Designing disorder into crystalline materials

Concluding remarks: Faraday Discussion on NMR crystallography

This Faraday Discussion explored the field of NMR crystallography, and considered recent developments in experimental and theoretical approaches, new advances in machine learning and in the generation and handling of large amounts of data. Applications to a wide range of disordered, amorphous and dynamic systems demonstrated the range and quality of information available from this approach and the challenges that are faced in exploiting automation and developing best practice. In these closing remarks I will reflect on the discussions on the current state of the art, questions about what we want from these studies, how accurate we need results to be, how we best generate models for complex materials and what machine learning approaches can offer. These remarks close with thoughts about the future direction of the field, who will be carrying out this type of research, how they might be doing it and what their focus will be, along with likely possible challenges and opportunities.

In Situ Programmable, Active, and Interactive Crystallization by Localized Polymerization

Additive manufacturing has sought active and interactive means of creating predictable structures with diverse materials. Compared to such active manufacturing tools, current crystallization strategies remain in statistical and passive programs of crystals via macroscale thermodynamic controllers, commonly lacking active means to intervene in crystal growth in a spatiotemporal manner. Herein, a strategy toward active and interactive programming and reprogramming of crystals, realized by real-time tangible feedback on growing crystals by delicately controlling the degree of in-situ, localized photopolymerization of polymeric structures via additive manufacturing is presented. Using this strategy, crystals can be seeded, guided, and even reprogrammed in a supersaturated liquid resin. In principle, the localized formation of sparse polymeric networks within supercooled resins can induce density fluctuation to trigger seed nucleation instantaneously, whereas the formation of dense networks can lower molecules' mobilities to inhibit crystal growth. Assisted by these active triggers and deterministic procedural aspects in additive manufacturing, growing crystals can be tangibly interacted through programmed polymeric structures, strengthening deterministic characteristics in crystal growth. It is suggested that crystal growth can be programmable with deterministic hierarchies within the created crystal's morphologies within the background of inherent stochasticity in crystallization, launching an era of convolutional growth of crystals.

Understanding orientational disorder in crystalline assemblies of hard convex polyhedra

Spontaneous self-assembly of hard convex polyhedra is known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of orientational phase with discrete rotational mobility has been reported in hard particle systems. In this paper, we present a new analysis method for characterizing the orientational phase of a crystal, which is based on algorithmic detection of unique orientations. Using this method, we collected complete statistics of discrete orientations along the Monte Carlo simulation trajectories and observed that particles were equally partitioned among them, with specific values of pairwise orientational differences. These features remained constant across the pressure range and did not depend on rotational mobility. The discrete mobility was characteristic of a distinct equilibrium thermodynamic phase, qualitatively different from the freely rotating plastic phase with continuous orientations. The high pressure behavior with frozen particle orientations was part of that same description and not a non-equilibrium arrested state. We introduced a precise notion of orientational order and demonstrated that the system was maximally disordered at the level of a unit cell, even though individual particles could only take a few discrete orientations. We report the existence of this phase in five polyhedral shapes and in systematically curated shape families constructed around two of them. The symmetry mismatch between the particle and the crystallographic point groups was found to be a predictive indicator for the occurrence of this phase.

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration-where the geometry of the net that the spins occupy precludes the generation of a simple ordered state-is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets-those which are both vertex- and edge-transitive-for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

In Situ Observation of Topotactic Linker Reorganization in the Aperiodic Metal-Organic Framework TRUMOF-1

We use in situ synchrotron X-ray diffraction measurements to monitor the solvothermal crystallization mechanism of the aperiodic metal-organic framework TRUMOF-1. Following an initial incubation period, TRUMOF-1 forms as a metastable intermediate that subsequently transforms into an ordered product with triclinic crystal symmetry. We determine the structure of this ordered phase, which we call msw-TRUMOF-1, and show that it is related to TRUMOF-1 through topotactic reorganization of linker occupancies. Our results imply that the connectivity of TRUMOF-1 can be reorganized, as required for data storage and manipulation applications.

High-pressure synthesis of Ruddlesden-Popper nitrides

Layered perovskites with Ruddlesden-Popper-type structures are fundamentally important for low-dimensional properties, for example, photovoltaic hybrid iodides and superconducting copper oxides. Many such halides and oxides are known, but analogous nitrides are difficult to stabilize due to the high cation oxidation states required to balance the anion charges. Here we report the high-pressure synthesis of three single-layer Ruddlesden-Popper (K2NiF4 type) nitrides-Pr2ReN4, Nd2ReN4 and Ce2TaN4-along with their structural characterization and properties. The R2ReN4 materials (R = Pr and Nd) are metallic, and Nd2ReN4 has a ferromagnetic Nd3+ spin order below 15 K. Thermal decomposition gives R2ReN3 with a Peierls-type distortion and chains of Re-Re multiply bonded dimers. Ce2TaN4 has a structural transition driven by octahedral tilting, with local distortions and canted magnetic Ce3+ order evidencing two-dimensional Ce3+/Ce4+ charge ordering correlations. Our work demonstrates that Ruddlesden-Popper nitrides with varied structural, electronic and magnetic properties can be prepared from high-pressure synthesis, opening the door to related layered nitride materials.

Ionic Liquid Crystals as Chromogenic Materials

Ionic liquid crystals (ILCs), a class of soft matter materials whose properties can be tuned by the wise pairing of the cation and anion, have recently emerged as promising candidates for different applications, combining the characteristics of ionic liquids and liquid crystals. Among those potential uses, this review aims to cover chromogenic ILCs. In this context, examples of photo-, electro- and thermochromism based on ILCs are provided. Furthermore, thermotropic and lyotropic ionic liquid crystals are also summarised, including the most common chemical and phase structures, as well as the advantages of confining these materials. This manuscript also comprises the following main experimental techniques used to characterise ILCs: Differential Scanning Calorimetry (DSC), Polarised Optical Microscopy (POM) and X-Ray Powder Diffraction (XRD). Chromogenic ILCs can be interesting smart materials for energy and health purposes.

