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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

pvplr-python: Python package implementation of PVplr for Performance Loss Rate (PLR) analysis

Due to software fragmentation, PV system modeling teams can be limited to language specific packages, preventing cross-sectional analysis of different modeling techniques and workflows. To this end, PVplr, a popular PV performance modeling R software package, has been ported to the Python programming language. To verify and test the robustness of the port, NSRDB data has been used to simulated PV installations at native resolution (~2 million Sites), with a variety of degradation rates, degradation patterns, and modules. Performance Ratios were calculated using the ported functions from pvplr-python and compared against Rdtools YoY values. Due to the complicated nature of degradation, a new metric has been proposed to quantify the performance loss of a system. The cumulative production loss, is the total amount of energy lost due to the degrading performance of the system. Cumulative production loss alleviates the problems with fitting linear functions to non-linear degradation. Cumulative Production loss was shown to better estimate the total lost revenue for non-linear degradation patterns. $XbX + UTC$ was found to most accurately predict the total lost revenue in simulated systems.

Kumar, Suraj↗
DOE OSTI2025

Optimal intrinsic alignment estimators in the presence of redshift-space distortions

We present estimators for quantifying intrinsic alignments in large spectroscopic surveys that efficiently capture line-of-sight (LOS) information while being relatively insensitive to redshift-space distortions (RSD). We demonstrate that changing the LOS integration range, pimax, as a function of transverse separation outperforms the conventional choice of a single pimax value. This is further improved by replacing the flat pimax cut with a LOS weighting based on shape projection and RSD. Although these estimators incorporate additional LOS information, they are projected correlations that exhibit signal-to-noise ratios comparable to 3D correlation functions, such as the IA quadrupole. Using simulations from Abacus Summit, we evaluate these estimators and provide recommended pimax values and weights for projected separations of 1 - 100 Mpc/h. These will improve measurements of intrinsic alignments in large cosmological surveys and the constraints they provide for both weak lensing and direct cosmological applications.

cosmology↗
DOE OSTI2023

Revisiting the definition of field capacity as a functional parameter in a layered agronomic soil profile beneath irrigated maize

The soil water content at the condition of field capacity (θ FC ) is a key parameter in irrigation scheduling and has been suggested to be determined by running a synthetic drainage experiment until the flux rate (q) at the bottom of the soil profile achieves a predefined negligible value (q FC ). We question the impact of q FC on the assessment of field capacity. Moreover, calculating θ FC as the integral mean of the water content profile when q is equal to q FC is strictly valid only for uniform soil profiles. By contrast, this practice is ambiguous and biased for stratified soil profiles due to the soil water content discontinuity at the layer interfaces. In this study, the concept of field capacity was revisited and adapted to practical agronomic heuristics. By resorting to the assessment of root-zone water storage capacity (W), we envision field capacity as a functional hydraulic parameter derived from synthetic irrigation scheduling scenarios to minimize drought stress, drainage, and nitrate leachate below the root zone. A functional analysis was carried out on a 135-cm-thick layered soil profile beneath maize in eastern Nebraska. On-farm irrigation scheduling applications and agricultural practices were recorded for 20 years (2001–2020) at a daily time step. Hydrus-1D was calibrated and validated with direct measurements of the soil water retention curve and soil water content data, respectively, in each soil layer. A set of functional field capacity values was derived from 24 irrigation scheduling scenarios, and the optimal water storage capacity at field capacity (W FC ) was approximately 50 cm (corresponding to about 80% saturation in the soil profile). An average irrigation amount of 217.5 mm distributed over 21 events was obtained by using optimal irrigation scheduling, which was initiated when the matric pressure head took on a value of –700 cm and the irrigation rate was set at 1.0 cm d –1 . This irrigation practice ensured water storage at approximately the same level (ideally at W FC ) by sustaining only evapotranspiration fluxes in the uppermost portion of the root zone and by limiting excessive drainage. This protocol can be transferred to other agricultural fields.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Surface Interactions and Confinement of Methane: A High Pressure Magic Angle Spinning NMR and Computational Chemistry Study

