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We study Ti 1s near-edge spectroscopy in PbTiO$_3$ at various temperatures above and below its tetragonal-to-cubic phase transition, and in SrTiO$_3$ at room temperature. Ab initio molecular dynamics (AIMD) runs on 80-atom supercells are used to determine the average internal coordinates and their fluctuations. We determine that one vector local order parameter is the dominant contributor to changes in spectral features: the displacement of the Ti ion with respect to its axial O neighbors in each Cartesian direction, as these displacements enhance the cross section for transitions to E$_{\rm g}$-derived core-hole exciton levels. Using periodic five-atom structures whose relative Ti-O displacements match the root-mean-square values from the AIMD simulations, and core-hole Bethe-Salpeter equation (BSE) calculations, we quantitatively predict the respective Ti 1s near-edge spectra. Properly accounting for atomic fluctuations greatly improves the agreement between theoretical and experimental spectra. The evolution of relative strengths of spectral features vs temperature and electric field polarization vector are captured in considerable detail. This work shows that local structure can be characterized from first-principles sufficiently well to aid both the prediction and the interpretation of near-edge spectra, Comment: 10 pages

We use first-principles density functional theory total energy and linear response phonon calculations to compute the Helmholtz and Gibbs free energy as a function of temperature, pressure, and cell volume in the flexible metal-organic framework material MIL-53(Cr) within the quasiharmonic approximation. GGA and metaGGA calculations were performed, each including empirical van der Waals (vdW) forces under the D2, D3, or D3(BJ) parameterizations. At all temperatures up to 500 K and pressures from -30 MPa to 30 MPa, two minima in the free energy versus volume are found, corresponding to the narrow pore ($np$) and large pore ($lp$) structures. Critical positive and negative pressures are identified, beyond which there is only one free energy minimum. While all results overestimated the stability of the $np$ phase relative to the $lp$ phase, the best overall agreement with experiment is found for the metaGGA PBEsol+RTPSS+U+J approach with D3 or D3(BJ) vdW forces. For these parameterizations, the calculated free energy barrier for the $np$-$lp$ transition is only 3 to 6 kJ per mole of Cr$_4$(OH)$_4$(C$_8$H$_4$O$_4$)$_4$.

In previous work, molecular dynamics simulations based on a first-principles-derived effective Hamiltonian for $Pb_{1-X}(Sc_{1/2}Nb_{1/2})O_{3-X}$~ (PSN), with nearest-neighbor Pb-O divacancy pairs, was used to calculate $X_{\rm [Pb-O]}$~vs.~T, phase diagrams for PSN with: ideal rock-salt type chemical order; nanoscale chemical short-range order; and random chemical disorder. Here, we show that the phase diagrams should include additional regions in which a glassy relaxor-phase (or state) is predicted. With respect to phase diagram topology, these results strongly support the analogy between relaxors and magnetic spin-glass-systems.

We model the remarkable thin-film Ba-Ti-O structures formed by heat treatment of an initial perovskite BaTiO$_3$ thin film on a Pt(111) surface. All structures contain a rumpled Ti-O network with all Ti threefold coordinated with O, and with Ba occupying the larger. mainly Ti$_7$O$_7$, pores. The quasicrystal structure is a simple decoration of three types of tiles: square, triangle and 30 degree rhombus, with edge lengths 6.85 Angstroms, joined edge-to-edge in a quasicrystalline pattern; observed crystalline Ba-Ti-O structures are built from these and other tiles. Simulated STM images reproduce the patterns seen experimentally, and identify the bright protrusions as Ba atoms. The models are consistent with all experimental observations.

