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At least 487 records · Page 27

Peripheral blood hematology, plasma biochemistry, and the optimization of an in vitro immune-based assay in the brown watersnake ( Nerodia taxispilota )

Reptiles represent a phylogenetic lineage that provides a unique link between ectothermic anamniotes and endothermic amniotes. Compared to mammalian and avian species, our understanding of the reptilian immune system is greatly lacking. This gap in knowledge is largely due to an absence of established immune-based assays or specific reagents for these species. In the present study, brown watersnakes (Nerodia taxispilota) were live-captured in the wild, sexed, weighed, measured, bled via the caudal vein and released. At 24 hr post-collection, peripheral blood leukocytes were enriched and evaluated with an established mammalian in-vitro lymphocyte proliferation assay. Snake peripheral blood leukocyte enrichment yielded > 90% lymphocytes with viabilities averaging 81.5%. Baseline physiologic data for N. taxispilota, including hematology and total solids, leukocyte differentials, cell recovery and plasma biochemistry, were also collected. Cells cultured with Concanavalin A exhibited significantly increased proliferation at both 72 and 96 hr. Furthermore, these preliminary results show that enriched peripheral blood from wild-caught N. taxispilota provides a sufficient yield of leukocytes that can be cultured and functionally evaluated using a standard mammalian in-vitro immune-based assay.

59 BASIC BIOLOGICAL SCIENCES↗

Scanning ultrafast electron microscopy reveals photovoltage dynamics at a deeply buried $p^- \mathrm{Si/SiO_2}$ interface

The understanding and control of charge carrier interactions with defects at buried insulator/semiconductor interfaces is essential for achieving optimum performance in modern electronics. In this work, we report on the use of scanning ultrafast electron microscopy (SUEM) to remotely probe the dynamics of excited carriers at a Si surface buried below a thick thermal oxide. Our measurements illustrate a previously unidentified SUEM contrast mechanism, whereby optical modulation of the space-charge field in the semiconductor modulates the electric field in the thick oxide, thus affecting its secondary electron yield. By analyzing the SUEM contrast as a function of time and laser fluence we demonstrate the diffusion mediated capture of excited carriers by interfacial traps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Second-harmonic and linear spectroscopy of $\textit{α}$-In 2 Se 3

We report spectroscopic measurements of optical transmission, ellipsometry, and second-harmonic generation (SHG) from as-grown vapor-deposited $\textit{α}$-In 2 Se 3 nanoflakes ranging in thickness from a single quintuple layer (QL) to bulk material. In this work, we compare these measurements with ab initio calculations of structural and optical properties. Linear optical measurements yield thickness-dependent band gaps and dielectric functions, while SHG diagnoses microscopic film structure and ferroelectric polarization. The rotational anisotropy of SHG for s-polarized incident photons of energy 1.4 eV reveals crystalline symmetry and orientation of individual QLs. Peak SHG intensity increases from one to three QLs, then decreases for larger numbers, tracking thickness-dependent trends in the second-order susceptibility components $χ^{xxx}$ and $χ^{zxx}$. Comparison of measured and calculated SHG spectra for s-polarized photons of energies between 1.2 and 1.7 eV incident upon two QL samples discriminates among candidate stacking arrangements, and favors an arrangement with electric polarization vectors of the two QLs pointing outward in opposite directions.

36 MATERIALS SCIENCE↗

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↗

Influence of the Guinier–Preston Zones on the Concentration Dependence of the Yield Point of the Aged Two-Component Alloys in Conditions of High-Speed Deformation

The glide of an ensemble of edge dislocations at the high-speed deformation of an aged binary metal alloy is theoretically analyzed. The yield stress of the alloy is a nonmonotone function of the second component concentration, which has a maximum and a minimum under certain conditions. The maximum corresponds to the transfer from the dominating influence of dislocation collective interaction on creation of a spectral gap to the prevalence of the influence of collective interaction of atoms of the second component. The minimum of the obtained curve corresponds to the transfer from the prevalence of the drag of the dislocation by the Guinier–Preston zones to the prevalence of its drag by the atoms of the second component.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Resolution requirements for energy conservation in kinetic plasma simulations