Characterization and modeling of the molecular-level behavior of simple hydrocarbon gases, such as methane, in the presence of both nonporous and nano-porous mineral matrices allows for predictive understanding of important processes in engineered and natural systems. In this study, changes in local electromagnetic environments of the carbon atoms in methane under conditions of high pressure (up to 130 bar) and moderate temperature (up to 346 K) were observed with 13C magic-angle spinning (MAS) NMR spectroscopy while the methane gas was mixed with two model solid substrates: a fumed non-porous, 12 nm particle size silica and a mesoporous silica with 200 nm particle size and 4 nm average pore diameter. Examination of the interactions between methane and the silica systems over temperatures and pressures that include the supercritical regime was allowed by a novel high pressure MAS sample containment system, which provided high resolution spectra collected under in situ conditions. For pure methane, no significant thermal effects were found for the observed 13C chemical shifts at all pressures studied here (28.2 bar, 32.6 bar, 56.4 bar, 65.1 bar, 112.7 bar, and 130.3 bar). However, the 13C chemical shifts of resonances arising from confined methane changed slightly with changes in temperature in mixtures with mesoporous silica. The chemical shift values of 13C nuclides in methane change measurably as a function of pressure both in the pure state and in mixtures with both silica matrices, with a more pronounced shift when meso-porous silica is present. Molecular-level simulations utilizing GCMC, MD and DFT confirm qualitatively that the experimentally measured changes are attributed to interactions of methane with the hydroxylated silica surfaces as well as densification of methane within nanopores and on pore surfaces.

confinement↗
DOE OSTI2019

Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation

The clumped isotopic composition of carbonate-CO 2 (denoted Δ 47 ) is a function of carbonate formation temperature and in natural samples can act as a recorder of paleoclimate, burial, or diagenetic conditions. The absolute abundance of heavy isotopes in the universal standards VPDB and VSMOW (defined by four parameters: R 13 VPDB , R 17 VSMOW , R 18 VSMOW , and λ ) impact calculated Δ 47 values. In this work, we investigate whether use of updated and more accurate values for these parameters can remove observed interlaboratory differences in the measured T-Δ 47 relationship. Using the updated parameters, we reprocess 14 published calibration data sets measured in 11 different laboratories, representing many mineralogies, bulk compositions, sample types, reaction temperatures, and sample preparation and analysis methods. Exploiting this large composite data set ( n = 1,253 sample replicates), we investigate the possibility for a “universal” clumped isotope calibration. We find that applying updated parameters improves the T-Δ 47 relationship (reduces residuals) within most labs and improves overall agreement but does not eliminate all interlaboratory differences. We reaffirm earlier findings that different mineralogies do not require different calibration equations and that cleaning procedures, method of pressure baseline correction, and mass spectrometer type do not affect interlaboratory agreement. We also present new estimates of the temperature dependence of the acid digestion fractionation for Δ 47 (Δ* 25-X ), based on combining reprocessed data from four studies, and new theoretical equilibrium values to be used in calculation of the empirical transfer function. Overall, we have ruled out a number of possible causes of interlaboratory disagreement in the T-Δ 47 relationship, but many more remain to be investigated.

58 GEOSCIENCES↗
DOE OSTI2017

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Here, our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Fractional Statistics

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

Physics↗
DOE OSTI2023

Shape polarization in the tin isotopes near N = 60 from precision g-factor measurements on short-lived 11/2 - isomers

