Calculation of complex chemical equilibria.
Nonlinear equations governing complex chemical and phase equilibria derived from thermodynamic principles and supplemented by solving algorithms and practical applications
NONLINEAR EQUATION↗
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Results for “phase equilibria”
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Probing ethane phase changes in bead pack via high-field NMR spectroscopy
Phase equilibria analysis in two-phase systems requires discernment of the individual phases as well as the interfacial region. The phase behavior of fluids in constraint geometries have been studied through several techniques. High-Field Nuclear Magnetic Resonance (HF-NMR) can be used to detect fluid phases, i.e. gas, liquid, or supercritical fluid, in the bulk or under confinement. In solution-state HF-NMR, each phase exhibits a distinct chemical shift that correlates to the phase density. In turn, the emergence of multimodal in NMR spectra reveals the coexistence of multiple phases in fluid systems. Our results for ethane show that HF-NMR can enable tracking phase changes in the bulk, but also in macro-scale (10–100's μm in pore size) porous systems at various pressure and temperature conditions, even when the system us out of equilibrium. Finally, these results creates potential opportunities to investigate phase changes influenced by confinement in porous systems, though additional steps are necessary.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Intermediate phases in some rare earth-ruthenium systems
The phase equilibria and crystal structures of intermediate phases were investigated in eight representative RE-Ru systems using powder X-ray diffraction and metallographic techniques. The Fe3C, Mn5C2 and Er5Ru3 structures occur in all but the Ce-Ru systems. Phases analogous to Er5Ru3 possess an unknown crystal structure similar to Er5Rh3(I). MgCu2 and MgZn2 type Laves phases are encountered in the light rare earth and heavy rare earth systems, respectively, and RERu2 phases, where RE = Nd and Sm, possess both the Laves phase structures. An intermediate phase, NdRu, with an unknown structure, occurs only in the Nd-Ru system. A bcc structure with 40 atoms per unit cell is encountered in the phases Er3Ru2 and Y3Ru2. The behavior of cerium in Ce-Ru alloys is unique in that four unidentified structures, not encountered in other RE-Ru systems, have been encountered. Also a phase designated as Ce3Ru is found with the Th7Fe3 type structure.
Sharifrazi, P.↗
Evolution of Indarch (EH4 Chondrite) at 1 GPa and High Temperature
The chondritic meteorites are materials that are as old as the solar system itself characterized by variations in bulk chemical and oxidation state, and have long been considered possible building blocks that accreted to form the terrestrial inner planets. Enstatite chondrites contain nearly FeO free enstatite, silicon-rich kamacite and various sulfides indicating formation under highly reducing conditions. These materials could have participated in the formation of the Earth. However, "fingerprinting" of meteoritic materials has shown that no known meteoritic class corresponds to a hypothetical bulk Earth composition in every aspect. To derive constraints on early accretion and differentiation processes and possibly resolve the debate on the formation of the Earth, it is required to study experimentally a variety of chondritic materials and investigate their melting relations and elemental partitioning behavior at variable pressure (P), temperature (T) and oxygen fugacities (fO2). Variations in fO2 can indeed change chemical features and phase equilibria dramatically. The P-T phase diagrams of peridotites and carbonaceous chondrites have been extensively studied experimentally up to pressures and temperatures corresponding to the transition zone and lower mantle. Even though partial melting experiments have been conducted at ambient pressure on the enstatite chondrite Indarch, enstatite meteorites have never been experimentally investigated at high PT. The following investigation focuses on the effect of the fO2 on the phase relations of Indarch, an EH4 chondrite.
