Self-consistent Method Research Articles

Pressure-dependent multiplet-excitation energies of α-Al2O3:Cr3+ by the first-principles method

We apply a method [Phys. Rev. B 108, 035141 (2023)], which can treat the multiplet excitations in the first-principles method, to a typical pressure indicator α-Al2O3:Cr3+. After optimizing the crystal structure under hydrostatic pressure from 0.0 to 35.0 GPa in the usual first-prinicple calculations, we obtain the multiplet energies in the method. That is, we conduct the exact diagonalization of the crystal-field model Hamiltonian which is directly determined based on the result of the quasiparticle self-consistent GW method. Our method has no parameters by hand. The calculated pressure dependences of the excitation energies agree well with those of experiments.

A Systematic Study of Two-Neutrino Double Electron Capture

In this paper, we update the phase-space factors for all two-neutrino double electron capture processes. The Dirac–Hartree–Fock–Slater self-consistent method is employed to describe the bound states of captured electrons, enabling a more realistic treatment of atomic screening and more precise binding energies of the captured electrons compared to previous investigations. Additionally, we consider all s-wave electrons available for capture, expanding beyond the K and L1 orbitals considered in prior studies. For light atoms, the increase associated with additional captures compensates for the decrease in decay rate caused by the more precise atomic screening. However, for medium and heavy atoms, an increase in the decay rate, up to 10% for the heaviest atoms, is observed due to the combination of these two effects. In the systematic analysis, we also include capture fractions for the first few dominant partial captures. Our precise model enables a close examination of low Q-value double electron capture in 152Gd, 164Er, and 242Cm, where partial KK captures are energetically forbidden. Finally, with the updated phase-space values, we recalculate the effective nuclear matrix elements and compare their spread with those associated with 2νβ−β− decay.

Spinel LiGa5O8 prospects as ultra-wideband-gap semiconductor: Band structure, optical properties, and doping

LiGa5O8 in the spinel type structure is investigated as a potential ultra-wideband-gap semiconductor. The band structure is determined using the quasiparticle self-consistent GW method, and the optical properties are calculated at the Bethe Salpeter Equation level including electron-hole interaction effects. The optical gap including exciton effects and an estimate of the zero-point motion electron phonon coupling renormalizations is estimated to be about 5.2±0.1 eV with an exciton binding energy of about 0.4 eV. Si doping as potential n-type dopant is investigated and found to be a promising shallow donor.

Non-equilibrium phase transitions in active rank diffusions

We consider N run-and-tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N = 2 leading to a stationary bound state in the attractive case. Here the evolution of the density fields is obtained in the large-N limit in terms of two coupled Burger's type equations. In the attractive case the exact stationary solution describes a non-trivial N-particle bound state, which exhibits transitions between a phase where the density is smooth with infinite support, a phase where the density has finite support and exhibits “shocks”, i.e., clusters of particles, at the edges, and a fully clustered phase. In the presence of an additional linear potential, the phase diagram, obtained for either sign of the interaction, is even richer, with additional partially expanding phases, with or without shocks. Finally, a general self-consistent method is introduced to treat more general interactions. The predictions are tested through extensive numerical simulations.

Systematic determination of a material’s magnetic ground state from first principles

We present a self-consistent method based on first-principles calculations to determine the magnetic ground state of materials, regardless of their dimensionality. Our methodology is founded on satisfying the stability conditions derived from the linear spin wave theory (LSWT) by optimizing the magnetic structure iteratively. We demonstrate the effectiveness of our method by successfully predicting the experimental magnetic structures of NiO, FePS3, FeP, MnF2, FeCl2, and CuO. In each case, we compared our results with available experimental data and existing theoretical calculations reported in the literature. Finally, we discuss the validity of the method and the possible extensions.

Efficient Quasiparticle Determination beyond the Diagonal Approximation via Random Compression.