Stereochemically Active Lone Pairs Stabilizing Intrinsic Vacancy Defects in Thermoelectric InTe

Harvesting waste heat efficiently with thermoelectric energy conversion requires materials with low thermal conductivity. Recently, it was demonstrated how dynamic lone pair expression in thermoelectric InTe is responsible for giant anharmonicity leading to a very low lattice thermal conductivity. InTe also contains correlated disorder of intrinsic defects due to vacancies, and this contributes to additional lowering of the thermal conductivity. Here we use the three-dimensional difference pair distribution function (3D-ΔPDF) to analyze 25 K single crystal diffuse X-ray scattering from InTe to unravel the local defect structure, and propose a microscopic structural model. Extended off-centering of In+ ions induced by vacancies allows for the local expression of stereochemically active lone pairs. The associated electronic stabilization is proposed to be a driving force for the formation of In+ vacancy defects in InTe.

Manipulating disorder within cathodes of alkali-ion batteries

The fact that ordered materials are rarely perfectly crystalline is widely acknowledged among materials scientists, but its impact is often overlooked or underestimated when studying how structure relates to properties. Various investigations demonstrate that intrinsic and extrinsic defects, and disorder generated by physicochemical reactions, are responsible for unexpectedly detrimental or beneficial functionalities. The task remains to modulate the disorder to produce desired properties in materials. As disorder is often correlated with local interactions, it is controllable. In this Review, we explore the structural disorder in cathode materials as a novel approach for improving their electrochemical performance. We revisit cathode materials for alkali-ion batteries and outline the origins and beneficial consequences of disorder. Focusing on layered, cubic rocksalt and other metal oxides, we discuss how disorder improves electrochemical properties of cathode materials and which interactions generate the disorder. We also present the potential pitfalls of disorder that must be considered. We conclude with perspectives for enhancing the electrochemical performance of cathode materials by using disorder.

Procrystalline Self-Assembly of Desymmetrized Pentaphenylcyclopentadiene

The interplay between the molecular shape and the intermolecular interaction plays a decisive role in self-assembled structures. Recently, inherent randomness of low ordered assemblies, resulting from lack of short- and long-range periodicities, has attracted significant attention due to the unique structural, electronic, and mechanical properties. Here, we present procrystalline self-assemblies of pentaphenyl cyclopentadienyl derivatives on Ag(111) and Au(111) with scanning tunneling microscopy, operating at 4.3 K under ultrahigh vacuum conditions. Two examples, using 5-fold symmetric molecules substituted with methyl or fluorine groups, show that weak interactions, such as π-π stacking, CH-π interactions, and CH···F hydrogen bonding, play a pivotal role in formation of the procrystalline assembly. Our results may give insights into the intricate relationship between the molecular shape and the intermolecular interaction in the formation of non-crystalline assemblies.

Hidden structures: a driving factor to achieve low thermal conductivity and high thermoelectric performance

The long-range periodic atomic arrangement or the lack thereof in solids typically dictates the magnitude and temperature dependence of their lattice thermal conductivity (κlat). Compared to crystalline materials, glasses exhibit a much-suppressed κlat across all temperatures as the phonon mean free path reaches parity with the interatomic distances therein. While the occurrence of such glass-like thermal transport in crystalline solids captivates the scientific community with its fundamental inquiry, it also holds the potential for profoundly impacting the field of thermoelectric energy conversion. Therefore, efficient manipulation of thermal transport and comprehension of the microscopic mechanisms dictating phonon scattering in crystalline solids are paramount. As quantized lattice vibrations (i.e., phonons) drive κlat, atomistic insights into the chemical bonding characteristics are crucial to have informed knowledge about their origins. Recently, it has been observed that within the highly symmetric 'averaged' crystal structures, often there are hidden locally asymmetric atomic motifs (within a few Å), which exert far-reaching influence on phonon transport. Phenomena such as local atomic off-centering, atomic rattling or tunneling, liquid-like atomic motion, site splitting, local ordering, etc., which arise within a few Å scales, are generally found to drastically disrupt the passage of heat carrying phonons. Despite their profound implication(s) for phonon dynamics, they are often overlooked by traditional crystallographic techniques. In this review, we provide a brief overview of the fundamental aspects of heat transport and explore the status quo of innately low thermally conductive crystalline solids, wherein the phonon dynamics is majorly governed by local structural phenomena. We also discuss advanced techniques capable of characterizing the crystal structure at the sub-atomic level. Subsequently, we delve into the emergent new ideas with examples linked to local crystal structure and lattice dynamics. While discussing the implications of the local structure for thermal conductivity, we provide the state-of-the-art examples of high-performance thermoelectric materials. Finally, we offer our viewpoint on the experimental and theoretical challenges, potential new paths, and the integration of novel strategies with material synthesis to achieve low κlat and realize high thermoelectric performance in crystalline solids via local structure designing.

Giant Modulation of Refractive Index from Picoscale Atomic Displacements

It is shown that structural disorder-in the form of anisotropic, picoscale atomic displacements-modulates the refractive index tensor and results in the giant optical anisotropy observed in BaTiS3, a quasi-1D hexagonal chalcogenide. Single-crystal X-ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS6 chains along the c-axis, and threefold degenerate Ti displacements in the a-b plane. 47/49Ti solid-state NMR provides additional evidence for those Ti displacements in the form of a three-horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. Scanning transmission electron microscopy is used to directly observe the globally disordered Ti a-b plane displacements and find them to be ordered locally over a few unit cells. First-principles calculations show that the Ti a-b plane displacements selectively reduce the refractive index along the ab-plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS3, this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity.