Berthet, S.↗
Molecular thermodynamics for scaling prediction: Case of membrane distillation
Membrane distillation (MD) for water treatment is significantly impaired by the scaling of dissolved minerals. The type and content of minerals generally measured as total dissolved solids (TDS) in hypersaline brines not only reduce the MD flux but also control the scaling behavior on the membrane surface. The scaling-induced pore blockage further reduces water flux and eventually leads to membrane wetting. The scaling problem is even more pronounced in the treatment of produced water (PW) as it contains 3–7 times higher TDS concentrations, compared to seawater. Theoretically, the necessary conditions for a salt to precipitate can be traced from its solubility product constant and activity of the constituents within the solution. Therefore, a comprehensive thermodynamic model is necessary to represent the electrolyte behavior and to predict the precipitation of different salts in a complex solution like PW. We pursued electrolyte Nonrandom Two Liquid Theory (eNRTL), a state-of-the-art electrolyte model, to address the PW fluid phase equilibria. With a fully parameterized eNRTL model, we predicted salt precipitations in two different PW samples and compared the results against the experimental findings. Furthermore, here we forecast the precipitation of salts in response to the change in PW concentration and temperature in the MD operation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Mechanisms of devitrification of grain boundary glassy phases in Si3N4 materials
Changes in the grain boundary (g.b.) phases of Si3N4 are analyzed, the effects of composition and thermal history on devitrification of the g.b. phases are determined, devitrification of the g.b. phases of Si3N are related to mechanical behavior and oxidation sensitivity of the material. The phase relationships that occur within the grain boundaries of Si3N4 containing various densification aids are reviewed. Comparisons of the effects of MgO, Y2O3, CeO2, and Y2O3 + AL2O3 are made in terms of the phase equilibria of the Si3N4 + SiO2 + additive compositional system. Two new equilibrium phase diagrams for the Si3N4-SiO2 and Y2O3 and Si3N4-SiO2-Ce2O3 systems are preented. The effects of Y2O3 vs CeO2 densification aids on the fracture surfaces of Si3N4 are compared. Auger electron spectroscopy shows that both oxides are concentrated within the fracture surface. Scanning electron microscopy shows evidence that Si3N4 with CeO2 formed an intergranular structure of fine grained oxynitride reaction products, as predicted by phase quilibria, whereas the Y2O3 containing sample shows evidence of an intergranular glassy phase.
Hench, L. L.↗
Advanced methods for preparation and characterization of infrared detector materials
Crystals were prepared by the Bridgman-Stockbarger method with a wide range of crystal growth rates and temperature gradients adequate to prevent constitutional supercooling under diffusion-limited, steady-state, growth conditions. The longitudinal compositional gradients for different growth conditions and alloy compositions were calculated and compared with experimental data to develop a quantitative model of solute redistribution during the crystal growth of the alloys. Measurements were performed to ascertain the effect of growth conditions on radial compositional gradients. The pseudobinary HgTe-CdTe constitutional phase diagram was determined by precision differential-thermal-analysis measurements and used to calculate the segregation coefficient of Cd as a function of x and interface temperature. Experiments were conducted to determine the ternary phase equilibria in selected regions of the Hg-Cd-Te constitutional phase diagram. Electron and hole mobilities as functions of temperature were analyzed to establish charge-carrier scattering probabilities. Computer algorithms specific to Hg(1-x)CdxTe were developed for calculations of the charge-carrier concentration, charge-carrier mobilities, Hall coefficient, and Dermi Fermi energy as functions of x, temperature, ionized donor and acceptor concentrations, and neutral defect concentrations.
Broerman, J. G.↗
Phase diagram to demarcate supercritical, transcritical, and continuous phase regimes for binary fluid equilibrium mixing relevant to combustion applications
Here, a robust methodology to develop phase diagrams of binary fluid mixtures at fixed thermo dynamic conditions (pressure, temperature, and mole fraction) as well as of two initially separated fluids undergoing mixing near critical conditions are presented for fluids and con ditions relevant to rockets, gas turbines, and diesel engine applications. Phase equilibria of mixtures is first examined to provide insight into the continuous-phase mixing behavior (including but not limited to supercritical behavior), and to develop a broadly applicable phase-diagram for binary fluid mixtures at fixed conditions. Next, adiabatic mixing theory and reduced Helmholtz equations of state are used to predict the thermodynamic conditions required to attain continuous-phase binary fluid mixing near critical conditions. Then, a 3D surface diagram (P,T fuel ,T amb ) separating single and two-phase regions is constructed by varying the ambient pressure and the initial temperatures of the two fluids. Polynomial fits of the 3D surfaces for 10 different binary mixtures are tabulated for nitrogen-alkane and methane-oxygen blends relevant to air-breathing and propellant based engines, respectively.
