Searcharxiv⌕ Search

arXiv subjects

Andrew J. Morris

Publications and source records attributed to Andrew J. Morris.

35 records · Page 2Linked to original sources
arXiv2017

Encapsulated Nanowires: Boosting Electronic Transport in Carbon Nanotubes

The electrical conductivity of metallic carbon nanotubes (CNTs) quickly saturates with respect to bias voltage due to scattering from a large population of optical phonons. Decay of these dominant scatterers in pristine CNTs is too slow to offset an increased generation rate at high voltage bias. We demonstrate from first principles that encapsulation of 1D atomic chains within a single-walled CNT can enhance decay of "hot" phonons by providing additional channels for thermalisation. Pacification of the phonon population growth reduces electrical resistivity of metallic CNTs by 51% for an example system with encapsulated beryllium.

cond-mat.mtrl-sci↗
arXiv2016

Structures and finite-temperature abundances of defects in In$_2$O$_3$-II from first-principles calculations

We have studied intrinsic defect complexes in In$_2$O$_3$ using ab initio random structure searching (AIRSS). Our first-principles density-functional-theory calculations predict the thermodynamic stability of several novel defect structures. We combine the static lattice energy and harmonic vibrational energy with the often-neglected configurational entropy to construct the free energy, which is minimised to predict defect abundances at finite temperatures. We predict that some of our new defect structures - in particular our {In,2V$_\mathrm{O}$} and {2In,3V$_\mathrm{O}$} defects - can exist in significant abundances at finite temperatures, and their densities of electronic states indicate that they could play an important role in the unexpectedly high density of n-type charge carriers observed in In$_2$O$_3$.

cond-mat.mtrl-sci↗
arXiv2015

$\textit{Ab initio}$ study of phosphorus anodes for lithium and sodium-ion batteries

Phosphorus has received recent attention in the context of high-capacity and high-rate anodes for lithium and sodium-ion batteries. Here, we present a first principles structure prediction study combined with NMR calculations which gives us insights into its lithiation/sodiation process. We report a variety of new phases phases found by AIRSS and the atomic species swapping methods. Of particular interest, a stable Na$_5$P$_4$-C2/m structure and locally stable structures found less than 10 meV/f.u. from the convex hull, such as Li$_4$P$_3$-P2$_1$2$_1$2$_1$, NaP$_5$-Pnma and Na$_4$P$_3$-Cmcm. The mechanical stability of Na$_5$P$_4$-C2/m and Li$_4$P$_3$-P2$_1$2$_1$2$_1$ has been studied by first principles phonon calculations . We have calculated average voltages which suggests that black phosphorus (BP) can be considered as a safe anode in lithium-ion batteries due to its high lithium insertion voltage, 1.5 V; moreover, BP exhibits a relatively low theoretical volume expansion compared with other intercalation anodes, 216\% ($ΔV/V$). We identify that specific ranges in the calculated shielding can be associated with specific ionic arrangements, results which play an important role in the interpretation of NMR spectroscopy experiments. Since the lithium-phosphides are found to be insulating even at high lithium concentrations we show that Li-P-doped phases with aluminium have electronic states at the Fermi level suggesting that using aluminium as a dopant can improve the electrochemical performance of P anodes.

cond-mat.mtrl-sci↗
arXiv2014

Thermodynamically stable lithium silicides and germanides from density-functional theory calculations

