Molten Salt Species Solubility Calculations Using Thermochimica's Gibbs Energy Minimizer (GEM)
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Lee, Kyoung [ORNL]↗
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Results for “Gibbs energy minimization”
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Acceleration of Thermochemistry Solves in MOOSE and Pronghorn
This work focuses on the development and implementation of strategies to accelerate thermochemical calculations within MOOSE-based multiphysics simulations, particularly for applications in MSRs. We highlight the inherent complexity of nuclear materials, which require a multiscale approach to accurately model their behavior across various physical domains, including mechanical, chemical, and thermal phenomena. Thermochemical equilibrium calculations are crucial for predicting material properties and enhancing the fidelity of these simulations. The integration of Thermochimica, a Gibbs energy minimizer, into MOOSE allows for the direct minimization of Gibbs energy at every point on the mesh. However, the computational cost of such integration is significant. To address this, we explored acceleration strategies such as multi-threading support and the use of a thermodynamic ValueCache to reduce redundant calculations. Additionally, we investigated modifications to Thermochimica to enable phase constraints and improve its coupling with phase-field models, which are essential for simulating microstructural evolution and corrosion in MSR. These efforts aim to optimize the computational efficiency and accuracy of multiphysics simulations, thereby supporting the development of reliable and efficient nuclear materials for next-generation reactor technologies.
36 - MATERIALS SCIENCE↗
Equilipy: a python package for calculating phase equilibria
The CALPHAD (CALculation of PHAse Diagram) approach (Nigel Saunders & Miodownik, 1998) provides predictions for thermodynamically stable phases in multicomponent-multiphase materials across a wide range of temperatures. Consequently, the CALPHAD calculations became an essential tool in materials and process design (Luo, 2015). Such design tasks frequently require navigating a high-dimensional space due to multiple components involved in the system. This increasing complexity demands high-throughput CALPHAD calculations, especially in the rapidly evolving field of alloy design. In response to the need, we developed Equilipy an open-source Python package designed for calculating phase equilibria of multicomponent-multiphase systems. Equilipy is specifically tailored for high-throughput CALPHAD calculations, offering parallel computations across multiple processors and nodes with the given NPT input conditions namely elemental compositions (N), pressure (P), and temperature (T). Equilipy utilizes the program structure and Gibbs energy functions from the Fortran-based program, Thermochimica (Piro et al., 2013), with incorporating a new Gibbs energy minimization algorithm. This algorithm, originally developed by Capitani and Brown in 1987 (Capitani & Brown, 1987), has been revised and implemented to enhance the stability and performance of calculations. The Fortran codes are precompiled and interfaced with Python via F2PY, ensuring high computation speed. Benchmark tests shown in Figure 1 demonstrate that Equilipy’s computation speed is comparable to those of established commercial software, TC-Python and PanPython. This result highlights its efficiency and potential applications in various scientific and industrial fields.
97 MATHEMATICS AND COMPUTING↗
Specification of Radionuclide Classes for MELCOR Molten Salt Reactor Simulations
MELCOR has been used extensively to facilitate virtual investigations into severe nuclear accidents for light-water reactors (LWRs). Non-light water reactors (non-LWRs) render some LWR-centric approaches potentially unsuitable. MELCOR has been instrumental in analyzing source terms for LWRs and has recently expanded its applicability to non-LWRs. To simplify radionuclide (RN) tracking, MELCOR currently groups elements into 17 classes, each containing representative species. This grouping, optimized for LWRs, is not appropriate for non-LWRs due to the different chemistry. This necessitates a reevaluation of radionuclide transport modeling. This report introduces a new class scheme for MELCOR tailored to MSR modeling, expanding the current 17 classes to 32 and are explained in the context of a UF 4 fueled FLiBe carrier MSR. It provides a discussion and justification for the new groupings and outlines a methodology for discovering and defining additional classes in MELCOR using a sample calculated RN inventory and a Gibbs energy minimizer (GEM).
