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At least 1,207 records · Page 67

Towards a Deeper Fundamental Understanding of (Al,Sc)N Ferroelectric Nitrides

Density functional theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely, the fourfold-coordinated wurtzite (WZ) polar structure and a five-fold coordinated paraelectric hexagonal phase (denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest-energy state within hexagonal symmetry as the Sc concentration increases from 0 to 0.4. Furthermore, the model points to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters-one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows us to reproduce their finite-temperature polar properties well and that a value of the axial ratio close to that of the ideal WZ structure implies a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices having, e.g., low operating voltages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural, Elastic, and Electronic Properties of CeN and LuN Using: Ab Initio Study

We report on the electronic, structural, and elastic property calculations conducted for the rare-earth (RE) nitride compounds in the rocksalt structure (CeN and LuN compounds) using the full-potential linear muffin-tin orbital method (FP-LMTO) based on the spin density functional theory (DFT) calculations using the LSDA + U approach (local spin density approximation with Hubbard-U corrections). The LSDA + U approximation is applied to the 4f as well as 5d states. Various space groups were considered including the NaCl (Fm-3m (225)), the cesium chloride [CsCl(Pm-3m (221))], and the zinc blende [ZnS(F-43m 216))]. Our obtained results indicate that the NaCl-type structure is stable than all the other phases, while the predicted elastic constants were found to satisfy the mechanical stability. The related mechanical properties such as the anisotropy factor (A), Poisson’s ratio (υ), Young’s modulus (E), and the shear modulus (G) for the same NaCl structure were also calculated. Finally, the band structure calculations of the CeN and LuN have revealed half-metallic and semiconductor behaviour, respectively. The obtained results are presented and in-depth discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form ana- lytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady- state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

Li, G.X.↗

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An Exchange-Correlation Functional Capturing Bulk Surface and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semilocal approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize our progress in addressing this issue. We describe the construction of the BSC exchange-correlation functional within the subsystem functional formalism which enables us to capture bulk, surface, and confinement physics with a single exchange-correlation functional. We report on the initial assessment of this functional within the jellium surface system and demonstrate that the BSC functional captures the confinement physics more accurately than standard semilocal exchange-correlation functionals. We conclude by outlining our future research objectives which focus on refining the functional form of the BSC functional and achieving significantly more accurate energetics of materials containing f and d electrons than existing semilocal functionals.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low-Energy E1 Strength Distributions of {sup 68}Ni

We study the effects of the coupling between one- and two-phonon components of the wave functions on the low-energy electric dipole response of {sup 6}8Ni in a microscopic model based on an effective Skyrme interaction SLy5. The finite rank separable approach for the quasiparticle random phase approximation is used. The effect of phonon-phonon coupling leads to the fragmentation of the E1 strength to a lower energy and improves the agreement with available experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty.

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual failure after some amount of elapsed time. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation of PLOAS with constant delay times, (iii) Approximation and illustration of PLOAS with constant delay times, (iv) Formal representation of PLOAS with aleatory uncertainty in delay times, (v) Approximation and illustration of PLOAS with aleatory uncertainty in delay times, (vi) Formal representation of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, (vii) Approximation and illustration of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, and (viii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

97 MATHEMATICS AND COMPUTING↗

Effect of Fe Doping and O Vacancies on the Magnetic Properties of Rutile TiO{sub 2}

Magnetism sources of Fe doping and O vacancies, which coexist in the presence of rutile TiO{sub 2}, are controversial and require a resolution. The effects of Fe doping and point defect on the magnetism of rutile TiO{sub 2} were studied using geometry optimization and energy calculation based on the first principle generalized gradient approximation + U method (GGA+U) of density functional theory. Fe/Vo ratio is 1:1 in rutile TiO{sub 2}. The next closest distance between Fe and Vo is 0.04082 nm. The formation energy of the doping system is the smallest. This doping system has the highest stability. The coexistence of Fe doping and O vacancy achieved ferromagnetic long-range order. The different ratios of Fe/Vo are 1:1, 1:2, 2:1, and 2:2. The magnetic properties of the doping system are significantly different. At a ratio of 2:1, the magnetic moment is the largest among all doping systems. Moreover, the Curie temperature of the doping system can be higher than room temperature. These findings can obtain dilute magnetic semiconductors with potential application value. At a Fe/V{sub O} ratio of 2:2, the Ti{sub 14}Fe{sub 2}O{sub 30} system produces a half-metallic property of 100% electron spin polarizability. This is the most valuable application for designing and preparing novel spintronic injection source dilute magnetic semiconductors. The magnetic source is mainly mediated by the holes generated by Fe doping and O vacancy complexes, thereby causing the spin polarization double exchange effect on the electron of Ti–3d orbital atoms near the O vacancy, O–2p electron orbital, and Fe–3d electron orbital. This feature is consistent with the following theories: the mean field approximation and the double exchange mechanism theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterizing the impact of model error in hydrologic time series recovery inverse problems