Water absorption in the metal-organic framework (MOF) material Cu-BTC, up to a concentration of 3.5 H$_2$O per Cu ion, is studied via density functional theory at the meta-GGA+U level. The stable arrangements of water molecules show chains of hydrogen-bonded water molecules and a tendency to form closed cages at high concentration. Water clusters are stabilized primarily by a combination of water-water hydrogen bonding and Cu-water oxygen interactions. Stability is further enhanced by van der Waals interactions, electric field enhancement of water-water bonding, and hydrogen bonding of water to framework oxygens. We hypothesize that the tendency to form such stable clusters explains the particularly strong affinity of water to Cu-BTC and related MOFs with exposed metal sites., Comment: 7 pages

First principles density functional theory DFT+U calculations and experimental neutron diffraction structure analyses were used to determine the low-temperature crystallographic and magnetic structure of bixbyite Mn2O3. The energies of various magnetic arrangements, calculated from first principles, were fit to a cluster-expansion model using a Bayesian method that overcomes a problem of underfitting caused by the limited number of input magnetic configurations. The model was used to predict the lowest-energy magnetic states. Experimental determination of magnetic structure benefited from optimized sample synthesis, which produced crystallite sizes large enough to yield a clear splitting of peaks in the neutron powder diffraction patterns, thereby enabling magnetic-structure refinements under the correct orthorhombic symmetry. The refinements employed group theory to constrain magnetic models. Computational and experimental analyses independently converged to similar ground states, with identical antiferromagnetic ordering along a principal magnetic axis and secondary ordering along a single orthogonal axis, differing only by a phase factor in the modulation patterns. The lowest-energy magnetic states are compromise solutions to frustrated antiferromagnetic interactions between certain corner-sharing MnO6 octahedra.

Density functional theory calculations are used to investigate a-MnO2, a structure containing a framework of corner and edge sharing MnO6 octahedra with tunnels in between. Placing K+ ions into the tunnels stabilizes a-MnO2 with respect to the rutile-structure b-MnO2 phase, in agreement with experiment. The computed magnetic structure has antiferromagnetic (ferromagnetic) Mn-Mn interactions between corner-sharing (edge-sharing) octahedra. Pure a-MnO2 is found to be a semiconductor with an indirect band gap of 1.3 eV. Water and related hydrides (OH-; H3O+) can also be accommodated in the tunnels; the equilibrium K-O distance increases with increasing oxygen hydride charge.

The structure of finite-area topological defects in graphene is described in terms of both the direct honeycomb lattice and its dual triangular lattice. Such defects are equivalent to cutting out a patch of graphene and replacing it with a different patch with the same number of dangling bonds. An important subset of these defects, bound by a closed loop of alternating 5- and 7-membered carbon rings, explains most finite-area topological defects that have been experimentally observed. Previously unidentified defects seen in scanning tunneling microscope (STM) images of graphene grown on SiC are identified as isolated divacancies or divacancy clusters.

Topological defects can affect the physical properties of graphene in unexpected ways. Harnessing their influence may lead to enhanced control of both material strength and electrical properties. Here we present a new class of topological defects in graphene composed of a rotating sequence of dislocations that close on themselves, forming grain boundary loops that either conserve the number of atoms in the hexagonal lattice or accommodate vacancy/interstitial reconstruction, while leaving no unsatisfied bonds. One grain boundary loop is observed as a "flower" pattern in scanning tunneling microscopy (STM) studies of epitaxial graphene grown on SiC(0001). We show that the flower defect has the lowest energy per dislocation core of any known topological defect in graphene, providing a natural explanation for its growth via the coalescence of mobile dislocations., Comment: 23 pages, 7 figures. Revised title; expanded; updated references

First-principles calculations were used to compute the dielectric permittivities of hypothetical [La,Sc]2O3 solid solutions in the cubic (bixbyite) and hexagonal La2O3 phases. Dielectric enhancement is predicted at small Sc concentrations due to the rattling ion effect. Similar calculations for a model amorphous La2O3 structure show little change in permittivity when a small amount of Sc is substituted for La. In this case, the local environment around the Sc changes in a way that compensates for the rattling ion effect., Comment: 4 pages, 3 figures

A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a model that underfits the data is generally used for this purpose. For arbitrarily precise data free from statistic noise, e.g. ab initio calculations, we argue that it is more appropriate to begin with a ensemble of models that overfit the data. Within a Bayesian framework, a most likely model can be defined that incorporates physical knowledge, provides error estimates for systems not included in the fit, and reproduces the original data exactly. We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3 solid solution., Comment: 10 pages, 3 figures, submitted to Physical Review Letters

A first-principles-based model is developed to investigate the influence of lead vacancies on the properties of relaxor ferroelectric Pb(Sc1/2Nb1/2)O3 (PSN). Lead vacancies generate large, inhomogeneous, electric fields that reduce barriers between energy minima for different polarization directions. This naturally explains why relaxors with significant lead vacancy concentrations have broadened dielectric peaks at lower temperatures, and why lead vacancies smear properties in the neighborhood of the ferroelectric transition in PSN. We also reconsider the conventional wisdom that lead vacancies reduce the magnitude of dielectric response., Comment: 11 pages, 1 figure

KTaO_3-based solid solutions exhibit a variety of interesting physical phenomena. To better understand these phenomena, we performed first-principles calculations on [K_{1-x}, Li_x]TaO_3 (KLT) and K[Ta_{1-x}, Nb_x]O_3 (KTN) supercells. Our results show Li displacements and potential barrier heights in KLT that are in excellent agreement with values obtained from experimental fits. Dramatic changes in B-site dynamical charges occur in KTN in response to changes in near neighbor (nn) coordination. These effects can be explained by heterogeneity in the local electronic dielectric permittivity., Comment: 4 figures

In this article, we motivate the detailed comparison of the physical properties of individual configurations of a ferroelectric solid solution as a means toward developing first principles models for these systems. We compare energies, dielectric constants epsilon_infinity, mode effective charges of local polar distortions, and the zero temperature piezoelectric behavior of several ordered Pb_3GeTe_4 supercells. Cluster expansions of these properties show the importance of second-neighbor effects, which can be related to symmetry-preserving relaxation and its effect on the symmetry breaking polar instabilities., Comment: 11 pages, LaTeX (aipproc), 1 eps figure

A method for the calculation of the temperature dependence of dielectric and piezoelectric responses, based on the use of a first-principles effective Hamiltonian, is described. Results are presented for the ferroelectric perovskite PbTiO3. While the method includes only the soft-mode contributions to the responses, it is argued to give a good description of the divergences or near-divergences of the response functions near the cubic-tetragonal transition. The expression of the response functions in terms of correlation functions is used to provide a real-space interpretation of the responses which clearly distinguishes between PbTiO3 and the related materials BaTiO3 and KNbO3., Comment: 10 pages, LaTeX (aipproc), three eps figures

We use first-principles density-functional total energy and polarization calculations to calculate the piezoelectric tensor at zero temperature for both cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest piezoelectric coefficient for the tetragonal configuration is enhanced by a factor of about three with respect to that of the cubic configuration. This can be attributed to both the larger strain-induced motion of cations relative to anions and higher Born effective charges in the tetragonal case. A normal mode decomposition shows that both cation ordering and local relaxation weaken the ferroelectric instability, enhancing piezoelectricity., Comment: 5 pages, revtex, 2 eps figures

In the substitutionally disordered narrow-gap semiconductor Pb_{1-x}Ge_xTe, a finite-temperature cubic-rhombohedral transition appears above a critical concentration $x \approx 0.005$. As a first step towards a first-principles investigation of this transition in the disordered system, a (hypothetical) ordered cubic Pb_3GeTe_4 supercell is studied. First principles density-functional calculations of total energies and linear response functions are performed using the conjugate-gradients method with ab initio pseudopotentials and a plane-wave basis set. Unstable modes in Pb_3GeTe_4 are found, dominated by off-centering of the Ge ions coupled with displacements of their neighboring Te ions. A model Hamiltonian for this system is constructed using the lattice Wannier function formalism. The parameters for this Hamiltonian are determined from first principles. The equilibrium thermodynamics of the model system is studied via Metropolis Monte Carlo simulations. The calculated transition temperature, T_c, is approximately 620K for the cubic Pb_3GeTe_4 model, compared to the experimental value of T_c \approx 350K for disordered Pb_{0.75}Ge_{0.25}Te. Generalization of this analysis to the disordered Pb_{1-x}Ge_xTe system is discussed., Comment: 38 pages, LaTeX, 11 PostScript figures