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At least 289 records · Page 16

Mark-18A Cold Runs

The Savannah River National Laboratory (SRNL) is tasked by the National Nuclear Security Administration (NNSA) to recover highly valued isotopes from irradiated Mark-18A (Mk-18A) targets. The Savannah River Site (SRS) has sixty-five Mk-18A targets available for the recovery of the high valued materials. The sixty-five Mk-18A targets are currently stored in the L-Area Basin and will be removed one at a time and individually transported to SRNL. Upon receipt at SRNL, the Mk-18A target material will be removed from the confinement, dissolved, chemically separated, and calcined to a stable oxide. The flowsheet is designed to recover the plutonium as well as the trivalent actinides. The remaining unrecovered material will be discarded to the high activity drain (HAD) system in SRNL. A specially designed cask was procured for transport of the targets from L-Area to SRNL. Once received at SRNL, the targets will be loaded into the back of Cell 7 and resized as they enter the cell. The resized targets (1/4 lengths) will then be processed one at a time through the following processes: caustic dissolution and filtration; acidic dissolution and filtration, Reillex anion exchange, diglycolamide (DGA) cation exchange; and DGA calcination. This processing will result in two product streams. The first is an aqueous plutonium solution which will be removed from the shielded cells and taken to a glovebox for further purification and conversion to an oxide. The second is a calcined oxide containing the Am and Cm as well as other lanthanide fission products which will be removed from the shielded cells using a bagless transfer system. Both materials will be packaged for shipment to Oak Ridge National Laboratory (ORNL). All equipment to carry out this process was designed, procured or fabricated, and installed in a mock-up facility (716-4A) at SRS to allow for simulation testing in a non-radioactive area. This equipment was then dismantled and transferred from 716-4A to 773-A and installed in the SRNL Shielded Cells. After installation in the shielded cells facility testing was performed using water followed by surrogates and cold chemicals. Issues were identified during these evaluations, including equipment issues as well as technical challenges. Many of the issues were rectified during performance of the cold runs, and the remaining have a resolution identified. Table ES-1 provides a summary of all issues identified during the cold run operations, as well as the status and identified resolutions to outstanding issues.

07 ISOTOPE AND RADIATION SOURCES↗

Studies on the Vitrification Potential of High Risk Spent Nuclear Fuels

This research explored vitrification of U-Zr nuclear fuel that exhibits an explosion hazard when processed by common nitric acid dissolution. Glass frits were chosen based on properties that had been previously measured as well as being demonstrated successfully in production at the Defense Waste Process Facility (DWPF). Zirconium and Aluminum metal powders were chosen to represent the spent fuels after literature demonstrated that the potential phase that causes the issue for explosive reaction in the effluent stream is tied to the Zirconium-III phase field. DSC measurements were carried out on various simulants and waste forms to better understand thermal behavior of these materials. Zirconium (Zr) was tested with both nitric acid and the new effluent flowsheet that is under development by the SRNL Chemical Process Control (CPC) group. The nitric acid test did show the expected exothermic behavior as well as how the behavior is affected by particle size of the powders used. In contrast, the effluent samples did not show an exothermic peak. However, the concentration of metal in the samples was orders of magnitude lower than in the nitric acid testing and further testing of the effect of concentration on the exothermicity that could be measured confirmed a dampened signal. Tests were run that included frit, both DWPF Frit 510 and Iron Phosphate frit, exhibiting complex curves that included multiple endothermic and exothermic peaks during heating and cooling. The final crucible samples appear similarly to the bulk glasses pointing to these peaks being a part of the dissolution of the simulant into the base glasses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluating Iodine Immobilization Technologies: Cermets, Polycermets, and Polyhalmets

