arXiv subjects

Andrew L. Goodwin

Publications and source records attributed to Andrew L. Goodwin.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2023

Geometrically-frustrated interactions drive structural complexity in amorphous calcium carbonate

Amorphous calcium carbonate (ACC) is an important precursor for biomineralisation in marine organisms. Among the key outstanding problems regarding ACC are how best to understand its structure and how to rationalise its metastability as an amorphous phase. Here, we report high-quality atomistic models of ACC generated by 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 Ca$\boldsymbol\cdots$Ca interaction potential governing ACC formation. This potential contains minima at two competing distances, corresponding to the two different ways in which carbonate ions bridge Ca$^{2+}$-ion pairs. We reveal an unexpected mapping to the Lennard-Jones--Gauss (LJG) model normally studied in the context of computational soft-matter, with the empirical LJG parameters for ACC taking values known to promote structural complexity. In this way we show that both the complex structure of ACC and its resilience to crystallisation are actually encoded in the geometrically-frustrated effective interactions between Ca$^{\boldsymbol 2+}$ ions.

cond-mat.mtrl-sci↗

arXiv2023

On the polytypism of layered $\textit{MX}_2$ materials

We revisit the problem of polytypism in layered $\textit{MX}_2$ materials, with a view to reinterpreting the phase space accessible to this family. Our starting point is to develop a simple, constructive and compact label for the most commonly observed stacking arrangements that is similar to the Glazer notation used to label tilt systems in perovskites. The key advantage of this label in the context of $\textit{MX}_2$ systems is that it contains sufficient information to generate the corresponding stacking sequences uniquely. Using a related approach, we generate a Cartesian representation of the phase space containing all possible $\textit{MX}_2$ polytypes, with the most common structures appearing as limiting cases. We argue that variation in (e.g. composition, or temperature, or pressure) may allow navigation of this phase space along continuous paths. This interpretation is shown to be consistent with the structural evolution of stacking-faulted $\textit{MX}_2$ systems as a function of temperature and composition. Our study highlights the potential for controlling composition/structure/property relationships amongst layered $\textit{MX}_2$ materials in ways that might not previously have been obvious.

cond-mat.mtrl-sci↗

arXiv2022

Direct interpretation of the X-ray and neutron 3D-$Δ$PDFs of yittria stabilized zirconia

Three dimensional difference pair distribution functions from X-ray and neutron diffraction experiments are reported for yttria stabilized zirconia (Zr$_{0.82}$Y$_{0.18}$O$_{1.91}$). We use a quantitative analysis of the signatures in the 3D-$Δ$PDFs to establish that oxygen ions neighbouring a vacancy shift by 0.515(5)~Å along $\langle 1,0,0 \rangle$ towards the vacancy while metal ions neighbouring a vacancy shift by 0.269(2)~Å along $\langle 1,1,1 \rangle$ away from the vacancy. The neutron 3D-$Δ$PDF shows a tendency for vacancies to cluster along $\langle \frac{1}{2},\frac{1}{2},\frac{1}{2}\rangle$, which results in 6-fold coordinated metal ions.

cond-mat.mtrl-sci↗

arXiv2022

Thermodynamic signatures of chain segmentation in dilute quasi-one dimensional Ising systems

Heat-capacity measurements are a useful tool for understanding the complex phase behaviour of systems containing one-dimensional motifs. Here we study the signature within such measurements of the incorporation of defects into quasi-one-dimensional (q-1D) systems. Using Monte Carlo simulations, we show that, on dilution by non-interacting sites, q-1D Ising models display a low-temperature signature not present in conventional three-dimensional models. Frustrated embeddings of 1D chains show similar features to unfrustrated embeddings, with the additional emergence of a finite ground-state entropy in the former, which arises from chain segmentation. We introduce a mean-field formulation which captures the low-temperature behaviour of the model. This theoretical framework is applied to the interpretation of experimental heat-capacity measurements of the Tb$_{1-ρ}$Y$_ρ$(HCOO)$_3$ family of magnetocalorics. We find good correspondence between simulation and experiment, establishing this system as a canonical example of dilute q-1D magnets.

cond-mat.stat-mech↗

arXiv2022

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 ($S=\frac{5}{2}$) occupy the nodes of a `trillium' hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration: 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 $\frac{1}{3}$-saturation magnetisation. We demonstrate that a simple nearest-neighbour Heisenberg antiferromagnet model accounts quantitatively for each observation, and hence Na[Mn(HCOO)$_3$] is the first experimental realisation of this model on the trillium net. We develop a mapping between this trillium model and that on the two-dimensional Shastry-Sutherland lattice, and demonstrate how both link geometric frustration within the classical spin liquid regime to a strong magnetocaloric response at low fields.

cond-mat.str-el↗

arXiv2022

Anomalous evolution of the magnetocaloric effect in dilute triangular Ising antiferromagnets $Tb_{1-x}Y_{x}(HCO_{2})_{3}$

