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A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Zhang, Yiqiang↗

4.32 Billion Year Old Impact Melts at Apollo 14: Dating the Procellarum Basin?

Introduction: Recent work has improved our understanding of lunar crustal structure and basin evolution on the Moon, but its early impact history and implications for solar system dynamics remain poorly established [1,2]. In particular, there is a derth of absolute ages, especially for the period >4.0 Ga, that could be related to basin-forming events. Here we present U-Pb isotopic data for Zr-rich minerals found in impact-melt fragments from Apollo 14 soil sample 14163 that, when combined with previously published data, dates an impact event at 4324±15 Ma. The compositions and ages of these impact-melt fragments provide unique information about the timing of early impact events and the composition of the lunar crust. Results: Fourteen rocklets ranging in size from 1 to 3 mm were extracted from soil 14163. Most are impactmelt rocks with 10-30% clasts of mostly pyroxene and plagioclase (100 to 500 μm) in a crystalline matrix. Textures of the matrix vary from subophitic, formed by intergrowths of 10-20 μm plagioclase and pyroxene crystals, to poikilitic, with plagioclase and pyroxene reaching 20-50 μm size. Some fragments that contain no visible clasts have similar textures are also interpreted as impact-melt rocks. All fragments contain notably large proportions of euhedral to subhedral ilmenite, zircon, apatite/merrillite and less abundant zirconolite and baddeleyite in the melt matrices. These grains often form intricate intergrowths with each other and rock-forming minerals, indicating their crystallization from the melt (Fig. 1). However, some slightly larger (~50 μm) zircon and phosphate grains can be interpreted as relict clasts based on their granular textures and relationships with the surrounding phases (Fig. 1). This implies that zircon and phosphate minerals were present in the target rocks. Some of these grains were profoundly remelted during the impact, which resulted in an oversaturation of the melt in Zr and P and crystallization of new grains of Zrrich minerals and phosphates during melt solidification. The presence of zircon and phosphates indicates that the melts were significantly enriched in KREEP components and ties their provenance to the Procellarum- KREEP Terrane (PKT) [3]. Combined U-Pb zircon data obtained for all fragments form two main clusters on a concordia diagram (Fig. 2), between about 4.3 and 3.9 Ga. Phosphate data mostly concentrate on the younger end of this age range but some analyses are almost as old as the older zircon grains (Fig. 2). Figure 1: Zircon (Zr) and phosphate (Apt; Mer) grains in impact melt fragments from Apollo 14 soil 14161. A-zircon grains crystallized from impact melt; B-phosphate grain inherited from the target; C- granular zircon grains Our interpretation of these data is that all U-rich minerals experienced variable resetting of the U-Pb system, with phosphate, where closure temperature is significantly lower than that in zircon, affected more profoundly by Pb loss than zircon. Our best estimate of the time of formation of zircon and phosphate is based on statistically valid analysis of grains interpreted texturally as grown from the impact melt (Fig. 2). Ten of these analyses define an age of 4324±15 Ma (MSWD=3.0, probability of fit P=0.002). Our best estimate for the time of resetting is obtained by combining data from phosphates that are statistically indistinguishable from 3.9 Ga within the analytical uncertainties. This group is represented by 18 analyses of 15 phosphate grains from different fragments (Fig. 2) and defines an age