The work in this report documents the efforts conducted to assess the feasibility of some of the ideas documented in Pacific Northwest National Laboratory invention disclosure reports (IDRs) including: 1) Iodine capture in polyacrylonitrile (PAN)-containing composite sorbents (32451-E). In this work, the composites evaluated included Ag0, Bi0, Cu0, Bi2S3, and Cu2S embedded in PAN. 2) Metal iodide removal from these sorbents through dissolution in dimethyl sulfoxide (DMSO) (32729-E). In this work, PAN dissolution was evaluated for multiple types of sorbents including Ag-Pan, Bi-PAN, Cu-PAN, Bi2S3-PAN, and Cu2S-PAN. 3) Using metal-sulfide sorbents for iodine capture (32647-E). In this work, the composites evaluated under this IDR included Ag2S, Bi2S3, and Cu2S embedded in PAN. 4) Using low-melting metals to immobilize (encapsulate) iodine-loaded and polymer-containing sorbents into polymer-ceramic-metal (called polycermet) or polymer-halide-metal (called polyhalmet) composite waste forms (32625-E). In this work, the iodine-loaded PAN composites included AgI-PAN, BiI-PAN, and CuI-PAN. 5) Ceramic-metal composite waste form synthesis of polymer-containing materials using low-melting metals like bismuth, tin, or bismuth-tin alloys (32537-E). In this work, the metals evaluated included Bi, 58Bi-42Sn eutectic. 6) Cermets for immobilizing commercial sorbents loaded with radioiodine (32806-E). In this work, AgIX (iodine-loaded silver faujasite zeolite) was evaluated in cermet form.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

TCF - Sustainable Well Cement for Geothermal, Thermal Recovery, and Carbon Storage wells

Primary cementing is the most important operation performed on a subterranean well. Cement, placed in the annulus between the casing and the formations, serves as a hydraulic seal preventing fluids and gas migrations, protecting steel casing from corrosion, and supporting the well structure. Poor cementing jobs can be directly responsible for wells not reaching their full capacity, casing corrosion, compromised well integrity and, in the worst-case scenarios, well collapse. Geothermal, thermal recovery, and carbon storage wells offer environments that are especially difficult for cements to survive while the required lifespan of these wells can be years. In these wells currently used cements cannot provide durable well integrity, and new solutions are necessary. The necessity of stabilizing the electric grid, increasing its flexibility, and providing energy on demand will further expand the market of durable cement solutions for applications in high-temperature underground reservoir thermal energy storage wells (HT RTES). The design challenges of special cement systems for such wells originate from chemistry limitations of currently used well cements, aggressive environments, temperature and repeated shock conditions associated with them, and very weak formations that are not uncommon in these wells. During the last 70 years the most common systems for thermal-well construction have been Ordinary Portland Cement (OPC) (absolute majority of the wells), silica-lime system, and high aluminum cement-containing formulations. The major issues of calcium-silicate hydrates, that form during the hydration of OPC resulting in hardened material, are their poor chemical resistance to acids due to the calcium interactions with acid anions followed by its eventual dissolution, even in mild acids, such as carbonic acid from CO 2 dissolution, and inadequate bonding to the steel causing serious casing corrosion problems (Sugama & Pyatina, 2019). Performance of OPC-based cement may be significantly improved with organic additives; however, those are limited by their temperature stability. An alternative to calcium-silicate cement was developed by BNL and commercialized by Halliburton as ThermaLock TM cement. Calcium-aluminate-phosphate-based chemistry of the material allowed overcoming acid-resistance problems of OPC, especially in CO 2 -rich geothermal environments. In 2012-2015, building upon this experience, BNL developed Thermal Shock Resistant Cement (TSRC) with the support of Geothermal Technology Office (GTO) of DOE. TSRC has high-temperature stable chemistry, superior properties of cement-metal casing bond and corrosion protection (4-times better than currently used OPC-based formulation), significantly outperforms common well-cements in thermal-shock tests, has self-healing properties, and like ThermaLock TM is CO 2 resistant incorporating carbonate ions into stable hydrates (Gill et al., 2012).

15 GEOTHERMAL ENERGY↗

Development of Li–S Battery Cells with High Energy Density and Long Cycling Life

Lithium–sulfur (Li–S) batteries are considered one of the most promising next-generation energy storage technologies for electric vehicles, owing to their high energy density (up to three times greater than current lithium-ion batteries) and the low cost of sulfur (approximately 100 times cheaper than conventional cobalt oxide). However, several challenges hinder their commercial viability, including the electronically and ionically insulating nature of sulfur, polysulfide dissolution, and lithium dendrite growth. These issues significantly limit battery energy density and cycle life and must be addressed to enable successful commercialization. Current strategies involving porous carbon structures, additives, and electrocatalyst engineering have not fully resolved the polysulfide dissolution problem. While polysulfide-free cathode materials offer a promising solution, they often suffer from low sulfur content, leading to reduced discharge capacity and sluggish reaction kinetics. To overcome these limitations, we have developed novel soluble-polysulfide-free sulfur cathode active materials with a high sulfur content (>50 wt%). By integrating these cathodes with functional binders, optimized electrolyte formulations, and refined electrode fabrication techniques, we demonstrate Li–S batteries with both high energy density and long cycle life. This advancement brings the realization of low-cost, high-energy Li–S batteries significantly closer to practical application.