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
High-Fidelity Multiphysics Assessment of the Molten Chloride Reactor Experiment (MCRE) Integrating Neutronics, Thermal-hydraulics and Thermochemistry
This work presents a MOOSE-based Multiphysics model of the LOTUS MSR reactor system. The model includes the coarse-mesh turbulent thermal-hydraulics including passive advection of delayed neutron precursors of the primary system through Pronghorn, the power density and neutronics calculation employing Griffin, and the chemical interactions through Gibbs energy minimization and redox potential with Thermochimica. Incorporating a plate-out model, the full multi-physics model is used to evaluate the effects of deposition and removal of solid compounds formed in the molten salt in the reactor surfaces, evaluating the concentrations and regions in which nickel, chromium and iron would be deposited. Results indicate an almost isothermal state of the fuel during operation at 25 kW that do not increase the plate-out effects due to low temperature gradients.
21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium
An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.
Palmer, Grant↗
A generalized chemistry version of SPARK
An extension of the reacting H2-air computer code SPARK is presented, which enables the code to be used on any reacting flow problem. Routines are developed calculating in a general fashion, the reaction rates, and chemical Jacobians of any reacting system. In addition, an equilibrium routine is added so that the code will have frozen, finite rate, and equilibrium capabilities. The reaction rate for the species is determined from the law of mass action using Arrhenius expressions for the rate constants. The Jacobian routines are determined by numerically or analytically differentiating the law of mass action for each species. The equilibrium routine is based on a Gibbs free energy minimization routine. The routines are written in FORTRAN 77, with special consideration given to vectorization. Run times for the generalized routines are generally 20 percent slower than reaction specific routines. The numerical efficiency of the generalized analytical Jacobian, however, is nearly 300 percent better than the reaction specific numerical Jacobian used in SPARK.
Carpenter, Mark H.↗
Thermodynamic constraints on the textural evolution of eucrite, EET 90020
Basaltic eucrites, which are possibly parts of the Vestan crust, formed as either lava flows or intrusions, and can offer insights into early crust formation. However most eucrites have experienced thermal metamorphism, which exacerbates the challenges of understanding these samples. A variety of petrogenetic models such as, partial melting of a primitive source, fractional crystallization of magmas emplaced in a primitive crust, and/or partial melting of a eucritic source coupled with melt mixing and assimilation have been proposed in order to explain observed petrologic and chemical characteristics of eucrites. EET 90020 is an unbrecciated eucrite that has experienced significant thermal metamorphism, with temperatures of metamorphic equilibration calculated to be ~840-1040°C. Its petrologic history remains contentious, in part due to differences in trace element analyses [10,17, this work], which has led to multiple metamorphic interpretations [8,10-11]. Here, we combined petrologic observations, chemical analyses, and thermodynamic modeling, to interpret micro-domain textures identified in EET 90020 and better constrain its petrologic history. Ultimately, the development of such textures is a direct result of the geologic processes operating on a young Vesta or similar asteroid. Sample description: We identified three textural domains in EET 90020 (Figure 1); (I) A coarse grain domain with granoblastic plagioclase and pyroxene, (II) a medium grain domain with curved grain boundaries between plagioclase and pyroxene, and (III) a fine grain domain dominated by tridymite that fills in interstitial space between spherical plagioclase. Major element chemistry in phases is consistent across domains. Pyroxene have distinctive high Ca lamellae (Wo40.92En28.1Fs31.0) forming from the low-Ca pigeonite host (Wo3.5En33.7Fs62.8). There are small amounts of fayalitic olivine along pyroxene/oxide grain boundaries, where pyroxenes have reacted with ilmenite/chromite clasts. Plagioclase is anorthitic (Avg ~An88), with little variation (An86-92.5). Trace element bulk rock analyses were collected via ICP-MS and