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At least 1,675 records · Page 93

On the high-temperature stability of the Al 8 Cu 3 Ce intermetallic in an additively manufactured Al-Cu-Ce-Zr alloy

High-temperature resistant eutectic Al alloys are crucial materials for lightweight and energy efficient design in the automotive and aviation industries. Additive manufacturing offers a pathway to refine eutectic microstructures and develop novel alloys with superior high-temperature strength. High-volume fraction intermetallic Al-Cu-Ce alloys have been developed to deliver high-temperature strength in combination with reduced hot-tearing susceptibility. Zr is added to provide additional strengthening via nanoscale Al 3 Zr precipitation, and to stabilize and avoid coarsening of the Al 8 Cu 3 Ce phase. However, the detailed interaction between Zr and Al 8 Cu 3 Ce remains unexplored. In this work, we show with synchrotron X-ray diffraction that laser powder bed fusion fabricated Al-Cu-Ce and Al-Cu-Ce-Zr alloys contain predominantly the Al 8 Cu 3 Ce intermetallic in the as-fabricated condition. Heat treatment of the Al-Cu-Ce alloy results in the Al 8 Cu 3 Ce → Al 8 Cu 4 Ce phase transformation. In the Al-Cu-Ce-Zr alloy, minor fractions of (Al,Cu,Si) 4 Ce and Al 2 Cu-θ are found in the as-fabricated condition, while Al 8 Cu 3 Ce remains stable during heat treatment. Atom probe microscopy quantifies intermetallic stoichiometries and reveals how Zr is enriched at the Al-matrix/Al 8 Cu 3 Ce interface acting as a diffusion barrier against solute exchange. Calibrated thermodynamic modeling underpins this as a kinetic effect. Here, a qualitative microstructural model summarizes, how Zr stabilizes Al 8 Cu 3 Ce against phase transformations and coarsening.

36 MATERIALS SCIENCE↗

Microstructure development and properties of micro-alloyed copper, Cu-0.3Zr-0.15Ag, produced by electron beam additive manufacturing

A micro-alloyed copper powder, Cu-0.3Zr-0.15Ag wt.%, was produced using gas atomization reaction synthesis. Zirconium was added to copper to sequester the oxygen present as copper oxide surface films on the powder particles. The as-received powders, as well as the intentionally oxidized powders were used to fabricate solid test articles by electron beam powder bed fusion additive manufacturing. Dense samples fabricated from as-received powder demonstrated nominal UTS, yield, and elongation values at 260 MPa, 150 MPa, and 34%, respectively. The average electrical conductivity of these samples was measured at 95% of the international annealed copper standard (IACS). Samples fabricated from the oxidized powder exhibited nominal UTS, yield, and elongation of 241 MPa, 146 MPa, and 43%, respectively, with an electrical conductivity of 95 % IACS. During characterization, it was observed that, rather than forming nano-scale dispersoids, the Zirconia (ZrO 2 ) appeared as discontinuous stringers in the metallographic cross-sections that crossed grain and melt pool boundaries. This was rationalized by tracing the presence of the micro-alloying addition of elemental zirconium, which was found to react with surface oxides dissociated in the melt pool to form ZrO 2 , which then solidified on the surface of the melt pool through an allotropic transformation to monoclinic ZrO 2 in discontinuous films and spheroids ranging in size from nanometers to microns. This was confirmed by microscopic analysis of the tops of the melt pools. On subsequent melt passes, these ZrO 2 structures were displaced and redistributed within the melt pool.

36 MATERIALS SCIENCE↗

Multi phenomena melt pool sensor data fusion for enhanced process monitoring of laser powder bed fusion additive manufacturing