The g factors of 11/2 - isomers in semimagic 109 Sn and 111 Sn (isomeric lifetimes $\tau$ = 2.9(3) ns and $\tau$ = 14.4(7) ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses LaBr3 detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, g(11/2 - ; 109 Sn) = -0.186(8) and g(11/2 - ; 111 Sn) = -0.214(4), are significantly lower in magnitude than those of the 11/2 - isomers in the heavier isotopes and depart from the value expected for a near pure neutron h 11/2 configuration. Broken-symmetry density functional theory calculations applied to the sequence of 11/2 - states reproduce the magnitude and location of this deviation. The g(11/2 - ) values are affected by shape core polarization; the odd Oh 11/2 neutron couples to J π = 2 + , 4 + , 6 + ... configurations in the weakly-deformed effective core, causing a decrease in the g-factor magnitudes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [ J. Appl. Phys. (1948), 19 , 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystalline powder samples.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Eyes On the Ground: Path Forward Analysis.

A previous report assesses our progress to date on the Eyes On the Ground project, and reviews lessons learned. In this report, we address the implications of those lessons in defining the most productive path forward for the remainder of the project. We propose two main concepts: Interactive Diagnosis and Model-Driven Assistance. Among these, the Model-Driven Assistance concept appears the most promising. The Model-Driven Assistance concept is based on an approximate but useful model of a facility, which provides a unified representation for storing, viewing, and analyzing data that is known about the facility. This representation provides value to both inspectors and IAEA headquarters, and facilitates communication between the two. The concept further includes a lightweight, portable field tool to aid the inspector in executing a variety of inspection tasks, including capture of images and 3-d scan data. We develop a detailed description of this concept, including its system components, functionality, and example use cases. The envisioned tool would provide value by reducing inspector cognitive load, streamlining inspection tasks, and facilitating communication between the inspector and teams at IAEA headquarters. We conclude by enumerating the top implementation priorities to pursue in the remaining limited time of the project. Approved for public release; further dissemination unlimited.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Moduli axions, stabilizing moduli, and the large field swampland conjecture in heterotic M-theory

We compute the F- and D-term potential energy for the dilaton, complex structure, and Kähler moduli of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds where, for simplicity, we choose ℎ 1,1 = ℎ 2,1 = 1. However, the formalism is immediately applicable to the “universal” moduli of Calabi-Yau threefolds with ℎ 1,1 = ℎ 1,2 > 1 as well. The F-term potential is computed using the nonperturbative complex structure, gaugino condensate and “world sheet instanton” superpotentials in theories in which the hidden sector contains an anomalous U⁡(1) structure group. The Green-Schwarz anomaly cancellation induces inhomogeneous “axion” transformations for the imaginary components of the dilaton and Kähler modulus—which then produce a D-term potential. V D is a function of the real components of the dilaton and Kähler modulus (s and t) that is minimized and precisely vanishes along a unique line in the s–t plane. Excitations transverse to this line have a mass m anom which is an explicit function of t. The F-term potential energy is then evaluated along the V D = 0 line. For values of t small enough that m anom ≳ M U —where M U is the compactification scale—we plot V F for a realistic choice of coefficients as a function of the Pfaffian parameter p. We find values of p for which V F has a global minimum at negative or zero vacuum density or a metastable minimum with positive vacuum density. In all three cases, the s, t, and associated “axion” moduli are completely stabilized. Finally, we show that, for any of these vacua, the large t behavior of the potential energy satisfies the “large scalar field” Swampland conjecture.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: In this study, we seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei, and the fission barrier of 240 Pu . Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. In conclusion, this result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Benchmarking and parameter sensitivity of physiological and vegetation dynamics using the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) at Barro Colorado Island, Panama

