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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The integrated miniaturized electrostatic analyzer: A space plasma environment sensor

The integrated Miniaturized Electrostatic Analyzer (iMESA) was a satellite-based ionospheric sensor that operated on NASA’s Space Test Program Satellite (STPSat-3) from December 2013 to July 2019. The instrument’s scientific objective was to (1) measure the plasma density in low Earth orbit, (2) measure the plasma temperature in low Earth orbit, and (3) quantify the spacecraft potential with respect to the ambient plasma potential in the ionosphere. iMESA sampled the ionosphere every 10 s by measuring the ion current density through the ESA as a result of the motion of the spacecraft through the plasma. Current density spectra were transmitted to the ground where they were post-processed into ion density spectra and then analyzed numerically to determine the ion density, ion temperature, and spacecraft potential. This article discusses the instrument design and simulation, the determination of a geometric factor, and data processing procedures and evaluates the final data product with regard to the mission success criteria. Here, the ion density and ion temperature captured by the iMESA instrument are on the same order and range as the values predicted in the literature. The spacecraft potential was also quantified. The conclusion after the evaluation of the instrument’s data product is that the scientific mission is successful on all three points.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Holistic Numerical Calibration of the iMESA Electrostatic Analyzer

A drifted Maxwellian velocity distribution is the most common model used to interpret the data from low-energy charged-particle instruments onboard spacecraft that are used to investigate the ambient plasma environment in the low Earth orbit (LEO). An original method is presented for determining the flow parameters (density, temperature, and flow energy) of such a distribution from the output of the integrated miniaturized electrostatic analyzer, which has been successfully flown on several LEO missions. Rather than attempting to deconvolve from the on-orbit data the analyzer’s response to an ideal, monoenergetic input, numerical simulation is used to predict and parameterize the response of the device to an input distribution that includes an isotropic, non-zero temperature, yielding a straightforward method for extracting the flow parameters from the spacecraft data. The method is computationally simple enough to be incorporated into a robust algorithm suitable for rapid batch processing or real-time analysis of data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Exploration of Options for Ultra-Fast Mass Spectroscopy for Pulsed Power Applications

Mega-ampere class pulsed power machines drive intense currents into small volumes to study high energy and density environments. Power lost during these events is a difficult and paramount problem to solve. For example, facilities such as Sandia National Laboratories’ Z machine experience meaningful power loss, which can be linked to non-linear ohmic heating at high currents (i.e., 26 MA on Z) leading to thermal desorption of contaminants and subsequent shunt plasma formation. Characterizing and understanding this type of thermal desorption is key to design optimizations necessary to minimize current loss, which will be even more important for next generation pulsed power. This type of characterization requires the ability to identify and determine concentration of analytes with nanosecond resolution given the pulse width of Z is on the order of 100 ns. This report summarizes progress on a small exploratory project focused on investigating options to meet this challenge using mass spectrometry. The main focus of these efforts utilized an Energy and Velocity Analyzer for Distributions of Electric Rockets intending to determine how quickly transient data could be resolved. This probe combines an electrostatic analyzer with a Wien velocity filter (ExB) to obtain ion energy and velocity distributions. Primary results from this exploratory project indicate significant additional work is needed to demonstrate a nanosecond time scale mass spectrometer for this application and also highlight that alternative detection methods such as laser-based diagnostics should be considered to meet the need for ultra-fast detection.