Finding actionable trends in laser-based metal additive manufacturing process monitoring data is challenging owing to the diversity and complexity of the underlying physical interactions. A single monitoring solution that captures a particular process phenomenon, such as a photodiode that tracks melt pool intensity, is not alone capable of evaluating process stability or detecting flaw formation with sufficient precision for routine application in industry. In this work, to improve flaw detection performance, we adopted a data fusion approach that captures multiple process phenomena. To demonstrate this, we acquired data from laser powder bed fusion (LPBF) builds of cylindrical specimens produced with different laser spot sizes, emulating defocusing due to process faults such as thermal lensing. The resulting specimens had porosity of varying types and severity, quantified by post-build non-destructive X-ray computed tomography, Archimedes density measurements, and destructive metallographic characterization. During the build, the melt pool state was monitored with two coaxial high-speed video cameras and a temperature field imaging system. Physically intuitive low-level melt pool signatures, such as melt pool temperature, shape and size, and spatter intensity were extracted from this high-dimensional, image-based sensor data. These process signatures were subsequently used as input features in relatively simple machine learning models, such as a support vector machine, which were trained to detect laser defocusing, and in addition, predict porosity type and severity. The results show that the data fusion approach significantly enhanced system performance by reducing the overall false positive rate from ~ 0.1 to ~ 0.001 without sacrificing the true positive rate (~0.90). These results were at par with a black-box, deep machine learning approach (convolutional neural network).

36 MATERIALS SCIENCE↗

High throughput structure–property relationship for additively manufactured 316L/IN625 alloy mixtures leveraging 2-step Bayesian estimation

While the fabrication of graded materials by directed energy deposition (DED) has led to accelerated materials discovery, the ability to rapidly explore sufficiently large material composition spaces is limited due to the time-intensive nature of conventional materials characterization techniques. The present study investigates the viability of small punch test (SPT) protocols for rapidly evaluating DED-fabricated alloy mixtures of stainless steel 316L (316L) and Inconel 625 (IN625). The SPT protocols evaluated in this study include both the recently established two-step Bayesian estimation framework as well as the empirical relationships established in prior literature. It is shown that these protocols are capable of reliably and quantitatively tracking the changes in the mechanical properties of the alloy mixtures studied. Enhancement of mechanical properties was observed with the addition of IN625 to 316L, which is attributed to the austenite stabilization in the matrix and the formation of fine δ - Ni3Nb precipitates. It is shown that CALPHAD-based Scheil model simulations predicted the formation of different precipitate phases for each composition. The novel protocols presented in this paper open new avenues for high throughput material explorations for additive manufacturing.

2-step Bayesian estimation↗

Additive manufacturing as a processing route for steel-aluminum bimetallic structures

Here we present results on the fabrication of steel-aluminum bi-metallic structures using directed energy deposition additive manufacturing. The challenges associated with the fabrication of a sharp transition from steel to aluminum are uncovered using ex-situ characterization techniques and thermo-mechanical modeling of the deposition process. It was found that the fabrication of a sharp steel-aluminum transition is challenging with extensive cracking observed at the interface. The cracking was attributed to the combined effect of residual stress development due to thermal expansion coefficient mismatch and the presence of ordered intermetallics with low ductility at the interface. Using a coupled thermodynamic and thermo-mechanical modeling approach, potential pathways to enable the fabrication of steel-aluminum bi-metallic structures using additive manufacturing are proposed. The results presented here can lay the foundation for future work on the fabrication of bi-metallic steel-aluminum structures using directed energy deposition.

36 MATERIALS SCIENCE↗

Effect of flame-retarding additives on surface chemistry in Li-ion batteries

This study examined the properties of 1 wt.% vinylene carbonate (VC), vinyl ethylene carbonate (VEC), and diphenyl octyl phosphate (DPOF) additive electrolytes as a promising way of beneficially improving the surface and cell resistance of Li-ion batteries. Surface film formation on the negative and positive electrodes was analyzed by electrochemical impedance spectroscopy (EIS), Fourier transform infrared (FT-IR) spectroscopy, and scanning electron microscopy (SEM). In conclusion, EIS, FT-IR spectroscopy and SEM results confirmed that DPOF is an excellent additive to the electrolyte in the Li-ion batteries due to the improved co-intercalation of the solvent molecules.

