arXiv subjects

Andrew L. Goodwin

Publications and source records attributed to Andrew L. Goodwin.

At least 19 recordsLinked to original sources

arXiv2026

Coupling of Cation and Anion Dynamics in Solid Electrolytes Revealed by Virtual Isotopic Substitution Molecular Dynamics

We characterise the interplay between cation-translational and anion-rotational dynamics on the model system $\rm \alpha\text{-}Li_{2}SO_{4}$ through virtual isotopic substitution molecular dynamics (VISMD) simulations. We independently control in turn the lithium translational- and sufate rotational- diffusivity by varying the masses of lithium and oxygen, respectively, showing that both diffusivities exhibit power-law relationships with the masses of each individual component. Changing either diffusivity produces an effect on the other; i.e. there exists a bidirectional coupling between anion and cation diffusive dynamics. From our variable-temperature/variable-mass dataset we demonstrate that the apparent activation energy for lithium diffusion depends strongly on the isotope mass, decreasing with accelerated sulfate dynamics; an observation which provides clear evidence of mode-coupling between cation and anion dynamics.

cond-mat.dis-nn↗

arXiv2026

Hidden Truchet Architecture in Zinc $p$-Hydroxybenzoate

We redetermine the structure of the disordered metal-organic framework Zn(hba) (hba$^{2-}$ = the dianion of 4-hydroxybenzoic acid). Using single-crystal X-ray diffraction measurements, we characterise the structured diffuse scattering that is experimentally observed for this material and which is characteristic of strongly correlated disorder. We use geometric and crystal chemical arguments to propose a general model for correlated disorder in Zn(hba), and then relate this model to a specific realisation of so-called Truchet tilings. Using Monte Carlo simulations, we proceed to show that the model so developed is simultaneously consistent with both the average crystal structure solution described previously, and the structured diffuse scattering reported here. The existence of ordered analogues with different, but related, chemistry suggests scope for control over correlated disorder in this family of metal-organic frameworks. Our study illustrates the potential for a Truchet-tile formalism to help describe and understand more generally the correlated disorder that occurs in framework materials - even amongst those that are chemically and crystallographically dissimilar.

cond-mat.mtrl-sci↗

arXiv2026

Responsive Disorder in a Metal-Organic Framework Enables Solid-State Reservoir Computing

Complex systems with nonlinear response mechanisms can be applied as reservoir computers for energy-efficient machine learning tasks. Historically explored at the macro- and meso-scale, physical reservoir computing has recently been extended to the atomic scale via chemical mixtures with strong and dynamic heterogeneity. Here we explore the possibility that configurational degeneracy within disordered materials might form the basis for solid-state atomic-scale reservoirs. Our proof-of-concept uses the disordered metal-organic framework DUT-8, which undergoes a series of disorder-disorder transitions on exposure to different guest species. We show that variations in X-ray diffuse scattering associated with these transitions function as suitable readouts for machine learning applications. A combination of nonlinearity and memory effects in the DUT-8 response allows the system to carry out both classification and time-series machine learning tasks with accuracies comparable to those of mesoscale physical reservoir computers. Our results suggest a new avenue for exploiting correlated disorder in solid phases whenever the nature of that disorder can be modulated through external perturbations-a phenomenon we term `responsive disorder'.

cond-mat.dis-nn↗

arXiv2026

Revisiting Jahn--Teller Transitions in Correlated Oxides with Monte Carlo Modeling

Jahn--Teller (JT) distortions are a key driver of physical properties in many correlated oxide materials. Cooperative JT distortions, in which long-range orbital order reduces the symmetry of the average structure macroscopically, are common in JT-distorted materials at low temperatures. This long-range order will often melt on heating, \textit{via} a transition to a high-temperature state without long-range orbital order. The nature of this transition has been observed to vary with different materials depending on crystal structure; in LaMnO$_3$ the transition has generally been interpreted as order-disorder, whereas in layered nickelates $A$NiO$_2$ ($A$=Li,Na) there is a displacive transition. Alternatively, recent theoretical work has suggested that previous attributions of order-disorder may in fact be a consequence of phonon anharmonicity, rather than persistence of JT distortions, which would suggest that the displacive transition may be more common than currently believed. In this work, we run Monte Carlo simulations with a simple Hamiltonian which is modified to include terms dependent on the JT amplitude $\rho$, which is allowed to vary within the simulation \textit{via} the Metropolis algorithm. Our simulations yield distributions of JT amplitudes consistent with displacive rather than order-disorder behaviour for both perovskites and layered nickelates, suggesting that displacive-like JT transitions may be more common than previously assumed in both perovskites and layered nickelates. We also find significant differences between the transition observed for perovskites compared with layered nickelates, which we attribute to differing extensivity of configurational entropy on the two lattices, showing the crucial role of lattice geometry in determining behaviour.