Calculations of excited states in the Green's function formalism often invokes the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. In this paper, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO2 on an extended gold surface with nearly 3000 electrons. We find that in the extended system the size of the problem can be compressed up to 95% using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determination of Dyson orbitals in large systems.

Using optical emission spectroscopy in atmospheric conditions to track the inflight reduction of plasma sprayed TiO2−x feedstock for thermoelectric applications

Thermal spray deposition (specifically Atmospheric Plasma Spraying, APS) is a well-established surface coating technology with a broad scope of applications (i.e., insulative coatings, tribological coatings, anti-corrosion coatings, etc.). In addition, there is a constant drive to introduce the APS process into new and emerging fields. One such niche application for APS would be sub-stoichiometric TiO2−x coatings with enhanced thermoelectric performance (compared to the bulk material). The APS process in this context has a unique ability—given the use of hydrogen as a plasma gas—to reduce TiO2−x material during processing. However, to this point, there is neither a reliable nor self-consistent method to assess (nor control by parametric optimization) the inflight reduction of molten oxide particles during processing. This study shows that using Optical Emission Spectroscopy (OES), it can be possible—even in atmospheric conditions—to identify characteristic emission peaks associated with the inflight reduction of TiO2 during APS. Using this OES data, the input spray processing parameters and their influence on coating microstructure and the degree of inflight reduction of the material will be shown. Results suggest under equilibrium conditions only a minimal amount of hydrogen gas is needed in the plasma to fulfill the TiO2 reduction.

Isovector properties of finite nuclei: Constraints from neutron stars observations

The nuclear symmetry energy plays a crucial role in the structure of finite nuclei and the bulk properties of neutron stars. However, its values at high densities are highly uncertain, and the corresponding experimental data have large errors. One way to determine or at least estimate these high-density values is through neutron star observations. Recently, observations of gravitational waves from binary neutron star mergers have provided useful information on their radius and tidal deformability, which are directly related to the symmetry energy. This work attempts to use recent observations to constrain the structure of finite nuclei. Specifically, we parameterize the equation of state (EoS) describing asymmetric and symmetric nuclear matter using the parameter η = (K0L2)1/3, where K0 is the incompressibility and L is the slope parameter, The parameter η regulates the stiffness of the EoS, and we expect its values to affect both finite nuclei and neutron star properties, especially given the important role of isovector interactions. It is natural to expect that constraints on η for finite nuclei will also imply constraints on neutron star properties and vice versa. In light of the above, we propose a simple yet self-consistent method to simultaneously examine the effects of η on the properties of finite nuclei and neutron stars. We found constraints on these systems by combining recent experimental data (PREX-2) and observational data from the LIGO and Virgo detectors.

Numerical analysis of an experimental ballistic test of Al/SiC functionally graded materials

Metal/ceramic functionally graded materials (FGMs) have been increasingly used for impact-resistant applications because of their ability to combine the strength of both components. However, understanding the local response of FGMs under ballistic impact conditions remains a complex nonlinear problem. Moreover, performing experimental investigations is difficult due to technical limitations in measuring critical parameters such as stress, strain, and pressure. That is why research in this field also concentrates on modeling methodologies, such as numerical simulations. In this study, a finite element model (FEM) was implemented to investigate the behavior of a particular metal/ceramic-based FGM impacted with fragment-simulating projectiles (FSPs). The studied FGMs, exhibiting an elastoplastic behavior, were composed of aluminum (Al) and silicon carbide (SiC). The ceramic volume fraction (Vc) varies according to a power-law distribution, through the thickness. Their effective material properties were evaluated using a homogeneization-based self-consistent method. FGM’s dynamic behavior was described using the dynamic Tamura-Tomota-Ozawa model (DTTO). The numerical simulations were in good correlation with experimental results. The importance of the DTTO model's introduction and the calibration of the plastic strain criterion in the failure modeling of FGMs were highlighted. In addition, it was observed that the variation in the composition exponent and grading continuity of mechanical properties has a significant effect on the predicted ballistic limit. It was finally noted that a linearly-composed 5-layerbased specimen exhibited a higher level of ballistic resistance.

Binary Vision: The Mass Distribution of Merging Binary Black Holes via Iterative Density Estimation

Binary black hole (BBH) systems detected via gravitational-wave emission are a recently opened astrophysical frontier with many unknowns and uncertainties. Accurate reconstruction of the binary distribution with as few assumptions as possible is desirable for inference of formation channels and environments. Most population analyses have, though, assumed a power law in binary mass ratio q, and/or assumed a universal q distribution regardless of primary mass. Methods based on kernel density estimation allow us to dispense with such assumptions and directly estimate the joint binary mass distribution. We deploy a self-consistent iterative method to estimate this full BBH mass distribution, finding local maxima in primary mass consistent with previous investigations and a secondary mass distribution with a partly independent structure, inconsistent both with a power law and with a constant function of q. We find a weaker preference for near-equal-mass binaries than in most previous investigations; instead, the secondary mass has its own “spectral lines” at slightly lower values than the primary, and we observe an anticorrelation between primary and secondary masses around the ∼10 M ⊙ peak.

Dust- and inclination-corrected star formation and interstellar medium scaling relations in nearby galaxies

ABSTRACT Following from our recent work, we present a detailed analysis of star formation and interstellar medium (ISM) scaling relations, done on a representative sample of nearby galaxies. H α images are analysed in order to derive the integrated galaxy luminosity, known as a more instantaneous and accurate star formation rate (SFR) tracer, and the required photometric and structural parameters. Dust- and inclination-corrected H α luminosities, SFRs, and related quantities are determined using a self-consistent method based on previous work prescriptions, which does not require the assumption of a dust attenuation curve and use of Balmer decrements (or other hydrogen recombination lines) to estimate the dust attenuation, with the advantage of determining dust opacities and dust masses along the way. We investigate the extent to which the dust and inclination effects bias the specific parameters of these relations, the scatter and degree of correlation, and which relations are fundamental or are just a consequence of others. Most of our results are consistent with errors with other similar studies, while others come in opposition or are inconclusive. By comparing the B-band optical and H α (star-forming) discs scale lengths, we found on average the star formation distribution to be more extended than the stellar continuum emission one (the ratio being 1.10), this difference increasing with stellar mass. Similarly, more massive galaxies have a more compact stellar emission surface density than the star formation one (average ratio of 0.77). The method proposed can be applied in larger scale studies of star formation and ISM evolution, for normal low- to intermediate-redshift galaxies.

Linear Response Equations Revisited: A Simple and Efficient Iterative Algorithm.

We present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent Field method that is both simple and efficient. The algorithm makes use of the well-established symmetric and antisymmetric combinations of trial vectors but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Numerical tests showed that the algorithm is robust and stable.

Self-consistent Analysis for Optimization of AlGaAs/GaAs Based Heterostructure

The heterostructures are suitable for developing high-performance electronic and optoelectronic devices. In this work, a significant interest in the design and analysis of compound semiconductor Aluminium Gallium Arsenide (AlGaAs) and Gallium Arsenide (GaAs) heterostructures has been realized. These structures are fabricated with alternating layers of GaAs (a direct bandgap material) and AlGaAs (an indirect bandgap material) and have been used to design a range of high-performance devices, including lasers, solar cells, and field-effect transistors. A 30 nm AlGaAs consisting of a middle layer between two GaAs layers with a GaAs substrate has been reported. This work has been carried out at 300 K utilizing a quantum transport and self-consistent method for the proposed AlGaAs/GaAs one-dimensional heterostructure with a gate length of 2 nm and a voltage varying from 0 to 0.1 V. The measured values of doping density (nd) and electron density (ne) of AlGaAs/GaAs one-dimensional heterostructure are 8.96 × 1011 cm−3 and 2 × 1026 cm−3, respectively. The system response to geometric changes in several parameters has been realized. Hence, confined restricted states were computed using wave functions and energies. The GaAs layer on top of quantum well heterostructure interfaces has been used to modulate the wave functions (eigenstates) resulting in pseudo-one dimensional or small-dimension eigenstates. In this work, a comprehensive analysis of 1D AlGaAs/GaAs heterostructure through benchmarking with several homo-structures (various thicknesses) has been performed.

Mathematical micro–macro modeling of fully coupled nonlinear magneto-elastic reinforced composites

In this paper, integral equation formulations and field-dependent micromechanical modeling of global nonlinear magneto-mechanical behavior of magneto-elastic composites under high strain and magnetic field are elaborated. The modeling is obtained based on an extension of micro–macro transition inclusion problem to nonlinear behavior using field-dependent and highly nonlinear localization tensors. A methodological procedure is elaborated based on newly introduced strain and magnetic field-dependent Green tensors, strain and magnetic field-dependent integral equations linked to tensors of Eshelby and micromechanical approaches. The field-dependent global moduli are predicted based on the Mori–Tanaka approach and self-consistent method. Iterative incremental schemes based on the Newton–Raphson and fixed-point algorithms are examined and established precise semi-analytic equations of the effective magneto-elastic properties of composites that are dependent on the magnetic-strain field for different types of inclusions. A numerical code is elaborated for numerical predictions and the obtained field-dependent effective magneto-elastic coefficients are obtained and presented for various volume fractions of inclusion, types and shapes of the reinforced nonlinear composites.

Pathways of two-body dissociation of BrCNq+ (q = 2, 3) induced by electron collision.

Pathways of two-body fragmentation of BrCNq+ (q = 2, 3) have been explored by combined experimental and theoretical studies. In the experiment, the BrCN molecule is ionized by 1keV electron impact and the created fragment ions are detected using an ion momentum imaging spectrometer. Six two-body fragmentation channels are identified. By measuring the momentum vectors of the fragment ions, the kinetic energy release (KER) distributions for these channels have been determined. Theoretically, the potential energy curves of BrCNq+ (q = 2, 3) as a function of Br-C and C-N internuclear distances are calculated by the complete active space self-consistent field method. By comparing the measured KER and theoretical predictions, pathways for the fragmentation channels are assigned. The relative branching ratios of the channels are also determined.

Variation in properties of double-walled zigzag and armchair silicon nanotubes depending on SW defects and applied electric fields by SCC-DFTB method

The geometric structure and electrical properties of the zigzag DWSiNT (8,0)@(12,0) and armchair DWSiNT (5,5)@(7,7) perfect tubes with the same diameter are simulated by self-consistent charge density functional tight binding method (SCC-DFTB). We considered the defective tubes by introducing three types of Stone-Wales (SW) defects, and further investigated the impact of both strong and weak electric fields on these defective tubes. Calculations demonstrate that the atomic arrangement regularity, degree of buckling, stability, energy gap, and charge distribution strongly depend on the type of perfect tubes. Following the introduction of the SW defects, the symmetry of the tubes disappeared, and there is a obvious atomic aggregation occurring at the defects. The armchair tubes demonstrate a higher stability compared to zigzag tubes and all exhibit metallic properties. SWⅡ and SWⅢ defects in zigzag tubes result in a transition from semiconductor to semi-metallic properties. The number of charge transfer increases, and the degree of atomic aggregation is more dispersed. The effect of applied electric field strength on perfect zigzag tubes is more obvious. The weak field has minimally impacted on the stability, and the strong field makes the stability improved to some extent. The presence of a strong field caused the energy gap values of (8,0)@(12,0) tube decrease sharply, and all tubes are transformed into semi-metal or metal. The weak electric field has a more pronounced regulation of band gap within the range of 0 V/nm - 0.3 V/nm on the inner tube. The consequences of this investigation can certainly be helpful in future experimental studies.