42 ENGINEERING↗
Theory-guided design of duplex-phase multi-principal-element alloys
Density-functional theory (DFT) is used to identify phase-equilibria in multi-principal-element and high-entropy alloys (MPEAs/HEAs), including duplex-phase and eutectic microstructures. Here, a combination of composition-dependent formation energy and electronic-structure-based ordering parameters were used to identify a transition from FCC to BCC favoring mixtures, and these predictions experimentally validated in the Al-Co-Cr-Cu-Fe-Ni system. A sharp crossover in lattice structure and dual-phase stability as a function of composition were predicted via DFT and validated experimentally. The impact of solidification kinetics and thermodynamic stability was explored experimentally using a range of techniques, from slow (castings) to rapid (laser remelting), which showed a decoupling of phase fraction from thermal history, i.e., phase fraction was found to be solidification rate-independent, enabling tuning of a multi-modal cell and grain size ranging from nanoscale through macroscale. Strength and ductility tradeoffs for select processing parameters were investigated via uniaxial tension and small-punch testing on specimens manufactured via powder-based additive manufacturing (directed-energy deposition). This work establishes a pathway for design and optimization of next-generation multiphase superalloys via tailoring of structural and chemical ordering in concentrated solid solutions.
36 MATERIALS SCIENCE↗
Linking the Spin Transition of Ferric Iron in δ‐(Al,Fe)OOH to Water Storage in the Lower Mantle
As the most massive geochemical reservoir, the lower mantle affects the Earth's budget of volatile elements, including hydrogen or H 2 O. The properties of minerals in the lower mantle are further affected by changes in the electronic configurations of iron cations, that is, by spin transitions. The feedback between spin transitions and potential storage of H 2 O in solid hydrous phases in the lower mantle, however, remains unexplored. By combining high‐pressure nuclear resonant inelastic X‐ray scattering and high‐pressure high‐temperature X‐ray diffraction experiments, we constrained the thermal equation of state of δ‐(Al,Fe)OOH, a member of the phase H solid solution. Based on the derived thermal equation of state of δ‐(Al,Fe)OOH and the underlying thermodynamic model, we calculate the excess Gibbs free energy that arises from the spin transition of ferric iron in this compound and evaluate the effect on phase equilibria. The results of our analysis show that the spin transition of ferric iron in phase H may significantly reduce the thermodynamic activity and hence the concentration of H 2 O in a coexisting hydrous melt. As a consequence, nominally anhydrous minerals of the lower mantle may become dehydrated in the presence of phase H. Our analysis further suggests that, under certain conditions, the spin transition may expand the thermal stability of Fe 3+ ‐bearing phase H and create a geochemical link between the storage of H 2 O in phase H and ferric iron in the lower mantle.
Buchen, Johannes [Univ. of Bayreuth (Germany); Cal↗
Metallic particles of high cobalt content in Apollo 15 soil samples.