The kinetic codes used to model the coupled dynamics of electromagnetic fields and charged particle transport have requirements for spatial, temporal, and charge resolution. These requirements may vary by the solution technique and scope of the problem. In this report, we investigate the resolution limits in the energy-conserving implicit particle-in-cell code CHICAGO. This report has the narrow aim of determining the maximum acceptable grid spacing for the dense plasmas generated in models of z-pinch target gases and power-flow electrode plasmas. In the 2D sample problem, the plasma drifts without external forces with velocity of 10 cm/µs. Simulations are scaled by plasma density to maintain uniform strides across the plasma and from the plasma to the boundaries. Additionally, the cloud-in-cell technique is used with 400 particles per cell and Δ t = 0.85× the Courant limit. For the linear cloud distribution, the criterion for conserving energy is Δ E/E tot < 0.01 for 50,000 time steps. The grid resolution is determined to crudely be Δx ≲ 3 l s , where l s is the electron collisionless skin depth. For the second-order cloud distribution the criterion is Δ E/E tot < 0.005 yielding Δx ≤ 15 l s . These scalings are functions of the chosen v d , Δ t , particles-per-cell, and number of steps.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Let’s Stick Together: Interplay of Moisture, Particle Size, and Anatomical Fraction in the Flowability of Corn Stover Crumbles

Handling of agricultural waste biomass feedstocks (such as corn stover) is a persistent challenge in the production of biofuels and chemicals at integrated biorefineries. Inconsistent flowability and high feedstock variability creates equipment downtime and processing challenges. This work investigates the influence of anatomical fractionation and moisture content on the bulk solids handling behavior of corn stover crumbles. A combination of rotational shear testing, tribological measurements, and surface and sorption characterization techniques (inverse gas chromatography (IGC), dynamic vapor sorption (DVS), and electron microscopy) were used to evaluate the contributions of particle composition, size, and surface properties to flow behavior. Shear and frictional testing revealed that moisture content has the greatest effect on flowability, significantly increasing unconfined yield strength (ƒ c ) and reducing the flow function coefficient (F F C), regardless of anatomical fraction. While differences in surface energy were observed between fractions, particularly in polar contributions (γ AB ), these did not correspond to meaningful differences in flow behavior. Coarser 6 mm particles exhibited poorer flow performance than 4 mm crumbles, likely due to broader particle size distributions and increased particle interlocking. Taken together, these results suggest that anatomical fractionation provides minimal benefit from a bulk handling perspective. Moisture content and particle size heterogeneity dominate handling behavior, reinforcing the utility of unfractionated corn stover in processing environments. These insights can inform the design of more efficient and reliable feedstock processing systems for agricultural biomass in integrated biorefineries.

09 BIOMASS FUELS↗

Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era

The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely sampled time-series are needed. Here, we present a new method for light curve period estimation based on quadratic mutual information (QMI). The presented method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated even when no single-band QMI yields the period. Period recovery performance as a function of average magnitude and sample size is measured using 30,000 synthetic multiband light curves of RR Lyrae and Cepheid variables generated by the LSST Operations and Catalog simulators. The results show that aggregating information from several bands is highly beneficial in LSST sparsely sampled time-series, obtaining an absolute increase in period recovery rate up to 50%. We also show that the QMI is more robust to noise and light curve length (sample size) than the multiband generalizations of the Lomb–Scargle and AoV periodograms, recovering the true period in 10%–30% more cases than its competitors. A python package with efficient Cython implementations of the QMI and other methods is provided.

79 ASTRONOMY AND ASTROPHYSICS↗

Principal factors in performance of indirect-drive laser fusion experiments

Progress in inertial confinement fusion depends on the accurate interpretation of experiments that are complex and difficult to explain with simulations. Results could depend on small changes in the laser pulse or target or physics that are not fully understood or characterized. In this paper we discuss an x-ray-driven platform [K. Baker et al., Phys. Rev. Lett. 121, 135001 (2018)] with fewer sources of degradation, and find the fusion yield can be described as a physically motivated function of laser energy, target scale, and implosion symmetry. This platform and analysis could enable a more experimental approach to the study and optimization of implosion physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Seismoacoustic Analysis of Chemical Explosions at the Nevada National Security Site

In recent years, two sets of chemical explosions have been conducted at the Nevada National Security Site (NNSS): 6 explosions from Phase I of the Source Physics Experiment (SPE) and 4 explosions from the Forensics Surface Events (FSE). We have estimated the explosive yield and depth-of-burial/height-of-burst of both from the synthesis of seismic and low-frequency acoustic data. Analysis of the seismic signal is performed using a waveform envelope technique. Using seismic data only, however, there is a tradeoff between the yield and depth or height of the explosion, which becomes especially acute for near-surface events. This tradeoff between yield and depth/height can be broken by including complementary analysis of the acoustic signal using the acoustic waveform inversion method. The acoustic signal also has a strong tradeoff between a yield and depth/height, but the slope is opposite that of the seismic for near-surface events. We use a likelihood function to combine the seismic and acoustic analysis and improve our estimates of yield and depth/height for these sets of explosions. The results are generally consistent with the known parameters, but can be improved upon by higher-frequency seismic analysis and improved acoustic impulse scaling for large scaled depths-of-burial. These events serve as prime examples of data fusion from multiple data streams. The challenge will be to apply the method to events at longer regional distances where the seismic signals will include phases traveling in the upper mantle, and the acoustic signals will be recorded as infrasound signals, which are subject to atmospheric variability.