of 3922±6 Ma (MSWD=1.2, P=0.23). Conversely, a minimum age of the target lithologies, remelted in the impact that produced the rocklets studied here (Fig. 2), can be determined from the five oldest analyses of zircon clasts at 4338±13 Ma (MSWD=1.5, P=0.2), which is indistinguishable from the age of the impact melt within the uncertainties. The obtained ages, combined with textural evidence, imply that the impact melt was formed at 4324±15 Ma, and that it occurred in a zircon-rich target with a minimum age of 4338±13 Ma. Further reworking occurred during a second impact event at 3922±6 Ma. Discussion: The younger age of 3922±6 Ma can be interpreted as the time of the Imbrium impact. The older age of 4324±15 Ma would then be the time of formation of the impact melt, which was then caught in the Imbrium ejecta either at the Apollo 14 landing site or within the target rocks of the Imbrium impact. The presence of abundant accessory phases such as zircons and phosphates is consistent with a substantial KREEP component in the analyzed particles. The current distribution of KREEP on the lunar surface appears to be strongly influenced by Imbrum ejecta [4] so interpretation of the 4.32 Ga age depends in part on assumed structure of the pre-impact crust and distribution of KREEP within the crust. If KREEP was present only in the deep crust at 4.32 Ga, then a basin-scale impact possibly analogous to Imbrium or larger may be necessary to excavate a KREEPy impact melt at this time. However, if KREEPy materials were present closer to the surface perhaps due to redistribution related to Mg-suite magmatism, then smaller impacts might be able to rework KREEPy compositions at shallower depths. The coherence of the data on the particles analysed here suggests a large volume of melt that has been preserved since 4.32 Ga, consistent with a large impact event. Relict zircons and mineral clasts suggests that the igneous crust in the vicinity of this impact was well developed by at least 4.34 Ga, similar to the model age of KREEP and older than the isochron ages of many Mg-suite cumulates [5]. A problem that confronts all lunar sample studies using the current collection is that the pre-Imbrium geology of the PKT (the source of these 4.32 Ga impact melts) is not well constrained. The South Pole-Aitken basin contains regions that are moderately enriched in Th, but its ejecta is Th-poor [6]; therefore these A14 fragments are probably not SPA ejecta. Alternatively, these fragments may represent formation of a hypothesized Procellarum basin [7] although the lack of a clearly defined basin ejecta signature is a potential problem with that interpretation. In any case, they provide a younger limit on the age of lunar differentiation and formation of KREEP within the lunar crust. Figure 2: U-Pb data for zircon and phosphate grains from impact melt fragments. A-all data; B-data used for age calculations. References: [1] Orgel C., Michael G., Fassett C. I., van der Bogert C. H., Riedel C., Kneissl T., and Hiesinger H. (2018) J. Geophys. Res. Planets 123, 748- 762. [2] Evans A. J., Andrews-Hanna J. C., Head J. W., Soderblom J. M., Solomon S. C., and Zuber M. T. (2018) J. Geophys. Planets. 123, 1596-1617. [3] Jolliff, B.L., Gillis, J.J., Haskin, L.A., Korotev, R.L. and Wieczorek, M.A. (2000) J. Geophys. Res: Planets 105, 4197-4216. [4] Haskin L. A. (1998) J. Geophys. Res. Planets 103, 1679-1689. [5] Borg L.E., Gaffney A.M., and Shearer C.K. (2015) MAPS 50, 715-732. [6] Moriarty, D.P., Watkins, R.N., Valencia, S.N., Kendall, J.D., Evans, A.J., Dygert, N. and Petro, N.E. (2021) J. Geophys. Res. Planets 126. [7] Zhu, M.H., Wünnemann, K., Potter, R.W., Kleine, T. and Morbidelli, A. (2019) J. Geophys. Res: Planets 124, 2117-2140

