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Export Control Requirements for Tritium Processing Design and R&D

This document will address requirements of export control associated with tritium plant design and processes. Los Alamos National Laboratory has been working in the area of tritium plant system design and research and development (R&D) since the early 1970’s at the Tritium Systems Test Assembly (TSTA). This work has continued to the current date with projects associated with the ITER project and other Office of Science Fusion Energy Science (OS-FES) funded programs. ITER is currently the highest funding area for the DOE OS-FES. Although export control issues have been integrated into these projects in the past a general guidance document has not been available for reference in this area. To address concerns with currently funded tritium plant programs and assist future projects for FES, this document will identify the key reference documents and specific sections within related to tritium research. Guidance as to the application of these sections will be discussed with specific detail to publications and work with foreign nationals.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Export Control Requirements for Tritium Processing Design and R&D

This document will address requirements of export control associated with tritium plant design and processes. Los Alamos National Laboratory has been working in the area of tritium plant system design and research and development (R&D) since the early 1970’s at the Tritium Systems Test Assembly (TSTA). This work has continued to the current date with projects associated with the ITER project and other Office of Science Fusion Energy Science (OS-FES) funded programs. ITER is currently the highest funding area for the DOE OS-FES. Although export control issues have been integrated into these projects in the past a general guidance document has not been available for reference in this area. To address concerns with currently funded tritium plant programs and assist future projects for FES, this document will identify the key reference documents and specific sections within related to tritium research. Guidance as to the application of these sections will be discussed with specific detail to publications and work with foreign nationals.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Application of SIAL{sup R} Solidification Technology for Processing of Problematic Waste Streams - 18267

SIAL{sup R} is a proven, safe, cost-effective and licensed waste solidification technology that has been used successfully for 20 years in Slovakia and the Czech Republic for processing of various problematic radioactive waste streams. This abstract presents and summarises the most interesting performance records of the SIAL{sup R} geopolymer solidification technology, the applied mobile devices as well as the characteristics of final products. Radioactive waste solidification into matrix SIAL{sup R} is based on polycondensation of inorganic aluminosilicate components with chemical composition similar to average cement. The main components of matrix SIAL{sup R} are natural inorganic raw materials containing SiO{sub 2}, Al{sub 2}O{sub 3}, CaO, MgO, Na{sub 2}O, K{sub 2}O, Fe{sub 2}O{sub 3}, and TiO{sub 2}. The treatment/solidification process is modified for individual radioactive streams with different compositions. To determine the most appropriate composition, the SIAL{sup R} application technology is laboratory tested on real samples of each individual waste stream identified for solidification. Then an appropriate mixture of aluminosilicate composition and other inorganic compounds is defined for a given solidification application. When determining the most appropriate mixture, other requirements are taken into consideration: maximum dose rate on the drum with solidified product, mass, volume, alpha radionuclide content in the final product, need for a waste's dewatering before solidification, dry matter content in the solidification product as well as other specific waste acceptance criteria (i.e., compressive strength, leachability, diffusion coefficients, radiation stability, biodegradability of matrix, distribution and partition coefficients, influence of frost and water presence to the product stability including long term physical stability in water, dustiness, flammability, time dependence of compression strength and water reduction, product homogeneity and also radiolytic G-value for hydrogen release, GH{sub 2}). The Amec Foster Wheeler baseline approach to implementing the SIAL{sup R} waste treatment process is structured on three steps - waste characterization, waste retrieval and pre-treatment and at last the solidification of pre-treated waste itself. The equipment used for the solidification process is relatively small, lightweight and designed for the specific application on site, directly 'in situ' or local to the tanks storing the sludge's/resins/other waste streams. This mitigates the problems normally experienced by transferring sticky, tight waste through long pipes. The equipment is normally 'tailor-made' to take into account the real space conditions and other existing facility requirements. At Bohunice and Dukovany sites, the facilities for encapsulation were designed to occupy existing areas of the plants in close proximity to the tanks where the waste was being stored. This allowed for the removal of the waste using Remote Operated Vehicles and for the waste to be immediately treated on site without the need for transportation thus saving both, time and resource. To date, SIAL{sup R} has been used successfully to immobilize approximately 2 x 10{sup 6} kg of waste which includes sludge, resin, crystalline borates and contaminated organic waste from Bohunice and Mochovce, Slovakia and approximately 300 m{sup 3} of spent ion exchange resins and sludge from tanks on site at the Dukovany NPP (Nuclear Power Plant) in the Czech Republic. The technology now has a track record of over 20 years which includes on-going research and development. The International missions WANO (the World Association of Nuclear Operators) and OSART (the Operational Safety Review Team) evaluated the SIAL{sup R} matrix technology at Dukovany NPP as an example of good practice. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