58 GEOSCIENCES↗

Dynamical edge modes and entanglement in Maxwell theory

Abstract Previous work on black hole partition functions and entanglement entropy suggests the existence of “edge” degrees of freedom living on the (stretched) horizon. We identify a local and “shrinkable” boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D entanglement entropy consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.

Physics↗

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

A remarkable case of basis set dependence: the false convergence patterns of the methyl anion

Here, the gas phase methyl anion, CH 3 ¯, has been difficult to study experimentally, and the extreme basis set dependence of its molecular properties has presented a comparable challenge to theoreticians. Reliable predictions for the electronic structure of CH 3 ¯ require the use of basis sets capable of describing both the diffuse and valence characteristics of the system. The present study examines the basis set dependence of the equilibrium geometry and harmonic vibrational frequencies of CH 3 ¯. Both Hartree–Fock and CCSD(T) levels of theories are used with cc-pVXZ (, T, Q, 5, 6) basis sets with up to triple augmentation to describe the diffuse nature of the electron distribution. We find that non-augmented basis sets systematically yield vibrational frequencies that are too high for the umbrella mode and too low for the C–H symmetric and antisymmetric stretch even when extrapolated to the complete basis set limit, displaying false convergence patterns. The inclusion of one set of augmented functions significantly improves the convergence of these properties, but again yields false convergence patterns. Only with the doubly augmented basis set do we approach the basis set limit for the CH 3 ¯ vibrational frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Amine Functionalized Electrospun Cellulose Nanofibers for Fluoride Adsorption from Drinking Water

In this study, we synthesized amine functionalized cellulose nanofiber based adsorbent for effective removal of dissolved fluoride ions from groundwater samples. Cellulose acetate was electrospun into nanofibers followed by deacetylation to yield cellulose nanofibers which were then treated with ethylenediamine to prepare amine functionalized cellulose fabric to be used as an adsorbent. As- synthesized adsorbent was first characterized by scanning electron microscopy and Fourier transform infrared spectroscopy for physiochemical characteristics. Fluoride adsorption studies were then carried out under batch mode to study the influence of various parameters on adsorption process. Amine functionalized cellulose nanofibrous mat was found to be effective with high adsorption efficiency for removal of fluoride ions from aqueous solution, even at low fluoride concentrations (< 5 mg L{sup −1}). Adsorption mechanism of fluoride onto prepared cellulose nanofibers based adsorbent was explained from the studies of isotherms, kinetic and thermodynamic parameters. Field studies conducted using this amine functionalized cellulose nanofibrous mat revealed the suitability and effectiveness of adsorbent for fluoride removal from contaminated groundwater.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Effects of Recovery Conditions and Aggregation Mechanisms on the Chemical and Physical Properties of Hybrid Poplar and Corn Stover Lignins

Heterogeneity in the physical properties and processing behavior of lignins recovered from biorefining process streams can hinder their effective utilization and industrial valorization. This work investigates lignin recovery by acidification from alkaline pretreatment liquors of varying sources (corn stover and hybrid poplar), compositions, solid contents, and incubation temperatures prior to filtration. Recovered lignins were characterized for filtration performance, mass yield, chemical composition, particle size and morphology, and color. A transition temperature was identified corresponding to marked shifts in lignin physical properties and was a function of the solid content and liquor source. Filtration below this temperature yielded slow-filtering, dark, brittle lignins with smoother particle surfaces, whereas precipitation above this threshold yielded fast-filtering, lighter, powdery lignins with rougher particle surfaces. The impact of temperature and concentration on universal cluster aggregation mechanisms was proposed to explain the differences between lignin particle properties and filtration behavior.

Aggregation↗

Predicting Biomass Yields of Advanced Switchgrass Cultivars for Bioenergy and Ecosystem Services Using Machine Learning