25 ENERGY STORAGE↗

FY24 Task 5: Leachate Disposition

Directly feeding sludge solids to the high-level waste (HLW) Waste Treatment Plant represents an alternative flowsheet seeking to initiate sludge processing as soon as possible. Key processing functions previously captured during baseline pretreatment operations include leaching and washing prior to solids concentration. These operations should be considered in the potential direct feed flowsheets to maximize waste feed loading, minimize HLW volume, and mitigate corrosion challenges associated with vitrification of high phosphate and fluoride concentrations. Additionally, single-shell tank (SST) retrievals and waste transfers to double-shell tanks (DSTs) in a direct feed flowsheet would likely also benefit from some level of leaching, washing, and solids concentration in order to reduce DST space and mission duration. These operations could occur in a new facility or potentially in available DSTs. If washing and leaching are utilized, an effective disposition pathway for the wash water and leachate solutions are needed. Three target species that benefit significantly from leaching and washing are phosphate, fluoride and aluminum. Phosphate (PO 4 3- ) and fluoride (F - ) can contribute substantially to the amount of carrier fluid needed for dissolution, and the resulting volume of liquid generated. Disposition of this retrieval solution should be evaluated in order to prevent crystallization of these anions throughout system processing. Since there is a high probability that any retrieval solutions will be at or near their PO 4 3- and F - solubility limits, evaporation or blending with a high Na supernate (>3.5 M) is not recommended for the wash water streams without a method to remove precipitants prior to solution disposal. Additionally, aluminum present in the southeast quadrant of the Hanford site represents roughly 60% of the waste solids in the initial processing tanks. These aluminum solids are in the form of gibbsite (Al(OH) 3 ) and can pose significant challenges for processing due to the fast-settling times and high solids loading associated with these materials. Easily remediated by caustic addition to the solids, these wash solutions could be processed through crystalline silicotitanate (CST) ion exchange columns to prepare the supernate solutions for disposition. The current target for feed conditions to the Low Activity Waste (LAW) melter are waste streams that contain nominally 5-6 M Na. Fractions within the tanks contain upwards of 0.2 M phosphate and fluoride in solution at 3.5 M Na. Concentrating these solutions above 5 M Na would result in an exceedance of the solubility limits, and potential for uncontrolled precipitation of the phosphate and fluoride crystal material. The resulting crystalline salt material is typically sodium fluoride phosphate, also referred to as natrophosphate (Na 7 FPO 4 ·19H 2 O). Salt phases are of importance in tank waste due to their chemical reactivity, which can result in precipitation, dissolution, or transformation, impacting any downstream processes (Bolling et al. 2020, Russell, Snow, and Peterson 2010). Salt generation and precipitation could pose challenges by causing system plugging and melter corrosion if left in the supernate stream, or limit sodium molarity of the supernate that would be accepted without incident in waste operations. To understand the impact of this salt generation, the crystallization of natrophosphate in multiple simulant feed matrices was studied to understand the implications of various tank waste supernate chemistries. Three matrices were examined: high PO 4 3- /low F - , low PO 4 3- /high F - , and an average matrix. Subsequent testing was performed with the average matrix with the inclusion of CsNO 3 , and a final run with the average matrix including CsNO 3 and a 137 Cs spike for tracer purposes.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Autonomous Infrared and Small (Wide) Angle X-Ray Scattering (IR-S(W)AXS) Capability