individual mineral analyses with LA-ICP-MS (Figure 2). The bulk sample has an observable enrichment in light rare earth elements, with a notable depletion in Eu. Plagioclase is enriched in LREEs, depleted in HREEs, and has a positive Eu anomaly while pyroxene is enriched in HREEs with a negative Eu anomaly. Variations in trace element analyses is likely influenced by the presence of phosphates because are highly enriched in REEs and have a dramatic effect on the bulk domain compositions. Thermodynamic modeling: The software package, Perple_X, was used to calculate mineral phase equilibria over a range of conditions using a Gibbs free energy minimization approach [12]. Models used all major/minor elements except P2O5. Thermodynamic properties from [13] were used to constrain endmember phase stabilities. Activity models were used to describe mixing in phases with solid solution. Isochemical P-T phase diagrams were constructed for the bulk thin section, and the coarse, medium and fine grain domain compositions. Domain compositions were determined using microprobe analyses of phases identified in each domain and observed modal mineral abundancies. Thermodynamically stable pyroxene compositions were extracted from model results and compared to pyroxene compositions collected via EMPA, allowing us to calculate temperatures for metamorphic equilibrium. Results: Results that use the coarse domain composition (Fig. 3a) demonstrate overlap at T ~ 1020°C indicating high T equilibration. There was no overlap for the medium and fine grain domains, or the bulk composition (e.g., Fig. 3b) indicating that these are not equilibrium assemblages. These results were replicated using data from [8,20]. Discussion: The disequilibrium results from the bulk rock, fine grain and medium grain models imply that EET 90020 was modified during and/or after peak metamorphism (open system behavior). However, this is in contrast to the coarse domain where it appears as if equilibrium was maintained. We suggest that this conflict is explained by highly localized equilibrium occurring at millimeter length-scales, which has been observed in terrestrial metamorphism where aqueous fluid infiltrate [14] or melt loss occurs [15]. It is unlikely that aqueous alteration was significant in modifying the bulk composition of EET 90020, because it lacks hydrated minerals. However, the presence of melt is supported by the presence of an abundance of curved grain boundaries and spherical grains in the medium and fine grain domains This contrasts the coarse domain, where grain boundaries are angular. Given the evidence for disequilibrium in the medium and fine grain domains, it would be inappropriate to draw additional conclusions about textural evolution using thermodynamic models of those domains. However, modeling results of the coarse grain domain, where equilibrium was maintained, can provide useful insights into the geologic evolution of EET 90020. We approximate maximum metamorphic temperatures, using the Ca component in pyroxene, at ~1020°C (Fig. 4), which is consistent with previous two-pyroxene thermometry [11]. At this temperature, up to 10 vol % melt can be produced in the coarse grain domain, which is at the boundary of minimum melt needed in order to segregate and form a melt network [16]. Tridymite and plagioclase would be the first minerals to melt out during heating starting ~990°C. This is consistent with the observed melt textures formed by tridymite and plagioclase in the fine grain domain. We suggest that a partial melting model best explains the textural development of EET 90020. Upon heating, melt generated was either trapped, resulting in no net change in the localized rock composition, or migrated, resulting in disequilibrium between pyroxene and the surrounding matrix. A positive Eu anomaly in plagioclase indicates that all of the plagioclase was melted previously. This is consistent with previous studies that have suggested that EET 90020 represents a residual eucrite that experienced partial melting and subsequent melt loss [8]. We speculate that partial melting could have occurred when EET 90020 was heated in the asteroid’s lower crust or adjacent to an intrusion [7]. Future work will study other, texturally heterogeneous samples to see if EET 90020 presents a unique circumstance or whether crustal partial melting was ubiquitous on the eucrite asteroid.
Eucrites↗
Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098
Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.