Hydrologic models are commonly over-smoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate high-resolution information. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased “observation noise” term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. In this paper, model error is considered for an important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of systematic model error on time series recovery for both well-determined and over-determined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. Finally, a possible diagnostic criterion for blind transfer function characterization is also uncovered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental determination of the valence band offsets of ZnGeN 2 and (ZnGe) 0.94 Ga 0.12 N 2 with GaN

A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN 2 /GaN heterointerface has inspired novel band-engineered III-N/ZnGeN 2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe) 1- x Ga 2 x N 2 , for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN 2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe) 0.94 Ga 0.12 N 2 the value was determined to be 1.29 eV, ~10%–20% lower than that of ZnGeN 2 . The experimental determination of the large band offset between ZnGeN 2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.

Physics↗

Free energy functionals for polarization fluctuations: Pekar factor revisited

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekar’s perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found for the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).

14 SOLAR ENERGY↗

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and here we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

74 ATOMIC AND MOLECULAR PHYSICS↗

TU-H-CAMPUS-IeP1-01: Bias and Computational Efficiency of Variance Reduction Methods for the Monte Carlo Simulation of Imaging Detectors

Purpose: Variance reduction techniques (VRTs) are employed in Monte Carlo simulations to obtain estimates with reduced statistical uncertainty for a given simulation time. In this work, we study the bias and efficiency of a VRT for estimating the response of imaging detectors. Methods: We implemented Directed Sampling (DS), preferentially directing a fraction of emitted optical photons directly towards the detector by altering the isotropic model. The weight of each optical photon is appropriately modified to maintain simulation estimates unbiased. We use a Monte Carlo tool called fastDETECT2 (part of the hybridMANTIS open-source package) for optical transport, modified for VRT. The weight of each photon is calculated as the ratio of original probability (no VRT) and the new probability for a particular direction. For our analysis of bias and efficiency, we use pulse height spectra, point response functions, and Swank factors. We obtain results for a variety of cases including analog (no VRT, isotropic distribution), and DS with 0.2 and 0.8 optical photons directed towards the sensor plane. We used 10,000, 25-keV primaries. Results: The Swank factor for all cases in our simplified model converged fast (within the first 100 primaries) to a stable value of 0.9. The root mean square error per pixel for DS VRT for the point response function between analog and VRT cases was approximately 5e-4. Conclusion: Our preliminary results suggest that DS VRT does not affect the estimate of the mean for the Swank factor. Our findings indicate that it may be possible to design VRTs for imaging detector simulations to increase computational efficiency without introducing bias.

60 APPLIED LIFE SCIENCES↗

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size, thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e., those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI algorithm. Furthermore, the cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, and (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with an increasing rank for the first three systems, even connected octuple excitations still appear important in Cr 2 , suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Implications of the fractional charge of hydroxide at the electrochemical interface

Rational design of materials that efficiently convert electrical energy into chemical bonds will ultimately depend on a thorough understanding of the electrochemical interface at the atomic level. Towards this goal, the use of density functional theory (DFT) at the generalized gradient approximation (GGA) level has been applied widely in the past 15 years. In the calculation of electrochemical reaction energetics using GGA-DFT, it is frequently implicitly assumed that ions in the Helmholtz plane have unit charge. However, the ion charge is observed to be fractional near the interface through both a capacitor model and through Bader charge partitioning. In this work, we show that this spurious charge transfer can be effectively mitigated by continuum charging of the electrolyte. Finally, we show that, similar to hydronium, the observed fractional charge of hydroxide is not due to a GGA level self-interaction error, as the partial charge is observed even when using hybrid level exchange–correlation functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Model for Approximately Stretched-Exponential Relaxation with Continuously Varying Stretching Exponents

Relaxation in glasses is typically approximated by a stretched-exponential form: \(f(t) = A \exp [-(t/\tau )^{\beta }]\) . Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corté et al. (Nat Phys 4:420–424, 2008 ) can be well approximated by a stretched exponential with an exponent \(\beta \) that depends on the strain amplitude: \(0.25< \beta < 1\) . In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.

36 MATERIALS SCIENCE↗

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. In this study, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead–spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k B T. We find that, for all melts and blends, interaction of a few k B T between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k B T and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

36 MATERIALS SCIENCE↗

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