Plant functional traits determine vegetation responses to environmental variation, but variation in trait values is large, even within a single site. Likewise, uncertainty in how these traits map to Earth system feedbacks is large. We use a vegetation demographic model (VDM), the Functionally Assembled Terrestrial Ecosystem Simulator (FATES), to explore parameter sensitivity of model predictions, and comparison to observations, at a tropical forest site: Barro Colorado Island in Panama. We define a single 12-dimensional distribution of plant trait variation, derived primarily from observations in Panama, and define plant functional types (PFTs) as random draws from this distribution. We compare several model ensembles, where individual ensemble members vary only in the plant traits that define PFTs, and separate ensembles differ from each other based on either model structural assumptions or non-trait, ecosystem-level parameters, which include (a) the number of competing PFTs present in any simulation and (b) parameters that govern disturbance and height-based light competition. While single-PFT simulations are roughly consistent with observations of productivity at Barro Colorado Island, increasing the number of competing PFTs strongly shifts model predictions towards higher productivity and biomass forests. Different ecosystem variables show greater sensitivity than others to the number of competing PFTs, with the predictions that are most dominated by large trees, such as biomass, being the most sensitive. Changing disturbance and height-sorting parameters, i.e., the rules of competitive trait filtering, shifts regimes of dominance or coexistence between early- and late-successional PFTs in the model. Increases to the extent or severity of disturbance, or to the degree of determinism in height-based light competition, all act to shift the community towards early-successional PFTs. In turn, these shifts in competitive outcomes alter predictions of ecosystem states and fluxes, with more early-successional-dominated forests having lower biomass. It is thus crucial to differentiate between plant traits, which are under competitive pressure in VDMs, from those model parameters that are not and to better understand the relationships between these two types of model parameters to quantify sources of uncertainty in VDMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

A benchmark photoelectron spectroscopic and theoretical study of the electronic stability of [B12H12]2-

We report a joint benchmark study on the electronic stability of closo-dodecaborate [B12H12]2- employing negative ion photoelectron spectroscopy and high level electronic structure methods. The photoelectron spectra of [B12H12]2-, measured at 266, 193 and 157 nm, yield the Adiabatic and Vertical Detachment Energies (ADE and VDE) of this dianion at 0.93 ± 0.05 eV and 1.15 ± 0.05 eV, respectively, along with a ~ 3 eV Repulsive Coulomb Barrier (RCB) against electron detachment. Theoretical calculations at various levels of electronic structure theory confirm the high stability of this dianion. The ADE and VDE values calculated at the CCSD(T)/aug-cc-PVQZ level are 0.92, and 1.16 eV, in excellent agreement with the experimental benchmark values. The comparison between the experimental and the theoretical values obtained at different levels of theory indicate that the PBE0 density functional represents a cost-effective method of sufficient accuracy to describe the molecular properties of this dianion and associated compounds. The theoretical RCB was modelled after the electrostatic potential (ESP) and point charge method (PCM) along three different detachment pathways, viz. along the B-H bond, perpendicular to a B-B bond, and normal to a B-B-B triangle. It was found that detachment of the electron along the B-H bond is preferred, as this pathway is associated with RCBs between 2.3 eV (PCM) and 3.3 eV (ESP), values that bracket the experimental estimate of ~ 3 eV.

Apra, Edoardo↗
DOE OSTI2025

Machine-learning-informed scattering correlation analysis of sheared colloids

We have carried out theoretical analysis, Monte Carlo simulations and machine-learning analysis to quantify microscopic rearrangements of dilute dispersions of spherical colloidal particles from coherent scattering intensity. Both monodisperse and polydisperse dispersions of colloids were created and underwent a rearrangement consisting of an affine simple shear and non-affine rearrangement using the Monte Carlo method. We calculated the coherent scattering intensity of the dispersions and the correlation function of intensity before and after the rearrangement and generated a large data set of angular correlation functions for varying system parameters, including number density, polydispersity, shear strain and non-affine rearrangement. Singular value decomposition of the data set shows the feasibility of machine-learning inversion from the correlation function for the polydispersity, shear strain and non-affine rearrangement using only three parameters. A Gaussian process regressor is then trained on the data set and can retrieve the affine shear strain, non-affine rearrangement and polydispersity with relative errors of 3%, 1% and 6%, respectively. Altogether, our model provides a framework for quantitative studies of both steady and non-steady microscopic dynamics of colloidal dispersions using coherent scattering methods.

