Multiple-scattering Theory Research Articles

Statistical physics of multicomponent alloys using KKR-CPA

We apply variational principles from statistical physics and the Landau theory of phase transitions to multicomponent alloys using the multiple-scattering theory of Korringa-Kohn-Rostoker (KKR) and the coherent potential approximation (CPA). This theory is a multicomponent generalization of the $S^{(2)}$ theory of binary alloys developed by G. M. Stocks, J. B. Staunton, D. D. Johnson and others. It is highly relevant to the chemical phase stability of high-entropy alloys as it predicts the kind and size of finite-temperature chemical fluctuations. In doing so it includes effects of rearranging charge and other electronics due to changing site occupancies. When chemical fluctuations grow without bound an absolute instability occurs and a second-order order-disorder phase transition may be inferred. The S$^{(2)}$ theory is predicated on the fluctuation-dissipation theorem; thus we derive the linear response of the CPA medium to perturbations in site-dependent chemical potentials in great detail. The theory lends itself to a natural interpretation in terms of competing effects: entropy driving disorder and favorable pair interactions driving atomic ordering. To further clarify interpretation we present results for representative ternary alloys CuAgAu, NiPdPt, RhPdAg, and CoNiCu within a frozen charge (or band-only) approximation. These results include the so-called Onsager mean field correction that extends the temperature range for which the theory is valid.

Sensitivity Analysis of Multiple Scattering Theory Applied to Tree Canopies at Microwave Frequencies

A sensitivity analysis of the multiple scattering theory applied to propagation in tree canopies is presented. This analysis aims at addressing the influence of input parameters on the canopy's equivalent scattering amplitude as well as the overall coherent and incoherent scattered fields. The main input parameters of interest were identified as frequency, number densities and dielectric parameters of branches and leaves, polarization, and a canopy shape. A number of graphical results are provided enabling to identify the key parameters of corresponding radio-wave propagation models based on the multiple scattering theory.

Azimuthal Angular Dependence of Plasmon Loss in Core-Level Photoemission with Multiple Scattering Theory

Azimuthal Angular Dependence of Plasmon Loss in Core-Level Photoemission with Multiple Scattering Theory

Investigation of the nuclear matter distribution of 56Ni by elastic proton scattering in inverse kinematics

We have measured the nuclear-matter distribution of the doubly-magic N = Z nucleus 56Ni by investigating elastic proton scattering in inverse kinematics. The radioactive beam of 56Ni was injected and stored in the experimental storage ring (ESR, GSI) and interacted with an internal hydrogen gas-jet target. The high revolution frequency of the ions in the ring enabled a high luminosity, despite the low density of the target being used. This way, measurements at very low momentum transfers became possible. By measuring the energy and the scattering angle of the recoiling protons, we were able to separate the elastic reaction channel from inelastic scattering to the first excited state of 56Ni and deduced the differential cross section of 56Ni Ni. The data were analyzed within the framework of the Glauber multiple-scattering theory in order to extract the nuclear-matter radius and radial matter distribution of 56Ni. Parameterizing the matter distribution with the phenomenological Symmetrized Fermi distribution, a preliminary value of 3.5 fm for the rms matter radius was deduced. This experiment was part of an EXL (EXotic nuclei studied in Light-ion induced reactions at storage rings) campaign at GSI in 2012 and was the first successful investigation of nuclear reactions with a stored radioactive beam ever.

Subwavelength focusing in bubbly media using broadband time reversal

Thanks to a Multiple Scattering Theory algorithm, we present a way to focus energy at the deep subwavelength scale, from the far-field, inside a cubic disordered bubble cloud by using broadband Time Reversal (TR). We show that the analytical calculation of an effective wavenumber performing the Independant Scattering Approximation (ISA) matches the numerical results for the focal extension. Subwavelength focusings of lambda/100 are reported for simulations with perfect bubbles (no loss). A more realistic case, with viscous and thermal losses, allows us to obtain a $\lambda/14$ focal spot, with a low volume fraction of scatterers (phi = 0.01). Bubbly materials could open new perspective for acoustic actuation in the microfluidic context.