J S Gorce↗
Modeling the Crystallization of Martian Igneous Compositions
The martian crust is dominated by basalts and ultramafic rocks [1]. Understanding the crystallization sequence of martian igneous rocks is critical for constraining the petrologic and geochemical evolution of the crust and mantle. Experimental studies have investigated the parental liquid compositions and crystallization behavior using martian meteorite compositions [2-7], as well as compositions measured by rovers on the martian surface [8,9]. While experiments deliver crucial results, they are often limited by time and resources. Therefore, modeling approaches are an ideal tool to complement experimental results. The application of the MELTS software package [10, 11], to calculate the crystallization of martian compositions, reproduces important compositional details of magma crystallization but significant uncertainties regarding the pressure of the olivine-pyroxene multiple saturation point have been reported [12], and in the temperatures of initial crystallization [12, 13]. Recently, a new melting model, MAGMARS, has been shown to reproduce martian primary melts more accurately [14]. Here, we constrain the applicability of Gibbs free energy minimization software Perple_X [15] for martian compositions by comparing our modeled results to experimentally derived crystallization paths for two martian compositions.
J Semprich↗
Phase Transitions and Melting in the Venusian Basaltic Crust: Implications for Crustal Recycling
Understanding phase transitions and melting in the Venusian crust and the associated changes in density are critical to constrain crustal thickness, recycling, and remelting processes. For example, average surface conditions on Venus of 92 bars and 460 °C correspond to low-grade metamorphic conditions on Earth equivalent to hornfels- and greenschist-facies. Further, the primary igneous mineralogy in the Venusian crust should be replaced by metamorphic minerals over time and potentially melt, as temperatures and pressures increase with depth along geothermal gradients. Here, we use Perple_X (Connolly, 2005), a Gibbs free energy minimization program to calculates table phase equilibria over a range of pressure and temperature conditions for whole-rock compositions of a dry basalt, alkali basalt, and peridotite. Further, we extract mineral abundancies along five geotherms of 5, 10, 15, 20 and 25 °C/km and calculate the rock density after the extraction of melt. On the coldest geotherm of 5 °C/km, melting would start at ~ 197 km and ~121 km in the basalt and alkali basalt, respectively, and therefore at depths that significantly exceed the estimated thickness of the Venusian crust (8-25 km). A density cross-over, where the crustal density would exceed that of the mantle could potentially induce delamination and is estimated to occur at ~ 40 km for both compositions. On the 10 °C/km geotherm, melting of the basalt starts at 65 km and melt extraction only causes a gradual densification due the formation of initially lower melt proportions. In contrast, the alkali basalt starts to melt at a depth of ~ 57 km and the subsequent densification of the residual composition could trigger delamination at ~ 60km depth. For hotter geotherms (i.e., 25 °C/km gradient), melting would occur at shallower depths of 21 – 23 km. However, the basalt will not get significantly denser than the mantle while the residuum of the alkali basalt would reach a density cross-over at 30 km. Hence, differences in Venusian crustal compositions can significantly influence the thickness of the crust on individual geotherms. Our results demonstrate that phase transitions and melting are strongly dependent on the assumed geotherm and could, combined with geodynamic models, further constrain crustal parameters.
Julia Semprich↗
Flux trapping in NbTiN strips
We use scanning superconducting quantum interference device (SQUID) microscopy to image vortices in superconducting structures fabricated from NbTiN thin films. We repeatedly cool superconducting strips with different width in an applied magnetic field and image the individual vortices. From these images we determine the threshold field at which the first vortex enters a strip and the number and configuration of vortices beyond this threshold field. We model the behavior of the vortices with and without considering the effect of pinning using numerical methods to minimize the Gibbs free energy of vortices in the strips. Our measurements provide a first benchmark to investigate the flux trapping properties of NbTiN thin films directly relevant to NbTiN-based superconducting digital circuits.
Bai, Ruiheng [Cornell University] (ORCID:000000025↗
An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium
An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.
Palmer, Grant↗
Algorithm For Hypersonic Flow In Chemical Equilibrium
Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.
Palmer, Grant↗
Molecular equilibrium with condensation
Minimization of the Gibbs energy of formation for species of chemical elements and compounds in their gas and condensed phases determines their relative abundances in a mixture in chemical equilibrium. The procedure is more general and more powerful than previous abundance determinations in multiphase astrophysical mixtures. Some results for astrophysical equations of state are presented, and the effects of condensation on opacity are briefly indicated.