M D Norman↗

Materials science research in microgravity

There are several important attributes of an extended duration microgravity environment that offer a new dimension in the control of the microstructure, processing, and properties of materials. First, when gravitational effects are minimized, buoyancy driven convection flows are also minimized. The flows due to density differences, brought about either by composition or temperature gradients will then be reduced or eliminated to permit a more precise control of the temperature and the composition of a melt which is critical in achieving high quality crystal growth of electronic materials or alloy structures. Secondly, body force effects such as sedimentation, hydrostatic pressure, and deformation are similarly reduced. These effects may interfere with attempts to produce uniformly dispersed or aligned second phases during melt solidification. Thirdly, operating in a microgravity environment will facilitate the containerless processing of melts to eliminate the limitations of containment for reactive melts. The noncontacting forces such as those developed from electromagnet, electrostatic, or acoustic fields can be used to position samples. With this mode of operation, contamination can be minimized to enable the study of reactive melts and to eliminate extraneous crystal nucleation so that novel crystalline structures and new glass compositions may be produced. In order to take advantage of the microgravity environment for materials research, it has become clear that reliable processing models based on a sound ground based experimental experience and an established thermophysical property data base are essential.

Perepezko, John H.↗

Compression-induced solidification of shock-melted cerium

Compression induced solidification has been observed in cerium on nanosecond timescales. For this study, a series of experiments were conducted on Sandia National Laboratories' Z Facility in which cerium was shock melted and subsequently shocklessly, or ramp, loaded across the melt line inducing solidification. The signature of solidification manifested in the recovery of material strength and the propagation of waves at the local elastic sound velocity. Density functional theory simulations of cerium along the experimental phase-space path exhibit spontaneous freezing to a tetragonal phase at the same pressure and closely predict the observed physical properties of solid and liquid cerium near melt.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Rapid solidification characteristics in melt spinning a Ni-base superalloy

The solidification kinetics involved in the process of melt spinning a Ni-base superalloy have been characterized. Through a correlation of ribbon thickness to melt puddle residence time, it was found that the solidification front velocity, V, is typically about 100 mm/sec at the ribbon surface not in contact with the spinning wheel. The rate of solidification varies within the ribbon, increasing with decreasing distance, S, from the wheel-contact surface as V = 3.65/s. Ribbon microstructure and texture characteristics are discussed in light of this kinetics result. The thickness-vs-time correlation was further analyzed to yield information about thermal history during ribbon formation. These thermal results are generally consistent with those deduced from dendrite arm spacing measurements.

Huang, S. C.↗

Long-Term Creep Behavior of a CoCrFeNi Medium-Entropy Alloy

We report that current research shows that high-entropy alloys (HEAs) can offer superior oxidation resistance compared to more traditional austenitic stainless steels with equivalent tensile mechanical performance. While many reports have been published on creep of CoCrFeNiMn, few focus on the CoCrFeNi family of low to medium entropy alloys. In this manuscript, uniaxial tensile creep test results for more than 46,000 accumulated hours are presented on the equiatomic CoCrFeNi alloy. The alloy was manufactured at NETL using a vacuum induction melt solidification approach with a computationally designed homogenization cycle. After completing the homogenization cycle, the ingot was first hot forged and then hot rolled into 10 mm thick plate, a product form that is relevant to many industries. Creep tests were performed in the temperature range of 600-650 °C using applied stresses from 120 to 189 MPa. This study builds upon previous results on the CoCrFeNiMn family of high-entropy alloys and offers a modicum of clarification about performance compared to small button melts by using ASTM standard test procedures and mechanical test specimens. The apparent creep activation energy and creep stress exponent were similar to those for CoCrFe medium-entropy and CoCrFeNiMn high-entropy alloys. The post-test creep microstructure showed some Cr segregation, which has also been noted for other CoCrFe alloys. The CoCrFeNi alloy also presents a double minimum or two minimum creep rate phenomena.

36 MATERIALS SCIENCE↗

Interface velocity dependent solute trapping and phase selection during rapid solidification of laser melted hypo-eutectic Al-11at.%Cu alloy

Microstructure formation of a hypo-eutectic Al-11Cu (atom percent) alloy during solidification after laser melting has been studied by transmission electron microscopy (TEM). The evolution of the solid-liquid-interface velocity, V SL , during the solidification process has been determined from direct observation by in-situ TEM. This enabled correlating V SL with development of four distinct microstructure zones. Crystal growth mode transitions from planar to cellular, cellular to dendritic, dendritic to cellular, and cellular to planar, have been observed for the accelerating solid-liquid-interface. The transition from coupled two-phase growth to the single-phase growth occurred for V SL = V a = (0.80±0.05) m/s, where V a is the velocity of absolute stability, at the onset of banded morphology grain formation. The in-situ and post-mortem TEM uniquely permitted determination of the non-equilibrium solidus for the rapidly solidifying Al-11Cu alloy. Experimental evidence for solute clustering and chemical ordering tendencies at length scales on the order of ≤ 5nm has been detected in the single-phase regions of the banded grains. The structural features of the single-phase bands have been interpreted as signatures of ‘frozen in’ configurations present in the liquid boundary layer adjacent to the growing crystal, which has a width of about 3nm. Finally, the nano-scale spatiotemporal resolution experimental TEM studies performed here provided quantitative metrics, e.g. the solidification interface velocity dependent solute concentration of the α-Al phase and the near-atomic scale structure in the single-phase bands, that are uniquely suitable for comparison with theory and model predictions for solidification microstructure development in multicomponent alloys after laser melting.