From Radtrack to eMWaste(r) G2 process-based integration

This paper provides a process-based examination of the integration of two separate but related software applications into Sandia National Laboratories’ (SNL’s) Radioactive and Mixed Waste Management Facility’s (RMWMF) data management system. First, data collection will be upgraded through the use of a new web-based Waste Description and Disposal Request (WDDR), which SNL personnel whose work creates radioactive and hazardous waste (generators) will use to characterize dozens of specific attributes of each waste parcel. Second, a commercial software package for data storage and manipulation — eMWaste® G2 by Attention IT — will replace two existing software applications and will track all radioactive and mixed waste at Sandia. Integrating these applications into a web-based system will give the RMWMF increased system flexibility, reduced reliance on key personnel, and improved document control, traceability and efficiency. To meet these goals and ensure the applications are developed in an efficient, quality-oriented environment, it is critical to first conduct a thorough evaluation of the affected processes. This paper will analyze the processes supported by the new applications and the requirements for a successful integration. A comprehensive analysis of both project flow and data management requirements, illustrated through original flow diagrams and other charts, will provide support to the development team and programmers as they work to integrate the applications into the new system.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Status Update - Installation and Operation of GeoMelt{sup R} ICV{sup TM} Process in the NNL's Central Laboratory on the Sellafield Site - 16410

Thermal treatment of nuclear waste in the UK has seen much renewed interest recently, owing to the advantages that can be gained in terms of reduced waste volumes, compatibility with reactive metals and organics and its ability to treat mixed generic wastes. Vitrification is a treatment option which destroys organics and some hazardous inorganics such as asbestos, reduces wasteform volume, and produces a robust leach resistant wasteform. Kurion's GeoMelt{sup R} In-Container Vitrification (ICV){sup TM} is a vitrification process where the treatment vessel can serve as an interim-storage, transport, and final long-term storage vessel - thus negating the need to pour glass into a separate container, effectively leading to a much simpler system than traditional waste melters. The UK's National Nuclear Laboratory (NNL) and Kurion have entered into a joint project to deploy an active waste ICV{sup TM} plant based on Kurion's GeoMelt{sup R} technology, at NNL's flagship Central Laboratory on the Sellafield site. NNL is the UK's national laboratory for civil nuclear science and technology, providing advice to government, protecting key skills, supporting industry and delivering national nuclear programs. NNL is bringing the Kurion GeoMelt{sup R} process alongside its existing capabilities in thermal waste treatment. Kurion provides technology solutions to minimize and stabilize nuclear and hazardous waste through its families of technologies: access, separation and stabilization processes. The GeoMelt{sup R} plant being installed at the NNL's Central Laboratory creates a platform to evaluate the vitrification technology for the variety of wastes from the NDA estate and creates a treatment path for problematic waste streams that currently have no disposition pathway. With the diverse facilities under NNL management coupled with the NNL's ability to import wastes from within the UK and Europe, this arrangement with Kurion provides waste owners with treatment disposition pathways for problematic wastes. The Kurion / NNL team completed non-radioactive commissioning of a GeoMelt{sup R} ICV{sup TM} treatment system in 2015. Commissioning consisted of performing two tests at NNL's Workington Laboratory. Commissioning Test 1 involved vitrification of 367 kg of glass frit over the course of approximately 18 hours. Commissioning Test 2 consisted of processing 470 kg of soil and additives in approximately 27 hours. The soil processed in the second test was non-radioactive soil from Sellafield and was used as an analog for radioactive soil to be processed during radioactive commissioning at the Central Laboratory at Sellafield. All commissioning test goals were easily achieved and all subsystems operated as designed. Radioactive commissioning will be carried out in early 2016. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Origin of Plutonium-244 in the Early Solar System