Configurational Disorder, Strong Anharmonicity, and Coupled Host Dynamics Lead to Superionic Transport in Li3YCl6 (LYC)

In superionic crystals, liquid-like ionic diffusivities often come hand-in-hand with ultra-low thermal conductivity and soft vibrational dynamics. However, generalized relationships between ion transport and vibrational dynamics remain elusive due to the diversity of superionic materials and complex underlying mechanisms. Here, the links between vibrational dynamics and ion transport in close-packed lithium halide ion conductor Li3YCl6 (LYC) are examined using a suite of atomistic first-principles methods. It is shown that configurational disorder, lattice anharmonicity, and coupled host-mobile ion vibrational dynamics together induce a transition to the superionic state. Statistical correlations between ionic hops and activation of the distribution of vibrational modes are found. However, typical phenomena associated with superionic conductors such as selective breakdown of zone-boundary soft phonons, or long wavelength transverse acoustic modes as in the 'phonon-liquid-electron crystal' concept, are not present. Instead, anharmonic zone-boundary modes aiding Li diffusion are found to broaden and soften selectively but persist across the superionic transition. These anharmonic modes couple Li ion motion with the vibrations of the flexible close-packed anion framework, which remains stable and facilitates ionic hopping. The results provide insights into how configurational disorder and soft-yet-resilient vibrational modes enable ionic hopping, particularly in 3D close-packed crystals.

Charge-Assisted Ionic Hydrogen-Bonded Organic Frameworks: Designable and Stabilized Multifunctional Materials

Hydrogen-bonded organic frameworks (HOFs) are a class of crystalline framework materials assembled by hydrogen bonds. HOFs have the advantages of high crystallinity, mild reaction conditions, good solution processability, and reproducibility. Coupled with the reversibility and flexibility of hydrogen bonds, HOFs can be assembled into a wide diversity of crystalline structures. Since the bonding energy of hydrogen bonds is lower than that of ligand and covalent bonds, the framework of HOFs is prone to collapse after desolventisation and the stability is not high, which limits the development and application of HOFs. In recent years, numerous stable and functional HOFs have been developed by π-π stacking, highly interpenetrated networks, charge-assisted, ligand-bond-assisted, molecular weaving, and covalent cross-linking. Charge-assisted ionic HOFs introduce electrostatic attraction into HOFs to improve stability while enriching structural diversity and functionality. In this paper, we review the development, the principles of rational design and assembly of charge-assisted ionic HOFs, and introduces the different building block construction modes of charge-assisted ionic HOFs. Highlight the applications of charge-assisted ionic HOFs in gas adsorption and separation, proton conduction, biological applications, etc., and prospects for the diverse design of charge-assisted ionic HOFs structures and multifunctional applications.

Sequence of Structural and Magnetic Phase Transitions in (NO)Mn6(NO3)13

New nitrosonium manganese(II) nitrate, (NO)Mn6(NO3)13, has been synthesized and structurally characterized. In the temperature range of 45-298 K, the crystal is hexagonal (centrosymmetric sp. gr. P63/m). Mn2+ ions are assembled into tubes along axis c with both NO3- filling and coating. The nitrosonium cation is located in the framework cavity and is disordered by a 3-fold axis. At the temperature TS1 = 190 K, a structural phase transition related to the libration of the intertube NO3 group and a small variation of Mn polyhedron is observed. Moreover, the anomalies in physical properties of (NO)Mn6(NO3)13 allow suggesting that ordering of NO+ units occurs at low temperatures. The antiferromagnetic ordering in this compound is preceded by the formation of a short-range correlation regime at about 25 K and takes place in two steps at TN1 = 12.0 K and TN2 = 8.4 K.

Impact of Correlated Disorder on Surface Superconductivity: Revealing the Robustness of the Surface Ordering Effect

Surface superconductivity, wherein electron pairing occurs at material surfaces or interfaces, has attracted a remarkable amount of attention since its discovery. Recent theoretical predictions have unveiled increased critical temperatures, especially at the surfaces of certain compounds and/or structures. The notion of "surface ordering" has been advanced to elucidate this phenomenon. Employing the framework of self-consistent Bogoliubov-de Gennes equations and a model incorporating correlated disorder, our study demonstrates the persistence of the surface ordering effect in the presence of weak to moderate bulk disorder. Intriguingly, our findings indicate that under moderate disorder conditions the surface critical temperature can be further increased, depending on the intensity and correlation of the disorder.

Femtosecond Electron Diffraction Reveals Local Disorder and Local Anharmonicity in Thermoelectric SnSe

In addition to long-range periodicity, local disorder, with local structures deviating from the average lattice structure, dominates the physical properties of phonons, electrons, and spin subsystems in crystalline functional materials. Experimentally characterizing the 3D atomic configuration of such a local disorder and correlating it with advanced functions remains challenging. Using a combination of femtosecond electron diffraction, structure factor calculations, and time-dependent density functional theory molecular dynamics simulations, the static local disorder and its local anharmonicity in thermoelectric SnSe are identified exclusively. The ultrafast structural dynamics reveal that the crystalline SnSe is composed of multiple locally correlated configurations dominated by the static off-symmetry displacements of Sn (≈0.4 Å) and such a set of locally correlated structures is termed local disorder. Moreover, the anharmonicity of this local disorder induces an ultrafast atomic displacement within 100 fs, indicating the signature of probable THz Einstein oscillators. The identified local disorder and local anharmonicity suggest a glass-like thermal transport channel, which updates the fundamental insight into the long-debated ultralow thermal conductivity of SnSe. The method of revealing the 3D local disorder and the locally correlated interactions by ultrafast structural dynamics will inspire broad interest in the construction of structure-property relationships in material science.

