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DOE OSTI2019

Using Nanoparticle X-ray Spectroscopy to Probe the Formation of Reactive Chemical Gradients in Diffusion-Limited Aerosols

For aerosol particles that exist in highly viscous, diffusion-limited states, steep chemical gradients are expected to form during photochemical aging in the atmosphere. Under these conditions, species at the aerosol surface are more rapidly transformed than molecules residing in the particle interior. To examine the formation and evolution of chemical gradients at aerosol interfaces, the heterogeneous reaction of hydroxyl radicals (OH) on ~200 nm particles of pure squalane (a branched, liquid hydrocarbon) and octacosane (a linear, solid hydrocarbon) and binary mixtures of the two are used to understand how diffusion limitations and phase separation impact the particle reactivity. Aerosol mass spectrometry is used to measure the effective heterogeneous OH uptake coefficient (γ eff ) and oxidation kinetics in the bulk, which are compared with the elemental composition of the surface obtained using X-ray photoemission. When diffusion rates are fast relative to the reaction frequency, as is the case for squalane and low-viscosity squalane–octacosane mixtures, the reaction is efficient (γ eff ~ 0.3) and only limited by the arrival of OH to the interface. However, for cases, where the diffusion rates are slower than reaction rates, as in pure octacosane and higher-viscosity squalane–octacosane mixtures, the heterogeneous reaction occurs in a mixing-limited regime and is ~10× slower (γ eff ~ 0.03). This is in contrast to carbon and oxygen K edge X-ray absorption measurements that show that the octacosane interface is oxidized much more rapidly than that of pure squalane particles. The O/C ratio of the surface (estimated to be the top 6–8 nm of the interface) is measured to change with rate constants of (3.0 ± 0.9) × 10 –13 and (8.6 ± 1.2) × 10 –13 cm 3 molecule –1 s –1 for squalane and octacosane particles, respectively. The differences in surface oxidation rates are analyzed using a previously published reaction-diffusion model, which suggests that a 1–2 nm highly oxidized crust forms on octacosane particles, whereas in pure squalane, the reaction products are homogeneously mixed within the aerosol. This work illustrates how diffusion limitations can form particles with highly oxidized surfaces even at relatively low oxidant exposures, which is in turn expected to influence their microphysics in the atmosphere.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Origins of quench in buffered chemical polished and low temperature baked SRF cavities

Electropolishing (EP) and buffered chemical polishing (BCP) are conventional surface preparation techniques for superconducting radiofrequency (SRF) cavities that remove damaged material from the cavity surface. One main issue with EP and BCP treated SRF cavities is high field Q-slope (HFQS), a drop in quality factor at high gradients that limits quench field. High gradient performance in EP cavities can be improved by applying a low temperature bake (LTB), but LTB does not consistently remove HFQS in BCP cavities. There is no consensus as to the why LTB is not effective on BCP prepared cavities, and the cause of HFQS in BCP cavities is not well understood. We examine the origins of quench in EP, BCP, EP+LTB, and BCP+LTB treated SRF cavities. We also show the effect of these treatments on the onset of HFQS, heating within the cavity up to quench, concentration of free hydrogen, and surface roughness.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Iron transformation mediates phosphate retention across a permafrost thaw gradient

Phosphorus limits primary productivity in many (Sub-)Arctic ecosystems and may constrain biological carbon sequestration. Iron (III) oxides strongly bind phosphate in soils but can dissolve under flooded, reducing conditions induced by permafrost thaw and ground collapse. The ability for iron to regulate phosphate storage and solubility in thawing permafrost landscapes remains unclear. Here, iron-rich sediments containing iron oxides and organic-bound iron were incubated with or without added phosphate in soils along a permafrost thaw gradient to evaluate how iron-phosphate associations respond to thaw-induced redox shifts. Iron oxides partially dissolved and released sorbed phosphate when incubated in soils underlain by degraded permafrost. Iron complexed by organic matter remained stable but provided no phosphate binding capacity. Phosphate addition enhanced iron oxide dissolution and phosphorus concentrations in associated microbial biomass. Our study demonstrates that the capacity for iron oxides to immobilize and retain phosphate in permafrost peatlands decreases with permafrost thaw.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Limit cycle oscillations in the zonal-flow-catalyzed interactions of ion-temperature-gradient turbulence

