Use of the R-matrix propagation technique to calculate the electronic energy levels of aperiodic structures - Application to an AlAs/GaAs quasiperiodic superlattice
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Vasquez, R. P.↗
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New Dimensions in the Theory of Excited States and X-ray Spectra (Final Report)
This Final Technical Report briefly summarizes the achievements during the lifetime of our DOE BES grant DE-FG02-97ER45623. The long-term goal of this project has been the development of quantitative theories of the interaction between radiation and matter, with a focus on x-ray spectroscopies. X-ray spectra have long been among the most important probes of atomic-scale structure and properties of matter, ranging from atoms and molecular systems to condensed matter and exotic states. These spectroscopies are widely used in investigations at the major DOE synchrotron x-ray facilities and related centers world-wide. In addition to fundamental theory, a major goal of our project has been the development of computational software that implements the theory for calculations of x-ray spectra of various materials throughout the periodic table. Due to the complex nature of x-ray spectra, quantitative theory is essential for its interpretation. The theory is challenging since it involves excited state electronic structure and many-body correlation effects that go beyond independent particle approximations like DFT or Hartree-Fock. Moreover, the experimental investigations typically involve a broad range of energy, time, and temperature scales, from the UV-Vis to hard x-ray energies of order 10 4 eV, and temperatures T from ambient up to the warm-dense-matter regime where the Fermi energy kBTF is of order a few eV, i.e., temperatures of order 105 Kelvin. This broad range of experimental conditions has fostered many novel theoretical approaches and computational techniques, many of which we have developed systematically over the duration of the grant. In contrast to the traditional wave-function approach of quantum theory and electronic structure methods, our theoretical approach is based on modern Green's function techniques. This approach is better suited for aperiodic structures, excited states, and broad spectral ranges, since it avoids the computational bottlenecks of sum-over-states approaches, as in the Fermi golden rule. This theoretical framework has been incorporated into efficient, user-friendly x-ray spectroscopy software which is now used routinely worldwide to simulate and analyze spectra. These theoretical tools provide an essential complement to synchrotron and next-generation light sources, which are used to investigate complex materials with ever increasing precision. Moreover, the synergism between theory, computation and experiment contributed by our research enhances scientific understanding and creates opportunities for innovations in materials and energy science and in many fields. As documented in this Report, this research grant has been remarkably successful in achieving these goals. In particular, this grant has supported the development of the x-ray spectroscopy software suite known as FEFF (named for an effective scattering amplitude f eff in the theory). The FEFF codes have become one of the premier tools for quantitative simulations of x-ray spectra as documented by many thousands of citations in the Web of Science and Google-Scholar.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Methane as a Diagnostic Tracer of Changes in the Brewer-Dobson Circulation of the Stratosphere
This study makes use of time series of methane (CH4/ data from the Halogen Occultation Experiment (HALOE) to detect whether there were any statistically significant changes of the Brewer-Dobson circulation (BDC) within the stratosphere during 1992-2005. The HALOE CH4 profiles are in terms of mixing ratio versus pressure altitude and are binned into latitude zones within the Southern Hemisphere and the Northern Hemisphere. Their separate time series are then analyzed using multiple linear regression (MLR) techniques. The CH4 trend terms for the Northern Hemisphere are significant and positive at 10 N from 50 to 7 hPa and larger than the tropospheric CH4 trends of about 3%decade(exp -1) from 20 to 7 hPa. At 60 N the trends are clearly negative from 20 to 7 hPa. Their combined trends indicate an acceleration of the BDC in the middle stratosphere of the Northern Hemisphere during those years, most likely due to changes from the effects of wave activity. No similar significant BDC acceleration is found for the Southern Hemisphere. Trends from HALOE H2O are analyzed for consistency. Their mutual trends with CH4 are anti-correlated qualitatively in the middle and upper stratosphere, where CH4 is chemically oxidized to H2O. Conversely, their mutual trends in the lower stratosphere are dominated by their trends upon entry to the tropical stratosphere. Time series residuals for CH4 in the lower mesosphere also exhibit structures that are anti-correlated in some instances with those of the tracer-like species HCl. Their occasional aperiodic structures indicate the effects of transport following episodic, wintertime wave activity. It is concluded that observed multi-year, zonally averaged distributions of CH4 can be used to diagnose major instances of wave-induced transport in the middle atmosphere and to detect changes in the stratospheric BDC.