42 ENGINEERING↗
DOE OSTI2024

Reexpansion of charged nanoparticle assemblies in concentrated electrolytes

Electrostatic forces in solutions are highly relevant to a variety of fields, ranging from electrochemical energy storage to biology. However, their manifestation in concentrated electrolytes is not fully understood, as exemplified by counterintuitive observations of colloidal stability and long-ranged repulsions in molten salts. Highly charged biomolecules, such as DNA, respond sensitively to ions in dilute solutions. Here, we use non-base-pairing DNA-coated nanoparticles (DNA-NP) to analyze electrostatic interactions in concentrated salt solutions. Despite their negative charge, these conjugates form colloidal crystals in solutions of sufficient divalent cation concentration. We utilize small-angle X-ray scattering (SAXS) to study such DNA-NP assemblies across the full accessible concentration ranges of aqueous CaCl 2 , MgCl 2 , and SrCl 2 solutions. SAXS shows that the crystallinity and phases of the assembled structures vary with cation type. For all tested salts, the aggregates contract with added ions at low salinities and then begin expanding above a cation-dependent threshold salt concentration. Wide-angle X-ray scattering (WAXS) reveals enhanced positional correlations between ions in the solution at high salt concentrations. Complementary molecular dynamics simulations show that these ion–ion interactions reduce the favorability of dense ion configurations within the DNA brushes below that of the bulk solution. Measurements in solutions with lowered permittivity demonstrate a simultaneous increase in ion coupling and decrease in the concentration at which aggregate expansion begins, thus confirming the connection between these phenomena. Our work demonstrates that interactions between charged objects continue to evolve considerably into the high-concentration regime, where classical theories project electrostatics to be of negligible consequence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory↗
DOE OSTI2023

Ion concentration ratio measurements of ion beams generated by a commercial microwave electron cyclotron resonance plasma source

A commercially available electron cyclotron resonance (ECR) plasma source (GenII Plasma Source, tectra GmbH) is widely used for surface processing. This plasma source is compatible with ultrahigh vacuum systems, and its working pressure is relatively low, around 10 –6 –10 –4 Torr even without differential pumping. Here, we report ion flux concentration ratios for each ion species in an ion beam from this source, as measured by a mass/energy analyzer that is a combination of a quadrupole mass spectrometer, an electrostatic energy analyzer, and focusing ion optics. In this study, the examined beams were those arising from plasmas produced from feed gases of H 2 , D 2 , N 2 , O 2 , Ar, and dry air over a range of input power and working pressures. H 2 (D 2 ) plasmas are widely used for nuclear fusion applications and, hence, the ion concentration ratios of H + , H 2 + , and H 3 + reported here will be useful information for research that applies this plasma source to well-controlled plasma-material interaction studies. Ion energy distributions, stability of operation, and impurity concentrations were also assessed for each of the plasma species investigated.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Understanding the selectivity of nonsteroidal anti-inflammatory drugs for cyclooxygenases using quantum crystallography and electrostatic interaction energy

Quantum crystallography methods have been employed to investigate complex formation between nonsteroidal anti-inflammatory drugs (NSAIDs) and cyclooxygenase (COX) enzymes, with particular focus on the COX-1 and COX-2 isoforms. This study analyzed the electrostatic interaction energies of selected NSAIDs (flurbiprofen, ibuprofen, meloxicam and celecoxib) with the active sites of COX-1 and COX-2, revealing significant differences in binding profiles. Flurbiprofen exhibited the strongest interactions with both COX-1 and COX-2, indicating its potent binding affinity. Celecoxib and meloxicam showed a preference for COX-2, consistent with their known selectivity for this isoform, while ibuprofen showed comparable interaction energies with both isoforms, reflecting its nonselective inhibition pattern. Key amino-acid residues, including Arg120, Arg/His513 and Tyr355, were identified as critical determinants of NSAID selectivity and binding affinity. The findings highlight the complex interplay between interaction energy and selectivity, suggesting that while electrostatic interactions play a fundamental role, additional factors such as enzyme dynamics and the hydrophobic effect also contribute to the therapeutic efficacy and safety profiles of NSAIDs. These insights provide valuable guidance for the rational design of NSAIDs with enhanced therapeutic benefits and minimized adverse effects.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Versatile system for ion energy measurements generated by pulsed laser ionization: Insights into electron-ion dynamics

Ion energy distributions generated by pulsed laser interactions with materials are essential for applications ranging from materials science to oncology. Ion energy characterization is particularly important for an emerging mass spectrometry technique called virtual-slit cycloidal mass spectrometry (VS-CMS). The ion energy distribution influences the design and performance of VS-CMS instruments, as well as the efficacy of laser-driven ionization methods in various fields. Several established techniques, including the retarding potential method, time-of-flight (TOF) analysis, and electrostatic energy analyzers, have been employed to measure ion energy distributions. The wide range of ion energies reported highlights the strong dependence of ion energy on laser parameters, target materials, and experimental conditions, as well as the necessity of making independent measurements of the ion energy distribution for specific laser systems and materials. This paper presents the design and characterization of a simple TOF-based apparatus for measuring ion energy distributions from pulsed laser ionization without external fields. This approach minimizes perturbation of electron-ion dynamics and enables simultaneous energy measurements at multiple spatial positions. Here, the apparatus was tested using a nanosecond pulsed Nd:YAG laser operating at 1064 nm, 532 nm, and 266 nm on solid copper sheets at various laser fluences. Simultaneous measurements at different distances provide new insights into ion-electron interactions post-ionization and demonstrate the influence of laser wavelength and fluence on ion energy distributions.

Ion energy↗
DOE OSTI2020

Calibration and Initial Results of Space Radiation Dosimetry Using the iMESA-R

The integrated Miniaturized Electrostatic Analyzer-Reflight (iMESA-R) is a space weather instrument designed to measure plasma density, temperature, and spacecraft charging, along with total ionizing dose and dose rate. A constellation consisting of five nearly identical instruments has been designed and developed to act as science payloads hosted on-board Department of Defense satellites operating in low-Earth orbit. To validate the dosimetry component of the iMESA-R, a radiation test study was performed to calibrate the dosimeter and ascertain the attenuation due to the instrument aluminum housing. An 80 curie Cobalt-60 radioisotope source emitting beta, X-ray, and gamma ray radiation decay products was used to calibrate the dosimeter response as a function of distance and instrument shielding. We present results of the calibration study along with initial on-orbit data presented from the first operational iMESA-R hosted on-board Space Test Program Satellite 5 in a polar Earth orbit. The initial on-orbit data demonstrate the ability to map the radiation environment, particularly the South Atlantic Anomaly and the auroral regions using total ionizing dose rate due to electrons of E > 1.5 MeV and protons of E > 25 MeV.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Optimization of laser-target parameters for the production of stable lithium beam

A laser ion source coupled with a radio frequency quadrupole linac accelerator is being proposed as a suitable system for the production of a low energy, high-current stable lithium beam. In order to maximize the lithium yield, plasmas generated by laser ablation of different materials based on lithium (Li, LiOH, and LiNbO3) have been characterized by using a Faraday cup and an electrostatic ion analyzer in the time of flight configuration. A wide range of laser power density has been investigated (109–1012 W/cm2) using two Nd:YAG lasers operating at different wavelengths (1064 nm and 532 nm), pulse durations (6 ns and 17 ns), and maximum energies (1400 mJ and 210 mJ). This paper outlines the pros and cons of the investigated materials by studying how the ion energy, yields, and charge state distributions are modified when the laser power density is changed. Considerable attention has been paid to the higher charge states of oxygen, which may occur with the same mass-to-charge ratio of Li3+. The analysis has evidenced that LiNbO3 represents a valid target since it allows minimizing the O6+/7Li3+ ratio down to 2.5% by using a laser power density of 1.8 × 1010 W/cm2. For such a condition, a Li3+ current of 1.4 mA/cm2 has been measured.

Cannavò, A. (ORCID:0000000309759630)↗
DOE OSTI2026

FLASH-therapy suitable single-pulse proton generation using TiH 2 under nanosecond laser irradiation

We investigated proton emission from titanium hydride (TiH 2 ) targets irradiated in vacuum by a 6-ns, 1064-nm Nd:YAG laser. Time-of-flight measurements with a Faraday cup and an electrostatic ion analyzer resolved distinct proton peaks at high pulse energies, with yields on the order of 10 9 protons per shot. Systematic scans over pulse energy and up to 1000 repeated shots showed that, while the peak amplitude gradually decreased, the integrated proton number remained nearly constant. This behavior is consistent with surface-induced broadening of the plasma expansion while bulk hydrogen is replenished by diffusion and repeated ablation of fresh TiH 2 layers. Using the measured proton numbers and pulse widths, a simple direct-plasma-injection-style scaling indicates peak currents of ∼100 mA and sub-microsecond pulse durations. The pulse structure and yield satisfy key ultra-high-dose-rate criteria and, together with sustained output over 1000 shots, support TiH 2 -based laser ion sources as practical candidates for FLASH-therapy (ultra-high-dose-rate)-oriented studies and injector development using direct plasma injection.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Ultra-black coatings for space instruments: a comparison of traditional Ebonol C processes and a method for future repeatability

Ultra-black coatings have served various roles in space instrumentation and hardware. The Ebonol C coating has been used for various missions requiring low reflectivity on aluminum substrates that are electrically conducting. This coating is produced through the formation of a cupric oxide structure on an intermediate layer of copper applied to the aluminum. For many years, this commercial formulation has been used ubiquitously for space instruments. The coating relies upon details of the copper base layer that have been trade secret at various finishing companies, and the availability of the Ebonol C formulated chemistry from the chemical supplier. In recent years, this product has been discontinued at various times, leaving vendors to either rely on expired stock or to formulate their own equivalents. Here, we detail the processing methods, chemistries, and resultant coating structures that produce reflectance performance equivalent to baseline historical reflectance data. This process detail will ensure equivalent performance for such coatings for future missions and link the performance to past and currently deployed instruments.

36 MATERIALS SCIENCE↗
DOE OSTI2026

pyEF: A Python Framework for QM and QM/MM Atom-Wise Electric Field Analysis

We introduce pyEF, a software package for computing molecular electric fields, electrostatic interaction energies, and electrostatic potentials from quantum mechanical (QM) atom-centered multipole expansions with atom-wise decomposable contributions. We demonstrate the computational efficiency and accuracy of this QM-derived electric field evaluation tool through several tests. To assess the influence of the underlying QM method and charge partitioning scheme on these electrostatic quantities, we analyze over 250 configurations of an acetone solute molecule in five solvents of variable polarity. We find that electric field calculations are highly sensitive to the choice of charge partitioning method. Even among real-space charge schemes, acetone Stark tuning rates differ by up to a factor of 2. Benchmarking computed solvent dipole moments against experimental bulk values, we conclude that the CM5, ADCH, and Hirshfeld-I charge schemes most reliably capture solvent electrostatics and therefore provide a more faithful foundation for computing electric fields. When constructed from these real-space charges, electric fields are nearly insensitive to basis set size and monotonically increase in magnitude with higher Fock exchange. We also demonstrate efficient convergence of QM electrostatics when more distant molecules are represented solely by MM point charges, reducing computational overhead. Leveraging these findings, we demonstrate the use of pyEF to deduce environmental effects on a transition metal complex from a Ga 4 L 6 12– nanocage and quantify the dominant role of organic linkers in orchestrating electrostatic preorganization.

electric fields↗
DOE OSTI2024

NbZr_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys niobium-zirconium (Nb-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach \cite{PAW}. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Nb and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on NERSC-Perlmutter and OLCF-Summit using the VASP 6.3.2. The VASP calculations for every atomic structure have been performed in 2 main steps: 1. Starting from an ideal body-centered-cubic (BCC) structure, geometry optimization with low precision has been executed to perform a preliminary optimization of the atomic structure. The output for this calculations is available in the files 0.CONTCAR, 0.OUTCAR, rlx1.out. 2. Using the atomic structure resulting from the preliminary geometry optimization, a second geometry optimization has been performed using normal precision. The output for this calculations is available in the files CONTCAR, OUTCAR, rlx2.out, vaspout.h5, and vasprun.xml. Cases 1-10 have been run without generating the file 'vaspout.h5'. Every chemical composition sampled across the composition range in the dataset has its own directory. The convention used to name the directories for binary alloys is AXBY, where A and B refer to the constituents, whereas X and Y are positive integers that represent the number of atoms for each constituent and their values still sum up to 128. Each atomic structure associated with a specific chemical composition has its own sub-directory within the directory of the corresponding chemical composition. The sub-directories for each atomic structure for each chemical composition are named 'case-*', where * is a positive integer that spans all the values from 1 through 100, extremes included. The files contained in each sub-directory 'case-*' for each atomic structure are as follows: FILES contained in each subdirectory with name "case-N" where N ranges between 11 and 100, extremes included: 1. INCAR: input file that contains various parameters and settings for controlling the behavior of the electronic structure calculations 2. KPOINTS: input file that specifies the Bloch vectors (k points) used to sample the Brillouin zone 3. 0.POSCAR: input file that defines the atomic structure of a system 4. 0.CONTCAR: output file that provides the atomic positions and cell parameters after the first geometry optimization has been run with the precision variable set to PREC=Low in the INCAR file 5. 0.OUTCAR: output file that contains detailed information about the progress of a calculation after the first geometry optimization has been run with the precision variable set to PREC=Low in the INCAR file 6. rlx1.out: file with diagnostic information about the execution of the first geometry optimization with precision variable set to PREC=Low in the INCAR file 7. POSCAR: input file that defines the atomic structure of a system after the first geometry optimization has been run at low precision. This represents the input for the second geometry optimization run with the precision variable set to PREC=Normal in the INCAR file 8. CONTCAR: output file that provides the atomic positions and cell parameters after the second geometry optimization has been run with the precision variable set to PREC=Normal in the INCAR file 9. OUTCAR: output file that contains detailed information about the progress of a calculation after the second geometry optimization has been run with the precision variable set to PREC=Normal in the INCAR file 10. rlx2.out: file with diagnostic information about the execution of the second geometry optimization with precision variable set to PREC=Normal in the INCAR file 11. vaspout.h5: hierarchical HDF5 file containing the inputs and outputs of a VASP calculation. To analyze the data in this file we recommend using py4vasp. This file is only produced if the VASP version used is compiled with HDF5 support 12. vasprun.xml: contains similar information to OUTCAR, but in an xml format. 13. CHGCAR: contains the charge density data of a system. This data is crucial for analyzing electronic structures, calculating electrostatic potential, and studying the distribution of charge in a crystal or molecular system FILES contained in each subdirectory with name "case-N" where N ranges between 1 and 10, extremes included: 1. INCAR: input file that contains various parameters and settings for controlling the behavior of the electronic structure calculations 2. KPOINTS: input file that specifies the Bloch vectors (k points) used to sample the Brillouin zone 3. {ID}.POSCAR: input file that defines the atomic structure of a system at the beginning of ID execution of geometry optimization with PREC=LOW 4. {ID}.CONTCAR: output file that provides the atomic positions and cell parameters at the end of ID execution of geometry optimization with PREC=LOW in the INCAR file 5. {ID}.OUTCAR: output file that contains detailed information about the progress of a calculation after the ID execution of geometry optimization that has been run with the precision variable set to PREC=Low in the INCAR file 6. rlx1.{ID}.out: file with diagnostic information about the execution of the ID execution of the geometry optimization with precision variable set to PREC=Low in the INCAR file 7. N{ID}.POSCAR: input file that defines the atomic structure of a system after the geometry optimization run at low precision. This represents the input for the ID execution of the second geometry optimization run with the precision variable set to PREC=Normal in the INCAR file 8. N{ID}.CONTCAR: output file that provides the atomic positions and cell parameters after the ID execution of the geometry optimization run with the precision variable set to PREC=Normal in the INCAR file 9. N{ID}.OUTCAR: output file that contains detailed information about the progress of a calculation after the ID execution of the geometry optimization run with the precision variable set to PREC=Normal in the INCAR file 10. rlx2.{ID}.out: file with diagnostic information about the ID execution of geometry optimization with precision variable set to PREC=Normal in the INCAR file 11. vaspout.h5: hierarchical HDF5 file containing the inputs and outputs of a VASP calculation. To analyze the data in this file we recommend using py4vasp. This file is only produced if the VASP version used is compiled with HDF5 support 12. vasprun.xml: contains similar information to OUTCAR, but in an xml format. 13. CHGCAR: contains the charge density data of a system. This data is crucial for analyzing electronic structures, calculating electrostatic potential, and studying the distribution of charge in a crystal or molecular system This research is sponsored by the Artificial Intelligence Initiative as part of the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. This work used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725, under Directorate Discretionary awards MAT025 (Materials Science) and LRN026 (Machine Learning), and INCITE award MAT201. This work also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, under award ERCAP0025216. REFERENCES (1) Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. review B 47, 558 (1993). (2) Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251 (1994) (3) Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. materials science 6, 15–50 (1996) (4) Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. review B 54, 11169 (1996) (5) Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. review b 59, 1758 (1999)

36 MATERIALS SCIENCE↗