We investigate the origin in the early Solar System of the short-lived radionuclide 244 Pu (with a half life of 80 Myr) produced by the rapid (r) neutron-capture process. We consider two large sets of r-process nucleosynthesis models and analyse if the origin of 244 Pu in the ESS is consistent with that of the other r and slow (s) neutron-capture process radioactive nuclei. Uncertainties on the r-process models come from both the nuclear physics input and the astrophysical site. The former strongly affects the ratios of isotopes of close mass ( 129 I/ 127 I, 244 Pu/ 238 U, and 247 Pu/ 235 U). The 129 I/ 247 Cm ratio, instead, which involves isotopes of a very different mass, is much more variable than those listed above and is more affected by the physics of the astrophysical site. We consider possible scenarios for the evolution of the abundances of these radioactive nuclei in the galactic interstellar medium and verify under which scenarios and conditions solutions can be found for the origin of 244 Pu that are consistent with the origin of the other isotopes. Solutions are generally found for all the possible different regimes controlled by the interval (δ) between additions from the source to the parcel of interstellar medium gas that ended up in the Solar System, relative to decay timescales. If r-process ejecta in interstellar medium are mixed within a relatively small area (leading to a long δ), we derive that the last event that explains the 129 I and 247 Cm abundances in the early Solar System can also account for the abundance of 244 Pu. Due to its longer half life, however, 244 Pu may have originated from a few events instead of one only. If r-process ejecta in interstellar medium are mixed within a relatively large area (leading to a short δ), we derive that the time elapsed from the formation of the molecular cloud to the formation of the Sun was 9-16 Myr.

79 ASTRONOMY AND ASTROPHYSICS↗

Detailed abundances for a large sample of giant stars in the globular cluster 47 Tucanae (NGC 104)

47 Tuc is an ideal target to study chemical evolution and globular cluster (GC) formation in massive more metal-rich GCs, as it is the closest massive GC. We present chemical abundances for O, Na, Al, Si, Ca, Ti, Fe, Ni, La, and Eu in 164 red giant branch stars in the massive GC 47 Tuc using spectra obtained with both the Hydra multifiber spectrograph at the Blanco 4 m telescope and the FLAMES multiobject spectrograph at the Very Large Telescope. We find an average [Fe/H] = –0.79 ± 0.09 dex, consistent with literature values, as well as overabundances of alpha-elements ([α/Fe] ∼ 0.3 dex). The n-capture process elements indicate that 47 Tuc is r process-dominated ([Eu/La] = +0.24), and the light elements O, Na, and Al exhibit star-to-star variations. The Na-O anticorrelation, a signature typically seen in Galactic GCs, is present in 47 Tuc, and extends to include a small number of stars with [O/Fe] ∼ –0.5. Additionally, the [O/Na] ratios of our sample reveal that the cluster stars can be separated into three distinct populations. A Kolmogorov-Smirnov test demonstrates that the O-poor/Na-rich stars are more centrally concentrated than the O-rich/Na-poor stars. The observed number and radial distribution of 47 Tuc's stellar populations, as distinguished by their light element composition, agrees closely with the results obtained from photometric data. We do not find evidence supporting a strong Na-Al correlation in 47 Tuc, which is consistent with current models of asymptotic giant branch nucleosynthesis yields.

