Design of crystal-like aperiodic solids with selective disorder-phonon coupling

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.

Correlated Anion Disorder in Heteroanionic Cubic TiOF2

Resolving anion configurations in heteroanionic materials is crucial for understanding and controlling their properties. For anion-disordered oxyfluorides, conventional Bragg diffraction cannot fully resolve the anionic structure, necessitating alternative structure determination methods. We have investigated the anionic structure of anion-disordered cubic (ReO3-type) TiOF2 using X-ray pair distribution function (PDF), 19F MAS NMR analysis, density functional theory (DFT), cluster expansion modeling, and genetic-algorithm structure prediction. Our computational data predict short-range anion ordering in TiOF2, characterized by predominant cis-[O2F4] titanium coordination, resulting in correlated anion disorder at longer ranges. To validate our predictions, we generated partially disordered supercells using genetic-algorithm structure prediction and computed simulated X-ray PDF data and 19F MAS NMR spectra, which we compared directly to experimental data. To construct our simulated 19F NMR spectra, we derived new transformation functions for mapping calculated magnetic shieldings to predicted magnetic chemical shifts in titanium (oxy)fluorides, obtained by fitting DFT-calculated magnetic shieldings to previously published experimental chemical shift data for TiF4. We find good agreement between our simulated and experimental data, which supports our computationally predicted structural model and demonstrates the effectiveness of complementary experimental and computational techniques in resolving anionic structure in anion-disordered oxyfluorides. From additional DFT calculations, we predict that increasing anion disorder makes lithium intercalation more favorable by, on average, up to 2 eV, highlighting the significant effect of variations in short-range order on the intercalation properties of anion-disordered materials.

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.

Inorganic Metal Thiocyanates

Metal thiocyanates were some of the first pseudohalide compounds to be discovered and adopt a diverse range of structures. This review describes the structures, properties, and syntheses of the known binary and ternary metal thiocyanates. It provides a categorization of their diverse structures and connects them to the structures of atomic inorganic materials. In addition to this description of characterized binary and ternary thiocyanates, this review summarizes the state of knowledge for all other binary metal thiocyanates. It concludes by highlighting opportunities for future materials development.

Thermal Transport Properties of Phonons in Halide Perovskites

Halide perovskites have emerged as promising candidates for various applications, such as photovoltaic, optoelectronic and thermoelectric applications. The knowledge of the thermal transport of halide perovskites is essential for enhancing the device performance for these applications and improving the understanding of heat transport in complicated material systems with atomic disorders. In this work, the current understanding of the experimentally and theoretically obtained thermal transport properties of halide perovskites is reviewed. This study comprehensively examines the reported thermal conductivity of methylammonium lead iodide, which is a prototype material, and provides theoretical frameworks for its lattice vibrational properties. The frameworks and discussions are extended to other halide perovskites and derivative structures. The implications for device applications, such as solar cells and thermoelectrics, are discussed.

Tuning electronic and phononic states with hidden order in disordered crystals

Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical properties of materials is not well understood. Using simple models for electronic and interatomic interactions, we show how crystals with identical average structures but different types of hidden order can have very different electronic and phononic band structures. Increasing the strength of local correlations within hidden-order states can open band gaps and tune mode (de)localisation-both mechanisms allowing for fundamental changes in physical properties without long-range symmetry breaking. Taken together, our results demonstrate how control over hidden order offers a new mechanism for tuning material properties, orthogonal to the conventional principles of (ordered) structure/property relationships.

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.