We investigate the effects of diamagnetic doping in the solid-solution series $Tb_{1-x}Y_{x}(HCO_{2})_{3}$, in which the parent $Tb(HCO_{2})_{3}$ phase has previously been shown to host a combination of frustrated and quasi-1D physics, giving rise to a triangular Ising antiferromagnetic ground state that lacks long range 3D order. Heat capacity measurements show three key features: (i) a low temperature Schottky anomaly is observed, which is constant as a function of x; (ii) the transition temperature and associated entropy change are both surprisingly robust to diamagnetic doping; and (iii) an additional contribution at T < 0.4 K appears with increasing x. The origin of this unusual behaviour is rationalised in terms of the fragmentation of quasi-1D spin chains by the diamagnetic $Y^{3+}$ dopant. Magnetocaloric measurements show a nonlinear dependence on x. The mass-weighted magnetocaloric entropy decreases across the series from the promising values in $Tb(HCO_{2})_{3}$; however, the magnetocaloric entropy per magnetic $Tb^{3+}$ ion first decreases then increases with increasing x. Our results establish $Tb_{1-x}Y_{x}(HCO_{2})_{3}$ as a model system in which to explore the functional ramifications of dilution in a low-dimensional magnet.

cond-mat.str-el↗

arXiv2022

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

Periodic tilings can store information if individual tiles are decorated to lower their symmetry. Truchet tilings - the broad family of space-filling arrangements of such tiles - offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. Here, we show that the crystalline metal-organic framework [OZn$_4$][1,3-benzenedicarboxylate]$_3$ (TRUMOF-1) is an atomic-scale realisation 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.

cond-mat.mtrl-sci↗

arXiv2021

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 characterised 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 we demonstrate 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. We use as the basis of our proof-of-concept study a toy model based on strongly-correlated disorder in diammine mercury(II) halides.

cond-mat.dis-nn↗

arXiv2021

Structural complexity in Prussian blue analogues

We survey the most important kinds of structural complexity in Prussian blue analogues, their implications for materials function, and how they might be controlled through judicious choice of composition. We focus on six particular aspects: octahedral tilts, A-site `slides', Jahn--Teller distortions, A-site species and occupancy, hexacyanometallate vacancies, and framework hydration. The promising K-ion cathode material K$_x$Mn[Fe(CN)$_6$]$_y$ serves as a recurrent example that illustrates many of these different types of complexity. Our article concludes with a discussion of how the interplay of various distortion mechanisms might be exploited to optimise the performance of this and other related systems, so as to aid in the design of next-generation PBA materials.

cond-mat.mtrl-sci↗

arXiv2020

Hybrid Perovskites, Metal--Organic Frameworks, and Beyond: Unconventional Degrees of Freedom in Molecular Frameworks

The structural degrees of freedom of a material are the various distortions most straightforwardly activated by external stimuli. A highly successful design strategy in materials chemistry involves controlling these individual distortions to produce useful functional responses. In a ferroelectric such as lead titanate, for example, the key degree of freedom involves displacements of Pb$^{2+}$; by coupling these together, the system interacts with electric fields. An exciting development has been to exploit the interplay between different distortions: $e.g.$ generating polarisation by combining different polyhedral rotations. Thus, degrees of freedom act as geometric `elements' that can be combined to engineer materials with interesting properties. Just as the discovery of new elements diversified chemical space, identifying new types of structural degrees of freedom is a key strategy for developing new functional materials. In this context, molecular frameworks are a fertile source of unanticipated distortion types, many of which have no parallel in conventional solid-state chemistry. Framework materials are solids whose structures are assembled from nodes and linkers to form scaffolding-like networks. These structures usually contain cavities, which may host additional ions for charge balance. In the well-established systems---such as lead titanate---these components are all atomic, but in molecular frameworks, at least one ion is molecular. Here, we survey the unconventional degrees of freedom introduced through the replacement of atoms by molecules. Our motivation is to understand the role these new distortions play in different materials properties. The various degrees of freedom are summarised and described in the context of experimental examples. We highlight a number of directions for future research, which demonstrate the extraordinary possibilities for this nascent field.

cond-mat.mtrl-sci↗

arXiv2020

Nature of Partial Magnetic Order in the Frustrated Antiferromagnet Gd2Ti2O7

Partially-ordered magnets are distinct from both spin liquids and conventional ordered magnets because order and disorder coexist in the same magnetic phase. Here, we determine the nature of partial order in the canonical frustrated pyrochlore antiferromagnet Gd$_2$Ti$_{2}$O$_{7}$. Using single-crystal neutron-diffraction measurements in applied magnetic field, magnetic symmetry analysis, inelastic neutron-scattering measurements, and spin-wave modeling, we show that its low-temperature magnetic structure involves two propagation vectors (2-$\mathbf{k}$ structure) with suppressed ordered magnetic moments and enhanced spin-wave fluctuations. Our experimental results support theoretical predictions of thermal fluctuation-driven order in Gd$_{2}$Ti$_{2}$O$_{7}$.