79 ASTRONOMY AND ASTROPHYSICS↗

Data and scripts associated with a manuscript investigating impacts of solid phase extraction on freshwater organic matter optical signatures and mass spectrometry pairing

This data package is associated with the publication “Investigating the impacts of solid phase extraction on dissolved organic matter optical signatures and the pairing with high-resolution mass spectrometry data in a freshwater system” submitted to “Limnology and Oceanography: Methods.” This data is an extension of the River Corridor and Watershed Biogeochemistry SFA’s Spatial Study 2021 (https://doi.org/10.15485/1898914). Other associated data and field metadata can be found at the link provided. The goal of this manuscript is to assess the impact of solid phase extraction (SPE) on the ability to pair ultra-high resolution mass spectrometry data collected from SPE extracts with optical properties collected on ambient stream samples. Forty-seven samples collected from within the Yakima River Basin, Washington were analyzed dissolved organic carbon (DOC, measured as non-purgeable organic carbon, NPOC), absorbance, and fluorescence. Samples were subsequently concentrated with SPE and reanalyzed for each measurement. The extraction efficiency for the DOC and common optical indices were calculated. In addition, SPE samples were subject to ultra-high resolution mass spectrometry and compared with the ambient and SPE generated optical data. Finally, in addition to this cross-platform inter-comparison, we further performed and intra-comparison among the high-resolution mass spectrometry data to determine the impact of sample preparation on the interpretability of results. Here, the SPE samples were prepared at 40 milligrams per liter (mg/L) based on the known DOC extraction efficiency of the samples (ranging from ~30 to ~75%) compared to the common practice of assuming the DOC extraction efficiency of freshwater samples at 60%. This data package folder consists of one main data folder with one subfolder (Data_Input). The main data folder contains (1) readme; (2) data dictionary (dd); (3) file-level metadata (flmd); (4) final data summary output from processing script; and (5) the processing script. The R-markdown processing script (SPE_Manuscript_Rmarkdown_Data_Package.rmd) contains all code needed to reproduce manuscript statistics and figures (with the exception of that stated below). The Data_Input folder has two subfolders: (1) FTICR and (2) Optics. Additionally, the Data_Input folder contains dissolved organic carbon (DOC, measured as non-purgeable organic carbon, NPOC) data (SPS_NPOC_Summary.csv) and relevant supporting Solid Phase Extraction Volume information (SPS_SPE_Volumes.csv). Methods information for the optical and FTICR data is embedded in the header rows of SPS_EEMs_Methods.csv and SPS_FTICR_Methods.csv, respectively. In addition, the data dictionary (SPS_SPE_dd.csv), file level metadata (SPS_SPE_flmd.csv), and methods codes (SPS_SPE_Methods_codes.csv) are provided. The FTICR subfolder contains all raw FTICR data as well as instructions for processing. In addition, post processed FTICR molecular information (Processed_FTICRMS_Mol.csv) and sample data (Processed_FTICRMS_Data.csv) is provided that can be directly read into R with the associated R-markdown file. The Optics subfolder contains all Absorbance and Fluorescence Spectra. Fluorescence spectra have been blank corrected, inner filter corrected, and undergone scatter removal. In addition, this folder contains Matlab code used to make a portion of Figure 1 within the manuscript, derive various spectral parameters used within the manuscript, and used for parallel factor analysis (PARAFAC) modeling. Spectral indices (SPS_SpectralIndices.csv) and PARAFAC outputs (SPS_PARAFAC_Model_Loadings.csv and SPS_PARAFAC_Sample_Scores.csv) are directly read into the associated R-markdown file. We acknowledge the Yakama Nation as owners and caretakers of the lands where we collected some of these data. We thank the Confederated Tribes and Bands of the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate sample collection and optimization of data usage according to their values and worldview.

54 ENVIRONMENTAL SCIENCES↗

gcamfaostat: An R package to prepare, process, and synthesize FAOSTAT data for global agroeconomic and multisector dynamic modeling

The gcamfaostat R package is designed for the preparation, processing, and synthesis of the Food and Agriculture Organization (FAO) Statistics (FAOSTAT) agroeconomic data. The primary purpose is to facilitate FAOSTAT data use in global economic and multisector dynamic models while ensuring transparency, traceability, and reproducibility. Here, we provide an overview of the development of gcamfaostat (v1.0) and demonstrate its capabilities in generating and maintaining agroeconomic data required for the Global Change Analysis Model (GCAM). Our initiative seeks to enhance the quality and accessibility of data for the global agroeconomic modeling community, with the aim of fostering more robust and harmonized outcomes in a collaborative, efficient, and open-source framework. One of the important features of the package is the possibility to construct the FAO Food Balance Sheets at the disaggregated commodity level (with over 500 commodities), which provides a comprehensive and detailed data input for a variety of analytical and modeling applications. The processed data and visualizations offered by gcamfaostat can also be valuable to a broader audience interested in gaining insights into the intricacies of global agriculture.

97 MATHEMATICS AND COMPUTING↗

Effect of ECAP Die Angles on Microstructure Mechanical Properties and Corrosion Behavior of AZ80 Mg Alloy

In this article, the effect of channel angles on material properties was investigated during equal channel angular pressing of AZ80 magnesium alloy using processing route R at 325 °C processing temperature. Channel angles of 90° and 110° and common corner angle 30° have been considered for this study. It has been revealed that the channel angle has a significant influence on deformation homogeneity, microhardness, ultimate tensile strength, ductility and corrosion behavior of Mg alloys. Investigation with reference to as-received AZ80 Mg alloy indicates 18.47% improvement in UTS and 76.07% enhancement in ductility after processing through 3P-90° and 2P-110° ECAP, respectively. Also, the corrosion rate reduces to 89.47% after processing the sample with 3P-110° ECAP die.

36 MATERIALS SCIENCE↗

ZIRCONIUM—HAFNIUM ISOTOPE EVIDENCE FROM METEORITES FOR THE DECOUPLED SYNTHESIS OF LIGHT AND HEAVY NEUTRON-RICH NUCLEI

Recent work based on analyses of meteorite and terrestrial whole-rock samples showed that the r- and s- process isotopes of Hf were homogeneously distributed throughout the inner solar system. We report new Hf isotope data for Calcium-Aluminum-rich inclusions (CAIs) of the CV3 carbonaceous chondrite Allende, and novel high-precision Zr isotope data for these CAIs and three carbonaceous chondrites (CM, CO, CK). Our Zr data reveal enrichments in the neutron-rich isotope {sup 96}Zr (≤1ε in {sup 96}Zr/{sup 90}Zr) for bulk chondrites and CAIs (∼2ε). Potential isotope effects due to incomplete sample dissolution, galactic and cosmic ray spallation, and the nuclear field shift are assessed and excluded, leading to the conclusion that the {sup 96}Zr isotope variations are of nucleosynthetic origin. The {sup 96}Zr enrichments are coupled with {sup 50}Ti excesses suggesting that both nuclides were produced in the same astrophysical environment. The same CAIs also exhibit deficits in r-process Hf isotopes, which provides strong evidence for a decoupling between the nucleosynthetic processes that produce the light (A ≤ 130) and heavy (A > 130) neutron-rich isotopes. We propose that the light neutron-capture isotopes largely formed in Type II supernovae (SNeII) with higher mass progenitors than the supernovae that produced the heavy r-process isotopes. In the context of our model, the light isotopes (e.g. {sup 96}Zr) are predominantly synthesized via charged-particle reactions in a high entropy wind environment, in which Hf isotopes are not produced. Collectively, our data indicates that CAIs sampled an excess of materials produced in a normal mass (12-25 M{sub ☉}) SNII.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

REPRODUCING THE OBSERVED ABUNDANCES IN RCB AND HdC STARS WITH POST-DOUBLE-DEGENERATE MERGER MODELS-CONSTRAINTS ON MERGER AND POST-MERGER SIMULATIONS AND PHYSICS PROCESSES

