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At least 217 records · Page 12

Engineering defect energy landscape of CoCrFeNi high-entropy alloys by the introduction of additional dopants

The concept of high-entropy alloys (HEAs) focusing on tuning the overall chemical complexity represents a novel alloy design strategy. In contrast, alloying of a metallic matrix with minor doping elements with limited and localized tunability has been a common practice to improve material performance. Combining the idea of globally engineering defect energy landscape in HEAs and the localized doping strategy in dilute alloys, in this work, we explore doping effects of minor elements in a HEA matrix to further enhance the overall and localized chemical tunability, aiming to improve its irradiation resistance. Specifically, we study the influence of minor Al, Cu, Ti, and Pd substitutional doping elements on defect energetics in a CoCrFeNi model HEA based on density-functional theory (DFT) calculations. The DFT results indicate that the formation and migration energies of vacancies can be strongly influenced when a dopant is introduced at the first nearest neighbor shells around a vacancy. On the other hand, interstitial energetics are only slightly affected. Among the four elements, Ti and Pd generally decrease vacancy formation energies and increase vacancy migration energies more significantly than Al and Cu. The doping effects become more pronounced when the concentration of the substitutional dopants increases. Based on the energy distributions obtained from DFT, we build a kinetic Monte Carlo (kMC) model to assess the impact of dopants on vacancy-mediated diffusivity in the doped HEAs. Our results suggest that Ti and Pd can lower the tracer diffusivity in the considered HEAs and act as trapping sites, whereas Cu may enhance the atomic transport. This work indicates that substitutional doping in HEAs is an effective strategy in metallurgy to further tune the defect and transport properties of complex alloys.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

MOCVD growth of Si-doped α-(AlGa) 2 O 3 on m-plane α-Al 2 O 3 substrates

We reported the growth of (AlGa) 2 O 3 layers on ($10\overline{10}$) α-Al 2 O 3 substrates using cold-wall metalorganic chemical vapor deposition, and the electrical characterization of Si-doped (AlGa) 2 O 3 layers. In the Ga 2 O 3 growth, the α phase was dominant at low growth temperature, achieving the growth rate of 2.4 μm h –1 at 650 °C. Sheet resistance and electrical conductivity of the Ga 2 O 3 layers with a Si concentration of 3 × 10 20 cm –3 were 1 × 10 4 Ω/square and 8.3 S cm –1 , respectively, at the measurement temperature of 500 °C. The Al composition in the (AlGa) 2 O 3 layers was controlled from 0% to 74%. In our initial attempts, we obtained electrically conductive α-(AlGa) 2 O 3 layers by Si doping (2 × 10 –9 S cm –1 in the sample with an Al composition of 56%). Finally, hybrid functional calculations suggest the conductivities are limited by compensation of Si through cation vacancy complexes, and not by the significant amounts of co-incorporated C and N that are predicted to be electrically passivated by hydrogen.

36 MATERIALS SCIENCE↗

Thermodynamic Stability and Site‐Specific Distribution of Graphitic and Pyridinic Nitrogen in Graphene Moiré on Ru(0001)

Abstract Graphene‐like materials are of interest for large‐scale hydrogen storage applications due to their lightweight, durable, and scalable properties. Nitrogen‐doping minimizes kinetic limitations in diffusion and recombination on surfaces, however, the role of graphitic nitrogen (GN) and pyridinic nitrogen (PN) is not well understood. Nitrogen‐doped graphene is synthesized on Ru(0001) using chemical vapor deposition (CVD) of pyridine and ion irradiation. Scanning tunneling microscopy (STM), x‐ray photoelectron spectroscopy (XPS), and density functional theory (DFT) are used to identify the structure, location, and thermodynamic stability of nitrogen species within the graphene moiré. CVD of pyridine results in a low nitrogen concentration (<0.1at%), while the post‐growth nitrogen ion irradiation allows us to increase the concentration further. The concentration of GN and PN is controlled by varying the ion dose and annealing temperature. Comparison of measured and simulated STM images of GN and PN yield an excellent agreement, allowing us to confidently establish that GN is preferentially located near the center of the Atop region, while PN is located in the valley region of the graphene moiré. This report explicitly confirms the site assignments and provides a foundation for the site synthesis and analysis of structural and electronic properties that drive the reactivity of N‐doped graphene.

Gedara, Buddhika S. A. [Physical and Computational↗

Using block-copolymer nanolithography as a tool to sensitively evaluate variation in chemical dry etching rates of semiconductor materials with sub-5 nm resolution

Ion implantation is a robust and established method to customize the electronic properties of Si. However, fabricating doped, ultrafine semiconductor nanostructures can be challenging. Ion implantation has well-established effects on the dry etch rates of Si, which becomes increasingly consequential as the target dimension shrinks below a few tens of nanometers. While dry etching arrays of block copolymer-templated nanoscale holes (pitch = 37.5 nm, diameter ~25 nm) into p-type, n-type, and undoped Si, we observed that the lateral etch rate was notably larger for the n-type regions than p-type or undoped regions. By doing image analyses on high resolution electron micrographs of the nanostructured hole arrays, we were able to extract the porosity and average radii of the holes with subnanometer sensitivity and compare the relative etch rates between different doping conditions. We found that degenerately doped n-type silicon consistently etches between approximately 17% and 27% faster in the lateral direction than p-type Si, resulting in significantly larger porosity and, consequently, less mechanical stability. