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DOE OSTI2025

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗

DOE OSTI2020

Sculpting Non-Machinable Porous Materials

The goal of this project was to establish the scientific basis for subtractive manufacturing (sculpting) of porous materials using ion beams. Using the catcher foil technique, complemented with molecular dynamics simulations, we studied the dependence of the sputtering yield of Ag and Au nanofoams as a function of foam monolith density, ion mass, and the beam incidence angle, and compared these dependencies to those measured for full-density solids. We found that the foam sputtering yield was considerably lower than for the full-density solid. The sputtering yield increased with beam incidence angle, and the open structure of the foam suppressed the development of collision cascades. We also found that the sputtering yield decreased with increasing foam density. The simulation revealed a significant redeposition of sputtered atoms in the foam.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Inflow, Outflow, Yields, and Stellar Population Mixing in Chemical Evolution Models

Chemical evolution models are powerful tools for interpreting stellar abundance surveys and understanding galaxy evolution. However, their predictions depend heavily on the treatment of inflow, outflow, star formation efficiency (SFE), the stellar initial mass function, the SN Ia delay time distribution, stellar yields, and stellar population mixing. Using flexCE, a flexible one-zone chemical evolution code, we investigate the effects of and trade-offs between parameters. Two critical parameters are SFE and the outflow mass-loading parameter, which shift the knee in [O/Fe]–[Fe/H] and the equilibrium abundances that the simulations asymptotically approach, respectively. One-zone models with simple star formation histories follow narrow tracks in [O/Fe]–[Fe/H] unlike the observed bimodality (separate high- α and low- α sequences) in this plane. A mix of one-zone models with inflow timescale and outflow mass-loading parameter variations, motivated by the inside-out galaxy formation scenario with radial mixing, reproduces the two sequences better than a one-zone model with two infall epochs. We present [X/Fe]–[Fe/H] tracks for 20 elements assuming three different supernova yield models and find some significant discrepancies with solar neighborhood observations, especially for elements with strongly metallicity-dependent yields. We apply principal component abundance analysis to the simulations and existing data to reveal the main correlations among abundances and quantify their contributions to variation in abundance space. For the stellar population mixing scenario, the abundances of α -elements and elements with metallicity-dependent yields dominate the first and second principal components, respectively, and collectively explain 99% of the variance in the model. flexCE is a python package available at https://github.com/bretthandrews/flexCE.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1981

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

Mark, W. D.↗

DOE OSTI2025

Fragmentation dynamics through geometrical distortion in low-energy electron attachment to carbon disulfide

The dissociation dynamics of dissociative electron attachment to carbon disulfide is studied using the velocity map imaging technique. Ion yields of the S− and CS− fragments are measured as a function of incident electron energy between 2 and 12 eV. Energy and angle-differential yields of the S− fragments are analyzed to investigate the dynamics of the CS2− anion around the 3.8-eV peak. The resonances involved in this fragmentation are identified and characterized in calculations using the well-known R-matrix method. Based on our measurements and the geometry dependence of the calculated resonances, we propose that a geometrical distortion of the transient negative-ion state of CS2 is necessary for S-CS bond dissociation to occur.

Paul, Anirban↗

DOE OSTI2026

Data for Sugar Accumulation Enhancement in Sorghum Stem is Associated with Reduced Reproductive Sink Strength and Increased Phloem Unloading Activity

Sweet sorghum has emerged as a promising source of bioenergy mainly due to its high biomass and high soluble sugar yield in stems. Studies have shown that loss-of-function Dry locus alleles have been selected during sweet sorghum domestication, and decapitation can further boost sugar accumulation in sweet sorghum, indicating that the potential for improving sugar yields is yet to be fully realized. To maximize sugar accumulation, it is essential to gain a better understanding of the mechanism underlying the massive accumulation of soluble sugars in sweet sorghum stems in addition to the Dry locus. We performed a transcriptomic analysis upon decapitation of near-isogenic lines for mutant (d, juicy stems, and green leaf midrib) and functional (D, dry stems and white leaf midrib) alleles at the Dry locus. Our analysis revealed that decapitation suppressed photosynthesis in leaves, but accelerated starch metabolic processes in stems. SbbHLH093 negatively correlates with sugar levels supported by genotypes (DD vs. dd), treatments (control vs. decapitation), and developmental stages post anthesis (3d vs.10d). D locus gene SbNAC074A and other programmed cell death-related genes were down regulated by decapitation, while sugar transporter-encoding gene SbSWEET1A was induced. Both SbSWEET1A and Invertase 5 were detected in phloem companion cells by RNA in situ assay. Loss of the SbbHLH093 homolog, AtbHLH093, in Arabidopsis led to a sugar accumulation increase. This study provides new insights into sugar accumulation enhancement in bioenergy crops, which can be potentially achieved by reducing reproductive sink strength and enhancing phloem unloading.

Transcriptomics↗

DOE OSTI2017

Recovery of Rare Earth Elements from Low-Grade Feedstock Leachates Using Engineered Bacteria

The use of biomass for sorption of rare earth elements (REEs) for bioremediation and biomining applications has been the subject of many recent investigations. However, REE adsorption by bioengineered systems has been scarcely documented, and rarely tested with complex natural feedstocks. In this study, we engineered E. coli cells for enhanced cell surface-mediated extraction of REEs. Using Lpp-OmpA as an anchor, up to 16 copies of a Lanthanide binding tag (LBT) per OmpA protein were displayed on the E. coli cell surface, resulting in a 2-fold increase in Tb adsorption capacity compared to control cells. To test the efficacy of engineered E. coli cells to extract REEs from complex source materials, biosorption was performed with leachates from two mine tailings and two rare earth deposits. Although control E. coli cells exhibited preferential adsorption of REEs over most metals, functionalization of the cell surface with LBT yielded several notable advantages. First, the efficiency of REE adsorption from all tested leachates was enhanced with distribution coefficients for individual REEs increased by 2-10 fold. Second, although, Cu, Al, Ga and Pb were found to be the best competitors for REE binding to the E. coli cell surface, LBT-display enhanced the cell surface affinity for REEs over all non-REEs except Cu. Third, LBT-display systematically enhanced the affinity of the cell surface for REEs as a function of decreasing atomic radii, providing a means to separate high value HREEs such as Dy and Tb from more common LREEs such as La. Altogether, our results demonstrate that REE biosorption of high efficiency and selectivity can be achieved by engineering the native bacterial surface.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Selective recovery of rare earth elements with ligand-functionalized polymers in fixed-bed adsorption columns

Rare earth elements (REE) are a group of valuable metals with growing demand and broad applications. Mineral ores, the traditional sources of REE, require significant capital investment and their refinement has been a source of environmental contamination. Industrial fluids and natural REE-bearing liquids are potential alternative sources for these metals. This work investigated the performance and REE selectivity of polymer resin beads functionalized with N,N-bis(phosponomethyl)glycine (BPG) for extraction of REE from saline solutions in fixed-bed adsorption columns. Competitive batch adsorption experiments were conducted with various metals (Nd, Gd, Ho, Al, Fe, Co, Ni, Ba, Pb, Th, and U) and the BPG-functionalized resins were up to 137 times more selective for REE than aminated resins. In column experiments, the BPG-functionalized resins preferentially adsorbed heavier metals and REE were strongly retained in the functionalized column, taking 270 times longer than the amine column to reach 10% breakthrough and 128 times longer to reach 50% breakthrough. REE bound to the BPG-functionalized resins were recovered with a dilute HNO3 solution, yielding REE concentrations up to 236 times higher than the influent feedstock. This work provides new insight into the operational performance of novel functionalized adsorbents for recovery of REE from saline fluids.

42 ENGINEERING↗

DOE OSTI2021

Stress-Induced Changes in Alternative Splicing Landscape in Rice: Functional Significance of Splice Isoforms in Stress Tolerance

Improvements in yield and quality of rice are crucial for global food security. However, global rice production is substantially hindered by various biotic and abiotic stresses. Making further improvements in rice yield is a major challenge to the rice research community, which can be accomplished through developing abiotic stress-resilient rice varieties and engineering durable agrochemical-independent pathogen resistance in high-yielding elite rice varieties. This, in turn, needs increased understanding of the mechanisms by which stresses affect rice growth and development. Alternative splicing (AS), a post-transcriptional gene regulatory mechanism, allows rapid changes in the transcriptome and can generate novel regulatory mechanisms to confer plasticity to plant growth and development. Mounting evidence indicates that AS has a prominent role in regulating rice growth and development under stress conditions. Several regulatory and structural genes and splicing factors of rice undergo different types of stress-induced AS events, and the functional significance of some of them in stress tolerance has been defined. Both rice and its pathogens use this complex regulatory mechanism to devise strategies against each other. This review covers the current understanding and evidence for the involvement of AS in biotic and abiotic stress-responsive genes, and its relevance to rice growth and development. Furthermore, we discuss implications of AS for the virulence of different rice pathogens and highlight the areas of further research and potential future avenues to develop climate-smart and disease-resistant rice varieties.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Simulations of x-ray absorption spectra for CO desorbing from Ru(0001) with transition-potential and time-dependent density functional theory approaches

The desorption of a carbon monoxide molecule from a Ru(0001) surface was studied by means of X-ray Absorption Spectra (XAS) computed with Transition Potential (TP-DFT) and Time Dependent (TD-DFT) DFT methods. By unraveling the evolution of the CO electronic structure upon desorption, we observed that at 2.3 Å from the surface, the CO molecule has already predominantly gas-phase character. While C 1s XAS is quite insensitive to changes in the C–O bond length, the O 1s excitation is very sensitive with the π* coming down in energy upon CO bond stretching, which competes with the increase in orbital energy due to the repulsive interaction with the metallic surface. We show in a systematic way that the TP-DFT method can describe the XAS rather well at the endpoints (chemisorbed and gas phase) but is affected by artificial charge transfer and/or incorrect spin treatment in the transition region in cases like CO, where there are low-lying π* orbitals and large exchange interactions between the core 1s and valence-acceptor π* orbitals. As an alternative, we demonstrate by comparing with experimental data that a linear response approach using TD-DFT employing common exchange-correlation functionals and finite-size clusters can yield a good description of the spectral evolution of the 1s → π* transition with correct spin and gas-to-chemisorbed chemical shifts in good agreement with experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1997

High-Resolution Studies of Extreme-Ultraviolet Emission from CO by Electron Impact

We report a high-resolution study (0.0036 nm full width at half maximum) of electron-impact-induced emission spectra of CO at 30-, 75-, and 100-eV electron-impact energies. The spectral features were acquired in optically thin conditions. At the specified resolution, attainable with our 3-m vacuum ultraviolet spectrometer, we observe rotationally resolved emission bands of CO in the extreme ultraviolet, from the vibronic states B (sup 1)sigma(sup +)(0), C (sup 1)sigma(sup+)(0), and E (sup 1)pi(0), to the ground state X (sup 1)sigma(sup +)(0). A simple model of these bands, based on the Honl-London factors and the rotational constants, is constructed and is shown to be in good agreement with the observed spectra. The predissociation yield for the E (sup 1)pi electronic state has been determined, showing that the E state has the largest predissociation cross section of CO for all singlet-state Rydberg series members. The excitation function of the [E (sup 1)pi(0) yields X (sup 1)sigma(sup +)(0)] transition, in the 0-800-eV impact energy range, is measured, permitting determination of the oscillator strength by using a modified Born approximation analytical fit.

Ciocca, Marco↗

DOE OSTI2021

Fragmentation of jets containing a prompt J$/\psi$ meson in PbPb and pp collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV

Jets containing a prompt J$/\psi$ meson are studied in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV, using the CMS detector at the LHC. Jets are selected to be in the transverse momentum range of 30 $\lt p_\mathrm{T} \lt$ 40 GeV. The J$/\psi$ yield in these jets is evaluated as a function of the jet fragmentation variable $z$, the ratio of the J$/\psi$$p_\mathrm{T} $ to the jet $p_\mathrm{T}$. The nuclear modification factor, $R_\mathrm{AA}$, is then derived by comparing the yield in lead-lead collisions to the corresponding expectation based on proton-proton data, at the same nucleon-nucleon center-of-mass energy. The suppression of the J$/\psi$ yield shows a dependence on $z$, indicating that the interaction of the J$/\psi$ with the quark-gluon plasma formed in heavy ion collisions depends on the fragmentation that gives rise to the J$/\psi$ meson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Effects of size, geometry, and testing temperature on additively manufactured Ti-6Al-4V titanium alloy