Anion-polarisation-directed short-range-order in antiperovskite Li2FeSO

Short-range ordering in cation-disordered cathodes can have a significant effect on their electrochemical properties. Here, we characterise the cation short-range order in the antiperovskite cathode material Li2FeSO, using density functional theory, Monte Carlo simulations, and synchrotron X-ray pair-distribution-function data. We predict partial short-range cation-ordering, characterised by favourable OLi4Fe2 oxygen coordination with a preference for polar cis-OLi4Fe2 over non-polar trans-OLi4Fe2 configurations. This preference for polar cation configurations produces long-range disorder, in agreement with experimental data. The predicted short-range-order preference contrasts with that for a simple point-charge model, which instead predicts preferential trans-OLi4Fe2 oxygen coordination and corresponding long-range crystallographic order. The absence of long-range order in Li2FeSO can therefore be attributed to the relative stability of cis-OLi4Fe2 and other non-OLi4Fe2 oxygen-coordination motifs. We show that this effect is associated with the polarisation of oxide and sulfide anions in polar coordination environments, which stabilises these polar short-range cation orderings. We propose that similar anion-polarisation-directed short-range-ordering may be present in other heterocationic materials that contain cations with different formal charges. Our analysis illustrates the limitations of using simple point-charge models to predict the structure of cation-disordered materials, where other factors, such as anion polarisation, may play a critical role in directing both short- and long-range structural correlations.

Dynamics in the ordered and disordered phases of barocaloric adamantane

High-entropy order-disorder phase transitions can be used for efficient and eco-friendly barocaloric solid-state cooling. Here the barocaloric effect is reported in an archetypal plastic crystal, adamantane. Adamantane has a colossal isothermally reversible entropy change of 106 J K^-1 kg^-1. Extremely low hysteresis means that this can be accessed at pressure differences less than 200 bar. Configurational entropy can only account for about 40% of the total entropy change; the remainder is due to vibrational effects. Using neutron spectroscopy and supercell lattice dynamics calculations, it is found that this vibrational entropy change is mainly caused by softening in the high-entropy phase of acoustic modes that correspond to molecular rotations. We attribute this difference in the dynamics to the contrast between an 'interlocked' state in the low-entropy phase and sphere-like behaviour in the high-entropy phase. Although adamantane is a simple van der Waals solid with near-spherical molecules, this approach can be leveraged for the design of more complex barocaloric molecular crystals. Moreover, this study shows that supercell lattice dynamics calculations can accurately map the effect of orientational disorder on the phonon spectrum, paving the way for studying the vibrational entropy, thermal conductivity, and other thermodynamic effects in more complex materials.

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.

Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites

We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-k orders. We propose experimental realizations of our model in rare-earth antiperovskites.

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.

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.

K-Ion Battery Cathode Design Utilizing Trigonal Prismatic Ligand Field

The intrinsic physical and chemical properties of materials are largely governed by the bonding and electronic structures of their fundamental building units. The majority of cathode materials contain octahedral TMO₆ (TM = transition metal), which dominates the redox chemistry during electrochemical operation. As a less symmetric form of TMO₆ , the trigonal prismatic geometry is not a traditionally favored coordination configuration as it tends to lose the crystal-field stabilization energy and thus generate large ligand repulsion. Herein, a K-ion battery cathode design, K₂ Fe(C₂ O₄ )₂ , is shown​, where the TMO₆ trigonal prism (TP) is not only electrochemically active but stable enough to allow for excellent cycling stability. Detailed synchrotron X-ray absorption spectroscopy measurements reveal the evolution of localized fine structure, evidencing the electrochemical activity, reversibility, and stability of the TP motif. The findings are expected to expand the toolbox for the rational design of electrode materials by taking advantage of TP as a structural gene.

Embracing Defects and Disorder in Magnetic Nanoparticles

Iron oxide nanoparticles have tremendous scientific and technological potential in a broad range of technologies, from energy applications to biomedicine. To improve their performance, single-crystalline and defect-free nanoparticles have thus far been aspired. However, in several recent studies, defect-rich nanoparticles outperform their defect-free counterparts in magnetic hyperthermia and magnetic particle imaging (MPI). Here, an overview on the state-of-the-art of design and characterization of defects and resulting spin disorder in magnetic nanoparticles is presented with a focus on iron oxide nanoparticles. The beneficial impact of defects and disorder on intracellular magnetic hyperthermia performance of magnetic nanoparticles for drug delivery and cancer therapy is emphasized. Defect-engineering in iron oxide nanoparticles emerges to become an alternative approach to tailor their magnetic properties for biomedicine, as it is already common practice in established systems such as semiconductors and emerging fields including perovskite solar cells. Finally, perspectives and thoughts are given on how to deliberately induce defects in iron oxide nanoparticles and their potential implications for magnetic tracers to monitor cell therapy and immunotherapy by MPI.

