We use a combination of X-ray pair distribution function (PDF) measurements, lattice dynamical calculations, and ab initio density functional theory (DFT) calculations to study the local structure and dynamics in various MPt(CN)6 Prussian blue analogues. In order to link directly the local distortions captured by the PDF with the lattice dynamics of this family, we develop and apply a new "interaction-space" PDF refinement approach. This approach yields effective harmonic force constants, from which the (experiment-derived) low-energy phonon dispersion relations can be approximated. Calculation of the corresponding Grüneisen parameters allows us to identify the key modes responsible for negative thermal expansion (NTE) as arising from correlated tilts of coordination octahedra. We compare our results against the phonon dispersion relations determined using DFT calculations, which identify the same NTE mechanism.
We report the magnetic behavior of the hybrid perovskites [Gua]Mn1-xFe2x/3â¡x/3(HCOO)3 (0 ≤ x ≤ 0.88), showing that vacancy ordering drives bulk ferrimagnetism for x > 0.6. The behavior is rationalized in terms of a simple microscopic model of percolation-induced ferrimagnetism. Monte Carlo simulations driven by this model reproduce the experimental dependence of magnetic susceptibility on x and show that, at intermediate compositions, domains of short-range vacancy order lead to the emergence of local magnetization. Our results open up a new avenue for the design of multiferroic hybrid perovskites.
The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone.
We explore the role and nature of torsional flexibility of carboxylate-benzene links in the structural chemistry of metal-organic frameworks (MOFs) based on Zn and benzenedicarboxlyate (bdc) linkers. A particular motivation is to understand the extent to which such flexibility is important in stabilising the unusual topologically aperiodic phase known as TRUMOF-1. We compare the torsion angle distributions of TRUMOF-1 models with those for crystalline Zn/1,3-bdc MOFs, including a number of new materials whose structures we report here. We find that both periodic and aperiodic Zn/1,3-bdc MOFs sample a similar range of torsion angles, and hence the formation of TRUMOF-1 does not require any additional flexibility beyond that already evident in chemically-related crystalline phases. Comparison with Zn/1,4-bdc MOFs does show, however, that the lower symmetry of the 1,3-bdc linker allows access to a broader range of torsion angles, reflecting a greater flexibility of this linker.
Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Caâ¯Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca2+-ion pairs. We reveal an unexpected mapping to the Lennard-Jones-Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca2+ ions.
Based on simple electrostatic and harmonic potential considerations, we derive a straightforward expression linking the composition of a Prussian blue analogue (PBA) to its propensity to undergo collective structural distortions. We demonstrate the existence of a threshold value, below which PBAs are undistorted and above which PBAs distort by a degree that is controlled by a geometric tolerance factor. Our analysis rationalizes the presence, absence, and magnitude of distortions in a wide range of PBAs and distinguishes their structural chemistry from that of other hybrid perovskites.
We study the phenomenology of cooperative off-centering of K+ ions in potassiated Prussian blue analogues (PBAs). The principal distortion mechanism by which this off-centering occurs is termed a "K-ion slide", and its origin is shown to lie in the interaction between local electrostatic dipoles that couple through a combination of electrostatics and elastic strain. Using synchrotron powder X-ray diffraction measurements, we determine the crystal structures of a range of low-vacancy K2M[Fe(CN)6] PBAs (M = Ni, Co, Fe, Mn, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect the common underlying physics responsible for K-ion slides and their evolution with temperature and composition. Monte Carlo simulations driven by a simple model of dipolar interactions and strain coupling reproduce the general features of the experimental phase behavior. We discuss the implications of our study for optimizing the performance of PBA K-ion battery cathode materials and also its relevance to distortions in other, conceptually related, hybrid perovskites.
The sodium-rich antiperovskites (NaRAPs) with composition Na3 OB (B=Br, Cl, I, BH4 , etc.) are a family of materials that has recently attracted great interest for application as solid electrolytes in sodium metal batteries. Non-Arrhenius ionic conductivities have been reported for these materials, the origin of which is poorly understood. In this work, we combined temperature-resolved bulk and local characterisation methods to gain an insight into the origin of this unusual behaviour using Na3 OBr as a model system. We first excluded crystallographic disorder on the anion sites as the cause of the change in activation energy; then identified the presence of a poorly crystalline impurities, not detectable by XRD, and elucidated their effect on ionic conductivity. These findings improve understanding of the processing-structure-properties relationships pertaining to NaRAPs and highlight the need to determine these relationships in other materials systems, which will accelerate the development of high-performance solid electrolytes.
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.
Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB2 phases. We test the validity of this assumption by comparing simplified and fully atomistic machine-learning models for local environments in ZIFs. Our work addresses the central question to what extent chemical information can be "coarse-grained" in hybrid framework materials.
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.
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.
Three-dimensional difference pair distribution functions (3D-ΔPDFs) from X-ray and neutron diffraction experiments are reported for yttria-stabilized zirconia (Zr0.82Y0.18O1.91). A quantitative analysis of the signatures in the three-dimensional difference pair distribution functions is used to establish that oxygen ions neighbouring a vacancy shift by 0.525â (5)â Å along ⟨1,â 0,â 0⟩ towards the vacancy while metal ions neighbouring a vacancy shift by 0.465â (2)â Å along ⟨1,â 1,â 1⟩ away from the vacancy. The neutron 3D-ΔPDF shows a tendency for vacancies to cluster along ⟨½,â ½,â ½⟩, which results in sixfold coordinated metal ions.
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.
The sodium-rich antiperovskites (NaRAPs) with composition Na3OB (B=Br, Cl, I, BH4, etc.) are a family of materials that has recently attracted great interest for application as solid electrolytes in sodium metal batteries. Non-Arrhenius ionic conductivities have been reported for these materials, the origin of which is poorly understood. In this work, we combined temperature-resolved bulk and local characterisation methods to gain an insight into the origin of this unusual behaviour using Na3OBr as a model system. We first excluded crystallographic disorder on the anion sites as the cause of the change in activation energy; then identified the presence of a poorly crystalline impurities, not detectable by XRD, and elucidated their effect on ionic conductivity. These findings improve understanding of the processing-structure-properties relationships pertaining to NaRAPs and highlight the need to determine these relationships in other materials systems, which will accelerate the development of high-performance solid electrolytes.
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.
Phonons , Monte Carlo Method , Thermal Conductivity , X-Rays
We report the synthesis, crystal structure, thermal response, and electrochemical behavior of the Prussian blue analogue (PBA) K2Cu[Fe(CN)6]. From a structural perspective, this is the most complex PBA yet characterized: its triclinic crystal structure results from an interplay of cooperative Jahn-Teller order, octahedral tilts, and a collective "slide" distortion involving K-ion displacements. These different distortions give rise to two crystallographically distinct K-ion channels with different mobilities. Variable-temperature X-ray powder diffraction measurements show that K-ion slides are the lowest-energy distortion mechanism at play, as they are the only distortion to be switched off with increasing temperature. Electrochemically, the material operates as a K-ion cathode with a high operating voltage and an improved initial capacity relative to higher-vacancy PBA alternatives. On charging, K+ ions are selectively removed from a single K-ion channel type, and the slide distortions are again switched on and off accordingly. We discuss the functional importance of various aspects of structural complexity in this system, placing our discussion in the context of other related PBAs.
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.
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.