Remsberg, E. E.↗
Wide-Stopband Aperiodic Phononic Filters
We demonstrate that a phonon stopband can be synthesized from an aperiodic structure comprising a discrete set of phononic filter stages. Each element of the set has a dispersion relation that defines a complete bandgap when calculated under a Bloch boundary condition. Hence, the effective stopband width in an aperiodic phononic filter (PnF) may readily exceed that of a phononic crystal with a single lattice constant or a coherence scale. With simulations of multi-moded phononic waveguides, we discuss the effects of finite geometry and mode-converting junctions on the phonon transmission in PnFs. The principles described may be utilized to form a wide stopband in acoustic and surface wave media. Relative to the quantum of thermal conductance for a uniform mesoscopic beam, a PnF with a stopband covering 1.6-10.4 GHz is estimated to reduce the thermal conductance by an order of magnitude at 75 mK.
bandgap↗
Probing the solidification of quasicrystals via joint experiment and simulation (Final Report)
Quasicrystals (QCs) possess long-range positional order but non-crystallographic orientational order. Their classically ‘forbidden’ symmetry has long attracted the interest of scientists worldwide. Despite their frequent observation in both metal alloys and soft matter structures in the 35 years since their discovery, little is known about how QCs evolve from a liquid, amorphous, or crystalline precursor. In this project, we sought to resolve the enigma of QC self-assembly through a combined experimental and computational program. The Shahani group employed in situ electron and synchrotron X ray imaging to peer into the growth dynamics of QCs in a liquid, covering a broad range of length scales and solidification pathways. Glotzer's team developed new simulation models incorporating phasonic defects — which are unique to quasicrystals — and used this model to investigate two grains growing together, closely mimicking the experimental conditions. While QCs remain exceptional structures, most compounds in the realm of intermetallics adopt non-trivial geometries. In fact, only around 6% of phases are comprised of the simplest sphere packings that researchers so readily associate with metals. State-of-the-art knowledge of phase transformations at the outset of this collaborative project did not encompass the remaining 94% of intermetallic compounds that possess complex and aperiodic structure types. Therefore, we expect that outcomes from this project will have immediate and profound impact on synthesis and processing science: our efforts will be used to not only explain the growth dynamics of QCs but also complex intermetallics more broadly.
36 MATERIALS SCIENCE↗
Field-induced magnetic phases in a qubit Penrose quasicrystal
Unveiling the fundamental dynamics of naturally or artificially formed magnetic quasicrystals in the presence of an external magnetic field remains a difficult problem that may have implications for the design of information processing devices. By embedding a qubit magnetic Penrose quasicrystal into a quantum annealer, we were able to reproduce the formation of magnetic phases driven by specific physical parameter selections, allowing us to distinguish a wide range of frustrated magnetic configurations at the single-spin scale. In our experiments, we observe some spins dynamically activate, while others remain static, all within an average magnetization space defined by competing structural and magnetic degrees of freedom. Static spin structure factors reveal ferromagnetic and ferrimagnetic modulations that are compatible with a variety of spin textures. This research demonstrates that introducing structural aperiodicity in magnetic devices that exploit spin degeneracy in a single, richly intraconnected finite object can enable the engineering of quantum states in both the effective low-temperature and thermally excited regimes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Toward a quantitative description of solvation structure: a framework for differential solution scattering measurements
Appreciating that the role of the solute–solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime—where sub-ångström spatial resolution is achieved—remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Near-field-driven radiative thermal dynamics in aperiodic photonic nanostructures
Harnessing structural correlations in near-field plasmonic and polaritonic systems hold untapped potential for controlling light–matter interactions at the nanoscale. By tuning these correlations, one can reshape mode localization, coupling, and spectral distribution which are properties central to manipulating energy transport and field enhancement in nanophotonic platforms. We exploit Vogel spirals, an aperiodic geometry where a single parameter dictates spatial correlations, to show how correlation strength reshapes the modal spectrum and transient dynamics of near-field coupling. As a proof of concept, we demonstrate that aperiodic configurations outperform both uncorrelated (random) and periodic arrays in controlling near-field radiative heat-transfer dynamics. These results establish deterministic aperiodic order as a powerful platform for tailoring correlated electromagnetic responses in next-generation nanophotonic devices.
36 MATERIALS SCIENCE↗
Scalable Synthesis and Characterization of Multilayer γ-Graphyne, New Carbon Crystals with a Small Direct Band Gap
γ-Graphyne is the most symmetric sp 2 /sp 1 allotrope of carbon, which can be viewed as graphene uniformly expanded through the insertion of two-carbon acetylenic units between all the aromatic rings. To date, synthesis of bulk γ-graphyne has remained a challenge. In this work, we report the synthesis of multilayer γ-graphyne through crystallization-assisted irreversible cross-coupling polymerization. A comprehensive characterization of this new carbon phase is described, including synchrotron powder X-ray diffraction, electron diffraction, lateral force microscopy, Raman spectroscopy, infrared spectroscopy, and cyclic voltammetry. Experiments indicate that γ-graphyne is a 0.48 eV band gap semiconductor, with a hexagonal a-axis spacing of 6.88 Å and an interlayer spacing of 3.48 Å, which is consistent with theoretical predictions. The observed crystal structure has an aperiodic sheet stacking. The material is thermally stable up to 240 °C but undergoes transformation at higher temperatures. While conventional 2D polymerization and reticular chemistry rely on error correction through reversibility, we demonstrate that a periodic covalent lattice can be synthesized under purely kinetic control. The reported methodology is scalable and inspires extension to other allotropes of the graphyne family.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quasicrystal stability and nucleation kinetics from density functional theory
The aperiodic order of quasicrystals bridges the amorphous and crystalline regime, so it has remained unclear whether quasicrystals are metastable or stable phases of matter. Density functional theory is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, in this work, we perform first-principles calculations on quasicrystal nanoparticles of increasing size, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn 7.33 and YbCd 5.7 are ground-state phases, thus revealing that translational symmetry is not a necessary condition for the zero-temperature stability of inorganic solids. Although we found the ScZn 7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is limited by nucleation, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques broadly open the door to first-principles investigations into the structure–bonding–stability relationships of aperiodic materials.