This article presents a comprehensive study concerning size and geometry effect on the ambient and high-temperature mechanical behavior of additively manufactured laser powder bed fusion Ti-6Al-4V alloy. Key mechanical property metrics are presented, including strain hardening rate, yield strength, and Young’s modulus as a function of thickness and testing temperature (ambient, 250 °C, and 450 °C). Here, the effect of specimen size on manufacturing-induced microstructural feature formation is demonstrated and discussed. A detailed analysis regarding Young’s modulus, yield strength, and strain hardening rate variation at elevated temperatures is also presented. Size effect and temperature-sensitive deformation mechanisms are linked to the underlying microstructural deformation mechanisms activated at respective temperatures. Counter-intuitively, this study determined that irrespective of the geometry, strain hardening rates increased as temperature increased. An in-depth microstructural examination is presented to explain the stated observation. The texture of Interrupted tensile test samples examined for ambient, 250 °C, and 450 °C post-yield was observed to be unchanged, indicating the strain hardening behavior was not texture dependent. Schmid factor analysis, coupled with experimental findings from previous work, was implemented to generate a hypothesis. This hypothesis suggests that the drop in critical resolved shear stress for basal and pyramidal slip systems, as temperature increases, paired with the high dislocation density of laser powder bed fusion Ti-6Al-4V, leads to dislocation entanglement and results in increased strain hardening at elevated temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2017

SUNSPOT AND STARSPOT LIFETIMES IN A TURBULENT EROSION MODEL

Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient D : an inverse power-law dependence D ∝ B {sup −ν} and a step-function dependence of D on the magnetic field magnitude B . Analytical self-similar solutions are presented for the power-law case, including solutions exhibiting “super fast” diffusion. For the step-function case, the heat-balance integral method yields approximate solutions, valid for moderately suppressed diffusion in the spot. The accuracy of the resulting solutions is confirmed numerically, using a method which provides an accurate description of long-time evolution by imposing boundary conditions at infinite distance from the spot. The new models may allow insight into the differences and similarities between sunspots and starspots.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

A function approximation approach to anomaly detection in propulsion system test data

Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.

Whitehead, Bruce A.↗

DOE OSTI2020

Improved Infrared Optical Constants from Pressed Pellets: II. Ellipsometric n and k Values for Ammonium Sulfate with Variability Analysis

Infrared spectral imaging is facilitated via the comparison of spectra recorded in situ to a databank of actual or synthetic infrared reflectance spectra. It has recently been shown that reference spectra corresponding to the many different morphological forms of the same chemical can be generated synthetically using the imaginary, k, and real, n, components of the complex refractive index, n~ = n + ik. One method to obtain the n and k vectors is infrared ellipsometry, which measures the changes in amplitude, tan ?, and phase, ?, of polarized light reflected from the sample both as a function of wavenumber and angle of incidence. The method requires specularly reflected light so best results are usually obtained with polished planar samples of large surface area. Due to the difficulties of obtaining such samples, however, we investigate the possibility of pressing powders of neat materials and obtaining the corresponding optical constants from the pellets. In this paper, variability in the sample pellet and preparation method is investigated, as is variability in the fitting procedure for the derived optical constants. The n/k vectors are derived from the measured ellipsometric parameters, tan ? and ?, as they are fit by an oscillator model which yield n(?) and k(?) vectors as a function of wavenumber, ?. Construction of the oscillator model is not automatic and depends on significant input from the analyst as well as the sample’s physical characteristics. For the pellet pressing, the experimental variability was found to be minimized for size-selected powdered samples as gauged by the minimal variance in ? and ? for three different pellets; similarly, the analytical precision for multiple measurements of the same pellet was also quite good, suggesting that a pressed pellet is a viable sample preparation method. The greatest variability came in the analytic fitting procedure with differences up to 20% arising from four different fits to the same data set. The final ellipsometric n/k data are compared to literature values obtained from crystalline (NH4)2SO4 samples as well as single-angle reflectance measurements that also used pressed pellets. Comparison with the previous literature values shows generally good agreement although higher k-values are observed for the independent sets of data derived from pressed pellets. These data are suggested as an improved set of optical constants for (NH4)2SO4.