cond-mat.str-el↗

arXiv2025

The Microscopic Nature of Orbital Disorder in LaMnO$_{3}$

We present a revised atomistic picture of the order-disorder transition in the archetypal orbital-ordered perovskite material, LaMnO$_{3}$. Our study uses machine-learning-driven molecular-dynamics simulations which describe the temperature evolution of pair distribution functions in close agreement with experiment. We find the orbital-disordered phase in LaMnO$_{3}$ to comprise a mixture of differing structural distortions with and without inversion symmetry, implying a mixture of different orbital arrangements. These distortions are highly dynamic with an estimated lifetime of $\sim 40$ fs at 1,000 K, and their fluctuations converge with the timescales of conventional thermal motion in the high-$T$ phase - indicating that the electronic instability responsible for static Jahn-Teller distortions at low temperature instead drives phonon anharmonicity at high temperatures. Beyond LaMnO$_{3}$, our work opens an avenue for studying a wider range of correlated materials.

cond-mat.mtrl-sci↗

arXiv2025

Autonomous interpretation of atomistic scattering data

Materials with bespoke properties have long been identified by computational searches, and their experimental realisation is now coming within reach through autonomous laboratories. Scattering experiments are central to verifying the atomic structures of autonomously synthesised materials. Yet, interpreting these measurements typically requires user expertise and manual processing, or machine learning (ML) models trained on predefined datasets, limiting fully autonomous materials discovery. Here, we introduce a differentiable optimisation framework that treats scattering calculations, energetics, and chemical constraints as a unified refinement problem. Capability demonstrations across molecules, crystal structures, nanoparticles, and amorphous matter show that this data-driven approach resolves structural degeneracies with multi-modal inputs - suggesting its usefulness for informing, and ultimately guiding, the operation of autonomous laboratories.

cond-mat.mtrl-sci↗

arXiv2025

Structural Complexity and Correlated Disorder in Materials Chemistry

Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if the disorder present is random: such systems can be described efficiently through statistical mechanics. True complexity emerges when structures are neither perfectly crystalline nor randomly disordered -- a middle ground once named ``organised complexity''. In current parlance, in our field, we use the term ``correlated disorder'' for this same regime, emphasising the presence and importance of non-random patterns.

cond-mat.dis-nn↗

arXiv2025

High-Quality Ultra-Fast Total Scattering and Pair Distribution Function Data using an X-ray Free Electron Laser

High-quality total scattering data, a key tool for understanding atomic-scale structure in disordered materials, require stable instrumentation and access to high momentum transfers. This is now routine at dedicated synchrotron instrumentation using high-energy X-ray beams, but it is very challenging to measure a total scattering dataset in less than a few microseconds. This limits their effectiveness for capturing structural changes that occur at the much faster timescales of atomic motion. Current X-ray free-electron lasers (XFELs) provide femtosecond-pulsed X-ray beams with maximum energies of approximately 24 keV, giving the potential to measure total scattering and the attendant pair distribution functions (PDFs) on femtosecond timescales. Here, we show that this potential has been realised using the HED scientific instrument at the European XFEL and present normalised total scattering data for 0.35 \r{A}-1 < Q < 16.6 \r{A}-1 and their PDFs from a broad spectrum of materials, including crystalline, nanocrystalline and amorphous solids, liquids, and clusters in solution. We analyse the data using a variety of methods, including Rietveld refinement, small-box PDF refinement, joint reciprocal-real space refinement, cluster refinement, and Debye scattering analysis. The resolution function of the setup is also characterised. We conclusively show that high-quality data can be obtained from a single approximately 30 fs XFEL pulse. Our efforts not only significantly increase the existing maximum reported Q-range for an S(Q) measured at an XFEL but also mean that XFELs are now a viable X-ray source for the broad community of people using reciprocal space total scattering and PDF methods in their research.