The production of advanced perennial bioenergy crops within marginal areas of the agricultural landscape is gaining interest due to its potential to sustainably produce feedstocks for biofuels and bioproducts while also improving the sustainability and resilience of commodity crop production. However, predicting the biomass yields of this production system is challenging because marginal areas are often relatively small and spread around agricultural fields and are typically associated with various abiotic conditions that limit crop production. Machine learning (ML) offers a viable solution as a biomass yield prediction tool because it is suited to predicting relationships with complex functional associations. The objectives of this study were to (1) evaluate the accuracy of commonly applied ML algorithms in agricultural applications for predicting the biomass yields of advanced switchgrass cultivars for bioenergy and ecosystem services and (2) determine the most important biomass yield predictors. Datasets on biomass yield, weather, land marginality, soil properties, and agronomic management were generated from three field study sites in two U.S. Midwest states (Illinois and Iowa) over three growing seasons. The ML algorithms evaluated in the study included random forests (RFs), gradient boosting machines (GBMs), artificial neural networks (ANNs), K-neighbors regressor (KNR), AdaBoost regressor (ABR), and partial least squares regression (PLSR). Coefficient of determination (R 2 ) and mean absolute error (MAE) were used to evaluate the predictive accuracy of the tested algorithms. Results showed that the ensemble methods, RF (R 2 = 0.86, MAE = 0.62 Mg/ha), GBM (R 2 = 0.88, MAE = 0.57 Mg/ha), and GBM (R 2 = 0.78, MAE = 0.66 Mg/ha), were the most accurate in predicting biomass yields of the Independence, Liberty, and Shawnee switchgrass cultivars, respectively. This is in agreement with similar studies that apply ML to multi-feature problems where traditional statistical methods are less applicable and datasets used were considered to be relatively small for ANNs. Consistent with previous studies on switchgrass, the most important predictors of biomass yield included average annual temperature, average growing season temperature, sum of the growing season precipitation, field slope, and elevation. This study helps pave the way for applying ML as a management tool for alternative bioenergy landscapes where understanding agronomic and environmental performance of a multifunctional cropping system seasonally and interannually at the sub-field scale is critical.

09 BIOMASS FUELS↗

Improved Lithium Iodide neutron scintillator with Eu 2 + activation II: Activator zoning and concentration effects in Bridgman-grown crystals

We have previously reported on the formation of Suzuki Phase precipitate particles as a result of the addition of the divalent activator ion Eu 2+ to the monovalent alkali halide host LiI. [Boatner et al. (2017)]. These precipitates form during Bridgman or other melt-growth processes, even at low Eu 2+ concentrations (e.g., 0.1% EuI 2 doping), and scatter the scintillation light reducing the optical transparency of the scintillator and adversely affecting its radiation-detection performance. In our prior work, we developed a two-stage thermal-treatment method for the post-growth removal of the Suzuki Phase particles and the realization of a significant improvement in the optical transparency and associated neutron-detection of LiI:Eu 2+ scintillators. These improvements resulted in neutron-detection performance that is superior to GS-20 glass and that allows for the application of pulse height gamma-ray discrimination over a wide range of gamma ray energies as opposed to pulse shape discrimination. Here in this paper, we apply the two-stage thermal-processing method for the removal of Suzuki phase precipitates and carry out an in-depth study, first, of the neutron scintillator performance versus the Eu 2+ activator-ion-concentration spatial variation as a result of zoning effects during the Bridgman growth of LiI:Eu and, second, of the effects of varying the initial Eu 2+ activator ion concentration prior to crystal growth. The Eu 2+ zoning variation results allow one to identify and select the most efficient location of the scintillation performance in a directionally solidified single-crystal boule. The present study of the initial activator concentration levels shows that there are, in fact, two distinct types of luminescence centers with varying performance properties — one that occurs only at low EuI 2 addition levels (e.g., 0.01 to 0.06 %EuI 2 ) and that is quickly replaced by a second luminescing center with increasing Eu content (e.g., at 0.1% EuI2). The light yield for the luminescing center formed using a Eu activator in LiI is a critical function of the Eu concentration in the range of 0.01 to 0.1 % EuI 2 , and a high light yield of 100,000 photons/neutron is observed at the 0.06 %EuIadditive level prior to thermal processing.

36 MATERIALS SCIENCE↗

A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements

We report that in the structural refinement of nanoparticles, discrete atomistic modeling can be used for small nanocrystals (< 15 nm), but becomes computationally unfeasible at larger sizes, where instead unit-cell-based small-box modeling is usually employed. However, the effect of the nanocrystal's shape is often ignored or accounted for with a spherical model regardless of the actual shape due to the complexities of solving and implementing accurate shape effects. Recent advancements have provided a way to determine the shape function directly from a pair distribution function calculated from a discrete atomistic model of any given shape, including both regular polyhedra (e.g. cubes, spheres, octahedra) and anisotropic shapes (e.g. rods, discs, ellipsoids) [Olds et al. (2015). J. Appl. Cryst. 48, 1651–1659], although this approach is still limited to small size regimes due to computational demands. In order to accurately account for the effects of nanoparticle size and shape in small-box refinements, a numerical or analytical description is needed. This article presents a methodology to derive numerical approximations of nanoparticle shape functions by fitting to a training set of known shape functions; the numerical approximations can then be employed on larger sizes yielding a more accurate and physically meaningful refined nanoparticle size. Lastly, the method is demonstrated on a series of simulated and real data sets, and a table of pre-calculated shape function expressions for a selection of common shapes is provided.

36 MATERIALS SCIENCE↗