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At least 307 records · Page 17

Multilayer interface tracking model of pure tungsten oxidation

Here, we present a numerical model to predict oxide scale growth on tungsten surfaces under exposure to oxygen at high temperatures. The model captures the formation of four thermodynamically-compatible oxide sublayers, WO 2 , WO 2.72 , WO 2.9 , and WO 3 , on top of the metal substrate. Oxide layer growth is simulated by tracking the oxide/oxide and oxide/metal interfaces using a sharp-interface Stefan model coupled to diffusion kinetics. The model is parameterized using selected experimental measurements and electronic structure calculations of the diffusivities of all the oxide subphases involved. We simulate oxide growth at temperatures of 600°C and above, extracting the power law growth exponents in each case, which we find to deviate from classical parabolic growth in several cases. We conduct a comparison of the model predictions with an extensive experimental data set, with reasonable agreement at most temperatures. While many gaps in our understanding still exist, this work is a first attempt at embedding the thermodynamic and kinetic complexity of tungsten oxide growth into a comprehensive mesoscale kinetic model that attempts to capture the essential features of tungsten oxidation to fill existing knowledge gaps and guide and enhance future tungsten oxidation models.

36 MATERIALS SCIENCE↗

Phase transformation and growth mechanism of RF sputtered ferroelectric lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 ) films

Lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 , PST), an order/disorder ferroelectric, is a potential candidate for electrocaloric cooling and pyroelectric infrared (IR) detector. In this work, we report the phase transformation kinetics from two series of samples containing pure amorphous and mixture of amorphous and pyrochlore to desired perovskite phase using postdeposition rapid thermal processing (RTP) as well as growth mechanism of RF sputtered PST thin films using excess lead target on platinized silicon (Pt/Ti/SiO 2 /Si) substrates. We find that small changes in the temperature ramp have a large effect on the degree of perovskite conversion (ferroelectric phase), orientation (crystallographic texture), and long-range order parameter (< S 111 >). Through isothermal annealing, we obtained optimal perovskite phase at ≥700°C temperature. The phase transformation is characterized by spontaneous formation of center-type in-plane radial rosette-like structures revealed by scanning electron microscopy. The PST perovskite crystallites were found to coexist with pyrochlore in RTP annealed films. The volume fractions for perovskite and pyrochlore phase were obtained from the analysis of “rosettes” and respective X-ray diffraction intensities which helped to determine various parameters associated with phase kinetics (n, k, and activation energy, Ea) and accompanying growth. The effective activation energies of perovskite transition and growth were found to be 332 ± 11 kJ/mol (345 ± 11 kJ/mol) and 114 ± 10 kJ/mol (122 ± 10 kJ/mol), respectively, for pure amorphous only (and mixed amorphous and pyrochlore) phase following nucleation-growth controlled Avrami's equation. A linear growth rate (n~1) for the perovskite phase indicates predominant interface-controlled process and diffusion-limited phenomena thus inhibiting rosette size owing to reactant depletion and soft impingement at the grain boundary. However, the growth behavior is isotropic in two-dimension parallel to the plane of the substrates for both sample series. Furthermore, lead loss was severe for in-situ growth and RTP combined with conventional furnace annealing than those of RTP only films, which were closer to stoichiometric albeit with excess lead and marginal oxygen vacancies (V o ).

36 MATERIALS SCIENCE↗

A Modified Sand’s Time Incorporating Li-Ion Transport Across the SEI: Basis for Understanding Li Dendrite Formation and Li-Metal Battery Electrolyte Selection

Abstract Understanding the initiation of lithium dendrites remains elusive, largely due to the intricate role of the solid electrolyte interphase (SEI) which forms on the Li surface during electrodeposition. Many studies have utilized the classical Sand’s equation to estimate the onset time when lithium dendrites begin to form. The Sand’s equation provides the time when the cation (Li+) concentration at the electrode-electrolyte interface approaches zero under diffusion-limited conditions in galvanostatic Li electrodeposition. However, recent experimental studies have revealed that the observed lithium dendrite onset time deviates considerably from the Sand’s time. Here, we show that this deviation from classical theory is likely due to the transport of Li+ ions through the SEI - a transport limitation that is much more dominant in controlling dendrite formation. We develop a ‘modified’ Sand's equation, incorporating the SEI layer and the diffusional transport across it to predict Li dendrite onset times. To validate this approach, we conducted Li electrodeposition experiments at various current densities using two distinct organic electrolytes. Analysis of the results demonstrates that the modified Sand's equation provides a more accurate prediction of dendrite onset times, highlighting the importance of incorporating SEI into transport models of Li plating in next-generation rechargeable Li-metal batteries.

Ma, Yuanman (ORCID:0000000200444811)↗

Diffusion bonding of metals.