Exploring disorder correlations in superconducting systems: spectroscopic insights and matrix element effects

Understanding the intricate interplay between disorder and superconductivity has become a key area of research in condensed matter physics, with profound implications for materials science. Recent studies have shown that spatial correlations of disorder potential can improve superconductivity, prompting a re-evaluation of some theoretical models. This paper explores the influence of disorder correlations on the fundamental properties of superconducting systems, going beyond the traditional assumption of spatially uncorrelated disorder. In particular, we investigate the influence of disorder correlations on key spectroscopic superconductor properties, including the density of states, as well as on the matrix elements of the superconducting coupling constant and their impact on the localization length. Our findings offer valuable insights into the role of disorder correlations in shaping the behavior of superconducting materials.

Modulation Strategies for the Preparation of High-Performance Catalysts for Urea Oxidation Reaction and Their Applications

Compared with the traditional electrolysis of water to produce hydrogen, urea-assisted electrolysis of water to produce hydrogen has significant advantages and has received extensive attention from researchers. Unfortunately, urea oxidation reaction (UOR) involves a complex six-electron transfer process leading to high overpotential, which forces researchers to develop high-performance UOR catalysts to drive the development of urea-assisted water splitting. Based on the UOR mechanism and extensive literature research, this review summarizes the strategies for preparing highly efficient UOR catalysts. First, the UOR mechanism is introduced and the characteristics of excellent UOR catalysts are pointed out. Aiming at this, the following modulation strategies are proposed to improve the catalytic performance based on summarizing various literature: 1) Accelerating the active phase formation to reduce initial potential; 2) Creating double active sites to trigger a new UOR mechanism; 3) Accelerating urea adsorption and promoting C─N bond cleavage to ensure the effective conduct of UOR; 4) Promoting the desorption of CO2 to improve stability and prevent catalyst poisoning; 5) Promoting electron transfer to overcome the inherent slow dynamics of UOR; 6) Increasing active sites or active surface area. Then, the application of UOR in electrochemical devices is summarized. Finally, the current deficiencies and future directions are discussed.

Synthetic control of correlated disorder in UiO-66 frameworks

Changing the perception of defects as imperfections in crystalline frameworks into correlated domains amenable to chemical control and targeted design might offer opportunities for the design of porous materials with superior performance or distinctive behavior in catalysis, separation, storage, or guest recognition. From a chemical standpoint, the establishment of synthetic protocols adapted to control the generation and growth of correlated disorder is crucial to consider defect engineering a practicable route towards adjusting framework function. By using UiO-66 as experimental platform, we systematically explored the framework chemical space of the corresponding defective materials. Periodic disorder arising from controlled generation and growth of missing cluster vacancies can be chemically controlled by the relative concentration of linker and modulator, which has been used to isolate a crystallographically pure "disordered" reo phase. Cs-corrected scanning transmission electron microscopy is used to proof the coexistence of correlated domains of missing linker and cluster vacancies, whose relative sizes are fixed by the linker concentration. The relative distribution of correlated disorder in the porosity and catalytic activity of the material reveals that, contrarily to the common belief, surpassing a certain defect concentration threshold can have a detrimental effect.

High-Entropy Oxides in the Mullite-Type Structure

High-entropy materials (HEMs) represent a new class of solid solutions containing at least five different elements. Their compositional diversity makes them promising as platforms for the development of functional materials. We synthesized new HEMs in a mullite-type structure and present five compounds, i.e., Bi2(Al0.25Ga0.25Fe0.25Mn0.25)4O9 and A2Mn4O10 with variations of A = Nd, Sm, Y, Er, Eu, Ce, and Bi, demonstrating the vast accessible composition space. By combining scattering, microscopy, and spectroscopy techniques, we show that our materials are mixed solid solutions. Remarkably, when following their crystallization in situ using X-ray diffraction and X-ray absorption spectroscopy, we find that the HEMs form through a metastable amorphous phase without the formation of any crystalline intermediates. We expect that our synthesis is excellently suited to synthesizing diverse HEMs and therefore will have a significant impact on their future exploration.

Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder - i.e., the local ordering principles - must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction - a method that allows single crystal diffraction measurements on sub-micron sized crystals - and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.

Breaking Rayleigh's Law with Spatially Correlated Disorder to Control Phonon Transport

Controlling thermal transport in insulators and semiconductors is crucial for many technological fields such as thermoelectrics and thermal insulation, for which a low thermal conductivity (κ) is desirable. A major obstacle for realizing low κ materials is Rayleigh's law, which implies that acoustic phonons, which carry most of the heat, are insensitive to scattering by point defects at low energy. We demonstrate, with large scale simulations on tens of millions of atoms, that isotropic long-range spatial correlations in the defect distribution can dramatically reduce phonon lifetimes of important low-frequency heat-carrying modes, leading to a large reduction of κ-potentially an order of magnitude at room temperature. We propose a general and quantitative framework for controlling thermal transport in complex functional materials through structural spatial correlations, and we establish the optimal functional form of spatial correlations that minimize κ. We end by briefly discussing experimental realizations of various correlated structures.