Limit-cycle oscillations are studied for ion temperature gradient turbulence, which, in the absence of large diamagnetic (mean) shear flows, saturates through energy transfer from unstable modes to large-scale stable modes via zonal-flow intermediary modes. Oscillations of zonal flow and turbulence levels are strongly constrained by the reactive, largely non-dissipative character of the zonal flows. Since existing predator–prey models for observed oscillations in experiments do not include energy transfer through zonal flows to stable modes, low-order fluid models with this physics are constructed and investigated. A simple three-wave truncation produces low-amplitude zonal flows that slowly oscillate around a zero mean, with turbulence oscillations between coupled wavenumbers that exceed linear frequencies by orders of magnitude. This inconsistency with experimental observations is caused by the weak non-linear drive of zonal flows in three-wave systems and the lack of multiple-wavenumber turbulent interactions. A more comprehensive model that preserves multiple wavenumber interactions within the context of conservative zonal-flow-mediated energy transfer to stable modes accurately reflects observed dynamics when the phase between stable and unstable modes is occasionally randomized.

Li, P. -Y. (ORCID:0000000295254171)↗

DOE OSTI2026

Ground and excited state gradients with end-to-end differentiable semiempirical quantum chemistry

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1988

On the origin of steep edges and filaments in vorticity and potential vorticity fields

High-resolution numerical calculations are shown which capture the fundamental process responsible for the intensification of vorticity gradients in an isolated vortex subject to externally imposed distrubances. Imposition of almost any weak strain or shear field in stripping away the relatively weak vorticity at the edge of the vortex and leaves it with gradients four to six orders of magnitude greater than in the initial state. Calculations displaying such enormous gradients have never been reported previously, because of the artificial eddy diffusivities that always limit such gradients in standard numerical models. The present calculations, which have no such limitations, have been made possible by the development of a novel and robust new numerical technique for vortex dynamics called contour surgery.

Dritschel, D. G.↗

NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗

NASA NTRS1994

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗

DOE OSTI2022

Continental-scale niche differentiation of dominant topsoil archaea in drylands

Archaea represent a diverse group of microorganisms often associated with extreme environments. However, an integrated understanding of biogeographical patterns of the specialist Haloarchaea and the potential generalist ammonia-oxidizing archaea (AOA) across large-scale environmental gradients remains limited. Here, we hypothesize that niche differentiation determines their distinct distributions along environmental gradients. To test the hypothesis, we use a continental-scale research network including 173 dryland sites across northern China. Our results demonstrate that Haloarchaea and AOA dominate topsoil archaeal communities. As hypothesized, Haloarchaea and AOA show strong niche differentiation associated with two ecosystem types mainly found in China's drylands (i.e. deserts vs. grasslands), and they differ in the degree of habitat specialization. The relative abundance and richness of Haloarchaea are higher in deserts due to specialization to relatively high soil salinity and extreme climates, while those of AOA are greater in grassland soils. Our results further indicate a divergence in ecological processes underlying the segregated distributions of Haloarchaea and AOA. Haloarchaea are governed primarily by environmental-based processes while the more generalist AOA are assembled mostly via spatial-based processes. Our findings add to existing knowledge of large-scale biogeography of topsoil archaea, advancing our predictive understanding on changes in topsoil archaeal communities in a drier world.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Extracting energy from ocean thermal and salinity gradients to power unmanned underwater vehicles: State of the art, current limitations, and future outlook