Diffusion bonding of metals, discussing interface joining processes and application to flueric devices, jet engine servovalves and porous woven structures

Kiwak, R. S.↗

Study of the Effects of Impurities on the Properties of Silicon Materials and Performance of Silicon Solar Cell

Numerical solutions were obtained from the exact one dimensional transmission line circuit model to study the following effects on the terrestrial performance of silicon solar cells: interband Auger recombination; surface recombination at the contact interfaces; enhanced metallic impurity solubility; diffusion profiles; and defect-impurity recombination centers. Thermal recombination parameters of titanium impurity in silicon were estimated from recent experimental data. Based on those parameters, computer model calculations showed that titanium concentration must be kept below 6x10 to the 12th power Ti/cu cm in order to achieve 16% AM1 efficiency in a silicon solar cell of 250 micrometers thick and 1.5 ohm-cm resistivity.

Sah, C. T.↗

The effect of thermal cycling to 1100 C on the alpha /Mo/ phase in directionally solidified gamma/gamma-prime-alpha alloys

Specimens of gamma/gamma-prime-alpha (Mo) eutectic alloy were thermally cycled or isothermally exposed at temperatures of 1075 to 1100 C. Transmission electron microscopy examination of cycled specimens indicated that even an exposure of 10 minutes effected noticeable changes in the shape of the alpha phase, and that the changes were cumulative as more cycles were added. The cross sections of fine, smooth fibers changed from rectangles to octagons, while lamellae and irregular shapes spheroidized. These effects are attributed to the differences in thermal expansion coefficients between the alpha phase and the gamma/gamma-prime matrix, and to the higher diffusion rates prevailing at elevated temperatures. Where the configuration of the alpha phase is a simple shape, such as a fiber, increasing the temperature eventually brings about a stress free interface between the alpha phase and the matrix by differential thermal expansion. Where the shape of the alpha phase is more complex, a stressed interface persists to higher temperatures where diffusion produces the more drastic morphological changes.

Harf, F. H.↗

Sources of atmospheric methane - Measurements in rice paddies and a discussion

Field measurements of methane fluxes from rice paddies, fresh water lakes, and saltwater marshes have been made to infer estimates of the size of these sources of atmospheric methane. The rice-paddy measurements, the first of their kind, show that the principal means of methane escape is through the plants themselves as opposed to transport across the water-air interface via bubbles or molecular diffusion. Nitrogen-fertilized plants release much more methane than unfertilized plants but even these measured rates are only one fourth as large as those inferred earlier by Koyama (1963, 1964) and on which all global extrapolations have been based to date. Measured methane fluxes from lakes and marshes are also compared to similar earlier data and it is found that extant data and flux-measurement methods are insufficient for reliable global extrapolations.

Cicerone, R. J.↗

Investigation of accelerated stress factors and failure/degradation mechanisms in terrestrial solar cells

Results of an ongoing research program into the reliability of terrestrial solar cells are presented. Laboratory accelerated testing procedures are used to identify failure/degradation modes which are then related to basic physical, chemical, and metallurgical phenomena. In the most recent tests, ten different types of production cells, both with and without encapsulation, from eight different manufacturers were subjected to a variety of accelerated tests. Results indicated the presence of a number of hitherto undetected failure mechanisms, including Schottky barrier formation at back contacts and loss of adhesion of grid metallization. The mechanism of Schottky barrier formation is explained by hydrogen, formed by the dissociation of water molecules at the contact surface, diffusing to the metal semiconductor interface. This same mechanism accounts for the surprising increase in sensitivity to accelerated stress conditions that was observed in some cells when encapsulated.

Lathrop, J. W.↗

Probing the chemistry of nickel/metal hydride battery cells using electrochemical impedance spectroscopy

Electrochemical Impedance Spectroscopy (EIS) is a valuable tool for investigating the chemical and physical processes occurring at electrode surfaces. It offers information about electron transfer at interfaces, kinetics of reactions, and diffusion characteristics of the bulk phase between the electrodes. For battery cells, this technique offers another advantage in that it can be done without taking the battery apart. This non-destructive analysis technique can thus be used to gain a better understanding of the processes occurring within a battery cell. This also raises the possibility of improvements in battery design and identification or prediction of battery characteristics useful in industry and aerospace applications. EIS as a technique is powerful and capable of yielding significant information about the cell, but it also requires that the many parameters under investigation can be resolved. This implies an understanding of the processes occurring in a battery cell. Many battery types were surveyed in this work, but the main emphasis was on nickel/metal hydride batteries.