Unlocking New Topologies in Zr-Based Metal-Organic Frameworks by Combining Linker Flexibility and Building Block Disorder

The outstanding diversity of Zr-based frameworks is inherently linked to the variable coordination geometry of Zr-oxo clusters and the conformational flexibility of the linker, both of which allow for different framework topologies based on the same linker-cluster combination. In addition, intrinsic structural disorder provides a largely unexplored handle to further expand the accessibility of novel metal-organic framework (MOF) structures that can be formed. In this work, we report the concomitant synthesis of three topologically different MOFs based on the same M₆O₄(OH)₄ clusters (M = Zr or Hf) and methane-tetrakis(p-biphenyl-carboxylate) (MTBC) linkers. Two novel structural models are presented based on single-crystal diffraction analysis, namely, cubic c-(4,12)MTBC-M₆ and trigonal tr-(4,12)MTBC-M₆, which comprise 12-coordinated clusters and 4-coordinated tetrahedral linkers. Notably, the cubic phase features a new architecture based on orientational cluster disorder, which is essential for its formation and has been analyzed by a combination of average structure refinements and diffuse scattering analysis from both powder and single-crystal X-ray diffraction data. The trigonal phase also features structure disorder, although involving both linkers and secondary building units. In both phases, remarkable geometrical distortion of the MTBC linkers illustrates how linker flexibility is also essential for their formation and expands the range of achievable topologies in Zr-based MOFs and its analogues.

Boosting the Sonodynamic Cancer Therapy Performance of 2D Layered Double Hydroxide Nanosheet-Based Sonosensitizers Via Crystalline-to-Amorphous Phase Transformation

Sonodynamic therapy (SDT) has been a promising therapeutic modality for cancer because of its superior advantages compared with other therapeutic strategies. However, the current sonosensitizers used for SDT normally exhibit low activity for ultrasound (US)-induced reactive oxygen species (ROS) generation. Herein, the crystalline-to-amorphous phase transformation is reported as a simple but powerful strategy to engineer ultrathin 2D CoW-LDH and NiW-LDH nanosheets as highly efficient sonosensitizers for SDT. The phase transformation of CoW-LDH and NiW-LDH nanosheets from polycrystalline to amorphous ones is achieved through a simple acid etching treatment. Importantly, compared with the polycrystalline one, the amorphous CoW-LDH (a-CoW-LDH) nanosheets possess higher ROS generation activity under US irradiation, which is ≈17 times of the commercial TiO₂ sonosensitizer. The results suggest that the enhanced performance of ultrathin a-CoW-LDH nanosheets for US-induced ROS generation may be attributed to the phase transformation-induced defect generation and electronic structure changes. After polyethylene glycol modification, the a-CoW-LDH nanosheets can serve as a high-efficiency sonosensitizer for SDT to achieve cell death in vitro and tumor eradication in vivo under US irradiation.

Direct synthesis of amorphous coordination polymers and metal–organic frameworks

Coordination polymers (CPs) and their subset, metal-organic frameworks (MOFs), can have porous structures and hybrid physicochemical properties that are useful for diverse applications. Although crystalline CPs and MOFs have received the most attention to date, their amorphous states are of growing interest as they can be directly synthesized under mild conditions. Directly synthesized amorphous CPs (aCPs) can be constructed from a wider range of metals and ligands than their crystalline and crystal-derived counterparts and demonstrate numerous unique material properties, such as higher mechanical robustness, increased stability and greater processability. This Review examines methods for the direct synthesis of aCPs and amorphous MOFs, as well as their properties and characterization routes, and offers a perspective on the opportunities for the widespread adoption of directly synthesized aCPs.

Emergence of high piezoelectricity from competing local polar order-disorder in relaxor ferroelectrics

Relaxor ferroelectrics are known for outstanding piezoelectric properties, finding a broad range of applications in advanced electromechanical devices. Decoding the origins of the enhanced properties, however, have long been complicated by the heterogeneous local structures. Here, we employ the advanced big-box refinement method by fitting neutron-, X-ray-based total scattering, and X-ray absorption spectrum simultaneously, to extract local atomic polar displacements and construct 3D polar configurations in the classical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3-PbTiO3. Our results demonstrate that prevailing order-disorder character accompanied by the continuous rotation of local polar displacements commands the composition-driven global structure evolution. The omnidirectional local polar disordering appears as an indication of macroscopic relaxor characteristics. Combined with phase-field simulations, it demonstrates that the competing local polar order-disorder between different states with balanced local polar length and direction randomness leads to a flattening free-energy profile over a wide polar length, thus giving rise to high piezoelectricity. Our work clarifies that the critical structural feature required for high piezoelectricity is the competition states of local polar rather than relaxor.

Truchet-tile structure of a topologically aperiodic metal-organic framework

When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. We show that the crystalline metal-organic framework [OZn₄][1,3-benzenedicarboxylate]₃ (TRUMOF-1) is an atomic-scale realization of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.

Charge Localization Induced by Pentagons on Ge(110)

The Ge(110) surface reconstructs into ordered and disordered phases, in which the basic unit is a five-membered ring of Ge atoms (pentagon). The variety of surface reconstructions leads to a rich electronic density of states with several surface states. Using scanning tunneling microscopy and spectroscopy, we have identified the exact origins of these surface states and linked them to either the Ge pentagons or the underlying Ge-Ge bonds. We show that even moderate fluctuations in the positions of the Ge pentagonal units induce large variations in the local density of states. The local density of states modulates in a precise manner, following the geometrical constraints on tiling Ge pentagons. These geometry-correlated electronic states offer a vast configurational landscape that could provide new opportunities in data storage and computing applications.