Thermal gradient energy-generation technologies for powering unmanned underwater vehicles (UUVs) or autonomous sensing systems in the ocean are mainly in the research development phase or commercially available at a limited scale, and salinity-gradient energy-generation technologies have not been adequately researched yet. The demand for self-powered UUVs suitable for long-term deployments has been growing, and further research related to small-scale ocean gradient energy systems is needed. In this study, we conducted a comprehensive review about harvesting energy from ocean thermal or salinity gradients for powering UUVs, focusing on gliders and profiling floats. Thermal gradient energy systems for UUVs based on phase change materials (PCM) cannot provide the energy required for powering autonomous sensing systems because of the systems' low energy conversion efficiency. Besides reducing energy consumption by developing more efficient electrical-mechanical systems, enhancing the thermal conductivity of the PCMs may help address this challenge by increasing the power generation rate of the UUVs. Several other emerging technologies, such as thermoelectric generators, shape memory alloys, and small-scale thermodynamic cycle systems, have shown potential for powering UUVs, but they are still only at the laboratory testing or conceptual design phase. The most advanced power generation technologies based on salinity gradients, reverse electrodialysis and pressure-retarded osmosis, are still not economically viable for large-scale deployment, mainly because of the high cost of the components required to operate in harsh saline environments. Our feasibility evaluation showed that existing salinity gradient power generation technologies are not directly feasible for powering UUVs in the open ocean.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Analytical and numerical studies of dark current in radiofrequency structures for short-pulse high-gradient acceleration

High-gradient acceleration is a key research area that could enable compact linear accelerators for future colliders, light sources, and other applications. In the pursuit of high-gradient operation, rf breakdown limits the attainable accelerating gradient in normal-conducting rf structures. Recent experiments at the Argonne Wakefield Accelerator suggest a promising approach: using short rf pulses with durations of a few nanoseconds. Experimental studies show that these 𝒪⁡(1⁢ ⁢ns) rf pulses can mitigate breakdown limitations, resulting in higher gradients. For example, an electric field of nearly 400 MV/m was achieved in an 𝑋-band photoemission gun driven by 6-ns-long rf pulses, with rapid rf conditioning and low dark current observed. Despite these promising results, the short-pulse regime remains an underexplored parameter space, and rf breakdown physics under nanosecond-long pulses requires further investigation. In this paper, we present analytical and numerical simulations of dark current dynamics in accelerating cavities operating in the short-pulse regime. We study breakdown-associated processes spanning different time scales, including field emission, multipacting, and plasma formation, using simulations of the 𝑋-band photogun cavities. The results reveal the advantages of using short rf pulses to reduce dark current and mitigate rf breakdown, offering a path toward a new class of compact accelerators with enhanced performance and reduced susceptibility to breakdown.

Linear accelerators↗

DOE OSTI2022

Phosphorus limitation of early growth differs between nitrogen‐fixing and nonfixing dry tropical forest tree species

Summary Tropical forests are often characterized by low soil phosphorus (P) availability, suggesting that P limits plant performance. However, how seedlings from different functional types respond to soil P availability is poorly known but important for understanding and modeling forest dynamics under changing environmental conditions. We grew four nitrogen (N)‐fixing Fabaceae and seven diverse non‐N‐fixing tropical dry forest tree species in a shade house under three P fertilization treatments and evaluated carbon (C) allocation responses, P demand, P‐use, investment in P acquisition traits, and correlations among P acquisition traits. Nitrogen fixers grew larger with increasing P addition in contrast to non‐N fixers, which showed fewer responses in C allocation and P use. Foliar P increased with P addition for both functional types, while P acquisition strategies did not vary among treatments but differed between functional types, with N fixers showing higher root phosphatase activity (RPA) than nonfixers. Growth responses suggest that N fixers are limited by P, but nonfixers may be limited by other resources. However, regardless of limitation, P acquisition traits such as mycorrhizal colonization and RPA were nonplastic across a steep P gradient. Differential limitation among plant functional types has implications for forest succession and earth system models.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1993

On the accuracy of limiters and convergence to steady state solutions

This paper addresses the practical problem of obtaining convergence to steady state solutions when limiters are used in conjunction with upwind schemes on unstructured grids. The base scheme forms a gradient and limits it by imposing monotonicity conditions in the reconstruction stage. It is shown by analysis in one dimension that such an approach leads to various schemes meeting TVD requirements in one dimension. It is further shown that these formally second order accurate schemes are less than second order accurate in practice because of the action of the limiter function in smooth regions of the solution. Modifications are proposed to the limiter that restore the second order accuracy. In multiple dimensions these schemes produce steady state solutions that are monotone and devoid of oscillations. However, convergence stalls after a few orders of reduction in the residual. With the modified limiter, on the other hand, it is shown that converged steady state solutions can be obtained.