Isaac, Bryan J.↗

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗

PV Technology for Low Intensity, Low Temperature (LILT) Applications

As a result of the recent NASA emphasis on smaller, lower cost space missions, PV is now being considered for a number of missions operating at solar distances of 3 AU or greater. In the past, many of these missions would utilize an RTG (radioisotope thermoelectric generator). Historically, silicon solar cell behavior at these distances has been compromised by a number of mechanisms including shunting, nonohmic back contacts, and the 'broken knee' curve shape. The former two can usually be neglected for modern silicon cells, but the latter has not been eliminated. This problem has been identified with localized diffusion at the top contact/silicon interface which leads to structural changes at the local junction. This is believed to create a resistive metal-semiconductor-like (MSL) interface in parallel with the junction which results in the characteristic forms of the LILT (low intensity, low temperature) 'broken knee'. This paper discusses a TaSiN contact barrier that will prevent the MSL structure in the junction.

spacecraft power LILT low temperature low intensit↗

(abstract) PV Technology for Low Intensity, Low Temperature (LILT) Applications

As a result of the recent NASA emphasis on smaller, lower cost space missions, PV is now being considered for a number of missions operating at solar distances of 3 AU or greater. In the past, many of these missions would utilize an RTG (radioisotope thermoelectric generator). Historically, silicon solar cell behavior at these distances has been compromised by a number of mechanisms including shunting, nonohmic back contacts, and the 'broken knee' curve shape. The former two can usually be neglected for modern silicon cells, but the latter has not been eliminated. This problem has been identified with localized diffusion at the top contact/silicon interface which leads to structural changes at the local junction. This is believed to create a resistive metal-semiconductor-like (MSL) interface in parallel with the junction which results in the characteristic forms of the LILT (low intensity, low temperature) 'broken knee'. This paper discusses a TaSiN contact barrier that will prevent the MSL structure in the junction.

spacecraft power LILT low temperature low intensit↗

Implications for Metallographic Cooling Rates, Derived from Fine-Scale Analytical Traverses Across Kamacite, Taenite, and Tetrataenite in the Butler Iron Meteorite

The "M-shaped" Ni concentrations across Widmanstatten patterns in iron meteorites, mesosiderites, and ordinary chondrites are commonly used to calculate cooling rates. As Ni-poor kamacite exolves from Ni-rich taenite, Ni concentrations build up at the kamacite-taenite interface because of the sluggish diffusivity of Ni. Quantitative knowledge of experimentally-determined Ni diffusivities, coupled with the shape of the M-profile, have been used to allow calculation of cooling rates that pertained at low temperatures, less than or equal to 500 C. However, determining Ni metallographic cooling rates are challenging, due to the sluggish diffusivity of Ni at low temperatures. There are three potential difficulties in using Ni cooling rates at low temperatures: (i) Ni diffusivities are typically extrapolated from higher-temperature measurements; (ii) Phase changes occur at low temperatures that may be difficult to take into account; and (iii) It appears that Ge in kamacite and taenite has continued to equilibrate (or attempted to equilibrate) at temperatures below those that formed the M-shaped Ni profile. Combining Ni measurements with those of other elements has the potential to provide a way to confirm or challenge Ni-determined cooling rates, as well as provide insight into the partitioning behaviors of elements during the cooling of iron meteorites. Despite these benefits, studies that examine elemental profiles of Ni along with other elements in iron meteorites are limited, often due to the low concentration levels of the other elements and associated analytical challenges. The Butler iron meteorite provides a good opportunity to conduct a multi-element analytical study, due to the higher concentration levels of key elements in addition to Fe and Ni. In this work, we perform combined analysis for six elements in the Butler iron to determine the relative behaviors of these elements during the evolution of iron meteorites, with implications for metallographic cooling rates.

Jones, J. H.↗

Electrode and Microstructure Dependence of Oxygen Diffusion in Ferroelectric Hafnium Zirconium Oxide Thin Films

Hafnia-based ferroelectrics hold promise to reduce energy demand for computing by enabling compute-in-memory and as non-volatile memories. The ferroelectric phase in this material system is, in part, stabilized by oxygen vacancies. While oxygen vacancies may be a necessity for phase stability, they limit device endurance through diffusion and accumulation into conducting channels. Herein, it is shown that oxygen diffusion is spatially variable within individual grains of ferroelectric hafnium zirconium oxide (HZO). Using 18 O tracers and finite difference modeling, it is shown that grain boundaries and regions near electrode interfaces allow for relatively rapid oxygen diffusion, with values as much as 10 4 larger than the grain cores. Further, the selection of electrode material affects the diffusion coefficients across all microstructural regions. HZO films in contact with TiN electrodes result in more oxygen-deficient HZO films and higher oxygen diffusion coefficients. Tungsten electrodes result in fewer vacancies and lower diffusion coefficients. Diffusion activation energy differences between the HZO with the two electrodes is reconciled by differing populations of charged and uncharged oxygen vacancies. This insight into the local vacancy populations and diffusion pathways provides a platform for designing hafnia-based films, deposition processes, and integration strategies to reduce vacancy gradients and improve performance.