36 MATERIALS SCIENCE↗

In Situ Monitoring of Crystal Growth Using MEPHISTO, Mission STS 87-Program USMP-4: Experimental Analysis

This report summarizes the results of the In situ Monitoring of Crystal Growth Using MEPHISTO (Material por l'Etude des Phenomenes Interessant de la Solidification sur Terre et en Orbite) experiment on USMP-4. The report includes microstructural and compositional data obtained during the first year of the post flight analysis, as well as numerical simulation of the flight experiment. Additional analyses are being continued and will be reported in the near future. The experiments utilized MEPHISTO hardware to study the solidification and melting behavior of bismuth alloyed with 1 at% tin. The experiments involved repeated melting and solidification of three samples, each approximately 90 cm long and 6mm in diameter. Half of each sample also included a 2 mm. diameter growth capillary, to assist in the formation of single grain inside. One sample provided the Seebeck voltage generated during melting and freezing processes. Another one provided temperature data and Peltier pulsed demarcation of the interface shape for post flight analysis. The third sample provided resistance and velocity measurements, as well as additional thermal data. The third sample was also quenched at the end of the mission to preserve the interface composition for post flight determination. A total of more than 45cm of directionally solidified alloy were directionally solidified at the end of the flight for post mission structural and compositional characterization. Metallurgical analysis of the samples has shown that the interfacial kinetics play a key role in controlling the morphological stability of faceted alloys. Substantial differences were observed in the Seebeck signal between the ground-based experiments and the space-based experiments. The temperature gradient in the liquid for the ground-based experiments was also significantly lower than the temperature gradient in the liquid for the space-based experiments. Both of these observations indicate significant influence of liquid convection for the ground-based experiments.

Abbaschian, Reza↗

Strength and ductility of additively manufactured 316L stainless steel: Impact of neutron irradiation and data variability

Here, this article presents the mechanical properties of additively manufactured (AM) 316L stainless steel processed via the laser powder bed fusion (LPBF) method, focusing on the effects of neutron irradiation on mechanical properties and the variability in strength and ductility data. The rapid melting-solidification process and multiple heating-cooling cycles inherent in LPBF typically result in a fine, metastable microstructure with significant local variability. AM 316L builds of varying thicknesses were fabricated, and SS-J3 miniature tensile specimens were machined from six different locations. These specimens were irradiated with fast neutrons to doses of 2 and 10 dpa at target temperatures of 300 °C and 600 °C. Post-irradiation tensile tests were conducted at room temperature, 300 °C, and 600 °C. Compared to conventional 316L stainless steel, AM 316L exhibited higher initial strength but lower ductility. Irradiation at 300 °C caused significant hardening and prompt necking at yield, with limited uniform ductility, although embrittlement was not observed up to 10 dpa. While neutron irradiation, particularly at 600 °C, increased the variability in strength and ductility data, no clear dependence of mechanical properties on build thickness or sampling location was found—contrary to the conventional perception that AM materials may exhibit high property variability. Furthermore, we observed that the variability in property data for LPBF-processed 316L was relatively low compared to that of wrought 316L stainless steel. This reduced variability in AM 316L steel may be attributed to its highly metastable, stress-containing microstructure, which is discussed in the context of general tensile property variations.

