arXiv subjects

Andrew J. Morris

Publications and source records attributed to Andrew J. Morris.

At least 19 recordsLinked to original sources

arXiv2026

Hierarchical Crystal Structure Prediction of Zeolitic Imidazolate Frameworks Using DFT and Machine-Learned Interatomic Potentials

Crystal structure prediction (CSP) is emerging as a powerful method for the computational design of metal-organic frameworks (MOFs). In this article we employ CSP to perform high-throughput exploration of the crystal energy landscape of zinc imidazolate (ZnIm2). As the most polymorphic member of the zeolitic imidazolate framework (ZIF) family, ZnIm2 has at least 24 reported structural and topological forms, and new polymorphs still being regularly discovered. With the aid of custom-trained machine-learned interatomic potentials (MLIPs) we have performed a high-throughput sampling of over 3 million randomly-generated crystal packing arrangements and identified 9609 energy minima characterized by 1484 network topologies, including 855 topologies that have not been reported before. All but one experimentally-reported structures of ZnIm2, falling within the search boundaries, were ultimately matched with the predicted structures, demonstrating the power of the CSP method in sampling experimentally-relevant ZIF structures. Finally, through a combination of topological analysis, density and porosity considerations, we have identified a set of structures representing promising targets for future experimental screening. as well as demonstrated how structures of mechanochemically-synthesized MOFs could be identified via matching experimental powder diffraction patterns with simulated patterns from the predicted structures.

cond-mat.mtrl-sci↗

arXiv2025

Tangential approach in the Dirichlet problem for elliptic equations

It is well-known that solvability of the $\mathrm{L}^{p}$-Dirichlet problem for elliptic equations $Lu:=-\mathrm{div}(A\nabla u)=0$ with real-valued, bounded and measurable coefficients $A$ on Lipschitz domains $Ω\subset\mathbb{R}^{1+n}$ is characterised by a quantitative absolute continuity of the associated $L$-harmonic measure. We prove that this local $A_{\infty}$ property is sufficient to guarantee that the nontangential convergence afforded to $\mathrm{L}^{p}$ boundary data actually improves to a certain \emph{tangential} convergence when the data has additional (Sobolev) regularity. Moreover, we obtain sharp estimates on the Hausdorff dimension of the set on which such convergence can fail. This extends results obtained by Dorronsoro, Nagel, Rudin, Shapiro and Stein for classical harmonic functions in the upper half-space.

math.AP↗

arXiv2025

AcceleratedKernels.jl: Cross-Architecture Parallel Algorithms from a Unified, Transpiled Codebase

AcceleratedKernels.jl is introduced as a backend-agnostic library for parallel computing in Julia, natively targeting NVIDIA, AMD, Intel, and Apple accelerators via a unique transpilation architecture. Written in a unified, compact codebase, it enables productive parallel programming with minimised implementation and usage complexities. Benchmarks of arithmetic-heavy kernels show performance on par with C and OpenMP-multithreaded CPU implementations, with Julia sometimes offering more consistent and predictable numerical performance than conventional C compilers. Exceptional composability is highlighted as simultaneous CPU-GPU co-processing is achievable - such as CPU-GPU co-sorting - with transparent use of hardware-specialised MPI implementations. Tests on the Baskerville Tier 2 UK HPC cluster achieved world-class sorting throughputs of 538-855 GB/s using 200 NVIDIA A100 GPUs, comparable to the highest literature-reported figure of 900 GB/s achieved on 262,144 CPU cores. The use of direct NVLink GPU-to-GPU interconnects resulted in a 4.93x speedup on average; normalised by a combined capital, running and environmental cost, communication-heavy HPC tasks only become economically viable on GPUs if GPUDirect interconnects are employed.

cs.DC↗

arXiv2025

Boundary value problems and Hardy spaces for singular Schrödinger equations with block structure