Quantification of gas-accessible microporosity in metal-organic framework glasses

Metal-organic framework (MOF) glasses are a new class of glass materials with immense potential for applications ranging from gas separation to optics and solid electrolytes. Due to the inherent difficulty to determine the atomistic structure of amorphous glasses, the intrinsic structural porosity of MOF glasses is only poorly understood. Here, we investigate the porosity features (pore size and pore limiting diameter) of a series of prototypical MOF glass formers from the family of zeolitic imidazolate frameworks (ZIFs) and their corresponding glasses. CO2 sorption at 195 K allows quantifying the microporosity of these materials in their crystalline and glassy states, also providing excess to the micropore volume and the apparent density of the ZIF glasses. Additional hydrocarbon sorption data together with X-ray total scattering experiments prove that the porosity features of the ZIF glasses depend on the types of organic linkers. This allows formulating design principles for a targeted tuning of the intrinsic microporosity of MOF glasses. These principles are counterintuitive and contrary to those established for crystalline MOFs but show similarities to strategies previously developed for porous polymers.

Compositionally Disordered Crystalline Compounds for Next Generation of Radiation Detectors

The review is devoted to the analysis of the compositional disordering potential of the crystal matrix of a scintillator to improve its scintillation parameters. Technological capabilities to complicate crystal matrices both in anionic and cationic sublattices of a variety of compounds are examined. The effects of the disorder at nano-level on the landscape at the bottom of the conduction band, which is adjacent to the band gap, have been discussed. The ways to control the composition of polycationic compounds when creating precursors, the role of disorder in the anionic sublattice in alkali halide compounds, a positive role of Gd based matrices on scintillation properties, and the control of the heterovalent state of the activator by creation of disorder in silicates have been considered as well. The benefits of introducing a 3D printing method, which is prospective for the engineering and production of scintillators at the nanoscale level, have been manifested.

Engineered disorder in CO2 photocatalysis

Light harvesting, separation of charge carriers, and surface reactions are three fundamental steps that are essential for an efficient photocatalyst. Here we show that these steps in the TiO2 can be boosted simultaneously by disorder engineering. A solid-state reduction reaction between sodium and TiO2 forms a core-shell c-TiO2@a-TiO2-x(OH)y heterostructure, comprised of HO-Ti-[O]-Ti surface frustrated Lewis pairs (SFLPs) embedded in an amorphous shell surrounding a crystalline core, which enables a new genre of chemical reactivity. Specifically, these SFLPs heterolytically dissociate dihydrogen at room temperature to form charge-balancing protonated hydroxyl groups and hydrides at unsaturated titanium surface sites, which display high reactivity towards CO2 reduction. This crystalline-amorphous heterostructure also boosts light absorption, charge carrier separation and transfer to SFLPs, while prolonged carrier lifetimes and photothermal heat generation further enhance reactivity. The collective results of this study motivate a general approach for catalytically generating sustainable chemicals and fuels through engineered disorder in heterogeneous CO2 photocatalysts.

Crystal structure and specific heat of calcium lanthanide oxyborates Ca4 LnO(BO3)3

Calcium lanthanide oxyborates Ca4 LnO(BO3)3 are of interest for their optical and electromechanical properties. Their crystal structure has been well characterised using powder and single-crystal X-ray diffraction but there remains some disagreement regarding cation ordering in these compounds. In this study, combined X-ray and neutron powder diffraction was employed to study the cation distribution and obtain accurate boron and oxygen atomic coordinates for six Ca4 LnO(BO3)3 compounds (Ln = Pr, Nd, Tb, Ho, Er, Yb) at room temperature and one (Ln = Tb) at 50 and 1.5 K. All compounds adopt the previously reported monoclinic structure with space group Cm. The Ln 3+ ions are disordered over two of the three metal sites, with the extent of disorder increasing across the lanthanide series with decreasing ionic radius. Low-temperature neutron data for Ca4TbO(BO3)3 showed a decrease in paramagnetic scattering on cooling but no obvious magnetic Bragg or diffuse scattering at the lowest temperature of 1.5 K. We report specific heat data at cryogenic temperatures for eight Ca4 LnO(BO3)3 compounds and relate the magnetic properties of these compounds to their structural behaviour.

Photoinduced Ultrafast Transition of the Local Correlated Structure in Chalcogenide Phase-Change Materials

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge_{2}Sb_{2}Te_{5} has been widely used in optical data storage and nonvolatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation, and time-dependent density-functional theory molecular dynamic simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5}. The randomly oriented Peierls distortion among unit cells in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5} is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in the individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ∼0.3  ps. In addition, the impact of the carrier relaxation and the large number of vacancies to the ultrafast structural response is quantified and discussed. Our Letter provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Traversing Double-Well Potential Energy Surfaces: Photoinduced Concurrent Intralayer and Interlayer Structural Transitions in XTe2 (X = Mo, W)

The microscopic arrangement of atoms and molecules is the determining factor in how materials behave and perform; i.e., the structure determines the property, a traditional paradigm in materials science. Photoexcitation-driven manipulation of the crystal structure and associated electronic properties in quantum materials provides opportunities for the exploration of exotic physics and practical applications; however, a generalized mechanism for such symmetry engineering is absent. Here, by ultrafast electron diffraction, structure factor calculation, and TDDFT-MD simulations, we report the photoinduced concurrent intralayer and interlayer structural transitions in the Td and 1T' phases of XTe₂ (X = Mo, W). We discuss the modification of multiple quantum electronic states associated with the intralayer and interlayer structural transitions, such as the topological band inversion and the higher-order topological state. The twin structures and the stacking faults in XTe₂ are also identified by ultrafast structural responses. The comprehensive study of the ultrafast structural response in XTe₂ suggests the traversal of all double-well potential energy surfaces (DWPES) by laser excitation, which is expected to be an intrinsic mechanism in the field of photoexcitation-driven global/local symmetry engineering and also a critical ingredient inducing the exotic properties in the non-equilibrium state in a large number of material systems.