cond-mat.str-el↗

arXiv2020

Mechanisms for collective inversion-symmetry breaking in dabconium perovskite ferroelectrics

Dabconium hybrid perovskites include a number of recently-discovered ferroelectric phases with large spontaneous polarisations. The origin of ferroelectric response has been rationalised in general terms in the context of hydrogen bonding, covalency, and strain coupling. Here we use a combination of simple theory, Monte Carlo simulations, and density functional theory calculations to assess the ability of these microscopic ingredients---together with the always-present through-space dipolar coupling---to account for the emergence of polarisation in these particular systems whilst not in other hybrid perovskites. Our key result is that the combination of A-site polarity, preferred orientation along $\langle111\rangle$ directions, and ferroelastic strain coupling drives precisely the ferroelectric transition observed experimentally. We rationalise the absence of polarisation in many hybrid perovskites, and arrive at a set of design rules for generating FE examples beyond the dabconium family alone.

cond-mat.mtrl-sci↗

arXiv2020

Understanding the Geometric Diversity of Inorganic and Hybrid Frameworks through Structural Coarse-Graining

Much of our understanding of complex structures is based on simplification: for example, metal-organic frameworks are often discussed in the context of "nodes" and "linkers", allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, by combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of "coarse-graining" atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB2 networks - including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density.

cond-mat.mtrl-sci↗

arXiv2019

Designing Disorder into Crystalline Materials

Crystals are a state of matter characterised 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 at the disposal of materials chemists that allow 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 to function in responsive media, thermoelectrics, topological phases, and information storage.

cond-mat.mtrl-sci↗

arXiv2019

Hidden Diversity of Vacancy Networks in Prussian Blue Analogues

Prussian blue analogues (PBAs) are a broad and important family of microporous inorganic solids, famous for their gas storage, metal-ion immobilisation, proton conduction, and stimuli-dependent magnetic, electronic and optical properties. The family also includes the widely-used double-metal cyanide (DMC) catalysts and the topical hexacyanoferrate/hexacyanomanganate (HCF/HCM) battery materials. Central to the various physical properties of PBAs is the ability to transport mass reversibly, a process made possible by structural vacancies. Normally presumed random, vacancy arrangements are actually crucially important because they control the connectivity of the micropore network, and hence diffusivity and adsorption profiles. The long-standing obstacle to characterising PBA vacancy networks has always been the relative inaccessibility of single-crystal samples. Here we report the growth of single crystals of a range of PBAs. By measuring and interpreting their X-ray diffuse scattering patterns, we identify for the first time a striking diversity of non-random vacancy arrangements that is hidden from conventional crystallographic analysis of powder samples. Moreover, we show that this unexpected phase complexity can be understood in terms of a remarkably simple microscopic model based on local rules of electroneutrality and centrosymmetry. The hidden phase boundaries that emerge demarcate vacancy-network polymorphs with profoundly different micropore characteristics. Our results establish a clear foundation for correlated defect engineering in PBAs as a means of controlling storage capacity, anisotropy, and transport efficiency.

cond-mat.mtrl-sci↗

arXiv2019

Room temperature spin-ice physics in cadmium cyanide

Spin-ices are frustrated magnets that support a particularly rich variety of emergent physics. Typically, it is the interplay of magnetic dipole interactions, spin anisotropy, and geometric frustration on the pyrochlore lattice that drives spin-ice formation. The relevant physics occurs at temperatures commensurate with the magnetic interaction strength, which for most systems is 1--5\,K. This low energy scale poses severe challenges for experimental studies of spin-ices and the practical exploitation of their unusual properties. Here, we show that non-magnetic cadmium cyanide (Cd(CN)$_2$) exhibits analogous behaviour to magnetic spin-ices, but does so on a temperature scale that is nearly two orders of magnitude greater. The electric dipole moments of cyanide ions in Cd(CN)$_2$ assume the role of magnetic pseudospins, with the difference in energy scale reflecting the increased strength of electric \emph{vs} magnetic dipolar interactions. As a result, spin-ice physics influences the structural behaviour of Cd(CN)$_2$ even at room temperature.

cond-mat.mtrl-sci↗

arXiv2018

Negative Hydration Expansion in ZrW2O8: 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$_8$. 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$_8$ is heavily disordered, with each configuration of strings forming a dense aperiodic `spaghetti'. This new connectivity contracts the unit cell \emph{via} large shifts in the Zr and W atom positions. Fluctuations of the undistorted parent structure towards this spaghetti phase emerge as the key NTE phonon modes in ZrW$_2$O$_8$ itself. The large relative density of NTE phonon modes in ZrW$_2$O$_8$ actually reflect the degeneracy of volume-contracting spaghetti excitations, itself a function of the particular topology of this remarkable material.

cond-mat.mtrl-sci↗