We obtain Riesz transform bounds and characterise operator-adapted Hardy spaces to solve boundary value problems for singular Schrödinger equations $-\mathrm{div}(A\nabla u)+aVu=0$ in the upper half-space $\mathbb{R}^{1+n}_{+}$ with boundary dimension $n\geq 3$. The coefficients $(A,a,V)$ are assumed to be independent of the transversal direction to the boundary, and consist of a complex-elliptic pair $(A,a)$ that is bounded and measurable with a certain block structure, and a non-negative singular potential $V$ in the reverse Hölder class $\mathrm{RH}^{q}(\mathbb{R}^{n})$ for $q\geq \max\{\frac{n}{2},2\}$. This block structure is significant because it allows for coefficients that are not symmetric but for which $\mathrm{L}^{2}(\mathbb{R}^{n})$-solvability persists due to recently obtained Kato square root type estimates. We find extrapolation intervals for exponents $p$ around $2$ on which the Dirichlet problem is well-posed for boundary data in $\mathrm{L}^{p}(\mathbb{R}^{n})$, and the associated Regularity problem is well-posed for boundary data in Sobolev spaces $\dot{\mathcal{V}}^{1,p}(\mathbb{R}^{n})$ that are adapted to the potential $V$, when $p>1$. The well-posedness of these Dirichlet problems and related estimates then allow us to solve the corresponding Neumann problem with boundary data in $\mathrm{L}^{p}$. The results permit boundary data in the Dziubanski--Zienkiewicz Hardy space $\mathrm{H}^{1}_{V}(\mathbb{R}^{n})$ and adapted Hardy--Sobolev spaces $\dot{\mathrm{H}}^{1,p}_{V}(\mathbb{R}^{n})$ when $p\leq 1$. We also obtain comparability of square functions and nontangential maximal functions for the solutions with their boundary data.

math.AP↗

arXiv2024

Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data

We develop a holomorphic functional calculus for first-order operators $DB$ to solve boundary value problems for Schrödinger equations $-\mathrm{div}\, A \nabla u + a V u = 0$ in the upper half-space $\mathbb{R}^{n+1}_+$ with $n\in\mathbb{N}$. This relies on quadratic estimates for $DB$, which are proved for coefficients $A,a,V$ that are independent of the transversal direction to the boundary, and comprised of a complex-elliptic pair $(A,a)$ that are bounded and measurable, and a singular potential $V$ in either $L^{n/2}(\mathbb{R}^n)$ or the reverse Hölder class $B^{q}(\mathbb{R}^n)$ with $q\geq\max\{\tfrac{n}{2},2\}$. In the latter case, square function bounds are also shown to be equivalent to non-tangential maximal function bounds. This allows us to prove that the (Dirichlet) Regularity and Neumann boundary value problems with $L^2(\mathbb{R}^n)$-data are well-posed if and only if certain boundary trace operators defined by the functional calculus are isomorphisms. We prove this property when the principal coefficient matrix $A$ has either a Hermitian or block structure. More generally, the set of all complex coefficients for which the boundary value problems are well-posed is shown to be open.

math.AP↗

arXiv2024

Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems

Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius. As compared to earlier results, Ricci curvature is only assumed to be bounded from below, and the weight is only assumed to be locally in A^2. The Kato square root estimate is proved under this weaker assumption. On compact Lipschitz manifolds we prove solvability estimates for solutions to degenerate elliptic systems with not necessarily self-adjoint coefficients, and with Dirichlet, Neumann and Atiyah-Patodi-Singer boundary conditions.

math.AP↗

arXiv2024

Developments and applications of the OPTIMADE API for materials discovery, design, and data exchange

The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the upcoming v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development.

cond-mat.mtrl-sci↗

arXiv2024

Structure prediction of stable sodium germanides at 0 and 10 GPa

In this work we used $\textit{ab-initio}$ random structure searching (AIRSS) to carry out a systematic search for crystalline Na-Ge materials at both 0 and 10 GPa. The high-throughput structural relaxations were accelerated using a machine-learned interatomic potential (MLIP) fit to density-functional theory (DFT) reference data, allowing $\sim$1.5 million structures to be relaxed. At ambient conditions we predict three new Zintl phases, Na$_3$Ge$_2$, Na$_2$Ge and Na$_9$Ge$_4$, to be stable and a number of Ge-rich layered structures to lie in close proximity to the convex hull. The known Na$_δ$Ge$_{34}$ clathrate and Na$_4$Ge$_{13}$ host-guest structures are found to be relatively stabilized at higher temperature by vibrational contributions to the free energy. Overall, the low energy phases exhibit exceptional structural diversity, with the expected mixture of covalent and ionic bonding confirmed using the electron-localisation function (ELF). The local Ge structural motifs present at each composition were determined using Smooth Overlap of Atomic Positions (SOAP) descriptors and the Ge-K edge was simulated for representatives of each motif, providing a direct link to experimental x-ray absorption spectroscopy (XAS). Two Ge-rich phases are predicted to be stable at 10 GPa; NaGe$_3$ and NaGe$_2$ have simple kagome and simple hexagonal Ge lattices respectively with Na contained in the pores. NaGe$_3$ is isostructural with the MgB$_3$ and MgSi$_3$ family of kagome superconductors and remains dynamically stable at 0 GPa. Removing the Na from NaGe$_2$ results in the hexagonal lonsdalite Ge allotrope, which has a direct band gap.