36 MATERIALS SCIENCE↗

Passivated Contacts for Direct Wafer Product (Final Technical Report)

This TCF project developed a thin-oxide (SiO 2 )/polycrystalline silicon (poly-Si) passivated contact solar cell on CubicPV's (formally 1366 Technologies, Inc.) Direct Wafer® Product (DWP) kerfless wafers. The project used two NREL-developed technologies described in U.S. Patent No. 9,911,873, Hydrogenation of Passivated Contacts and U.S. Patent Application Serial No. 15/890,172, Doped Passivated Contacts . The project was motivated by a potential higher efficiency cell (compared to a PERC cell) using passivated contacts on the ultra-low cost kerfless wafers grown using the Direct Wafer process. The hope was to accelerate market adoption of the cell and wafer by delivering the lowest LCOE in the PV industry. The project tested both n-type and p-type SiO 2 /poly-Si passivated contacts grown by thermal oxidation and plasma enhanced chemical vapor deposition (PECVD) of the poly-Si layer on DWP with varying wafer resistivities. Both deposition techniques are industry standards and thus economically viable methods for commercializing the contacts. The results indicated that both n-type and p-type poly-Si passivated contacts can be formed on polycrystalline DWP wafers, but implied open-circuit voltages (i Voc ) were limited to below 0.65 mV (compared with ~ 730 mV on n-Cz wafers). Diffusion of H to the Si/SiO 2 /poly-Si interface was key to obtaining high i Voc values. In this study, H was diffused from a high-temperature SiN x layer deposited over the poly-Si layer during a high-temperature firing step, similar to one used for screen printed metals. The study concluded that poly-Si passivated contacts on DWP wafers passivated the surface of the wafers as well as PERC passivated surfaces, which use a less expensive dielectric layer stack. The project showed that Direct Wafer Product wafers grown by CubicPV could produce high i Voc values (~0.647 mV), which could produce a cell over 20% efficient with proper processing and metallization. These cells, though not economically viable in 2024 as a stand-alone cell, could be integrated with a wide-bandgap top solar cell to form a two-junction tandem cell that could be viable under certain circumstances. This is because the bottom cell of a 30%, two-terminal tandem only needs to be a 20% cell under one-sun conditions. Thus, the DWP could be an ideal low-cost wafer for tandems. The project also revealed that a TOPCon type cell could be formed on a p-type DWP wafer using a P-diffused emitter and a p-type poly-Si contact. In fact, the p-type version of the poly-Si contact out-performed the n-type version for a variety of wafer resistivities, from highly doped to lowly doped. This curiosity requires more work to understand because on Cz wafers, the n-type poly-Si contact is of much higher quality than the p-type version.

14 SOLAR ENERGY↗

Electroepitaxy of multicomponent systems - Ternary and quarternary compounds

A theoretical model is presented which accounts for the electroepitaxial growth kinetics and composition of multicomponent compounds in terms of mass transport in the liquid and phase diagram relationships. The mass transport in the interface is dominated by electromigration in the absence of convection and by diffusion in the presence of convection. The composition of the solid is controlled by the Peltier effect at the growth interface and by the diffusion and mobility constants of the solute components and the growth velocity (current density). Thus, for a given solution composition, the composition of the solid can be varied by varying the current density. For a given current density the composition remains constant even in the case of relatively thick epitaxial layers. All aspects of the model were found to be in good agreement with the growth and composition characteristics of Ga/x-1/Al/x/As layers.

Bryskiewicz, T.↗

Solidification Furnace for In Situ Observation of Bulk Transparent Systems and Image Analysis Methods

This paper aims to describe the experimental framework of the Directional Solidification Insert (DSI), installed onboard the International Space Station (ISS), dedicated to the in situ and real-time characterization of the dynamic selection of the solid-liquid interface morphology in bulk samples of transparent materials under diffusive growth conditions. The in situ observation of the solid-liquid interface is an invaluable tool for gaining knowledge on the time-evolution of the interface pattern because the initial morphological instability evolves nonlinearly and undergoes a reorganization process. The result of each experiment, characterized by the sample concentration, a thermal gradient and a pulling rate, is a large number of images. Interpretation of these images necessitates a robust identification of each cell/dendrite position and size during the entire solidification. Several image analysis methods have been developed to achieve this goal reliably despite varying contrast and noise levels, and are described in details. Typical solidification experiments are presented and the dynamics of the pattern formation are analyzed to illustrate the application of the image analysis methods.

Programming languages↗

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↗