Pressure Induced Disorder-Order Phase Transitions in the Al4Cr Phases

An ordered ω-Al4Cr phase synthesized recently by a high-pressure sintering (HPS) approach was calculated to be stable by density function theory (DFT), implying that high pressure can accelerate the disorder-order phase transitions. The structural building units of the ω-Al4Cr phase as well as the non-stoichiometric disordered ε-Al4Cr and μ-Al4Cr phases have been analyzed by the topological “nanocluster” method in order to explore the structural relations among these phases. Both the ε-and μ-Al4Cr phases contain the typical Macky or pseudo-Macky cluster, and their centered positions were all occupied by Cr atoms, which all occupy the high-symmetry Wyckoff positions. The mechanism of the pressure-induced disorder-order phase transitions from the ε-/μ-Al4Cr to the ω-Al4Cr phase has been analyzed. and the related peritectic and eutectoid reactions have been re-evaluated. All results suggest that the stable ω-Al4Cr phase are transformed from the μ-Al4Cr phase by the eutectoid reaction that is accelerated by high-pressure conditions, whereas the ε-Al4Cr phase should form by the peritectic reaction.

Nanostructured Metallic Glass in a Highly Upgraded Energy State Contributing to Efficient Catalytic Performance

Metallic glasses (MGs), with high density of low coordination sites and high Gibbs free energy state, are novel promising and competitive candidates in the family of electrochemical catalysts. However, it remains a grand challenge to modify the properties of MGs by control of the disordered atomic structure. Recently, nanostructured metallic glasses (NGs), consisting of amorphous nanometer-sized grains connected by amorphous interfaces, have been reported to exhibit tunable properties compared to the MGs with identical chemical composition. Here, it is demonstrated that electrodeposited Ni-P NG is characterized by an extremely high energy state due to its heterogeneous structure, which significantly promotes the catalytic performance. Moreover, the Ni-P NG with a heterogeneous structure is a perfect precursor for the fabrication of unique honey-like nanoporous structure, which displays superior catalytic performance in the urea oxidation reaction (UOR). Specifically, modified Ni-P NG requires a potential of mere 1.36 V at 10 mA cm^-2 , with a Tafel slope of 13 mV dec^-1 , which is the best UOR performance in Ni-based alloys. The present work demonstrates that the nanostructurization of MGs provides a universal and effective pathway to upgrade the energy state of MGs for the design of high-performance catalysts in energy conversion.

Interplay of thermal diffuse scattering and correlated compositional disorder in KCl1-xBrx

Single-crystal X-ray diffuse scattering measurements are reported of the compositional series KCl1-xBrx, a model system for the broader family of disordered rocksalts. Using a combination of Monte Carlo simulations and lattice dynamical calculations, we show that the observed diffuse scattering is well described in terms of (i) non-statistical anion distributions, (ii) local lattice relaxations accompanying Cl/Br substitution, and (iii) the contribution from low-energy phonons. It is found that a tendency for compositional domain formation broadens the thermal diffuse scattering by splitting and softening the acoustic phonon branches. This effect, which is strongest for intermediate compositions, is seen in both experiment and calculation alike. These results establish a link between local compositional order and unconventional lattice dynamics in this system, and reinforce emerging design principles of exploiting compositional fluctuations to tailor physical properties, such as thermal conductivity, that depend on phonon broadening.

Geometric Frustration on the Trillium Lattice in a Magnetic Metal-Organic Framework

In the dense metal-organic framework Na[Mn(HCOO)_{3}], Mn^{2+} ions (S=5/2) occupy the nodes of a "trillium" net. We show that the system is strongly magnetically frustrated: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 1/3-saturation magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2-k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

Designing Magnetism in High Entropy Oxides

In magnetic systems, spin and exchange disorder can provide access to quantum criticality, frustration, and spin dynamics, but broad tunability of these responses and a deeper understanding of strong limit disorder are lacking. Here, it is demonstrated that high entropy oxides present a previously unexplored route to designing materials in which the presence of strong local compositional disorder may be exploited to generate tunable magnetic behaviors-from macroscopically ordered states to frustration-driven dynamic spin interactions. Single-crystal La(Cr0.2 Mn0.2 Fe0.2 Co0.2 Ni0.2 )O3 films are used as a model system hosting a magnetic sublattice with a high degree of microstate disorder in the form of site-to-site spin and exchange type inhomogeneity. A classical Heisenberg model simplified to represent the highest probability microstates well describes how compositionally disordered systems can paradoxically host magnetic uniformity and demonstrates a path toward continuous control over ordering types and critical temperatures. Model-predicted materials are synthesized and found to possess an incipient quantum critical point when magnetic ordering types are designed to be in direct competition, this leads to highly controllable exchange bias behaviors previously accessible only in intentionally designed bilayer heterojunctions.

High Entropy Oxide Relaxor Ferroelectrics

Relaxor ferroelectrics are important in technological applications due to strong electromechanical response, energy storage capacity, electrocaloric effect, and pyroelectric energy conversion properties. Current efforts to discover and design materials in this class generally rely on substitutional doping as slight changes to local compositional order can significantly affect the Curie temperature, morphotropic phase boundary, and electromechanical responses. In this work, we demonstrate that moving to the strong limit of compositional complexity in an ABO₃ perovskite allows stabilization of relaxor responses that do not rely on a single narrow phase transition region. Entropy-assisted synthesis approaches are utilized to synthesize single-crystal Ba(Ti_0.2Sn_0.2Zr_0.2Hf_0.2Nb_0.2)O₃ [Ba(5B)O] films. The high levels of configurational disorder present in this system are found to influence dielectric relaxation, phase transitions, nanopolar domain formation, and Curie temperature. Temperature-dependent dielectric, Raman spectroscopy, and second-harmonic generation measurements reveal multiple phase transitions, a high Curie temperature of 570 K, and the relaxor ferroelectric nature of Ba(5B)O films. The first-principles theory calculations are used to predict possible combinations of cations to design relaxor ferroelectrics and quantify the relative feasibility of synthesizing these highly disordered single-phase perovskite systems. The ability to stabilize single-phase perovskites with various cations on the B-sites offers possibilities for designing high-performance relaxor ferroelectric materials for piezoelectric, pyroelectric, and electrocaloric applications.