cond-mat.mtrl-sci↗

arXiv2023

The importance of electronic correlations in exploring the exotic phase diagram of layered Li$_x$MnO$_2$

Using ab initio dynamical mean-field theory we explore the electronic and magnetic states of layered Li$_x$MnO$_2$ as a function of $x$, the state of charge. Constructing real-space Wannier projections of Kohn-Sham orbitals based on the low-energy subspace of Mn $3d$ states and solving a multi-impurity problem, our approach focuses on local correlations at Mn sites. The antiferromagnetic insulating state in LiMnO$_2$ has a moderate Néel temperature of $T_N=296\,K$ in agreement with experimental studies. Upon delithiation the system proceeds through a number of states: ferrimagnetic correlated metals at $x$=0.92, 0.83; multiple charge disproportionated ferromagnetic correlated metals with large quasiparticle weights at $x$=0.67, 0.50, 0.33; ferromagnetic metals with small quasiparticle weights at $x$=0.17, 0.08 and an antiferromagnetic insulator for the fully delithiated state, $x=0.0$. At moderate states of charge, $x=0.67-0.33$, a mix of +3/+4 formal oxidation states of Mn is observed, while the overall nominal oxidation of Mn state changes from +3 in LiMnO$_2$ to +4 in MnO$_2$. In all these cases the high-spin state emerges as the most likely state in our calculations considering the full $d$~manifold of Mn based on the proximity of $e_g$ levels in energy to $t_{2g}$. The quasiparticle peaks in the correlated metallic states were attributed to polaronic states based on previous literature for similar isoelectronic JT driven materials, arising due to non-Fermi liquid type behaviour of the strongly correlated system.

cond-mat.str-el↗

arXiv2023

Low-dimensional metal-organic magnets as a route towards the S=2 Haldane phase

Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are connected by organic linkers, are promising candidates for next-generation quantum technologies. MOMs readily form low-dimensional structures, and so are ideal systems to realise physical examples of key quantum models, including the Haldane phase, where a topological excitation gap occurs in integer-spin antiferromagnetic (AFM) chains. Thus far the Haldane phase has only been identified for $S=1$, with $S \geq 2$ still unrealised because the larger spin imposes more stringent requirements on the magnetic interactions. Here, we report the structure and magnetic properties of CrCl$_2$(pym) (pym=pyrimidine), a new quasi-1D $S=2$ AFM MOM. We show, using X-ray and neutron diffraction, bulk property measurements, density-functional theory calculations and inelastic neutron spectroscopy (INS) that CrCl$_2$(pym) consists of AFM CrCl$_2$ spin chains ($J_1=-1.13(4)\;$meV) which are weakly ferromagnetically coupled through bridging pym ($J_2=0.10(2)\;$meV), with easy-axis anisotropy ($D=-0.15(3)\;$meV). We find that although small compared to $J_1$, these additional interactions are sufficient to prevent observation of the Haldane phase in this material. Nevertheless, the proximity to the Haldane phase together with the modularity of MOMs suggests that layered Cr(II) MOMs are a promising family to search for the elusive $S=2$ Haldane phase.

cond-mat.str-el↗

arXiv2022

Finite Temperature Effects on the X-ray Absorption Spectra of Crystalline Aluminas from First Principles

By including phonon-assisted transitions within plane-wave DFT methods for calculating the X-ray absorption spectrum (XAS) we obtain the Al K-edge XAS at 300 K for two Al$_2$O$_3$ phases. The 300 K XAS reproduces the pre-edge peak for $α$-Al$_2$O$_3$, which is not visible at the static-lattice level of approximation. The 300 K XAS for $γ$-Al$_2$O$_3$ correctly describes two out of the three experimental peaks. We show that the second peak arises from 1s to mixed $s$-$p$ transitions and is absent in the 0 K XAS. This letter serves as a basis for future applications, as the method is generalizable to any atom and edge.