Single phase alpha-kamacite containing more than 3.2 wt % Co and gamma-taenite containing from 30 to 60 wt % Ni from the Apollo 15 soils - 15031, 15071, 15081, 15261, and 15271 - have been examined by metallographic and electron microprobe techniques. In addition two phase alpha + gamma particles from soils 14003, 15071, 15261, and 15271 with Ni and Co contents well outside the meteoritic range have also been examined. Two distinct types of alpha-gamma structure occur, one analogous to 'clear taenite' in ordinary chondrites, and the other analogous to a 'Widmanstaetten' structure in Ni-rich ataxites. The measured Ni gradients in the two-phase particles are very similar to those meteorites having the same structure. However the Co content is much higher than the meteoritic samples, up to 12 wt % in the alpha phase. Approximate phase equilibria data for the Fe-Ni-Co system indicate equilibration of the two-phase particles during cooling to approximately 350 C. Estimates of cooling rates and second-phase growth times indicate that the maximum time necessary for the development of the high-Co two-phase structures is roughly 25 to 100 m.y. These estimates argue for the development of the two-phase structures during formation of the lunar crust, at a depth of 10 to 20 km beneath the moon's surface.
Axon, H. J.↗
Formation of a metastable ferromagnetic tau phase during containerless melt processing in Mn-Al-C alloys
This paper reports the production of a metastable ferromagnetic tau phase directly from the melt in Mn(0.55)Al(0.433)C(0.017), using a containerless processing method involving levitation melting followed by quenching. Using the results from differential thermal analysis measurements and an analysis of the phase equilibria, it was found that the minimum amount of undercooling level required for ferromagnetic metastable tau phase formation in this alloy was Delta T = 87 K. The attainment of this undercooling may be facilitated by the application of containerless melt processing.
Kim, Y. J.↗
Undercooling minimization in ultrasound coupled DTA measurements of molten salts
Molten salts are ionic liquids that are used for the electrolytic pyroprocessing of metals and as heat transfer fluids in very high temperature processes. Recently, halide-based molten salt reactors (MSR) have gained momentum for high density and environmentally responsible electricity generation. The function of these reactors and their fuel cycle depend on a knowledge of the halide salt’s thermodynamic properties [1]. Therefore, high accuracy phase equilibria of MSR relevant base halide and actinide containing salts are needed. Modern thermal analysis of the phase transitions of halide salts is usually done during heating at relatively high scan rates with commercial devices. Normally such measurements are adequate for pure or pseudo-binary salts. However, as the number of components in the mixture increases, accurately resolving the liquidus becomes increasingly difficult. Reversing the scanning mode greatly increases the sensitivity of phase transition measurements but can decrease accuracy due to undercooling [2] — a common occurrence in molten halide systems [3]. This work presents the development of a differential thermal analysis (DTA) cell intended for use in radiological gloveboxes. Non-contact ultrasonic agitation of the halide salt is implemented to limit kinetic limitations on crystallization during cooling to minimize undercooling [4]. Measurements on halide salts are also presented to elucidate the effect of non-contact mixing on undercooling. Reference [1] S. Boyd and C. Taylor, “3 - Chemical fundamentals and applications of molten salts,” in Molten Salt Reactors and Thorium Energy, T. J. Dolan, Ed., Woodhead Publishing, 2017, pp. 29–91. doi: 10.1016/B978-0-08-101126-3.00003-8. [2] K. Nitsch, A. Cihlár, and M. Rodová, “Molten state and supercooling of lead halides,” J. Cryst. Growth, vol. 264, no. 1, pp. 492–498, Mar. 2004, doi: 10.1016/j.jcrysgro.2004.01.011. [3] L. Rycerz, “Practical remarks concerning phase diagrams determination on the basis of differential scanning calorimetry measurements,” J. Therm. Anal. Calorim., vol. 113, no. 1, pp. 231–238, Jul. 2013, doi: 10.1007/s10973-013-3097-0. [4] Md. H. Zahir, S. A. Mohamed, R. Saidur, and F. A. Al-Sulaiman, “Supercooling of phase-change materials and the techniques used to mitigate the phenomenon,” Appl. Energy, vol. 240, pp. 793–817, Apr. 2019, doi: 10.1016/j.apenergy.2019.02.045.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Testing and Application of Commercial Thermodynamics Software for Solid-Gas Equilibria in Planetary Science Applications