Additively manufactured 316L stainless steel↗

Multi-GPU porting of a phase-change cascaded lattice Boltzmann method for three-dimensional pool boiling simulations

The Lattice Boltzmann method (LBM) has proven effective in simulating phase-change phenomena, such as melting, solidification, evaporation, and boiling. In this work, we develop a highly parallelized multi-GPU implementation of LBM for three-dimensional pool boiling simulations. The code is based on the OpenACC programming model, which enables the code to be deployed efficiently on multi-core CPUs, GPUs, and potentially other accelerators, without the need for architecture-specific rewrites. To support large-scale simulations, the domain is decomposed and distributed across multiple compute nodes using MPI. We demonstrate that the code exhibits excellent scaling properties, with ideal strong-scaling running with up to 256 GPUs on the MareNostrum5 cluster.

97 MATHEMATICS AND COMPUTING↗

Manufacturing in space and materials sciences on Skylab

Two main groups of manufacturing and materials studies were performed during the Skylab missions. The first group of experiments studied processes which are important in orbital assembly and construction, including melting, solidification, brazing, welding, and cutting. The second group concerned the manufacture of specific materials, including metallic alloys, single crystals, doped semiconductors, composite materials, and multicomponent superconductors. The present paper discusses several specific experiments conducted on Skylab. In general, the processes tested produced materials of higher quality in space than they would have on earth. The experiments prove that the elimination of gravitational forces has a decisive effect on a number of materials processes.

Stuhlinger, E.↗

Novel duplex vapor-electrochemical method for silicon solar cells

A process was developed for the economic production of high purity Si from inexpensive reactants, based on the Na reduction of SiF4 gas. The products of reaction (NaF, Si) are separated by either aqueous leaching or by direct melting of the NaF-Si product mixture. Impurities known to degrade solar cell performance are all present at sufficiently low concentrations so that melt solidification (e.g., Czochralski) will provide a silicon material suitable for solar cells.

Nanis, L.↗

Core Formation on Asteroid 4 Vesta: Iron Rain in a Silicate Magma Ocean

Geochemical observations of the eucrite and diogenite meteorites, together with observations made by NASA's Dawn spacecraft, suggest that Vesta resembles H chondrites in bulk chemical composition, possibly with about 25% of a CM-chondrite like composition added in. For this model, the core is 15% by mass (or 8 volume %) of the asteroid. The abundances of moderately siderophile elements (Ni, Co, Mo, W, and P) in eucrites require that essentially all of the metallic phase in Vesta segregated to form a core prior to eucrite solidification. Melting in the Fe-Ni-S system begins at a cotectic temperature of ~940 deg. C. Only about 40% of the total metal phase, or 3-4 volume % of Vesta, melts prior to the onset of silicate melting. Liquid iron in solid silicate initially forms isolated pockets of melt; connected melt channels, which are necessary if the metal is to segregate from the silicate, are only possible when the metal phase exceeds about 5 volume %. Thus, metal segregation to form a core does not occur prior to the onset of silicate melting.

Kiefer, Walter S.↗

Improved Mechanical Performance in FDM Cellular Frame Structures through Partial Incorporation of Faces

The utilization of lattice-type cellular architectures has seen a significant increase, owing to their predictable shape and the ability to fabricate templated porous materials through low-cost 3D-printing methods. Frames based on atomic lattice structures such as face-centered cubic (FCC), body-centered cubic (BCC), or simple cubic (SC) have been utilized. In FDM, the mechanical performance has been impeded by stress concentration at the nodes and melt-solidification interfaces arising from layer-by-layer deposition. Adding plates to the frames has resulted in improvements with a concurrent increase in weight and hot-pocket-induced dimensional impact in the closed cells formed. In this paper, we explore compressive performance from the partial addition of plates to the frames of a SC-BCC lattice. Compression testing of both single unit cells and 4 × 4 × 4 lattices in all three axial directions is conducted to examine stress transfer to the nearest neighbor and assess scale-up stress transfer. Our findings reveal that hybrid lattice structure unit cells exhibit significantly improved modulus in the range of 125% to 393%, specific modulus in the range of 13% to 120%, and energy absorption in the range of 17% to 395% over the open lattice. The scaled-up lattice modulus increased by 8% to 400%, specific modulus by 2% to 107%, and energy absorption by 37% to 553% over the lattice frame. Parameters that emerged as key to improved lightweighting.