Computationally efficient simulation methodology for railway repair welding: Cyclic plasticity, phase transformations and multi-phase homogenization

The in-situ railway repair welding process consists of multiple weld passes, which makes it significantly different from other rail welding processes. In this study, finite element simulations of repair welding are performed to predict the resulting microstructure and residual stresses. To accurately simulate the material behavior, the modeling includes phase transformation kinetics, cyclic hardening plasticity, transformation induced plasticity, and multi-phase homogenization. More specifically, four different homogenization methods are investigated: isostrain, isostress, self-consistent and linear mixture rule. The performance of the material modeling is demonstrated by simulating multiple weld passes using a classical three-bar welding experiment. Based on the results, the self-consistent method and linear mixture rule are used in a 3D full-scale railhead repair weld simulation, in which the former generates a more realistic mechanical response. The immense computational cost associated with 3D full-scale, full-detail multi-pass welding simulations is addressed by exploring different model reduction schemes. From this study, a 2D generalized plane strain model, extended with out-of-plane axial and bending stiffness, is found to replicate the full-scale model at a mere fraction of the computational cost. Finally, the longitudinal residual stress distribution obtained from the reduced model is shown to correlate well with experimental measurements.

Effective mechanical properties of frozen hydrogel with ice inclusions

Hydrogel exhibits attractive mechanical properties that can be regulated to be extremely tough, strong and resilient, adhesive and fatigue-resistant, thus enabling diverse applications ranging from tissue engineering scaffolds, flexible devices, to soft machines. As a liquid-filled porous material composed of polymer networks and water, the hydrogel freezes at subzero temperatures into a new material composed of polymer matrix and ice inclusions: the frozen hydrogel displays dramatically altered mechanical properties, which can significantly affect its safety and reliability in practical applications. In this study, based upon the theory of homogenization, we predicted the effective mechanical properties (e.g., Young's modulus, shear modulus, bulk modulus and Poisson ratio) of a frozen hydrogel with periodically distributed longitudinal ice inclusions. We firstly estimated its longitudinal Young's modulus, longitudinal Poisson ratio and plane strain bulk modulus using the self-consistent method, and then its longitudinal and transverse shear modulus using the generalized self-consistent method; further, the results were employed to calculate its transverse Young's modulus and transverse Poisson ratio. We validated the theoretical predictions against both finite element (FE) simulation and experimental measurement results, with good agreement achieved. We found that the estimated transverse Poisson ratio ranges from 0.3 to 0.53 and, at low volume fraction of ice inclusions, exhibits a value larger than 0.5 that exceeds the Poisson ratios of both the polymer matrix and the ice inclusion (typically 0.33–0.35). Compared with other homogenization methods (e.g., the rule of mixtures, the Halpin-Tsai equations, and the Mori-Tanaka method), the present approach is more accurate in predicting the effective mechanical properties (in particular, the transverse Poisson ratio) of frozen hydrogel. Our study provides theoretical support for the practical applications of frozen liquid-saturated porous materials such as hydrogel.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues.

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

Numerical and analytical studies of attenuation coefficient in 2D matrix-inclusion composites with randomly distributed circular inclusions

This paper studies the analytical and numerical evaluation of the scattering-induced attenuation coefficient of elastic waves in 2D matrix-inclusion composites with a random distribution of inclusions. An analytical self-consistent homogenization method is recalled to estimate the phase velocity and attenuation coefficient. Afterward, a finite element-based numerical approach is introduced for calculating the phase velocity and attenuation coefficient. The analytical and numerical results are compared for different area fractions and inclusion sizes, and the limitations of both methods are investigated. It is shown that the results are in good agreement when the area fraction of inclusions is less than 10%. Due to the limitation of the analytical approach, the numerical method is used for obtaining the attenuation coefficient of a particular 3D-printed composite with a quasi-incompressible matrix used for replicating the biological tissues in ultrasonic imaging.