Thin water films are 2-D, nanoconfined layers that form on solid surfaces exposed to humid atmospheres—environments ubiquitous across catalysis, corrosion science, soil science, and subsurface geochemistry. At relative humidity (RH) values below saturation, these films are Å–nm thick and exhibit properties that differ sharply from bulk water, including disrupted H-bonding and impeded mass transport. Owing to their high surface-to-volume ratio, dissolution of the solid can rapidly drive strong supersaturation with respect to secondary phases. Reactivity in thin water films is highly sensitive to film thickness, and critically, thickness evolves during reaction because the hygroscopicity of the interfacial system changes as ions accumulate or diminish in the film and as reaction products transform. To accurately probe and control these dynamics, a capability is needed that can measure and automatically maintain a constant water-film thickness while simultaneously monitoring solid dissolution, nucleation, and growth. This project developed an autonomous Infrared/Small Angle X-ray Scattering-Wide Angle X-ray Scattering (IR/(W)SAXS) for investigating reactivity in thin water films on solid surfaces exposed to humidified gases. The capability consists of an IR spectrometer, a (W)SAXS instrument, and a mass flow controller system for generating variably humidified gas flows to a custom reaction cell. Progress on each of the major components of the capability are detailed below.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Finding ways to reduce nuclear waste: searching for the unknown one step at a time

In my home country, Venezuela, research has been stagnant. Due to the political turmoil and the crisis, many educated people have left the country in search for a better life. This has caused a deficit in any technological and scientific advances, making Venezuela one of the first South American countries to have its rate of publications decline by 29% in 2013. Currently, Venezuela lacks the infrastructure and the means to keep up with the research progress as compared to other countries in South America, such as Brazil. Since coming to the United States (US), and currently working for a national laboratory, the active research environment endorses a wide range of careers and engineering programs that allow researchers to thrive at any given field. Researchers have access to funds and tools to succeed in developing materials for the future. There are 17 national laboratories in the US, and all of these have a different research focus/objective. As examples, Los Alamos National Laboratory and Sandia National Laboratory focus is on national homeland security, weapon science, radiation effects, among others. Argonne National Laboratory focuses on nuclear energy, energy storage, high performance computing, etc. At Idaho National Laboratory (INL) the research focuses on innovating nuclear energy and clean energy resources, critical infrastructure materials, along with fuel cycle solutions to manage, dispose and find ways to recycle current and future radiological waste. Compared to other national laboratories, INL focuses slightly more on applied processes and how nuclear energy can be innovated to next reactor design and technologies. The research being conducted at INL made me apply for a Seaborg distinguished postdoctoral position. For the position itself, the researcher must submit a proposal related to actinide chemistry on a research field area. In this position, 50% of my time will be focused on my own proposal. The proposal that I am working on is focused on the innovation of nuclear energy and fuel cycle recycling, which is why I was mainly interested on working at this national laboratory. To give a bit more context of what my proposal is about, a little bit of background is necessary: After the nuclear fuel (UO2) is used in a reactor, the fuel matrix is then characterized by various fission products (FP). Among these FP (including rare earth elements, alkali/alkaline earths, and actinides), many can potentially be recovered through nuclear reprocessing technologies. In pyroprocessing, the used nuclear fuel undergoes electrochemical dissolution into a molten chloride salt mixture in an electrorefiner. Initially, uranium is reduced onto an inert cathode by applied potentials. However, numerous remaining FPs accumulate in the melt and pose challenges for recovery by an inert electrode, particularly the rare earth elements (e.g., Nd, Gd, Pr, Sm) due to their multivalent oxidation states and tendencies toward side reactions, leading to their dissolution in the electrolyte. These recovery challenges result in inefficiencies and necessitate the continual discarding of the molten chloride salt, thereby generating additional waste. Furthermore, the presence of rare earth elements and other fission products in the molten salt electrolyte alters its physical and chemical properties, affecting both uranium recovery efficiency and the longevity of the molten chloride salt. To improve the recovery efficiency of the FP, specifically rare earth elements, I am investigating the fundamental interactions between rare earth elements in the molten chloride salt and their metallic form. The kinetic pathways and the chemical reactions of these elements will give insights on how the recovery efficiency can be improved. The interactions and speciation of these elements are being studied by spectro-electrochemistry at high temperature environments in quartz and other ceramic materials (e.g., alumina crucibles). Some of the challenges I am facing specifically relates the reactivity of some of these elements with different glass and crucible materials. Although my research focuses on fundamental science, it will benefit the applied process by generating new scientific knowledge and closing the gap for an efficient recycling of the waste: one step at a time.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