FDM↗

Rapid solidification of levitation melted Ni-Sn alloy droplets with high undercooling

Experimental results obtained by high-speed optical temperature sensing for the rapid solidification of highly undercooled, levitation-melted Ni-Sn alloy droplets are presented. These data suggest a solidification model proceeding according to overlapping steps: (1) dendritic growth within the bulk undercooled melt, (2) continued recalescence as supersaturation of the interdendritic liquid dissipates, (3) fine-scale remelting within the dendrites, (4) ripening of the fine structure, and (5) solidification of remaining liquid at the end of recalescence.

Shiohara, Yuh↗

Quantifying Equiaxed vs Epitaxial Solidification in Laser Melting of CMSX-4 Single Crystal Superalloy

The competition between epitaxial vs. equiaxed solidification has been investigated in CMSX-4 single crystal superalloy during laser melting as practiced in additive manufacturing. Single-track laser scans were performed on a powder-free surface of directionally solidified CMSX-4 alloy with several combinations of laser power and scanning velocity. Electron backscattered diffraction (EBSD) mapping facilitated identification of new orientations, i.e., “stray grains” that nucleated within the fusion zone along with their area fraction and spatial distribution. Using high-fidelity computational fluid dynamics simulations, both the temperature and fluid velocity fields within the melt pool were estimated. This information was combined with a nucleation model to determine locations where nucleation has the highest probability to occur in melt pools. In conformance with general experience in metals additive manufacturing, the as-solidified microstructure of the laser-melted tracks is dominated by epitaxial grain growth; nevertheless, stray grains were evident in elongated melt pools. It was found that, though a higher laser scanning velocity and lower power are generally helpful in the reduction of stray grains, the combination of a stable keyhole and minimal fluid velocity further mitigates stray grains in laser single tracks.

36 MATERIALS SCIENCE↗

Influence of alloy solidification path on melt pool behavior in additive manufacturing

Numerical models used to study transport phenomena in laser-powder bed fusion processes often rely on assumptions and simplifications to reduce their computational expense. One common simplification is in the description of latent heat evolution during the solid-liquid phase change (i.e., the solidification pathway), justified by the fact that the mushy zone thickness is similar to the numerical grid spacing used for continuum transport models. The lack of resolution of transport phenomena in the mushy zone motivates the use of computationally convenient solidification paths such as linear or sigmoidal relationships over pathways derived from fundamental solidification theory such as equilibrium or Scheil models. In the present work, an uncertainty quantification (UQ) framework is used to analyze the influence of solidification pathway selection on the solidification dynamics and melt pool geometries in laser based additive manufacturing (AM) of IN625. Results show the solidification pathway has a quantifiable influence on the cooling rate at the liquidus isotherm, mushy zone thickness, and solidification time. Due to similarities in the latent heat evolution at the beginning of solidification, the equilibrium and Scheil models predict similar cooling rates near the liquidus isotherm, however the wider freezing range of Scheil leads to a wider mushy zone compared to equilibrium. The non-physical latent heat release profiles of sigmoidal and linear paths lead to significant overpredictions of cooling rates at the liquidus isotherm compared to equilibrium and Scheil. Finally, these results indicate that careful consideration should be given to the choice of solidification pathway to ensure reliable model predictions.

36 MATERIALS SCIENCE↗

Segregation effects during solidification in weightless melts

The generalized problem of determining the temperature and solute concentration profiles during directional solidification of binary alloys with surface evaporation was mathematically formulated. Realistic initial and boundary conditions were defined, and a computer program was developed and checked out. The programs computes the positions of two moving boundaries, evaporation and solidification, and their velocities. Temperature and solute concentration profiles in the semiinfinite material body at selected instances of time are also computed.

Li, C.↗