cond-mat.mtrl-sci↗

arXiv2021

OPTIMADE, an API for exchanging materials data

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification.

cond-mat.mtrl-sci↗

arXiv2020

Unboundedness of potential dependent Riesz transforms for totally irregular measures

We prove that, for totally irregular measures $μ$ on $\mathbb{R}^{d}$ with $d\geq3$, the $(d-1)$-dimensional Riesz transform $$ T_{A,μ}^{V}f(x) = \int_{\mathbb{R}^d} \nabla_{1}\mathcal{E}_{A}^{V}(x,y) f(y) \, d μ(y) $$ adapted to the Schrödinger operator $L_{A}^{V} = -\mathrm{div} A \nabla + V$ with fundamental solution $\mathcal{E}_{A}^{V}$ is not bounded on $L^{2}(μ)$. This generalises recent results obtained by Conde-Alonso, Mourgoglou and Tolsa for free-space elliptic operators with Hölder continuous coefficients $A$ since it allows for the presence of potentials $V$ in the reverse Hölder class $RH_{d}$. We achieve this by obtaining new exponential decay estimates for the kernel $\nabla_{1} \mathcal{E}_{A}^{V}$ as well as Hölder regularity estimates at local scales determined by the potential's critical radius function.

math.CA↗

arXiv2020

Computational Investigation of Copper Phosphides as Conversion Anodes for Lithium-Ion Batteries

Using first principles structure searching with density-functional theory (DFT) we identify a novel $Fm\bar{3}m$ phase of Cu$_2$P and two low-lying metastable structures, an $I\bar{4}3d$--Cu$_3$P phase, and a $Cm$--Cu$_3$P$_{11}$ phase. The computed pair distribution function of the novel $Cm$--Cu$_3$P$_{11}$ phase shows its structural similarity to the experimentally identified $Cm$--Cu$_2$P$_7$ phase. The relative stability of all Cu--P phases at finite temperatures is determined by calculating the Gibbs free energy using vibrational effects from phonon modes at 0 K. From this, a finite-temperature convex hull is created, on which $Fm\bar{3}m$--Cu$_2$P is dynamically stable and the Cu$_{3-x}$P ($x < 1$) defect phase $Cmc2_1$--Cu$_8$P$_3$ remains metastable (within 20 meV/atom of the convex hull) across a temperature range from 0 K to 600 K. Both CuP$_2$ and Cu$_3$P exhibit theoretical gravimetric capacities higher than contemporary graphite anodes for Li-ion batteries; the predicted Cu$_2$P phase has a theoretical gravimetric capacity of 508 mAh/g as a Li-ion battery electrode, greater than both Cu$_3$P (363 mAh/g) and graphite (372 mAh/g). Cu$_2$P is also predicted to be both non-magnetic and metallic, which should promote efficient electron transfer in the anode. Cu$_2$P's favorable properties as a metallic, high-capacity material suggest its use as a future conversion anode for Li-ion batteries; with a volume expansion of 99% during complete cycling, Cu$_2$P anodes could be more durable than other conversion anodes in the Cu--P system with volume expansions greater than 150%.

cond-mat.mtrl-sci↗

arXiv2019

Cation Disorder and Lithium Insertion Mechanism of Wadsley--Roth Crystallographic Shear Phases

Wadsley--Roth crystallographic shear phases form a family of compounds that have attracted attention due to their excellent performance as lithium-ion battery electrodes. The complex crystallographic structure of these materials poses a challenge for first-principles computational modelling and hinders the understanding of their structural, electronic and dynamic properties. In this article, we study three different niobium-tungsten oxide crystallographic shear phases (Nb$_{12}$WO$_{33}$, Nb$_{14}$W$_{3}$O$_{44}$, Nb$_{16}$W$_5$O$_{55}$) using an enumeration-based approach and first-principles density-functional theory calculations. We report common principles governing the cation disorder, lithium insertion mechanism, and electronic structure of these materials. Tungsten preferentially occupies tetrahedral and block-central sites within the block-type crystal structures. The lithium insertion proceeds via a three-step mechanism, associated with an anisotropic evolution of the host lattice. Our calculations reveal an important connection between long-range and local structural changes: in the second step of the mechanism, the removal of local structural distortions leads to the contraction of the lattice along specific crystallographic directions, buffering the volume expansion of the material. Niobium-tungsten oxide shear structures host small amounts of localised electrons during initial lithium insertion due to the confining effect of the blocks, but quickly become metallic upon further lithiation. We argue that the combination of local, long-range, and electronic structural evolution over the course of lithiation is beneficial to the performance of these materials as battery electrodes. The mechanistic principles we establish arise from the compound-independent crystallographic shear structure, and are therefore likely to apply to Ti/Nb oxide or pure Nb oxide shear phases.