Function from configurational degeneracy in disordered framework materials

We develop the concepts of combinatorial mechanics, adaptive flexibility, and error-correcting codes as applications of disordered framework materials.

Ring structure of selected two-dimensional procrystalline lattices

Recent work has introduced the term "procrystalline" to define systems which lack translational symmetry but have an underlying high-symmetry lattice. The properties of five such two-dimensional (2D) lattices are considered in terms of the topologies of rings which may be formed from three-coordinate sites only. Parent lattices with full coordination numbers of four, five, and six are considered, with configurations generated using a Monte Carlo algorithm. The different lattices are shown to generate configurations with varied ring distributions. The different constraints imposed by the underlying lattices are discussed. Ring size distributions are obtained analytically for two of the simpler lattices considered (the square and trihexagonal nets). In all cases, the ring size distributions are compared to those obtained via a maximum entropy method. The configurations are analyzed with respect to the near-universal Lemaître curve (which connects the fraction of six-membered rings with the width of the ring size distribution) and three lattices are highlighted as rare examples of systems which generate configurations which do not map onto this curve. The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

A simple model for vacancy order and disorder in defective half-Heusler systems

Defective half-Heusler systems X 1-x YZ with large amounts of intrinsic vacancies, such as Nb1-x CoSb, Ti1-x NiSb and V1-x CoSb, are a group of promising thermoelectric materials. Even with high vacancy concentrations they maintain the average half-Heusler crystal structure. These systems show high electrical conductivity but low thermal conductivity arising from an ordered YZ substructure, which conducts electrons, while the large amounts of vacancies in the X substructure effectively scatters phonons. Using electron scattering, it was recently observed that, in addition to Bragg diffraction from the average cubic half-Heusler structure, some of these samples show broad diffuse scattering indicating short-range vacancy order, while other samples show sharp additional peaks indicating long-range vacancy ordering. Here it is shown that both the short- and long-range ordering can be explained using the same simple model, which assumes that vacancies in the X substructure avoid each other. The samples showing long-range vacancy order are in agreement with the predicted ground state of the model, while short-range order samples are quenched high-temperature states of the system. A previous study showed that changes in sample stoichiometry affect whether the short- or long-range vacancy structure is obtained, but the present model suggests that thermal treatment of samples should allow controlling the degree of vacancy order, and thereby the thermal conductivity, without changes in composition. This is important as the composition also dictates the amount of electrical carriers. Independent control of electrical carrier concentration and degree of vacancy order should allow further improvements in the thermoelectric properties of these systems.

Quasicrystal-related mosaics with periodic lattices interlaid with aperiodic tiles

Quasicrystals, which have long-range orientational order without translational symmetry, are incompatible with the theory of conventional crystals, which are characterized by periodic lattices and uniformly repeated unit cells. Reported here is a novel quasicrystal-related solid state observed in two Al-Cr-Fe-Si alloys, which can be described as a mosaic of aperiodically distributed unit tiles in translationally periodic structural blocks. This new type of material possesses the opposing features of both conventional crystals and quasicrystals, which might trigger wide interest in theory, experiments and the potential applications of this type of material.