Proton-three-nucleon nuclei elastic scattering: three-body force effect

Elastic scattering differential cross sections at 0.6 GeV for p-3H and at 0.6, 0.715 and 1 GeV for p-3He are calculated in the framework of the multiple-scattering theory of Glauber. A simple approach for the three-body force effect is used. We have found that the three-body force effect appears in the range of momentum transfer squared $$ q^{2} \ge 0.2\; ( {\text{GeV/c)}}^{ 2} $$ and plays an important role to obtain a good fit with the experimental data at the first minimum region.

Electron transport in graphene/graphene side-contact junction by plane-wave multiple-scattering method

Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a ``side-contact'' geometry which causes the current to flow perpendicular to the sheets within the device. Such geometry presents a challenge to first-principles transport methods. We solve this problem by implementing a plane-wave-based multiple-scattering theory for electron transport. This implementation improves the computational efficiency over the existing plane-wave transport code, scales better for parallelization over large number of nodes, and does not require the current direction to be along a lattice axis. As a first application, we calculate the tunneling current through a side-contact graphene junction formed by two separate graphene sheets with the edges overlapping each other. We find that transport properties of this junction depend strongly on the AA or AB stacking within the overlapping region as well as the vacuum gap between two graphene sheets. Such transport behaviors are explained in terms of carbon orbital orientation, hybridization, and delocalization as the geometry is varied.

Electron impact ionization of metastable 2P-state hydrogen atoms in the coplanar geometry

Triple differential cross sections (TDCS) for the ionization of metastable 2P-state hydrogen atoms by electrons are calculated for various kinematic conditions in the asymmetric coplanar geometry. In this calculation, the final state is described by a multiple-scattering theory for ionization of hydrogen atoms by electrons. Results show qualitative agreement with the available experimental data and those of other theoretical computational results for ionization of hydrogen atoms from ground state, and our first Born results. There is no available other theoretical results and experimental data for ionization of hydrogen atoms from the 2P state. The present study offers a wide scope for the experimental study for ionization of hydrogen atoms from the metastable 2P state.

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number $L_{max}=(l,m)_{max}$, while scattering matrices, which determine spectral properties, are truncated at $L_{tr}=(l,m)_{tr}$ where phase shifts $\delta_{l>l_{tr}}$ are negligible. Historically, $L_{max}$ is set equal to $L_{tr}$; however, a more proper procedure retains free-electron and single-site contributions for $L_{max}>L_{tr}$ with $\delta_{l>l_{tr}}$ set to zero [Zhang and Butler, Phys. Rev. B {\bf 46}, 7433]. We present a numerically efficient and accurate \emph{augmented}-KKR Green's function formalism that solves the KKR secular equations by matrix inversion [$\mathcal{R}^3$ process with rank $N(l_{tr}+1)^2$] and includes higher-order $L$ contributions via linear algebra [$\mathcal{R}^2$ process with rank $N(l_{max}+1)^2$]. Augmented-KKR yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. For fcc Cu, bcc Fe and L$1_0$ CoPt, we present the formalism and numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus $L_{max}$ for a given $L_{tr}$.

Scattering by an array of perforated cylinders with a porous core.

In this work multiple scattering by an array of perforated cylindrical shells with a porous core has been investigated. A semi-analytical model to predict scattering from such cylindrical units is presented in the context of the multiple scattering theory (MST), and validated against laboratory experiments. The suggested semi-analytical multiple scattering model uses an impedance expression to include the perforated shell in the scattering coefficients, which is a compact way to describe a composite scatterer in MST. Calculation results of a small array are shown to be in excellent agreement with measured data. Predictions and data show that perforated cylinders with empty cavities exhibit a strong and narrow insertion loss peak at resonance, though simultaneously suffer from amplification below resonance. By adding porous material in the core of the scatterer adverse effects below the resonance peak were suppressed. In addition, it was found that the reduction peak broadens, though at a cost of a reduced peak amplitude. Finally, it has been shown that adding porous material in a perforated shell will introduce partial absorption of the incoming field, which can be optimized by adjusting the perforation ratio of the shell.