cond-mat.mtrl-sci↗

arXiv2019

First-Principles Study of Localised and Delocalised Electronic States in Crystallographic Shear Phases of Niobium Oxide

Crystallographic shear phases of niobium oxide form an interesting family of compounds that have received attention both for their unusual electronic and magnetic properties, as well as their performance as intercalation electrode materials for lithium-ion batteries. Here, we present a first-principles density-functional theory study of the electronic structure and magnetism of H-Nb$_2$O$_5$, Nb$_{25}$O$_{62}$, Nb$_{47}$O$_{116}$, Nb$_{22}$O$_{54}$, and Nb$_{12}$O$_{29}$. These compounds feature blocks of niobium-oxygen octahedra as structural units, and we show that this block structure leads to a coexistence of flat and dispersive energy bands, corresponding to localised and delocalised electronic states. Electrons localise in orbitals spanning multiple niobium sites in the plane of the blocks. Localised and delocalised electronic states are both effectively one-dimensional and are partitioned between different types of niobium sites. Flat bands associated with localised electrons are present even at the GGA level, but a correct description of the localisation requires the use of GGA+U or hybrid functionals. We discuss the experimentally observed electrical and magnetic properties of niobium suboxides in light of our results, and argue that their behaviour is similar to that of $n$-doped semiconductors, but with a limited capacity for localised electrons. When a threshold of one electron per block is exceeded, metallic electrons are added to existing localised electrons. We propose that this behaviour of shear phases is general for any type of $n$-doping, and should transfer to doping by alkali metal (lithium) ions during operation of niobium oxide-based battery electrodes. Future directions for theory and experiment on mixed-metal shear phases are suggested.

cond-mat.mtrl-sci↗

arXiv2018

Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations

We prove that the Dirichlet problem for degenerate elliptic equations $\mathrm{div}(A \nabla u) = 0$ in the upper half-space $(x,t)\in \mathbb{R}^{n+1}_+$ is solvable when $n\geq2$ and the boundary data is in $L^p_μ(\mathbb{R}^n)$ for some $p<\infty$. The coefficient matrix $A$ is only assumed to be measurable, real-valued and $t$-independent with a degenerate bound and ellipticity controlled by an $A_2$-weight $μ$. It is not required to be symmetric. The result is achieved by proving a Carleson measure estimate for all bounded solutions in order to deduce that the degenerate elliptic measure is in $A_\infty$ with respect to the $μ$-weighted Lebesgue measure on $\mathbb{R}^n$. The Carleson measure estimate allows us to avoid applying the method of $ε$-approximability, which simplifies the proof obtained recently in the case of uniformly elliptic coefficients. The results have natural extensions to Lipschitz domains.

math.AP↗

arXiv2017

Single-Atom Scale Structural Selectivity in Te Nanowires Encapsulated inside Ultra-Narrow, Single-Walled Carbon Nanotubes

Extreme nanowires (ENs) represent the ultimate class of crystals: They are the smallest possible periodic materials. With atom-wide motifs repeated in one dimension (1D), they offer a privileged perspective into the Physics and Chemistry of low-dimensional systems. Single-walled carbon nanotubes (SWCNTs) provide ideal environments for the creation of such materials. Here we present a comprehensive study of Te ENs encapsulated inside ultra- narrow SWCNTs with diameters between 0.7 nm and 1.1 nm. We combine state-of-the-art imaging techniques and 1D-adapted ab initio structure prediction to treat both confinement and periodicity effects. The studied Te ENs adopt a variety of structures, exhibiting a true 1D realisation of a Peierls structural distortion and transition from metallic to insulating behaviour as a function of encapsulating diameter. We analyse the mechanical stability of the encapsulated ENs and show that nanoconfinement is not only a useful means to produce ENs, but may actually be necessary, in some cases, to prevent them from disintegrating. The ability to control functional properties of these ENs with confinement has numerous applications in future device technologies, and we anticipate that our study will set the basic paradigm to be adopted in the characterisation and understanding of such systems.

cond-mat.mtrl-sci↗