cond-mat.mtrl-sci↗

arXiv2025

The interplay between Jahn-Teller distortions and structural degrees of freedom on pseudocubic states in manganite perovskites

The average structure of the solid solution LaMn$_{1-x}$Ga$_x$O$_3$ (LMGO) has been investigated from a symmetry-motivated approach utilizing synchrotron x-ray and neutron powder diffraction techniques. We show experimentally that a trilinear coupling term ($\Gamma_5^+$M$_2^+$M$_3^+$) between shear strain, octahedral rotation, and the $C$-type orbital ordering mode is responsible for driving the orthorhombic to pseudocubic phase transition occurring in the composition range 0.5 $<$ $x$ $<$ 0.6. Our Monte Carlo simulations elucidate the macroscopic origin of this coupling to shear strain, and point to its importance with respect to controlling the orbital order-disorder transitions. We find that the emergence of the pseudocubic state can be rationalized by considering the competition between this trilinear term and a linear-quadratic term of the out-of-phase octahedral tilting with strain ($\Gamma_5^+$(R$_5^-$)$^2$). Illustrating the general nature of these results, we construct a simple function that captures the change in Landau free energy at the order-disorder transition, in parameters that are trivial to relate to the concentration of Jahn--Teller active species, temperature, tolerance factor and unit cell strain, for a broad range of manganite perovskites. Our results point to the fact that far from the pseudocubic state being a symptom of orbital disorder, it is in many cases more correctly to view it as a cause. The results have a broad impact on the study of orbital ordering physics in the perovskite materials and on chemical and physical control parameters through which to tune the richness of the intertwined physical properties.

cond-mat.str-el↗

arXiv2025

The structure and topology of an amorphous metal-organic framework

Amorphous metal-organic frameworks are an important emerging materials class that combine the attractive physical properties of the amorphous state with the versatility of metal-organic framework (MOF) chemistry. The structures of amorphous MOFs have largely been inferred by drawing analogies to crystalline polymorphs and inorganic glasses, but ultimately the validity of such structural models has been challenging to establish either experimentally or computationally. Here we use a unified data-driven approach, combining experimental scattering data and active machine learning for interatomic potentials, to determine the structure of an amorphous zeolitic imidazolate framework (a-ZIF) -- the canonical amorphous MOF. Our results reveal clear differences between the structure of a-ZIF and that of other amorphous tetrahedral networks, allowing us to invalidate the long-standing assumption that these inorganic and hybrid glasses are topologically equivalent. To this end, we introduce a systematic notation for the network topology of amorphous solids, building a bridge to the successful use of topology analysis in crystalline MOFs and to materials informatics. Our work provides insights into the structure and topology of the archetypal amorphous MOF and opens up new avenues for modelling and understanding amorphous framework materials more generally.

cond-mat.mtrl-sci↗

arXiv2024

Displacive Jahn--Teller transition in NaNiO$_2$

Below its Jahn--Teller transition temperature, $T_\mathrm{JT}$, NaNiO$_2$ has a monoclinic layered structure consisting of alternating layers of edge-sharing NaO$_6$ and Jahn-Teller-distorted NiO$_6$ octahedra. Above $T_\mathrm{JT}$ where NaNiO$_2$ is rhombohedral, diffraction measurements show the absence of a cooperative Jahn-Teller distortion, accompanied by an increase in the unit cell volume. Using neutron total scattering, solid-state Nuclear Magnetic Resonance (NMR), and extended X-ray absorption fine structure (EXAFS) experiments as local probes of the structure we find direct evidence for a displacive, as opposed to order-disorder Jahn-Teller transition at $T_\mathrm{JT}$. This is supported by \textit{ab initio} molecular dynamics (AIMD) simulations. To our knowledge this study is the first to show a displacive Jahn-Teller transition in any material using direct observations with local probe techniques.