density functional theory↗
Defect-Free Growth of Decagonal Quasicrystals around Obstacles
Quasicrystals are aperiodic solids with exotic physical properties. The mechanisms driving their growth are far from understood, particularly in the presence of rigid obstacles. Here, using in situ synchrotron x-ray tomography and molecular dynamics simulations, we investigate the interaction between decagonal quasicrystals and obstacles (shrinkage pores) during solidification of an Al 79 Co 6 Ni 15 alloy. The results reveal defect-free quasicrystal growth around the pores, independent of pore size and geometry. Our findings point to a universal feature of aperiodic solids: their ability to accommodate structural disruptions due to additional (phasonic) degrees of freedom. This Letter opens new possibilities for synthesizing large-scale, single quasicrystals from a liquid metal precursor.
alloys↗
Shaker-structure interaction modeling and analysis for nonlinear force appropriation testing
Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.
42 ENGINEERING↗
Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations
Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. Here, in this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Unravelling Disorder in Aperiodic Crystals – Diffuse Scattering and Atomic Resolution Holography
The atomic–scale disorder of aperiodic crystals, and quasicrystals in particular, is inherently difficult to explore by experimental methods due to their complex atomic arrangements. Two advanced characterization techniques, a revived and an emerging one, offer direct experimental access even to such complex atomic structures: Diffuse Scattering and Atomic Resolution Holography. Finally, in this overview, we introduce their specific application to aperiodic crystals and discuss their merits and difficulties.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Vortical interactions in turbulent thermoacoustic systems
This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately 52° between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. As a result, we further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.
Sahay, Ankit [Indian Institute of Technology Madra↗
Particle Dynamics in a Diblock-Copolymer-Based Dodecagonal Quasicrystal and Its Periodic Approximant by X-Ray Photon Correlation Spectroscopy
Temperature-dependent X-ray photon correlation spectroscopy (XPCS) measurements are reported for a binary diblock copolymer blend that self-assembles into an aperiodic dodecagonal quasicrystal (DDQC) and a periodic Frank-Kasper σ phase approximant. The measured structural relaxation times are Bragg scattering wavevector-independent and are five times faster in the DDQC than the σ phase, with minimal temperature dependence. Further, the underlying dynamical relaxations are ascribed to differences in particle motion at the grain boundaries within each of these tetrahedrally close-packed assemblies. These results identify unprecedented particle dynamics measurements of tetrahedrally-coordinated micellar block polymers, thus expanding the application of XPCS to ordered soft materials.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Scanning tunneling microscopy of ferrocenecarboxylic acid assemblies on Ag(111): a comparison to Au(111)
Scanning tunneling microscopy was used to investigate the arrangement of ferrocenecarboxylic acid (FcCOOH) monolayers on the Ag(111) surface. Four distinct structures were observed, none of which had previously been observed on other surfaces. Structural analysis indicates that these assemblies are primarily composed of dimers. VASP calculations support the molecular assignments of the monolayer structures, while ESI-MS experiments confirm that dimers are the predominant species in solution. Of particular note, the cyclic pentamers and aperiodic packing observed for FcCOOH on Au(111) were not observed, despite (1) the similarity of the Ag(111) and Au(111) surfaces in reactivity, flatness, and lattice constant, and (2) prior explanation of the Au(111) monolayer in terms of molecule–molecule interactions alone. It is clear that while the surface does not have a template structure, it has a significant influence on which structures are formed.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Simulation of enhanced light extraction from periodic, disordered, and quasi-periodic OLED structures
Here we have developed a rigorous scattering matrix theory of light emission from periodically structured media using a Green’s function approach. We computationally simulate the spectral power inside the structure, incorporating Purcell factor enhancements, and find internal waveguiding modes and plasmonic losses. We simulate the light-outcoupling factor η out and describe how corrugations and structured media can enhance η out . We have extended our framework to describe non-periodic disordered arrays as well as aperiodic quasi-crystalline arrays. Flat organic light-emitting diodes (OLEDs) have low outcoupling with η out ~20% since most of the light is trapped in waveguided modes in higher index layers or lost to plasmonic excitations at the metal cathode. Periodically corrugated OLEDs can achieve highly enhanced η out ~65%-70% for pitch values between 1000 and 2000 nm, representing an enhancement factor >3 over planar structures. Periodic corrugations strongly diffract trapped waveguided and plasmonic modes to the emissive air cone. Disordered templates also can cause significant enhanced outcoupling with η out ~50%-55% for smaller nearest-neighbor separations of 300–400 nm. Quasi-crystalline tilings can also lead to enhancements of η out ~50%-55%. This framework can be utilized to design novel structured media that can generate high light extraction.
42 ENGINEERING↗