36 MATERIALS SCIENCE↗

Enhanced Curie temperature and piezoelectric properties of (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 lead-free ceramics after the addition of LiTaO3

Highlights: • The Curie temperature and piezoelectric properties of BCZT ceramics can be obviously enhanced by the addition of LiTaO{sub 3}. • The Curie temperature of (Ba{sub 0.85}Ca{sub 0.15})(Zr{sub 0.10}Ti{sub 0.90})O{sub 3} ceramics improved from 93 ℃ to 102 ℃. • (Ba{sub 0.85}Ca{sub 0.15})(Zr{sub 0.10}Ti{sub 0.90})O{sub 3} ceramic with x = 0.3 mol.% LiTaO{sub 3} demonstrates optimal piezoelectric properties. • The giant electrostrictive coefficients (Q{sub 33} ≈ 0.040-0.050 m{sup 4}/C{sup 2}) were also obtained in LT-doped BCZT ceramics. - Abstract: Polycrystalline (Ba{sub 0.85}Ca{sub 0.15})(Zr{sub 0.10}Ti{sub 0.90})O{sub 3}–xLiTaO{sub 3} ceramics were designed and synthesized using a solid-state reaction to improve both the Curie temperature and the electrical properties of (Ba{sub 0.85}Ca{sub 0.15})(Zr{sub 0.10}Ti{sub 0.90})O{sub 3} lead-free piezoelectric ceramics. The effect that the addition of LiTaO{sub 3} has on the structure and electrical properties of BCZT ceramics was studied systemically. The results show that the Curie temperature and the piezoelectric properties of BCZT can be substantially enhanced by adding LiTaO{sub 3.} The Curie temperature increased from 93 °C to 102 °C after adding LT of 0.3 mol.%. X-ray diffraction and Raman spectral analysis of the ceramics reveal the coexistence of orthorhombic (O) and tetragonal (T) phases. This coexistence of O and T phases at room temperature helps improve the ferroelectric and piezoelectric properties. The ceramic with x = 0.3 mol.% exhibits the highest values for d{sub 33} = 433 pC/N, d{sub 33}{sup *} = 858 pm/V (at 1 kV/mm) and k{sub p} = 44.6%. Furthermore, giant electrostrictive coefficients (Q{sub 33} ≈ 0.040–0.050 m{sup 4}/C{sup 2}) were also obtained for these LT-doped BCZT ceramics. These properties confirm that BCZT-xLT is a promising candidate system for lead-free piezoelectric ceramic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Sulfonated polybenzimidazole membrane with graphene oxide additive for 2,3-butanediol/water separation: A molecular simulation

Membrane separation for 2,3-butanediol (2,3-BDO) recovery from fermentation broth is highly valued for sustainable and renewable processes, but it requires efficient membrane materials. Here, this work evaluates the sulfonated polybenzimidazole (sPBI) and its graphene oxide (GO) doped composite membrane for separating 2,3-BDO and water via atomistic simulations. Density functional theory calculations are applied to identify various forms of sPBI structures and quantify their binding interactions with 2,3-BDO and water. Classical molecular dynamic simulations are used to evaluate the structural changes, diffusivity, and selectivity of 2,3-BDO and water in different sPBI models, GO surfaces, and GO-doped sPBI composite models. Our results suggest that sPBI slightly increases the crystallinity of the membrane structures, enhances the adsorption strength for both 2,3-BDO and water, and improves the water/2,3-BDO selectivity by 2–3 times. The GO surfaces display a maximum selectivity at a surface coverage of 0.1–0.15 for both hydroxyl and epoxy surface groups. The addition of GO flakes to sPBI creates new interaction sites for 2,3-BDO and water at the interface of sPBI and GO, and the water/2,3-BDO selectivity of GO-doped sPBI models is further increased up to 3 times. This work illustrates how the integrated addition of sPBI and GO flakes offers a promising approach to selective separation of 2,3-BDO and water, providing theoretical guidance for polybenzimidazole-based membranes in the potential application of 2,3-BDO recovery.