Density-functional-theory (DFT) calculations have been performed on the Li-Si and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play an important technological rôle as Li-ion battery (LIB) anodes. The calculations comprise structural optimisations on crystal structures obtained by swapping atomic species to Li-Si and Li-Ge from the X-Y structures in the International Crystal Structure Database, where X={Li,Na,K,Rb,Cs} and Y={Si,Ge,Sn,Pb}. To complement this at various Li-Si and Li-Ge stoichiometries, ab initio random structure searching (AIRSS) was also performed. Between the ground-state stoichiometries, including the recently found Li$_{17}$Si$_{4}$ phase, the average voltages were calculated, indicating that germanium may be a safer alternative to silicon anodes in LIB, due to its higher lithium insertion voltage. Calculations predict high-density Li$_1$Si$_1$ and Li$_1$Ge$_1$ $P4/mmm$ layered phases which become the ground state above 2.5 and 5 GPa respectively and reveal silicon and germanium's propensity to form dumbbells in the Li$_x$Si, $x=2.33-3.25$ stoichiometry range. DFT predicts the stability of the Li$_{11}$Ge$_6$ $Cmmm$, Li$_{12}$Ge$_7$ $Pnma$ and Li$_7$Ge$_3$ $P32_12$ phases and several new Li-Ge compounds, with stoichiometries Li$_5$Ge$_2$, Li$_{13}$Ge$_5$, Li$_8$Ge$_3$ and Li$_{13}$Ge$_4$.

cond-mat.mtrl-sci↗
arXiv2014

Square Function Estimates in Spaces of Homogeneous Type and on Uniformly Rectifiable Euclidean Sets

We announce a local $T(b)$ theorem, an inductive scheme, and $L^p$ extrapolation results for $L^2$ square function estimates related to the analysis of integral operators that act on Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The inductive scheme is a natural application of the local $T(b)$ theorem and it implies the stability of $L^2$ square function estimates under the so-called big pieces functor. In particular, this analysis implies $L^p$ and Hardy space square function estimates for integral operators on uniformly rectifiable subsets of the Euclidean space.

math.AP↗
arXiv2013

The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\infty$ coefficients

We consider layer potentials associated to elliptic operators $Lu=-{\rm div}(A \nabla u)$ acting in the upper half-space $\mathbb{R}^{n+1}_+$ for $n\geq 2$, or more generally, in a Lipschitz graph domain, where the coefficient matrix $A$ is $L^\infty$ and $t$-independent, and solutions of $Lu=0$ satisfy interior estimates of De Giorgi/Nash/Moser type. A "Calderón-Zygmund" theory is developed for the boundedness of layer potentials, whereby sharp $L^p$ and endpoint space bounds are deduced from $L^2$ bounds. Appropriate versions of the classical "jump-relation" formulae are also derived. The method of layer potentials is then used to establish well-posedness of boundary value problems for $L$ with data in $L^p$ and endpoint spaces.

math.AP↗
arXiv2013

Lithiation of silicon via lithium Zintl-defect complexes

An extensive search for low-energy lithium defects in crystalline silicon using density-functional-theory methods and the ab initio random structure searching (AIRSS) method shows that the four-lithium-atom substitutional point defect is exceptionally stable. This defect consists of four lithium atoms with strong ionic bonds to the four under-coordinated atoms of a silicon vacancy defect, similar to the bonding of metal ions in Zintl phases. This complex is stable over a range of silicon environments, indicating that it may aid amorphization of crystalline silicon and form upon delithiation of the silicon anode of a Li-ion rechargeable battery.

cond-mat.mtrl-sci↗
arXiv2013

$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local $T(b)$ theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for $L^p$ and Hardy space versions of these estimates are also established. Moreover, we prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.

math.AP↗
arXiv2012

An ab initio study of intrinsic defects in zirconolite

Zirconolite, CaZrTi2O7, is a proposed ceramic for the use in disposal of highly active nuclear waste. Density functional theory (DFT) has been used, in conjunction with a random search technique, to identify the stable interstitial sites for the intrinsic defects in zirconolite. There is a significant dependence on charge states for the vacancy defect structures, with the formation of an O2 molecule in certain charge states of Ti and Zr vacancies. The low coordination of the oxygen ions provided sites on which DFT localised holes associated with the cation vacancies. The Frenkel defect energies, calculated from the combination of the vacancy and interstitial formation energies, show that the oxygen defects have a strong dependence on the chemical environment, with a range of 1.5 eV between the oxygen Frenkel pair energies.

cond-mat.mtrl-sci↗
arXiv2012

Energetics of hydrogen/lithium complexes in silicon analyzed using the Maxwell construction