Venkatakrishnan, V.↗

DOE OSTI2025

Turbulence suppression at extreme plasma densities on DIII-D and EAST

Recent high-poloidal-beta (high-βP) experiments on DIII-D and EAST have made coordinated breakthroughs for high confinement quality at high density near the Greenwald limit. Density gradient amplification of turbulence suppression at high βP can explain both of these achievements. Experiments on DIII-D have achieved Greenwald fraction (fGr = line-averaged density/Greenwald density) above 1 simultaneously with normalized energy confinement (H98y2) around 1.5, as required in fusion reactor designs but never before verified in tokamak experiments with the divertor configuration. A synergy between increased H98y2 and fGr is observed with strong gas puffing, due to the build-up of an internal transport barrier at large radius in the temperature and density channels. Transport simulations reveal that the favorable trend of reduced turbulent energy transport at higher density is only expected when increasing the density gradient at high local safety factor and high β, thus at high βP to ensure strong α-stabilization. These conditions are crucial to many conceptual designs for steady-state reactors. New experiments on EAST have nearly doubled the ion temperature at fGr ∼ 0.9, consistent with predict-first modeling results based on the same physics revealed from the DIII-D analysis. All previous EAST long-pulse H-modes have Ti ≪ Te near plasma axis. Transport modeling indicates that the profiles are limited by ion-temperature-gradient modes at mid-radius. The modeling also suggested potential solutions, including reducing magnetic shear, enhancing density gradients, and higher impurity concentration. Following this guidance, EAST experiments directly show a strong enhancement of Ti achieved with a combination of a second plasma current ramp-up, a density gradient increase, and a Zeff perturbation by a short pulse (100 ms) of impurity injection, as predicted by the earlier modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2008

Spacecraft Design Thermal Control Subsystem

The Thermal Control Subsystem engineers task is to maintain the temperature of all spacecraft components, subsystems, and the total flight system within specified limits for all flight modes from launch to end-of-mission. In some cases, specific stability and gradient temperature limits will be imposed on flight system elements. The Thermal Control Subsystem of "normal" flight systems, the mass, power, control, and sensing systems mass and power requirements are below 10% of the total flight system resources. In general the thermal control subsystem engineer is involved in all other flight subsystem designs.

Jupiter Icy Moon Orbiter (JIMO)↗

DOE OSTI2026

Nutrient limitation shapes functional traits of mycorrhizal fungi and phosphorus-cycling bacteria across an elevation gradient