2,3-butanediol↗

Relationship between ductility and the porosity of additively manufactured AlSi10Mg

Additive manufacturing via selective laser melting can result in variable levels of internal porosity both between build plates and within components from the same build. In this work, sample porosity levels were compared to tensile properties for 176 samples spanning eight different build plates. Sample porosity was measured both by Archimedes density, which provided an estimation of overall porosity, and by observation of voids in the fracture surface, which provided an estimation of the porosity at the failure plane. The porosity observed at the fracture surface consistently demonstrated higher porosity than that suggested by Archimedes density. The porosity values obtained from both methods were compared against the mechanical results. Sample porosity appears to have some correlation to the ultimate tensile strength, yield strength, and modulus, but the strongest relationship is observed between porosity and ductility. Three different models were used to relate the fracture surface porosity to the ductility. The first method was a simple linear regression analysis, while the other two models have been used to relate porosity to ductility in cast alloys. It is shown that all three models fit the data well over the observed porosity ranges, suggesting that the models taken from casting theory can extend to additively manufactured metals. Finally, it is proposed that the non-destructive Archimedes method could be used to estimate an approximate sample ductility through the use of correlations realized here. Such a relationship could prove useful for design and for a deeper understanding of the impact of pores on tensile behavior.

36 MATERIALS SCIENCE↗

Minor titanium addition markedly improves the co-deformability of copper-tantalum composites

We investigated the microstructures of equal channel angular extrusion (ECAE) processed sintered composites of copper (Cu) and tantalum (Ta). These composites were produced with nominal Ta volume percentages ranging from 25% to 75%. Additional composites of the same nominal Ta content were prepared with a minor amount of titanium (Ti) added to facilitate interphase bonding. Ti addition was found to markedly improve the strength and co-deformability of the composites, allowing reliable extrusion of Cu-Ta composites with novel microstructures. A major influence of the Ti appears to be to soften the Ta, which contributes to improved co-deformability by reducing the flow stress mismatch between the composite constituents. Here, a change in the fracture surface morphology in the Ti-modified composite compared to the unmodified composite suggests that the Ti may also improve cohesion between Cu and Ta by reducing Ta surface oxides.

36 MATERIALS SCIENCE↗

A synergistic approach to improve the cellulose nanofibril dispersion in poly(lactic acid) composites as feedstocks for extrusion-based additive manufacturing

Hybrid fiber-reinforced polymer composites (HFRPs) are multifunctional materials that bear more than one characteristic benefit. In this study, hybrid cellulose fibers, e.g., pulp fiber (PF) and cellulose nanofibril (CNF), were used for reinforcing poly(lactic acid) (PLA). A synergistic approach was applied to disperse CNF. The low-surface-tension solvent (ethanol), together with PF templating, assisted the dispersion of CNF in PLA. The HFRP achieved a higher tensile strength (∼70 MPa, 29% increase from PLA) and modulus (∼7 GPa, 46% increase from PLA), as well as a higher heat deflection temperature (∼60℃, 6℃ increase compared to neat PLA), compared to single-reinforcement FRPs. Additionally, the formulation was demonstrated to be potentially suitable for large-scale additive manufacturing.

Bista, Bivek [University of Maine]↗

An additively manufactured AlCuMnZr alloy microstructure and tensile mechanical properties

In this study, selective laser melting (SLM) was used to fabricate an AlCuMnZr alloy. The microstructural features that resulted from additive manufacturing (AM) were significantly refined compared to the corresponding cast alloy features. A combination of fine equiaxed and columnar grains along with in-situ formation of θ' precipitates during AM leads to enhanced yield strength (up to 300°C) in the as-fabricated AM alloy. The refinement of brittle intermetallics and a bimodal grain size distribution leads to improved tensile elongation in the AM alloy. The results illustrate the microstructural advantages that can result from additive processing over conventionally processed microstructures.

36 MATERIALS SCIENCE↗

First measurement of the cross section for top quark pair production with additional charm jets using dileptonic final states in pp collisions at $\sqrt{s}$= 13 TeV

The first measurement of the inclusive cross section for top quark pairs ($t\bar{t}$) produced in association with two additional charm jets is presented. The analysis uses the dileptonic final states of $t\bar{t}$ events produced in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 41.5 fb -1 recorded by the CMS experiment at the LHC. A new charm jet identification algorithm provides input to a neural network that is trained to distinguish among $t\bar{t}$ events with two additional charm ($t\bar{t}c\bar{c}$), bottom ($t\bar{t}b\bar{b}$), and light-flavour or gluon ($t\bar{t}LL$) jets. By means of a template fitting procedure, the inclusive $t\bar{t}c\bar{c}$, $t\bar{t}b\bar{b}$, and $t\bar{t}LL$ cross sections are simultaneously measured, together with their ratios to the inclusive $t\bar{t}$ + two jets cross section. This provides measurements of the $t\bar{t}c\bar{c}$ and $t\bar{t}b\bar{b}$ cross sections of 10.1 ± 1.2 (stat) ± 1.4 (syst) pb and 4.54 ± 0.35 (stat) ± 0.56 (syst) pb, respectively, in the full phase space. The results are compared and found to be consistent with predictions from two different matrix element generators with next-to-leading order accuracy in quantum chromodynamics, interfaced with a parton shower simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Insights on keto-hydroperoxide formation from O 2 addition to the beta-tetrahydrofuran radical