The ability to calculate chemical equilibria from thermochemical constants (e.g., H, S, Cp) or other experimental data is a tool widely employed by scientists. However, phase equilibria for planetary science problems is limited by easy access to libraries of thermochemical data, as well as the software to invert that data. Many academic software packages are focused on specific types of problems (e.g., aqueous solutions or melting and crystallization of magmas). This focus makes them excellent tools for specific uses, but poorer tools for other scenarios, especially those involving elements or chemical species that are less well-studied in that specific scientific field (e.g. NaCl vapor). Amongst the more general thermodynamic software tools, there are closed academic software packages, open-source options, as well as commercial software. We have explored the extent to which commercial chemistry/chemical engineering software may be able to satisfy the need for thermochemical modeling packages that can accommodate the diverse species and conditions of planetary science problems. Here we compare the output of software package HSC Chemistry™ (Metso Outotec) to published vapor-solid phase diagrams for a variety of major and minor elements. HSC Chemistry™ has been used in several recent geochemical studies of terrestrial volcanic systems [2- 4]. However, it has not to our knowledge been benchmarked against peer-reviewed model results for the conditions and compositions relevant to planetary science. We present one such comparison here, the low- pressure environment of the solar nebula, using literature data. In short, we find excellent agreement between HSC Chemistry™ and the well-regarded academic software package CONDOR. These preliminary results suggest that at least some commercial software packages are capable of robust thermochemical calculations for planetary science.
planetary science↗
The formation of ore mineral deposits on the Moon: A feasibility study
Most of the ore deposits on Earth are the direct result of formation by hydrothermal solutions. Analogous mineral concentrations do not occur on the Moon, however, because of the absence of water. Stratified ore deposits form in layered instrusives on Earth due to fractional crystallization of magma and crystal settling of high-density minerals, particularly chromium in the mineral chromite. We have evaluated the possibility of such mineral deposition on the Moon, based upon considerations of 'particle settling velocities' in lunar vs. terrestrial magmas. A first approximation of Stoke's Law would seem to indicate that the lower lunar gravity (1/6 terrestrial) would result in slower crystal settling on the Moon. However, the viscosity of the silicate melt is the most important factor affecting the settling velocity. The viscosities of typical lunar basaltic melts are 10-100 times less than their terrestrial analogs. These lower viscosities result from two factors: (1) lunar basaltic melts are typically higher in FeO and lower in Al2O3, Na2O, and K2O than terrestrial melts; and (2) lunar igneous melts and phase equilibria tend to be 100-150 C higher than terrestrial, largely because of the general paucity of water and other volatile phases on the Moon. Therefore, particle settling velocities on the Moon are 5-10 times greater than those on Earth. It is highly probable that stratiform ore deposits similar to those on Earth exist on the Moon. The most likely ore minerals involved are chromite, ilmenite, and native FeNi metal. In addition, the greater settling velocities of periodotite in lunar magmas indicate that the buoyancy effects of the melt are less than on Earth. Consequently, the possibility is considerably less than on Earth of deep-seated volcanism transporting upper mantle/lower crustal xenoliths to the surface of the Moon, such as occurs in kimberlites on Earth.
Taylor, Lawrence A.↗
Experimental Constraints on the Origin of Lunar High-Ti Ultramafic Glasses
Phase equilibria and dissolution rate experiments are used to develop a petrogenetic model for the high-Ti lunar ultramafic glasses. Near-liquidus phase relations of the Apollo 14 black glass, the most Ti-rich lunar ultramafic glass, are determined to 2.2-GPa. The liquidus is saturated with Cr-spinel at 1-atm, olivine between approximately 0.5- and 1.5-GPa, and low-Ca pyroxene + Cr-spinel above 1.5-GPa. Ilmenite does not crystallize near the liquidus and implies that high-Ti ultramafic glasses are not produced by melting of an ilmenite-saturated source. We infer that high-Ti ultramafic magmas are derived from low-Ti ultramafic parent magmas by assimilation of ilmenite +/- clinopyroxene +/- urKREEP +/- pigeonite in the shallow lunar interior. Heat is provided by adiabatic ascent of the low-Ti ultramafic primary magmas from the deeper lunar interior and crystallization of olivine during assimilation. The assimilation reaction is modeled by mass balance and requires that ilmenite and high-Ca pyroxene are assimilated in a approximately 3:1 ratio, a much higher ratio than the proportion in which these minerals are thought to exist in the lunar interior. In an effort to understand the kinetic controls on this reaction, the dissolution of ilmenite is examined experimentally in both low- and high-Ti lunar magmas. We find that ilmenite dissolves incongruently to Cr-spinel and a high-Ti melt. The dissolution reaction proceeds by a diffusion-controlled mechanism. An assimilation model for the origin of high-Ti melts is developed that leaves the magma ocean cumulates in their initial stratigraphic positions and obviates source hybridization models that require lunar overturn.