Gaussian process regression↗
DOE OSTI2022

Simple new methods for deducing lifetimes in recoil distance Doppler-shift measurements

In this work, new approaches for lifetime determination using data from recoil distance Doppler-shift experiments are presented based on the fundamental properties of the functions describing the time evolution of the population of excited nuclear states. To some extent, one of them represents a contraction of the well-known Differential decay-curve method (DDCM) by using the most reliable data point [the maximum of the $n_i(t)$ function describing the population of level $\textit{i}$ in time] and a purely numerical procedure avoiding any fitting of decay curves. The combination with the standard DDCM analysis is promising for improving the reliability and the precision of the results for the lifetimes obtained. The novel part of the approach consists of using a chain of equations at the consecutive maxima of the ni(t) functions, which allow us to precisely determine the ratio of the lifetimes of two consecutive levels and, in the case where one of these lifetimes is known, to determine the unknown one. In addition, a simple integral derivation of the lifetime is presented involving the peak areas measured at different distances, and an application of the first moments (expectation values and centroids in time) of the $n_i(t)$ functions for determining lifetimes is also demonstrated to be useful.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

On the Equality of Values in the Monge and Kantorovich Problems

This paper is concerned with the study of conditions under which the Monge and Kantorovich problems with a continuous cost function on a product of two completely regular spaces and two given atomless Radon measures-projections on these spaces have equal values of the corresponding infima.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Hardness and modulus of Fe2B, Fe3(C,B), and Fe23(C,B)6 borides and carboborides in the Fe-C-B system

Highlights: • Hardness and modulus of the Fe{sub 2}B, Fe{sub 3}(C,B), Fe{sub 23}(C,B){sub 6} and M{sub 7}C{sub 3} phases are analyzed. • Hardness and modulus of the Fe{sub 3}(C,B) phase are increasing with its B content. • Size effects are apparent for hardness of Fe{sub 2}B, Fe{sub 3}(C,B), Fe{sub 23}(C,B){sub 6} and M{sub 7}C{sub 3}. • The model of Nix and Gao was used to evaluate the load-independent hardness H{sub 0}. • Hardness ranking is Fe{sub 2}B > M{sub 7}C{sub 3} > Fe{sub 3}(C,B) > Fe{sub 23}(C,B){sub 6} - Abstract: This work provides a comparative and comprehensive study of the indentation hardness and indentation modulus of iron-rich borides and carboborides of types Fe{sub 2}B, Fe{sub 3}(C,B), and Fe{sub 23}(C,B){sub 6}. In addition, the hardness and elastic modulus of Cr-rich M{sub 7}C are investigated for comparative purposes. We investigated the impact of increasing B content and indentation size effect (ISE). The phases of interest were stabilized in cast Fe-C-B alloys that varied with respect to the B / (B + C) ratio and heat treatment. The resulting microstructures were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and wavelength X-ray spectroscopy (WDS). Dynamic in-situ nanoindentation experiments based on the method of continuous stiffness measurement (CSM) were coupled to SEM and EBSD investigations to determine the mechanical properties of the individual borides and carboborides as a function of the indentation depth. The results were compared to values obtained for the Cr-rich M{sub 7}C{sub 3} carbide. It was found that the hardness of the B-rich Fe{sub 3}(C{sub ,}B) phase is considerably higher than pure Fe{sub 3}C and increases with increasing B content. The ISE was present in all investigated phases, and the hardness decreased as a function of indentation depth. The hardness at infinite indentation depth H{sub 0} was estimated according to the model of Nix and Gao. The Fe{sub 2}B phase was found to be the hardest phase (H{sub 0} = 19.04 GPa), followed by M{sub 7}C{sub 3} (H{sub 0} = 16.43 GPa), Fe{sub 3}(C,B) (H{sub 0} = 11.18 to 12.24 GPa), and Fe{sub 23}(C,B){sub 6} (H{sub 0} = 10.39 GPa).

36 MATERIALS SCIENCE↗