optical constants, ellipsometry, ammonium sulfate,↗

DOE OSTI2024

Measurement of Neutron Multiplicity in Charged Current Neutrino Interactions on Oxygen

The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a 26-ton gadolinium-doped water Cherenkov detector located 100~meters downstream in the Booster Neutrino Beam (BNB) at the Fermi National Accelerator Laboratory (Fermilab). Its primary goals are to (1) measure the neutron yield from $\nu_\mu$ interactions as a function of momentum transfer $Q^2$ so that neutrino-nucleus interaction models can be better constrained, and (2) demonstrate the power of novel, fast-timing detectors with the first deployment of Large Area Picosecond PhotoDetectors (LAPPDs). Current knowledge of neutrino-nucleus interactions fall short in modeling the topologies of such interactions, leading to inaccurate reconstruction of event kinematics such as particle energy, direction, and vertex. As a consequence, the accuracy of cross section measurements is impacted, which is necessary for precise physics measurements. Neutrons are an indication of inelasticity and affect the determination of the energy of the parent neutrino. Quantifying the neutron yield is a step towards reducing the associated uncertainties, and thus improving our understanding of these complex interactions and benefiting the next generation of long-baseline neutrino experiments. ANNIE will make use of LAPPDs to measure neutron multiplicity of CC-0$\pi$ $\nu_\mu$ interactions on oxygen, making it the first experiment to deploy an array of these photodetectors. Because the LAPPD is a novel photodetection technology, much customization is required to integrate it into existing electronics. The first half of this thesis covers the significant progress made towards the first deployment of the LAPPD system. From its test stand at Fermilab, the LAPPD system was systematically tested and put together until deployment readiness was achieved. I present my contributions to the design, fabrication, and testing of the waterproof housing and cables, and the commissioning of the LVHV board that powers the LAPPD and its readout electronics. These efforts brought the LAPPD system significantly closer to deployment, and eventually first data. The second half of this thesis presents the vertex and energy reconstruction algorithms developed to analysis the beam data with PMT-only information. While much progress has been made towards the deployment of LAPPDs, with several in the detector tank, efforts to integrate the LAPPD datastream are in progress. Thus, I developed a ring edge detection technique using PMT data to fit the muon vertex and determine its energy. The analysis in this thesis finds average neutron yields of $\Bar{n}_{data} = 0.452 \pm 0.039 (\text{stat}) \pm 0.27 (\text{sys})$ for a selection of muon neutrino candidates in the fiducial volume of ANNIE and corrected with an averaged neutron detection efficiency. An equivalent analysis for simulated beam data results in an average neutron yield of $\Bar{n}_{MC} = 0.582 \pm 0.018 (\text{stat}) \pm 0.25 (\text{sys})$. Future work includes application of efficiency corrections at a positional level, quantification of all systematic uncertainties, and neutron multiplicity measurements with other event topologies.

43 PARTICLE ACCELERATORS↗

NASA NTRS1981

Laser annealing of ion implanted CZ silicon for solar cell junction formation

The merits of large spot size pulsed laser annealing of phosphorus implanted, Czochralski grown silicon for function formation of solar cells are evaluated. The feasibility and requirements are also determined to scale-up a laser system to anneal 7.62 cm diameter wafers at a rate of one wafer/second. Results show that laser annealing yields active, defect-free, shallow junction devices. Functional cells with AM 1 conversion efficiencies up to 15.4% for 2 x 2 cm and 2 x 4 cm sizes were attained. For larger cells, 7.62 cm dia., conversion efficiencies ranged up to 14.5%. Experiments showed that texture etched surfaces are not compatible with pulsed laser annealing due to the surface melting caused by the laser energy. When compared with furnace annealed cells, the laser annealed cells generally exhibited conversion efficiencies which were equal to or better than those furnace annealed. In addition, laser annealing has greater throughput potential.

Katzeff, J. S.↗