Cyclic ethers provide an interesting case study of low-temperature oxidation chemistry, especially in relevance to biofuels. A recent experimental study revealed new questions regarding the low-temperature oxidation mechanism of tetrahydrofuran (THF) concerning the formation of keto-hydroperoxides. In particular, keto-hydroperoxides originating from the THF-β radical were not captured accurately by current literature models, motivating this work to calculate the energetics of the first and second O 2 -addition pathways for THF radicals. Electronic structure calculations at the CCSD(T)/cc-pV∞Z//M06-2X/cc-pVTZ level of theory were used to generate potential energy surfaces for the α-C and β-C THF radicals and subsequent pathways to the formation of the keto-hydroperoxide isomers. These are the first theoretical calculations of the second O 2 -addition radical pathways for the THF-β radical. Results from the theorical work provided further insight into the low-temperature oxidation of THF. This included identifying the pathways most likely to form the keto-hydroperoxide isomers observed in prior experimental work; and detecting that the shortcomings in prior models are likely due to uncertainties in R + THF abstraction reaction rates. Here, these conclusions will motivate future work for accurate THF kinetic model development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bay capping via acetylene addition to polycyclic aromatic hydrocarbons: Mechanism and kinetics

The bay-capping mechanism on PAH armchair edges and the kinetics of acetylene addition to 6–6–5 and 5–6–5 bays have been explored by ab initio/RRKM-ME calculations. The bays on the edges were modeled by C 21 H 11 and C 20 H 9 radicals produced by H abstractions from 7H-benzo[c]cyclopenta[e]pyrene and dicyclopenta[cf]pyrene. The C 20 H 9 + C 2 H 2 reaction is shown to have a low entrance barrier and to rapidly form the capped product, indaceno[2,1,8,7-cdefg]pyrene, along with ethynyl substituted dicyclopenta[cf]pyrene at temperatures above 1400 K. The reactivity of C 21 H 11 is shown to be governed by the location of the unpaired electron; the π radical R1 formed by H abstraction from the CH 2 group in 7H-benzo[c]cyclopenta[e]pyrene reacts with C 2 H 2 very slowly owing to a high entrance barrier, with the bay-capping rate constant approaching 10 -16 cm 3 molecule -1 s -1 only at temperatures above 2000K. Further, this result reaffirms that the growth of π aryl radicals via acetylene addition is inefficient and reflects the generally low reactivity of such radicals where the spin density is highly delocalized over the entire polyaromatic system. Alternatively, the σ C 21 H 11 radical R2 produced by H abstraction from the five-membered ring at the bay rapidly reacts with C 2 H 2 forming the bay-capped product, with the rate constant on the order of 10 -12 cm 3 molecule -1 s -1 at T≥1500K. Rate constants for the capping reactions at the 6–6–5 and 5–6–5 bays are compared with those at the 6–0–6, 6–6–6, and 6–5–6 bays. The site-specific bay-capping rate constants have been utilized in kMC simulations of the PAH growth and the results showed measurable differences when the 6–6–5 and 5–6–5 bay-capping reactions are taken into account, including an increase of the growth rate and the formation of closed-shell PAH and a rise of the number of embedded five-membered rings accompanied with a slight decrease of their overall amount.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stimulation of anaerobic organic matter decomposition by subsurface organic N addition in tundra soils