Sound propagation in the presence of a resonant surface

The interactions between acoustic waves and an array of resonators are studied. The resonators are arranged periodically on an impedance surface so that the scale separation between sound wavelength and the array period is achieved. An asymptotic multi-scale model which accounts for viscous and thermal losses in the resonators is developed and is used to derive an effective surface admittance. It is shown that the boundary conditions at the surface are substantially modified around the resonance frequency. The pressure field on the surface is nearly canceled leading to a phase shift between the reflected and the incident waves. The array can also behave as an absorbing layer. The predictions of the homogenized model are compared with multiple scattering theory (MST) applied to a finite size array and the limitations of the former are identified. The influence of the surface roughness and local scattering on the reflected wave is discussed.

Temperature dependence of the local structure and lattice dynamics of wurtzite-type ZnO

Temperature-dependent (10–300K) Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra of polycrystalline wurtzite-type ZnO were analyzed using ab initio multiple-scattering theory and taking into account anisotropy of the crystallographic structure and thermal disorder. We employed two different simulation approaches: classical molecular dynamics (MD) and reverse Monte Carlo coupled with an evolutionary algorithm (RMC/EA method). The accuracy of several force-field models, which are commonly used in the MD simulations of bulk and nanostructured ZnO, was tested based on a comparison between the experimental and simulated Zn K-edge EXAFS spectra. It was found that available force-field models fail to describe accurately many-atom distribution functions. A more accurate solution was obtained with the RMC/EA method, which allowed us also to resolve the non-equivalent groups of atoms in the first two coordination shells around the absorbing Zn atom and to follow the changes of structural parameters as the temperature varied. It was found that upon increasing temperature the structure of ZnO becomes more anisotropic due to the increase of internal parameter u of the oxygen Wyckoff position (2b) and related Zn0–O2 distances.

The Dual Wavelength Ratio Knee: A Signature of Multiple Scattering in Airborne Ku–Ka Observations

AbstractDeep convective systems observed by the High Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar during the 2011 Midlatitude Continental Convective Clouds Experiment (MC3E) field campaign in Oklahoma provide the first evidence of multiple-scattering effects simultaneously at Ku and Ka band. One feature is novel and noteworthy: often, in correspondence to shafts with strong convection and when moving from the top of the cloud downward, the dual wavelength ratio (DWR) first increases as usual in Ku–Ka-band observations, but then it reaches a maximum and after that point it steadily decreases all the way to the surface, forming what will be hereinafter referred to as a knee. This DWR knee cannot be reproduced by single-scattering theory under almost any plausible cloud microphysical profile. On the other hand, it is explained straightforwardly with the help of multiple-scattering theory when simulations involving hail-bearing convective cores with large horizontal extents are performed. The DWR reduction in the lower troposphere (i.e., DWR increasing with altitude) is interpreted as the result of multiple-scattering pulse stretching caused by the highly diffusive hail layer positioned high up in the atmosphere, with Ka multiple scattering typically exceeding that occurring in the Ku channel. Since the effects of multiple scattering increase with increasing footprint size, if multiple-scattering effects are present in the aircraft measurements, they are likely to be more pronounced in the spaceborne dual-frequency Ku–Ka radar observations, envisaged for the NASA–Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM) Mission, launched in February 2014. This notional study supports the idea that DWR knees will be observed by the GPM radar when overflying high-density ice shafts embedded in large convective systems and suggests that their explanation must not be sought in differential attenuation or differential Mie effects but via multiple-scattering effects.

The single-site Green’s function and Krein’s theorem

An important step in electronic structure calculations using multiple-scattering theory is obtaining the density of states for the central site from the Green’s function for that site. We have found that the Krein’s spectral displacement function for the central site contributes significantly to the understanding of these calculations. We argue that these insights can lead to improvements in the robustness of MST electronic structure codes without negatively impacting their performance.

Impact of molecular orbital distribution on photoelectron intensity for picene film

The recent development in the theoretical evaluation of photoelectron intensity from π-electronic states delocalized over a molecule is discussed. By comparing the experimental photoelectron angular distribution (PAD) from the organic molecular assemblies with computed PAD we show that the use of the initial-state orbitals by density functional theory and the final continuum states by multiple-scattering theory is suited for simulations of angle-resolved photoelectron spectrum (ARPES) and PAD. We demonstrate that the ARPES and PAD simulations are useful to characterize the top five π-electronic states for picene (C22H14) film.

Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media

Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves have not been investigated so far. We study theoretically the polarization and coherence properties of electromagnetic waves produced by a dipole source in a three-dimensional uncorrelated disordered medium. The spatial field correlation matrix is calculated analytically using a multiple-scattering theory for polarized light. This allows us to provide a formal description of the light depolarization process in terms of ``polarization eigenchannels'' and to derive analytical formulas for the spatial coherence of multiply scattered light.

Gilbert damping tensor within the breathing Fermi surface model: anisotropy and non-locality

In magnetization dynamics, the Gilbert damping α is often taken as a parameter. We report on a theoretical investigation of α, taking into account crystal symmetries, spin–orbit coupling and thermal reservoirs. The tensor is calculated within the Kamberský breathing Fermi-surface model. The computations are performed within a tight-binding electronic structure approach for the bulk and semi-infinite systems. Slater–Koster parameters are obtained by fitting the electronic structure to first-principles results obtained within the multiple-scattering theory. We address the damping tensor for the bulk and surfaces of the transition metals Fe and Co. The role of various contributions are investigated: intra- and interband transitions, electron and magnetic temperature as well as surface orientation. Our results reveal a complicated non-local, anisotropic damping that depends on all three thermal reservoirs.

X-ray absorption near-edge spectroscopy study on Ge-doped Li7La3Zr2O12: enhanced ionic conductivity and defect chemistry

Ge-doped Li7La3Zr2O12 (LLZ) is prepared via the conventional solid-state reaction. Our results showed that doping Ge of less than 1 wt% could stabilize the cubic phase of garnet-type LLZ and also increase its ionic conductivity up to 8.28×10−4 S/cm at room temperature. When the content of Ge dopant is higher, GeO2 impurity phase would appear and there coexists cubic and tetragonal mixed structures, lowering the conductivity. By combining X-ray absorption near-edge spectroscopy and full multiple-scattering theory, we find that Ge more likely enters into the Li and La crystallographic sites instead of the Zr site, which provides understanding of the micro-structural modulation by Ge dopants and the subsequent enhancement in the ionic conductivity.

Two-dimensional broadband acoustic black hole for underwater applications

Transformation acoustics using sub-wavelength elements to obtain homogenized properties has been utilized increasingly in recent years to manipulate the propagation of acoustic waves. Gradient index (GRIN) lenses are designed by varying local properties of the elements through a given geometry for a variety of devices including focusing lenses and black holes. This study presents a cylindrical, two-dimensional acoustic black hole for underwater applications. The black hole designed focuses acoustic energy to the center of the cylinder using a radially decreasing sound speed profile. An absorbing core then prevents scattering of the acoustic waves into the surrounding fluid. Transformation acoustics was used to design the index gradient through the black hole structure and multiple scattering theory (MST) was used to predict the scattering profile over a broadband range of frequencies. The black hole was constructed of concentric rings of silicone rubber cylinders, which behave as effective fluids in a multiple scattering configuration. Experimental realization of the black hole structure was fabricated and analyzed with measured pressure intensity agreeing with predicted results. [Work sponsored by the Office of Naval Research.]

Green's function theory for predicting device-to-device variability

Due to random dopant fluctuations, the device-to-device variability is a serious challenge to emerging nanoelectronics. In this work we present theoretical formalisms and numerical simulations of quantum-transport variability, based on the Green's function technique and the multiple-scattering theory. We have developed a general formalism using the diagrammatic technique within the coherent-potential approximation that can be applied to a wide range of disorder concentrations. In addition, we have developed a method by using a perturbative expansion within the low-concentration approximation that is extremely useful for typical nanoelectronic devices having low dopant concentration. Applying both formalisms, transport fluctuations due to random impurities can be predicted without lengthy brute force computation of ensembles of device structures. Numerical implementations of the formalisms are demonstrated using both tight-binding models and first-principles models.