In nutrient-limited high-elevation ecosystems, plants rely on arbuscular mycorrhizal (AM) fungi to provide mineral phosphorus (P) in the form of phosphate (PO43-). AM fungi gather these nutrients from phosphorus-cycling bacteria (PCBs) that can mineralize PO43- from organic matter and solubilize mineral-bound P. How climate, soil factors, and nutrient limitation influence AM fungi and PCB assembly remains unclear. We collected soil from montane meadows across a 1,000-m elevation gradient on three replicate mountainsides and analyzed AM fungal marker genes, P-cycling genes from shotgun metagenomes, and edaphic measurements. High-elevation soils had nearly 50-fold less soil PO₄³⁻ and 60% more AM fungal hyphae than low-elevation soils. AM fungal turnover was linked to changes in pH, organic carbon, and PO₄³-. The composition of 198 P-cycling genes was influenced by the AM fungal community structure. Drivers of individual PCB functional genes, including pH and organic carbon, varied with gene phylogeny. We found a trade-off in P-cycling strategies across elevation: P-rich, low-elevation soils supported root-colonizing AM fungi and organic P-mineralizing bacteria. P-poor, high-elevation soils were dominated by stress-tolerant AM fungi and mineral P-solubilizing bacteria. Our results suggest that AM fungi and PCB community turnover across elevation are both shaped by pH, organic carbon, and P availability. With continued climate warming, the structure and function of mountaintop ecosystems might shift to resemble lower elevations, disrupting long-established and specialized microbial assemblages, with consequences for P-cycling dynamics and the total P available to plant communities.IMPORTANCEPhosphorus (P) limits plant productivity in high-elevation ecosystems, yet the microbial networks that mobilize P, including arbuscular mycorrhizal (AM) fungi and phosphorus-cycling bacteria (PCBs), remain under-characterized in these nutrient-poor soils. We show that across a 10,00-m elevation gradient, AM fungi and P-cycling gene assemblages shift predictably with pH, organic carbon, and phosphate availability. Higher elevations, with less available P, select for stress-tolerant AM fungal taxa and PCB strategies geared toward mineral solubilization, while low-elevation sites favor root colonization by AM fungi and organic P mineralization. These results suggest that nutrient limitation can constrain microbial community assembly in consistent ways across landscapes. High mountain soils are low in P and rely on a network of underground AM fungi and PCB to deliver nutrients to plants. This study shows how those underground relationships reorganize with elevation and how climate change could collapse long-standing microbial strategies by pushing high-elevation ecosystems toward lowland conditions. As soils warm and dry, the microbial scaffolding that supports alpine plant life may become increasingly unstable.

arbuscular mycorrhizal fungi↗

DOE OSTI2022

Experiments On A Conduction Cooled Superconducting Radio Frequency Cavity With Field Emission Cathode

To achieve Ampere-class electron beam accelerators the pulse delivery rate need to be much higher than the typical photo injector repetition rate of the order of a few kilohertz. We propose here an injector which can, in principle, generate electron bunches at the same rate as the operating RF frequency. A conduction-cooled superconducting radio frequency (SRF) cavity operating in the CW mode and housing a field emission element at its region of high axial electric field can be a viable method of generating high-repetition-rate electron bunches. In this paper, we report the development and experiments on a conduction-cooled Nb3Sn cavity with a niobium rod intended as a field emitter support. The initial experiments demonstrate 0.4 MV/m average accelerating gradient, which is equivalent of peak gradient of 3.2 MV/m. The measured RF cavity quality factor is 1.4 x 10$^8$ slightly above our goal. The achieved field gradient is limited by the relatively low input RF power and by the poor coupling between the external power supply and the RF cavity. With ideal coupling the field gradient can be as high as 0.6 MV/m still below our goal of about 1 MV/m.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

A Subspace-Inclusive Sampling Method for the Computational Design of Compositionally Graded Alloys

Abstract Compositionally graded alloys, a subclass of functionally graded materials (FGMs), utilize localized variations in composition with a single metal part to achieve higher performance than traditional single material parts. In previous work [Kirk, T., Galvan, E., Malak, R., and Arroyave, R., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” J. Mech. Des., 140, p. 111410. 10.1115/1.4040816], the authors presented a computational design methodology that avoids common issues which limit a gradient alloy’s feasibility, such as deleterious phases, and optimizes for performance objectives. However, the previous methodology only samples the interior of a composition space, meaning designed gradients must include all elements in the space throughout the gradient. Because even small amounts of additional alloying elements can introduce new deleterious phases, this characteristic often neglects potentially simpler solutions to otherwise unsolvable problems and, consequently, discourages the addition of new elements to the state space. The present work improves upon the previous methodology by introducing a sampling method that includes subspaces with fewer elements in the design search. The new method samples within an artificially expanded form of the state space and projects samples outside the true region to the nearest true subspace. This method is evaluated first by observing the sample distribution in each subspace of a 3D, 4D, and 5D state space. Next, a parametric study in a synthetic 3D problem compares the performance of the new sampling scheme to the previous methodology. Lastly, the updated methodology is applied to design a gradient from stainless steel to equiatomic NiTi that has practical uses such as embedded shape memory actuation and for which the previous methodology fails to find a feasible path.

Engineering↗