A top-down strategy for amorphization of hydroxyl compounds for electrocatalytic oxygen evolution

Amorphous materials have attracted increasing attention in diverse fields due to their unique properties, yet their controllable fabrications still remain great challenges. Here, we demonstrate a top-down strategy for the fabrications of amorphous oxides through the amorphization of hydroxides. The versatility of this strategy has been validated by the amorphizations of unitary, binary and ternary hydroxides. Detailed characterizations indicate that the amorphization process is realized by the variation of coordination environment during thermal treatment, where the M-OH octahedral structure in hydroxides evolves to M-O tetrahedral structure in amorphous oxides with the disappearance of the M-M coordination. The optimal amorphous oxide (FeCoSn(OH)6-300) exhibits superior oxygen evolution reaction (OER) activity in alkaline media, where the turnover frequency (TOF) value is 39.4 times higher than that of FeCoSn(OH)6. Moreover, the enhanced OER performance and the amorphization process are investigated with density functional theory (DFT) and molecule dynamics (MD) simulations. The reported top-down fabrication strategy for fabricating amorphous oxides, may further promote fundamental research into and practical applications of amorphous materials for catalysis.

Unusual Properties of Hydrogen-Bonded Ferroelectrics: The Case of Cobalt Formate

Hybrid organic-inorganic perovskites is a class of materials with diverse chemically tunable properties and outstanding potential for multifunctionality. We use first-principles simulations to predict room temperature ferroelectricity in a representative of the formate family, [NH_{2}NH_{3}][Co(HCOO)_{3}]. The ferroelectricity arises as a "by-product" of structural transition driven by the stabilization of the hydrogen bond. As a consequence the coupling with the electric field is relatively weak giving origin to large intrinsic coercive fields and making material immune to the depolarizing fields known for its detrimental role in nanoscale ferroelectrics. Insensitivity to the electric field and the intrinsic dynamics of the order-disorder transition in such material leads to the supercoercivity defined as significant increase in the coercive field with frequency. Room temperature polarization measurements provide further support for the predictions.

Orbital Order Melting at Reduced Dimensions

The orbital degree of freedom, strongly coupled with the lattice and spin, is an important factor when designing correlated functions. Whether the long-range orbital order is stable at reduced dimensions and, if not, what the critical thickness is remains a tantalizing question. Here, we report the melting of orbital ordering, observed by controlling the dimensionality of the canonical e_g¹ orbital system LaMnO₃. Epitaxial films are synthesized with vertically aligned orbital ordering planes on an orthorhombic substrate, so that reducing film thickness changes the two-dimensional planes into quasi-one-dimensional nanostrips. The orbital order appears to be suppressed below the critical thickness of about six unit cells by changing the characteristic phonon modes and making the Mn d orbital more isotropic. Density functional calculations reveal that the electronic energy instability induced by bandwidth narrowing via the dimensional crossover and the interfacial effect causes the absence of orbital order in the ultrathin thickness.

Large π-Conjugated Metal-Organic Frameworks for Infrared-Light-Driven CO2 Reduction

It remains challenging to excite traditional photocatalysts through near-infrared (NIR) light. Attempts to use NIR-light-response materials for photochemical reduction usually suffer from inapposite band position due to extremely narrow band gaps. Here, we report that large π-conjugated organic semiconductor engineered metal-organic framework (MOF) can result in NIR-light-driven CO₂ reduction catalyst with high photocatalytic activity. A series of mesoporous MOFs, with progressively increased macrocyclic π-conjugated units, were synthesized for tuning the light adsorption range and catalytic performance. Attainment of these MOFs in single-crystal form revealed the identical topology and precise spatial arrangements of constituent organic semiconductor units and metal clusters. Furthermore, the ultrafast spectroscopic studies confirmed the formation of charge separation state and the mechanism underlying photoexcited dynamics. This combined with X-ray photoelectron spectroscopy and in situ electron paramagnetic resonance studies verified the photoinduced electron transfer pathway within MOFs for NIR-light-driven CO₂ reduction. Specifically, tetrakis(4-carboxybiphenyl)naphthoporphyrin) MOF (TNP-MOF) photocatalyst displayed an unprecedentedly high CO₂ reduction rate of over 6630 μmol h^-1 g^-1 under NIR light irradiation, and apparent quantum efficiencies (AQE) at 760 and 808 nm were over 2.03% and 1.11%, respectively. The photocatalytic performance outperformed all the other MOF-based photocatalysts, even visible-light-driven MOF-based catalysts.

Multi-mode excitation drives disorder during the ultrafast melting of a C4-symmetry-broken phase

Spontaneous C4-symmetry breaking phases are ubiquitous in layered quantum materials, and often compete with other phases such as superconductivity. Preferential suppression of the symmetry broken phases by light has been used to explain non-equilibrium light induced superconductivity, metallicity, and the creation of metastable states. Key to understanding how these phases emerge is understanding how C4 symmetry is restored. A leading approach is based on time-dependent Ginzburg-Landau theory, which explains the coherence response seen in many systems. However, we show that, for the case of the single layered manganite La0.5Sr1.5MnO4, the theory fails. Instead, we find an ultrafast inhomogeneous disordering transition in which the mean-field order parameter no longer reflects the atomic-scale state of the system. Our results suggest that disorder may be common to light-induced phase transitions, and methods beyond the mean-field are necessary for understanding and manipulating photoinduced phases.

Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides.