Real-space Model Research Articles

Real-space phase-field simulation of piezoresponse force microscopy accounting for stray electric fields

Piezoresponse force microscopy (PFM) is a powerful scanning-probe technique used to characterize important aspects of the microstructure in ferroelectrics. It has been widely applied to understand domain patterns, domain nucleation and the structure of domain walls. In this paper, we apply a real-space phase-field model to consistently simulate various PFM configurations. We model the PFM tip as a charged region that is external to the ferroelectric, and implement a boundary element method to efficiently and accurately account for the external stray fields that mediate the interactions between the tip and the ferroelectric. Our phase-field model and the solution method together are able to account for the electrical fields both within the specimen as well as those outside, and also consistently solve for the resulting electromechanical response with the same phase-field model. We apply this to various problems: first, the effect of crystal lattice orientation on the induced tip displacement and rotation; second, PFM scanning of a 90° domain wall that emerges at a free surface; third, the effect of closure domain microstructure on PFM response; fourth, the effect of surface modulations on PFM response; and fifth, the effect of surface charge compensation on PFM response.

Free surface domain nucleation in a ferroelectric under an electrically charged tip

This paper examines the process of domain nucleation in ferroelectric perovskites at a free surface due to electrical fields applied through a charged tip above the surface. We use a real-space phase-field model to model the ferroelectric, and apply a boundary element-based numerical method that enables us to accurately account for the stray electric fields outside the ferroelectric and the interactions through electric fields between the external tip and ferroelectric. We calculate the induced domain patterns, the stress and internal electric fields, and the induced surface displacement for various relative orientations of the crystal lattice with respect to the free surface. The effect of the external spatially inhomogeneous electric field leads to the formation of complex domain patterns and nominally incompatible microstructures. Two key findings are: first, in c axis films, a new domain forms beneath the tip through 180° switching and this new domain has the opposite piezo-response as the original domain, leading to a distinct displacement signature on the surface; and second, in a axis films, domain nucleation occurs at lower applied field because polarization rotates to align with the applied field, whereas in c axis films, the polarization magnitude reduces until 180° switching occurs at a higher applied field. We also see that the calculated domain patterns differ significantly from analytical approximations that are often used.

Communication: A density functional with accurate fractional-charge and fractional-spin behaviour for s-electrons

We develop a new density-functional approach combining physical insight from chemical structure with treatment of multi-reference character by real-space modeling of the exchange-correlation hole. We are able to recover, for the first time, correct fractional-charge and fractional-spin behaviour for atoms of groups 1 and 2. Based on Becke's non-dynamical correlation functional [A. D. Becke, J. Chem. Phys. 119, 2972 (2003)] and explicitly accounting for core-valence separation and pairing effects, this method is able to accurately describe dissociation and strong correlation in s-shell many-electron systems.

On Occupied-orbital Dependent Exchange-correlation Functionals: From Local Hybrids to Becke’s B05 Model

Abstract Recent work in the field of occupied-orbital dependent (OOD) exchange-correlation functionals in density functional theory is reviewed. The main emphasis is put on the development of so-called local hybrid functionals, and on the nontrivial self-consistent implementation of complex OOD functionals. Local hybrids employ a so-called local mixing function (LMF) to govern their position-dependent exact-exchange admixture. Recently proposed LMFs have provided local hybrids of remarkable accuracy in the computation of thermochemical data and classical reaction barriers, and with good performance for some magnetic-resonance parameters. These local hybrids mix only local and exact exchange and exhibit very few semi-empirical parameters. Further refinement and the efficient implementation of local hybrids offers the prospect of a new level of accuracy in Kohn-Sham density functional calculations. Two levels of the self-consistent implementation of OOD functional are discussed: one may either stop after the derivation of the functional derivatives with respect to the orbitals (FDOs), leading to nonlocal potentials. This is discussed for local hybrids and for general OOD functionals up to and including the complicated B05 real-space model of nondynamical correlation. Alternatively, one may append an additional transformation to local and multiplicative potentials based on the optimized effective potential (OEP) approach or of approximations to the OEP. Numerical results for various properties are reviewed briefly, ranging from nonself-consistent energies via FDO-based calculations to OEP-transformed potentials.

Quantitative analysis of fine nano-sized precipitates in low-carbon steels by small angle neutron scattering

The small angle neutron scattering (SANS) technique was used to determine the nano-sized precipitates in interstitial free (IF) and low-carbon (LC) steels with a hot-rolling temperature. The real-space direct model fitting method was applied to quantitatively analyze the SANS data. The magnetic and chemical properties of precipitates in the samples were also investigated by separation and comparison of nuclear and magnetic SANS scattering data. The size distribution of precipitates in the IF steel is in good agreement with the microstructure observation using transmission electron microscopy. The results revealed that the IF steel had two types of non-magnetic precipitates, Ti4C2S2 and TiC, with the average size of about 30 nm in diameter and little difference in chemical composition. In case of commercial LC steel, the fine and large precipitates are identified as MnS and Fe3C, respectively. The average size of spherical MnS precipitates was about 4.8 nm in radius and the distribution is isotropic. It is likely that the LC steels have almost the same composition and a similar size as precipitates such as MnS and Fe3C with different finishing delivery temperatures. Interestingly, the average size and volume fraction of fine precipitates showed no significantly changes under the different finishing delivery temperatures.

Modeling: What has it Really Contributed?

We often read that neutron scattering sees “where atoms are and how they move.” In truth, this is an indirect view in reciprocal space. Modeling's contribution has been to make this a reality by confronting neutron-scattering data with a real-space model (Figure 1). To do this properly, we need good algorithms and computing power, but the advantages are many-fold:

On the self-consistent implementation of general occupied-orbital dependent exchange-correlation functionals with application to the B05 functional

Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke's real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)].

MAIN 2008: real-space model fitting – as good as it gets

<i>MAIN 2008</i>: real-space model fitting – as good as it gets

Publisher's Note: Entanglement between remote spin-qubits in one dimension by scattering in the real-space Anderson model [Phys. Rev. B77, 195308 (2008)

Publisher's Note: Entanglement between remote spin-qubits in one dimension by scattering in the real-space Anderson model [Phys. Rev. B<b>77</b>, 195308 (2008)

Entanglement between remote spin-qubits in one dimension by scattering in the real-space Anderson model

The possibility of generating entanglement between two solid-state electron spin-qubits by spin-dependent scattering of a third, propagating electron is attractive. A process of this kind could work well beyond the range of the direct interaction between the two spins. In this study, the binding of electrons in one-dimensional structures is theoretically modeled using a real-space analog of the Anderson model. The respective binding sites are arranged in two different geometries. The first is a straightforward series arrangement, and the second a parallel arrangement in which the binding sites are embedded in either arm of an Aharonov-Bohm style ring. For the series arrangement, the entanglement between the bound electrons is calculated and is shown to be low (concurrence ) starting configuration with an overall probability of success up to 0.5.

Single-Line Diffraction Profile Analysis Method Used for Evaluation of Microstructural Parameters in the Plain Ferritic Steel upon Tensile Straining

The modification of the Transformed Model Fitting /TMF/ [1] method developed for evaluation of the single-line profiles from high-resolution neutron powder diffractometers is proposed [2]. More sophisticated real-space model [3] is used for the distortion and crystallite size broadening of the diffraction lines. The new PC program based on this model has been tested on neutron diffraction profiles collected in situ upon tensile deformation tests of the plain ferritic steel. The deformation test was performed in the incremental mode in which each individual deformation step was followed by unloading. The neutron diffraction spectra were collected both upon loading and unloading and behavior of the diffraction profiles in elastic as well as in plastic region of the deformation curve was examined in detail. Comparison of microstress values in loaded/unloaded state and in elastic and plastic region offers interesting possibility to separate the contribution of the type II and type III microstresses.

Entanglement of static and flying qubits in degenerate mesoscopic systems

The entanglement of flying qubits with static qubits in the solid state is important in the development of quantum computing. It has recently been shown theoretically that the spin-dependent scattering of a propagating electron from a bound electron is sufficient to give full entanglement between the qubits embodied in their respective spins [J. H. Jefferson et al., Europhys. Lett. 74, 764 (2006); D. Gunlycke et al., J. Phys.: Condens. Matter 18, S851 (2006)]. In this paper a generalized, real-space Anderson model is introduced for a quasi-one-dimensional structure consisting of a binding site coupled to ideal leads. Degeneracy of both the binding site and the leads is incorporated to represent, for example, conduction band degeneracy in carbon nanotubes. The model is used to calculate the spin-dependent scattering behavior and resultant static-flying qubit entanglement created by the scattering process. Degeneracy (and more generally, multiplicity) in the binding site gives rise to inelastic scattering processes. In the elastic scattering regime, a degenerate binding site gives rise to antiresonant structures in the transmission spectrum. Additional degeneracy in the leads restricts this effect to the second set of leads, raising the possibility of spin filtration, though this is eliminated in the inelastic scattering regime. Degeneracy in the binding site also gives rise to multiple resonances in transmission that will improve the probability of obtaining entangled pairs relative to the nondegenerate case. This effect is maximized when the components of the degenerate binding site are symmetrically coupled to the leads.

Colloidal crystal–fluid interfaces

In this article we show that colloidal systems are excellent model systems to experimentally study crystal–fluid interfaces. Using confocal microscopy it is possible to investigate static and dynamic interfacial properties in three dimensions and on the single particle level. The combination of real-space microscopy and colloidal model systems may provide a possible route to directly access the anisotropic interfacial free energy and the kinetic growth coefficient of crystal–fluid interfaces.

The Structure of Ferrihydrite, a Nanocrystalline Material.

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The Structure of Ferrihydrite, a Nanocrystalline Material

Despite the ubiquity of ferrihydrite in natural sediments and its importance as an industrial sorbent, the nanocrystallinity of this iron oxyhydroxide has hampered accurate structure determination by traditional methods that rely on long-range order. We uncovered the atomic arrangement by real-space modeling of the pair distribution function (PDF) derived from direct Fourier transformation of the total x-ray scattering. The PDF for ferrihydrite synthesized with the use of different routes is consistent with a single phase (hexagonal space group P6(3)mc; a = approximately 5.95 angstroms, c = approximately 9.06 angstroms). In its ideal form, this structure contains 20% tetrahedrally and 80% octahedrally coordinated iron and has a basic structural motif closely related to the Baker-Figgis delta-Keggin cluster. Real-space fitting indicates structural relaxation with decreasing particle size and also suggests that second-order effects such as internal strain, stacking faults, and particle shape contribute to the PDFs.

Evidence of disorder in cubic zirconium tungstate from the temperature dependence ofRaman spectra

The cubic phase of zirconium tungstate exhibits a larger number of vibrational Ramanmodes in the frequency region of the symmetric stretching mode of tungstate ions thanpermitted by group-theoretical analysis for a perfectly ordered lattice. This suggeststhe existence of disorder in the tungstate sublattice. The additional modes areidentified and assigned on the basis of their relative intensities and temperaturedependences of line-widths. Using a real-space model for misoriented tetrahedral ions,the occurrence of four disorder modes is explained. From the evolution of theintensities of different components of the symmetric stretching mode as a function oftemperature, the disorder is found to be largely static (frozen-in) in nature. As eachtungstate ion carries a net dipole moment, randomly misoriented tetrahedral unitscan result in a dipole glass, explaining a recently reported glass-like behaviourof thermal conductivity. The proposed disordered configurations of tungstateions are indeed found to be energetically stable from first-principles simulationstudies.

A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries

Ferroelectric perovskites are used in various transducer, memory and optical applications due to their attractive properties. In these applications, the ferroelectric materials often have complex geometries and electrode arrangements, and are subjected to domain switching. Therefore, it is important to understand the domain pattern that forms in these geometries. However, models of domain evolution often make assumptions like periodicity and complete shielding which make them unrealistic for these applications. In this paper, we develop a phase-field approach that can study domain patterns and domain evolution in complex geometries with no a priori assumption on geometry, electrode arrangement, and dielectric properties. The key idea is a boundary element method to resolve the electrostatic fields. We illustrate the method by examining the closure domains that form at a free surface and domain switching under cyclic electric field in a device with interdigitated electrodes.

Compositional dependence of the local structure ofSexTe1−xalloys: Electron energy-loss spectra, real-space multiple-scattering calculations, and first-principles molecular dynamics

In this work we present an investigation on the composition dependence of the local structure in ${\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ crystalline alloys analyzing their experimental energy-loss spectra with the aid of a real-space multiple-scattering modeling approach and first-principles molecular dynamics. The concourse of this latter technique is essential for a proper modeling of the alloy spectra. From our results, it can be inferred that ${\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ alloys exhibit a high degree of substitutional disorder ruling out the existence of fully ordered alternating copolymer chains of Se and Te atoms.

Normalization of the effective exchange hole in Becke's nondynamical correlation model: Closed-form analytic representation

An analytical approximation to the implicit ‘ x-function’ appearing in a recent real-space model for non-dynamical correlation (A. D. Becke, J. Chem. Phys. 119 (2003) 2972) has been constructed as a continuous function sewed of three pieces. The ansatz avoids iterative techniques. The x-Function enters the expression of the so-called normalization of the effective exchange hole, which provides a measure of the importance of nondynamical correlation (NDC) effects at a given point in space. Our approximation has been evaluated in quantum-chemical calculations of several reaction energies. Differences between the results obtained with and without analytical approximation are very small and far below the ‘chemical accuracy’ threshold. The present analytical approximation to the x-function should aid future self-consistent implementations of the NDC model.

Coherent Single Photon Transport in a One-Dimensional Waveguide Coupled with Superconducting Quantum Bits

A recent theoretical analysis and experimental results show that interesting transport properties of a single microwave photon emerge when a quantum bit in a cavity is coupled to a one-dimensional waveguide. Here we adopt a real-space model Hamiltonian to give a unified approach which accounts for the experimental results, and make new predictions on the properties of single photon transport, such as the general Fano line shape, symmetric vacuum Rabi splitting for a leaky cavity at resonance, and a one-photon switching capability.