We present that increasing nitrogen (N) availability in Arctic soils could stimulate the growth of both plants and microorganisms by relieving the constraints of nutrient limitation. It was hypothesized that organic N addition to anoxic tundra soil would increase CH 4 production by stimulating the fermentation of labile substrates, which is considered the rate-limiting step in anaerobic C mineralization. We tested this hypothesis through both field and lab-based experiments. In the field experiment, we injected a solution of 13 C- and 15 N-labeled glutamate 35 cm belowground at a site near Nome on the Seward Peninsula, Alaska, and observed the resulting changes in porewater geochemistry and dissolved greenhouse gas concentrations. The concentration of free glutamate declined rapidly within hours of injection, and the 15 N label was recovered almost exclusively as dissolved organic N within 62 h. These results indicate rapid microbial assimilation of the added N and transformation into novel organic compounds. We observed increasing concentrations of dissolved CH 4 and Fe(II), indicating rapid stimulation of methanogenesis and Fe(III) reduction. Low molecular weight organic acids such as acetate and propionate accumulated despite increasing consumption through anaerobic C mineralization. A laboratory soil column flow experiment using active layer soil collected from the same site further supported these findings. Glutamate recovery was low compared to a conservative bromide tracer, but concentrations of NO 3 - and NH 4 + remained low, consistent with microbial uptake of the added N. Similar to the field experiment, we observed both increasing Fe(II) and organic acid concentrations. Lastly, together, these results support our hypothesis of increased fermentation in response to organic N addition and suggest that increasing N availability could accelerate CH 4 production in tundra soils.

54 ENVIRONMENTAL SCIENCES↗

Ionic liquids as oil additives for lubricating oxygen-diffusion case-hardened titanium

This study attempts to use ionic liquids (ILs) as oil additives to lubricate oxygen-diffusion (OD) case-hardened titanium for improved friction and wear behavior. Four oil-soluble ILs were used as additives in a base oil for boundary lubrication of an OD-treated Ti-6Al-4V surface sliding against a bearing steel ball. The ILs improved the friction behavior to various extents and the two phosphate ILs clearly outperformed the conventional ZDDP. Unlike ZDDP that adversely caused a higher material loss, ILs exhibited excellent wear protection suggesting good material-chemical compatibility. Particularly, the carboxylate IL protected the OD-Ti surface from any measurable wear. As a result, the morphology and chemical composition of the worn surfaces and tribofilms were examined to gain insights of the anti-wear mechanism.

36 MATERIALS SCIENCE↗

Decreased PCDD/F formation when co-firing a waste fuel and biomass in a CFB boiler by addition of sulphates or municipal sewage sludge

Highlights: • Two strategies to reduce PCDD/F formation when co-firing solid recovered fuel (SRF) and biomass. • They were co-combustion with municipal sewage sludge (MSS) and addition of ammonium sulphate. • PCDD/Fs were significantly reduced for a biomass rich in chlorine when adding ammonium sulphate. • MSS had a suppressing effect on PCDD/F formation during co-combustion with SRF. • A link is presented between gaseous alkali chlorides, chlorine in deposits and PCDD/F formation. - Abstract: Polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) are formed during waste incineration and in waste-to-energy boilers. Incomplete combustion, too short residence times at low combustion temperatures (<700 °C), incineration of electronic waste and plastic waste containing chlorine are all factors influencing the formation of PCDD/Fs in boilers. The impact of chlorine and catalysing metals (such as copper and iron) in the fuel on PCDD/F formation was studied in a 12 MW{sub th} circulating fluidised bed (CFB) boiler. The PCDD/F concentrations in the raw gas after the convection pass of the boiler and in the fly ashes were compared. The fuel types were a so-called clean biomass with low content of chlorine, biomass with enhanced content of chlorine from supply of PVC, and solid recovered fuel (SRF) which is a waste fuel containing higher concentrations of both chlorine, and catalysing metals. The PCDD/F formation increased for the biomass with enhanced chlorine content and it was significantly reduced in the raw gas as well as in the fly ashes by injection of ammonium sulphate. A link, the alkali chloride track, is demonstrated between the level of alkali chlorides in the gas phase, the chlorine content in the deposits in the convection pass and finally the PCDD/F formation. The formation of PCDD/Fs was also significantly reduced during co-combustion of SRF with municipal sewage sludge (MSS) compared to when SRF was fired without MSS as additional fuel.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