CWMD Nuclear Forensics Quarterly Report

Analysis and evaluation of nuclear debris is a key component to identify forensic signatures in a post-detonation environment. Currently, methods exist and are practiced in obtaining signatures from post-detonation debris. However, efforts to reduce the timeline in obtaining signatures is continuous within nuclear forensics research and will be forwarded by this research. This education and research project will explore combined material chemistry and separations of radionuclides to provide actionable signatures in less time than standard methods. The research will use the phase distribution of radionuclides in debris to develop targeted and rapid dissolution methods. These dissolution methods will be coupled with microfluidics to achieve samples suitable for analysis within reduced timelines.

and nuclear chemistry↗

Direct Processing of Lithium Chloride Based Waste Salt in a Ceramic Waste Form

Ceramic waste form materials were fabricated with a LiCl based salt mixture to demonstrate the suitability of direct processing of waste salt from an all LiCl pyroprocessing flow sheet on the formation, microstructure, and durability of ceramic waste forms. Materials were successfully synthesized by using the simplified direct processing technique with salt loadings of 5, 7.5, and 10 wt% at the laboratory scale. Materials fabricated with LiCl based salt indicated full conversion of zeolite to sodalite occurred to form products with low open porosity. This indicates that the Na 2 O content of NBS4 glass is suitable for processing salt chemistries which do not contain NaCl. Generated sodalite was microencapsulated by the glass binder, halite occlusions were detected within sodalite domains at all salt loadings, and a Cs-rich phase believed to be Cs-pollucite was detected in the material made with the lowest salt loading (5 wt%). Salt inclusions were encapsulated within the binder glass at all loadings, and found to consist primarily of NaCl with Cs present. A small amount of salt was found at the surface of the wasteform made with the highest salt loading of 10 wt%, which may indicate an upper limit to the amount of salt that can be accommodated or incomplete mechanical mixing of the reagents. Durability testing by using the ASTM C1308 method indicated that initial rapid dissolution of exposed halite inclusion phases was directly correlated to salt loading. Wasteform degradation during all tests occurred primarily due to dissolution of the sodalite phase. Durability of the binder glass was found to increase as the waste salt loading increased. Results for the release of cations from the salt indicate the changes in wasteform durability and halite inclusion chemistry are strongly influenced by ion exchange phenomena between the salt and the glass. This appears to be the result of the relatively stronger affinity for the glass phase of Li, compared to that of other cations such as Na and Cs. The effects from cation exchange were diminished at lower salt loadings.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Simplified procedure for emission spectrochemical analysis

Procedure involves dissolution of samples to prepare them for analysis, and uses single set of experimental conditions to analyze wide variety of materials and compositions without compromising analysis accuracy. Automated spectrometer alloys per sample analysis time of four minutes after sample dissolution.

Gordon, W. A.↗

Research on rechargeable oxygen electrodes

Studies were carried out on a number of factors which may influence the behavior of the platinum electrocatalyst of oxygen electrodes for use in rechargeable metal-oxygen batteries or hydrogen-oxygen fuel cells. The effects of pretreatments for various potentials and added ionic species, which could be present in such systems, were studied with reguard to: (1) the state of surface oxidation, (2) platinum dissolution, (3) the kinetics of oxygen evolution and reduction (including the role of hydrogen peroxide), and (4) changes in porous electrode structure. These studies were carried out on smooth platinum, platinized platinum, and Teflon-bonded platinum black electrodes in carefully purified electrolyte solutions. The main factors which appear to affect rechargeable oxygen electrode performance and life are: (1) the buildup of a refractory anodic layer on extended cycling, and (2) the dissolution of platinum.