cond-mat.mtrl-sci↗

arXiv2024

Rules governing Jahn-Teller order in Prussian blue analogues

Jahn-Teller distortions of transition-metal coordination environments link orbital occupancies to structure. In the solid state, such distortions can be strongly correlated through the propagation of strain and/or through orbital interactions. Cooperative Jahn-Teller (CJT) order of this kind affects the electronic, magnetic, and structural properties of the materials in which it occurs. Conventionally studied in dense ceramics, CJT order also occurs in hybrid materials, albeit the underlying phenomenology is not well established. Here we use synchrotron powder X-ray diffraction measurements to identify the compositional factors governing cooperative Jahn-Teller order in a series of Prussian blue analogue (PBA) families. We develop a simple microscopic model based on the dual considerations of strain and crystal-field stabilisation that rationalises the stability, extent of CJT order, and crystallite strain measured experimentally. This model shows how PBA compositions might be tuned to control the emergence and nature of CJT effects, and predicts universal phase behaviour for JT-active PBAs more generally. Our results establish a microscopic framework for understanding and controlling CJT effects in PBAs, and reveal an interplay between compositional, structural, and orbital degrees of freedom closely analogous to that of the manganite perovskites.

cond-mat.mtrl-sci↗

arXiv2023

Enhanced elastic stability of a topologically disordered crystalline metal--organic framework

By virtue of their open network structures and low densities, metal--organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to increase the connectivity of the underlying MOF network, which necessarily increases material density and reduces porosity. Here we demonstrate an alternative paradigm, whereby elastic stability is enhanced in a MOF with an aperiodic network topology. We use a combination of variable-pressure single-crystal X-ray diffraction measurements and coarse-grained lattice-dynamical calculations to interrogate the high-pressure behaviour of the topologically aperiodic system TRUMOF-1, which we compare against that of its ordered congener MOF-5. We show that the topology of the former quenches the elastic instability responsible for pressure-induced framework collapse in the latter, much as irregularity in the shapes and sizes of stones acts to prevent cooperative mechanical failure in drystone walls. Our results establish aperiodicity as a counterintuitive design motif in engineering the mechanical properties of framework structures, relevant to MOFs and larger-scale architectures alike.

cond-mat.mtrl-sci↗

arXiv2023

Understanding defects in amorphous silicon with million-atom simulations and machine learning

The structure of amorphous silicon 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 show that atomistic machine-learning methods can reveal the complex structural and energetic landscape of defects in amorphous silicon. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and more than ten thousand defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned local atomic energies to develop a universal classification of the different types of defects in amorphous silicon. The results suggest a revision of the established floating-bond model by showing that fivefold-coordinated atoms in amorphous silicon exhibit a wide range of local environments, and 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 modelling and understanding defects in disordered materials beyond silicon alone.

cond-mat.mtrl-sci↗

arXiv2023

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.

cond-mat.mtrl-sci↗

arXiv2023

Coarse-grained versus fully atomistic machine learning for zeolitic imidazolate frameworks

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB$_{2}$ 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.

physics.chem-ph↗

arXiv2023

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 intentional 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. Correlated disorder 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. 3D-ΔPDFs visualise and quantify local deviations from the average structure and enable a straightforward interpretation of the single crystal diffuse scattering data in terms of a three-dimensional local order model. Comparison of the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia demonstrates the reliability of the newly proposed approach.

cond-mat.mtrl-sci↗

arXiv2023

Anion-polarisation-directed short-range-order in antiperovskite Li$_2$FeSO

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 Li$_2$FeSO, 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 OLi$_4$Fe$_2$ oxygen coordination with a preference for polar cis-OLi$_4$Fe$_2$ over non-polar trans-OLi$_4$Fe$_2$ 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-OLi$_4$Fe$_2$ oxygen coordination and corresponding long-range crystallographic order. The absence of long-range order in Li$_2$FeSO can therefore be attributed to the relative stability of cis-OLi$_4$Fe$_2$ and other non-OLi$_4$Fe$_2$ 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 similar anion-polarisation-directed short-range-ordering may be present in other heterocationic materials that contain cations with different formal charges. Our analysis also 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.

cond-mat.mtrl-sci↗