Wagner, T. P.↗
Formation of thin sulfide rinds on the CM parent body
Many of the textures that are observed in CM chondrites have been alternately assigned nebular, parent-body, or combined nebular-parent body origins. Since it is very difficult to substantiate the production of complex textures in the nebula, an alternate approach to this problem is to rigorously determine which of the observable textures could have been produced by reasonable aqueous alteration processes on the CM parent body. Potential parent body reactions involving S deserve special attention because S-bearing phase define many important CM textures, such as rims. We have examined the possibility that the thin (about 5 microns) rinds of sulfides observed around some partially dissolved olivines within the chondrules and matrixes of CM chondrites were formed by the preferential precipitation of sulfides at or near dissolving olivine boundaries during parent-body alteration. Our model defines two infinite and parallel planes of olivine that are separated by pure water. Average separation distances between olivine grains in CM chondrites at the time of accretion (about 100-200 microns) were estimated by assuming a closed system fluid/rock ratio of 45% and varying the bimodal grain-size distribution. We restrict our calculations to the case of an isochemical system with sufficient bisulfide in solution to account for precipitation of pyrrhotite at STP. Our model examines the possibility that dissolving olivines with compositions between Fo(sub 0.9) and Fo(sub 0.4) can produce a strong gradient of Fe(2+) at pHs from 7 to 12 such that the precipitation of pyrrhotite will be initiated at the olivine-fluid boundary. Since CM phase equilibria is consistent with highly reducing conditions, Fe released by olivines would largely remain in solution as Fe(2+) until the solubility product of a Fe(2+) bearing phase was exceeded. Our calculations indicate that all examined combinations of olivine composition and pH yield a strong Fe(2+) gradient at the time the pyrrhotite solubility is exceeded near the olivine-fluid boundary. This favors the initiation of sulfide precipitation around dissolving olivines. However, sulfide rinds are not observed around all partially dissolved olivine grains in CM chondrites, which suggests that the availability of aqueous sulfide species limits the production of the thin sulfide rinds.
Browning, L. B.↗
A brief review on strain engineering of ferroelectric K x Na 1- x NbO 3 epitaxial thin films: Insights from phase-field simulations
Strains play a pivotal role in determining the phase equilibrium, domain configuration, and functional properties of the low-dimensional ferroelectrics. There is growing interest in the strain engineering of ferroelectric K x Na 1- x NbO 3 (KNN) epitaxial thin films, which exhibit excellent physical properties and promise as eco-friendly alternatives to lead-based ferroelectrics for microdevice applications. Further, advances have been made in understanding the phase equilibria and transitions, domains and domain walls, and their relations to the physical properties of KNN epitaxial thin films using a combination of experiments and theoretical modeling, particularly phase-field simulations. Here, we review recent progress in these aspects and showcase the phase-field method for establishing strain phase diagrams, elucidating the domain and domain wall structures at equilibrium, and predicting the structure–property relationships in ferroelectric KNN thin films. We also discuss challenges and opportunities to further advance our understanding of KNN thin films and potentially unlock new functionalities by leveraging phase-field simulations.
36 MATERIALS SCIENCE↗