Sharp, C. M.↗
Mineral equilibrium in fractionated nebular systems
We investigated the equilibrium mineral assemblages in chemically fractionated nebular systems, using a computer routine that finds the set of minerals and gases which minimizes the Gibbs free energy of a system with stipulated elemental abundances. Diagrams are presented showing the equilibrium mineralogy, as a function of temperature (400-2300 K), for unfractionated solar material and five fractionated systems. The fractionated systems were defined by mixing, in various proportions, the following four volatility components that solar material can be divided into: refractory dust, carbonaceous matter, ices, and H2 gas. Dust enrichment is seen to increase temperatures of condensation/evaporation and the Fe(2+) content of mafic minerals and to permit existence of stable melt phases. Enrichment of dust and organic matter produces mineral assemblages that are similar in many ways to those of enstatite chondrites, but with mafic minerals that are far more reduced than those in primitive enstatite chondrites. Enrichment of dust, organics, and ices leads to highly ferrous mineralogies even at the highest temperatures but does not predict the stability of hydrous phases above about 450 K.
Wood, John A.↗
Tables and charts of equilibrium thermodynamic properties of ammonia for temperatures from 500 to 50,000 K.
Equilibrium thermodynamic properties for pure ammonia were generated for a range of temperature from 500 to 50,000 K and pressure from 0.01 to 40 MN/sq m and are presented in tabulated and graphical form. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, specific heat at constant pressure, specific heat at constant volume, isentropic exponent, and species mole fractions. These properties were calculated by the method which is based on minimization of the Gibbs free energy. The data presented herein are for an 18-species ammonia model. Heats of formation and spectroscopic constants used as input data are presented. Comparison of several thermodynamic properties calculated with the present program and a second computer code is performed for a range of pressure and for temperatures up to 30,000 K.
Simmonds, A. L.↗
Structures Self-Assembled Through Directional Solidification
Nanotechnology has created a demand for new fabrication methods with an emphasis on simple, low-cost techniques. Directional solidification of eutectics (DSE) is an unconventional approach in comparison to low-temperature biomimetic approaches. A technical challenge for DSE is producing microstructural architectures on the nanometer scale. In both processes, the driving force is the minimization of Gibb's free energy. Selfassembly by biomimetic approaches depends on weak interaction forces between organic molecules to define the architectural structure. The architectural structure for solidification depends on strong chemical bonding between atoms. Constituents partition into atomic-level arrangements at the liquid-solid interface to form polyphase structures, and this atomic-level arrangement at the liquid-solid interface is controlled by atomic diffusion and total undercooling due to composition (diffusion), kinetics, and curvature of the boundary phases. Judicious selection of the materials system and control of the total undercooling are the keys to producing structures on the nanometer scale. The silicon-titanium silicide (Si-TiSi2) eutectic forms a rod structure under isothermal cooling conditions. At the NASA Glenn Research Center, directional solidification was employed along with a thermal gradient to promote uniform rods oriented with the thermal gradient. The preceding photomicrograph shows the typical transverse microstructure of a solidified Si-TiSi2 eutectic composition. The dark and light gray regions are Si and TiSi2, respectively. Preferred rod orientation along the thermal gradient was poor. The ordered TiSi2 rods have a narrow distribution in diameter of 2 to 3 m, as shown. The rod diameter showed a weak dependence on process conditions. Anisotropic etch behavior between different phases provides the opportunity to fabricate structures with high aspect ratios. The photomicrographs show the resulting microstructure after a wet chemical etch and a dry plasma etch. The wet chemical etches the silicon away, exposing the TiSi2 rods, whereas plasma etching preferentially etches the Si-TiSi2 interface to form a crater. The porous architectures are applicable to fabricating microdevices or creating templates for part fabrication. The porous rod structure can serve as a platform for fabricating microplasma devices for propulsion or microheat exchangers and for fabricating microfilters for miniatured chemical reactors. Although more work is required, self-assembly from DSE can have a role in microdevice fabrication.
Dynys, Frederick W.↗