The R Coronae Borealis (RCB) stars are hydrogen-deficient, variable stars that are most likely the result of He-CO WD mergers. They display extremely low oxygen isotopic ratios, {sup 16}O/{sup 18}O {approx_equal} 1-10, {sup 12}C/{sup 13}C {>=} 100, and enhancements up to 2.6 dex in F and in s-process elements from Zn to La, compared to solar. These abundances provide stringent constraints on the physical processes during and after the double-degenerate merger. As shown previously, O-isotopic ratios observed in RCB stars cannot result from the dynamic double-degenerate merger phase, and we now investigate the role of the long-term one-dimensional spherical post-merger evolution and nucleosynthesis based on realistic hydrodynamic merger progenitor models. We adopt a model for extra envelope mixing to represent processes driven by rotation originating in the dynamical merger. Comprehensive nucleosynthesis post-processing simulations for these stellar evolution models reproduce, for the first time, the full range of the observed abundances for almost all the elements measured in RCB stars: {sup 16}O/{sup 18}O ratios between 9 and 15, C-isotopic ratios above 100, and {approx}1.4-2.35 dex F enhancements, along with enrichments in s-process elements. The nucleosynthesis processes in our models constrain the length and temperature in the dynamic merger shell-of-fire feature as well as the envelope mixing in the post-merger phase. s-process elements originate either in the shell-of-fire merger feature or during the post-merger evolution, but the contribution from the asymptotic giant branch progenitors is negligible. The post-merger envelope mixing must eventually cease {approx}10{sup 6} yr after the dynamic merger phase before the star enters the RCB phase.

79 ASTRONOMY AND ASTROPHYSICS↗

Low cost solar aray project: Experimental process system development unit for producing semiconductor-grade silicon using the silane-to-silicon process

This phase consists of the engineering design, fabrication, assembly, operation, economic analysis, and process support R&D for an Experimental Process System Development Unit (EPSDU). The mechanical bid package was issued and the bid responses are under evaluation. Similarly, the electrical bid package was issued, however, responses are not yet due. The majority of all equipment is on order or has been received at the EPSDU site. The pyrolysis/consolidation process design package was issued. Preparation of process and instrumentation diagram for the free-space reactor was started. In the area of melting/consolidation, Kayex successfully melted chunk silicon and have produced silicon shot. The free-space reactor powder was successfully transported pneumatically from a storage bin to the auger feeder twenty-five feet up and was melted. The fluid-bed PDU has successfully operated at silane feed concentrations up to 21%. The writing of the operating manual has started. Overall, the design phase is nearing completion.

Source record↗

Development of an Efficient and Cost-Effective Enzymatic Process for Production of (R)-[3,5-bis(trifluoromethyl)phenyl] Ethanol Using Carbonyl Reductase Derived from Leifsonia sp. S749

(R)-[3,5-bis(trifluoromethyl) phenyl] ethanol [(R)-3,5-BTPE] is a crucial chiral intermediate for the synthesis of the NK-1 receptor antagonists aprepitant, rolapitant and fosaprepitant. The carbonyl reductase KR01 from Leifsonia sp. S749, discovered by protein sequence alignment, could convert 3′,5′-bis(trifluoromethyl) acetophenone (3,5-BTAP) into (R)-3,5-BTPE with excellent activity and enantioselectivity. In order to enhance the conversion efficiency at high substrate concentrations, the reaction conditions were optimized by response surface analysis. The results showed that 600 g/L 3,5-BTAP was bioreduced to (R)-3,5-BTPE (> 99.9% enantiomeric excess) by the recombinant Escherichia coli/pET-28a (+)-KR01 whole cells, with a 98.3% conversion and 59 g/L/h productivity under the optimized reaction conditions. In addition, the recombinant E. coli cells could be repeatedly used up to seven times in the reaction mixture containing 90% isopropanol (IPA). This is the highest substrate loading and productivity for the bioreduction of 3,5-BTAP by carbonyl reductase ever reported, and this method represents an efficient and cost-effective process for production of (R)-3,5-BTPE.

60 APPLIED LIFE SCIENCES↗

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max , while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr , which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L max > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2 ] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2 ]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr .

36 MATERIALS SCIENCE↗