Giner, J.↗

Electrochemical behavior of the boron anode in aqueous solutions

The electrochemical oxidation of p-type boron in 0.2 N NaNO3 solutions of pH 0.4 to 13.1 was studied by galvanostatic techniques. The capacitance of the electrode, Tafel slopes, and a limited analysis of reaction mechanisms are reported. The anodic dissolution in acid solution is a charge-transfer-limited one-electron reaction to form a monovalent species in the over-potential region of 0.25 to 0.70 V. The dissolution in basic solution is most probably a one-electron charge-transfer reaction from a monovalent to divalent species involving three hydroxyl ions. Open circuit potentials were mixed potentials, probably due to hydrogen formation at open circuit but not contributing to the electrochemical reaction at the applied overpotential. Exchange current, estimated by extrapolation of the Tafel line to the standard oxidation potential for the boron reaction, were of the order of 10 to the minus 6th power A/cm2 in acid solution and 10 to the minus 12th power A/cm2 in basic solution. The reaction order of the rate determining acidic and basic reactions was determined with regard to (H+) and (OH-). The level of illumination had no effect on the electrochemical behavior of the electrode.

Delduca, B. S.↗

A study of gas solubilities and transport properties in fuel cell electrolytes

An analysis of the rate of heat generation on the dissolution of sparingly soluble gas in electrolytes was made, and it leads to the conclusion that the temperature changes to be expected are much too small to be measured with precision owing to the slowness of the gas dissolution. It appears that more accurate gas solubility measurements are the only real hope of improved precision in heats of solution and other thermodynamic properties.

Walker, R. D. J.↗

Interfacial impurities and the reaction between Si and evaporated Al

As commonly formed, the interface between substrate Si and evaporated Al is laden with impurities. Subsequent heating causes modest dissolution of Si into solid Al, the dissolution morphology being influenced by the interface impurities. In the present experiments, the amount of Si dissolving was considerably enhanced, causing sufficient interface movement to carry most interfaces clear of the original impurities. Under these conditions, the Si/Al interface assumes, during brief heat treatment, a simple shape composed of a few 111 plane-type facets. Such Si/Al interfaces produced in situ should be useful for low-temperature solid-state growth of Si.

Best, J. S.↗

Adsorption and chemical reaction of gaseous mixtures of hydrogen chloride and water on aluminum oxide and application to solid-propellant rocket exhaust clouds

Hydrogen chloride (HCl) and aluminum oxide (Al2O3) are major exhaust products of solid rocket motors (SRM). Samples of calcination-produced alumina were exposed to continuously flowing mixtures of gaseous HCl/H2O in nitrogen. Transient sorption rates, as well as maximum sorptive capacities, were found to be largely controlled by specific surface area for samples of alpha, theta, and gamma alumina. Sorption rates for small samples were characterized linearly with an empirical relationship that accounted for specific area and logarithmic time. Chemisorption occurred on all aluminas studied and appeared to form from the sorption of about a 2/5 HCl-to-H2O mole ratio. The chemisorbed phase was predominantly water soluble, yielding chloride/aluminum III ion mole ratios of about 3.3/1 suggestive of dissolved surface chlorides and/or oxychlorides. Isopiestic experiments in hydrochloric acid indicated that dissolution of alumina led to an increase in water-vapor pressure. Dissolution in aqueous SRM acid aerosol droplets, therefore, might be expected to promote evaporation.

Cofer, W. R., III↗

Mechanism and models for zinc metal morphology in alkaline media

Based on experimental observations, a mechanism is presented to explain existence of the different morphologies of electrodeposited zinc in alkaline solution. The high current density dendrites appear to be due to more rapid growth on the nonbasal crystallographic planes than on the basal plane. The low current density moss apparently results from dissolution from the nonbasal planes at low cathodic voltages. Electrochemical models were sought which would produce such a phenomenon. The fundamental plating mechanism alone accounts only for different rates on different planes, not for zinc dissolution from a plane in the cathodic region. Fourteen models were explored; two models were in accord with the proposed mechanism. One involves rapid disproportionation of the zinc +1 species on the nonbasal planes. The other involves a redox reaction (corrosion) between the zinc-zincate and hydrogen-water systems.

May, C. E.↗

Modelling of TGS growth in space

Attention is called to the necessity of programming the temperature downward in order to maintain a constant growth rate in the absence of convection. Trial and error numerical computations are performed to find the first approximation for the required isothermal dissolution period, linear ramp, and polynomial temperature variation period. The linear ramp rate is limited by the specified maximum temperature gradient. The isothermal dissolution turns out to be unnecessary. The linear ramp must be stopped before the polynomial period is begun in order to avoid overshooting the specified maximum growth rate. After a few hours, the temperature profile approaches steady-state behavior.

Liu, L. C.↗