Ultralow thermal conductivity from transverse acoustic phonon suppression in distorted crystalline α-MgAgSb

Low thermal conductivity is favorable for preserving the temperature gradient between the two ends of a thermoelectric material, in order to ensure continuous electron current generation. In high-performance thermoelectric materials, there are two main low thermal conductivity mechanisms: the phonon anharmonic in PbTe and SnSe, and phonon scattering resulting from the dynamic disorder in AgCrSe2 and CuCrSe2, which have been successfully revealed by inelastic neutron scattering. Using neutron scattering and ab initio calculations, we report here a mechanism of static local structure distortion combined with phonon-anharmonic-induced ultralow lattice thermal conductivity in α-MgAgSb. Since the transverse acoustic phonons are almost fully scattered by the compound's intrinsic distorted rocksalt sublattice, the heat is mainly transported by the longitudinal acoustic phonons. The ultralow thermal conductivity in α-MgAgSb is attributed to its atomic dynamics being altered by the structure distortion, which presents a possible microscopic route to enhance the performance of similar thermoelectric materials.

Ultrafast calculation of diffuse scattering from atomistic models

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391-399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 10², making refinement of atomistic models to large diffuse-scattering volumes practical.

Negative Hydration Expansion in ZrW_{2}O_{8}: Microscopic Mechanism, Spaghetti Dynamics, and Negative Thermal Expansion

We use a combination of x-ray diffraction, total scattering, and quantum mechanical calculations to determine the mechanism responsible for hydration-driven contraction in ZrW_{2}O_{8}. The inclusion of H_{2}O molecules within the ZrW_{2}O_{8} network drives the concerted formation of new W─O bonds to give one-dimensional (─W─O─)_{n} strings. The topology of the ZrW_{2}O_{8} network is such that there is no unique choice for the string trajectories: the same local changes in coordination can propagate with a large number of different periodicities. Consequently, ZrW_{2}O_{8}·H_{2}O is heavily disordered, with each configuration of strings forming a dense aperiodic "spaghetti." This new connectivity contracts the unit cell via large shifts in the Zr and W atom positions. Fluctuations of the undistorted parent structure towards this spaghetti phase emerge as the key negative thermal expansion (NTE) phonon modes in ZrW_{2}O_{8} itself. The large relative density of NTE phonon modes in ZrW_{2}O_{8} actually reflects the degeneracy of volume-contracting spaghetti excitations, itself a function of the particular topology of this remarkable material.

Ab initio study of the nature and stability of the defects and multi-vacancies in TaN. Comparison with TiN

First principles calculations have been carried out to study the native single-defects and multi-vacancies in TaN and TiN with a cubic rocksalt structure mainly used as diffusion barriers. Our results indicate that vacancies are the most stable single-defects in both compounds and that nitrogen interstitial defects in tetrahedral interstitial site are significantly more stable in TaN than in TiN. The interactions between vacancies are attractive in TaN in contrast to the case of TiN. The vacancies show a much larger tendency to cluster and to form bi- and tri- vacancies in TaN than in TiN. We suggest that the number of d electrons might explain this difference in the defect stability. These results will have impact on the use of these materials as diffusion barrier.

A Chiral 3 D Net with 2 D Cairo Pentagonal Tiling Projection in Site-Modified CuCN/CuSCN Networks

A novel isohedral 3-periodic net (i.e. a net with one kind of tile), showing a Cairo pentagonal tiling projection on the Euclidean plane, has been identified in a series of site-modified CuCN/CuSCN networks, namely, [Cu₆ (SCN)₂ (CN)₆ ⋅Ni(tpy)₂ ]_n (1), [Cu₆ (SCN)(CN)₇ ⋅Ni(tpy)₂ ]_n (2) and [Cu₆ (CN)₈ ⋅Ni(tpy)₂ ]_n (3) (tpy=2,2':6'',2''-terpyridine). These infinite inclusion compounds were prepared via a solvothermal sulfur migration reaction with subtle modification to fine-tune the sulfur content. The chiroptical activity of single crystals, which arises from the intrinsically chiral net, was confirmed by X-ray diffraction and solid-state circular dichroism spectra.

Defects and disorder in metal organic frameworks

The wide-ranging properties of metal organic frameworks (MOFs) rely in many cases on the presence of defects within their structures and the disorder that is inevitably associated with such defects.