of iso-oriented single-crystalline particles with an individual size between 1 -1000 nm. [1][2][3][4][5] Their physical properties are largely determined by structural coherence, for which the angular correlation between their individual atomic lattices and the underlying superlattice of nanocrystals (NC) is a key ingredient. 1,2 Colloidal NCs stabilized by organic surfactants have been shown to pose excellent building blocks for the design of synthetic MCs with tailored structural properties which are conveniently obtained by self-assembly of NCs from solution on a solid or liquid substrate by exploiting ligand-ligand 3 interactions. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] Typically, the utilized ligands consist of wide-gap, bulky hydrocarbons which render the MCs insulating. [26][27][28][29][30][31][32][33] MCs obtained in this way exhibit average grain sizes of ~150 µm 2 , which enables a detailed characterization by electron and/or X-ray microscopy. 34 Since the optoelectronic properties of PbS NC ensembles bear many opportunities for applications in solar cells or photodetectors, a number of ligand exchange procedures with small organic or inorganic molecules as well as single atom passivation strategies have been developed, all of which greatly increase the carrier mobilities within the SL of NCs. 28,33,[35][36][37][38][39][40][41][42][43][44] Due to the short interparticle spacing imposed by these ligands, structural coherence is mostly lost in such superlattices, but in rare cases it has been demonstrated that significant long-range order and even mesocrystallinity can be preserved. 25,35,45 However, a persisting problem of these protocols is that they are prone to introduce defects in the superlattice structure with some degree of granularity and signifi...

We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC.Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the multicritical scaling theory over a full temperature range of the hexatic phase existence. 1The influence of angular correlations on structural and physical properties of complex fluids, colloidal suspensions and liquid crystals (LCs) remains one of fundamental and unresolved problems in modern condensed matter physics [1]. A prominent example of a system with angular correlations is the hexatic phase that combines the properties of both crystals and liquids [2]. The two-dimensional (2D) hexatic phase shows a sixfold quasi-long range bond-orientational (BO) order, while the positional order is short range [3]. The hexatic phase is a general phenomenon that was observed in a number of systems of various physical nature, such as 2D colloids [4][5][6], electrons at the surface of helium [7], 2D superconducting vortexes [8,9] and, particularly, in liquid crystals [10][11][12][13].The hexatic phase was predicted by Halperin and Nelson [14] as an intermediate state in 2D crystal melting. According to their theory the hexatic phase arises as a consequence of the broken translational symmetry of a 2D crystal induced by dissociation of dislocation pairs.This mechanism does not work in 3D crystals, however, the 3D hexatic phase was observed experimentally in LCs [10]. The multicritical scaling theory (MCST) developed by Aharony and coworkers [15] based on renormalization group approach to critical phenomena enabled quantitative characterization of the BO order in the hexatic phase and, particularly, allowed to study a crossover from 2D to 3D behavior [11,16]. In spite of the extensive experimental and theoretical work the origin of the hexatic phase in LCs and the features of the hexatic -smectic phase transition remain puzzling and controversial.The structure of hexatics is traditionally studied by means of x-ray or electron diffraction in a single-domain area of a hexatic film (see for reviews [17][18][19]). The quantitative characteristics of the BO order, the so-called BO order parameters [12], are typically determined by fitting the measured azimuthal intensity distribution by the Fourier cosine series. In contrast to this approach in the present work we performed spatially resolved x-ray diffraction studies of free standing LC films. Measured x-ray data were analyzed by means of direct Fourier transformation and by using angular x-ray cross-correlation analysis (XCCA) [20][21][22][23]. The latter method enabled a direct d...

Trees are used by animals, humans and machines to classify information and make decisions. Natural tree structures displayed by synapses of the brain involves potentiation and depression capable of branching and is essential for survival and learning. Demonstration of such features in synthetic matter is challenging due to the need to host a complex energy landscape capable of learning, memory and electrical interrogation. We report experimental realization of tree-like conductance states at room temperature in strongly correlated perovskite nickelates by modulating proton distribution under high speed electric pulses. This demonstration represents physical realization of ultrametric trees, a concept from number theory applied to the study of spin glasses in physics that inspired early neural network theory dating almost forty years ago. We apply the tree-like memory features in spiking neural networks to demonstrate high fidelity object recognition, and in future can open new directions for neuromorphic computing and artificial intelligence.