We have studied hydrogen/lithium complexes in crystalline silicon using density-functional-theory methods and the ab initio random structure searching (AIRSS) method for predicting structures. A method based on the Maxwell construction and convex hull diagrams is introduced which gives a graphical representation of the relative stabilities of point defects in a crystal and enables visualization of the changes in stability when the chemical potentials are altered. We have used this approach to study lithium and hydrogen impurities in silicon, which models aspects of the anode material in the recently-suggested lithium-ion batteries. We show that hydrogen may play a role in these anodes, finding that hydrogen atoms bind to three-atom lithium clusters in silicon, forming stable {H,3Li} and {2H,3Li} complexes, while the {H,2Li} complex is almost stable.

cond-mat.mtrl-sci↗
arXiv2011

Local Hardy Spaces of Differential Forms on Riemannian Manifolds

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most exponential volume growth. In particular, if $D$ is the Hodge--Dirac operator on $M$ and $Δ=D^2$ is the Hodge--Laplacian, then the local geometric Riesz transform ${D(Δ+aI)^{-{1}/{2}}}$ has a bounded extension to $h^p_D$ for all $p\in[1,\infty]$, provided that $a>0$ is large enough compared to the exponential growth of $M$. A characterisation of $h^1_{\mathcal D}$ in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms $H^p_D(\wedge T^*M)$ introduced by Auscher, McIntosh and Russ.

math.DG↗
arXiv2011

The Kato Square Root Problem on Submanifolds

We solve the Kato square root problem for divergence form operators on complete Riemannian manifolds that are embedded in Euclidean space with a bounded second fundamental form. We do this by proving local quadratic estimates for perturbations of certain first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincaré inequality holds. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.

math.AP↗
arXiv2009

Ultracold atoms at unitarity within quantum Monte Carlo

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. The ratio of the energy of the interacting to the non-interacting gas for a system of 128 particles is calculated to be 0.4517(3) in VMC and 0.4339(1) in the more accurate DMC method. The spherically-averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, but the two-body density matrices and condensate fractions show some differences. Our best estimate of the condensate fraction of 0.51 is a little smaller than values from other quantum Monte Carlo calculations.

cond-mat.quant-gas↗
arXiv2009

Hydrogen/nitrogen/oxygen defect complexes in silicon from computational searches

Point defect complexes in crystalline silicon composed of hydrogen, nitrogen, and oxygen atoms are studied within density-functional theory (DFT). Ab initio Random Structure Searching (AIRSS) is used to find low-energy defect structures. We find new lowest-energy structures for several defects: the triple-oxygen defect, {3O}, triple oxygen with a nitrogen atom, {N, 3O}, triple nitrogen with an oxygen atom, {3N,O}, double hydrogen and an oxygen atom, {2H,O}, double hydrogen and oxygen atoms, {2H,2O} and four hydrogen/nitrogen/oxygen complexes, {H,N,O}, {2H,N,O}, {H,2N,O} and {H,N,2O}. We find that some defects form analogous structures when an oxygen atom is replaced by a NH group, for example, {H,N,2O} and {3O}, and {H,N} and {O}. We compare defect formation energies obtained using different oxygen chemical potentials and investigate the relative abundances of the defects.

cond-mat.mtrl-sci↗
arXiv2008

Hydrogen/silicon complexes in silicon from computational searches

Defects in crystalline silicon consisting of a silicon self-interstitial atom and one, two, three, or four hydrogen atoms are studied within density-functional theory (DFT). We search for low-energy defects by starting from an ensemble of structures in which the atomic positions in the defect region have been randomized. We then relax each structure to a minimum in the energy. We find a new defect consisting of a self-interstitial and one hydrogen atom (denoted by {I,H}) which has a higher symmetry and a lower energy than previously reported structures. We recover the {I,H_2} defect found in previous studies and confirm that it is the most stable such defect. Our best {I,H_3} defect has a slightly different structure and lower energy than the one previously reported, and our lowest energy {I,H_4} defect is different to those of previous studies.

cond-mat.mtrl-sci↗
arXiv2007

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, Σ-- and we obtain a systematic discrimination of these two effects by turning the vertex in Σon and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in Σleads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in Σis unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.

cond-mat.mtrl-sci↗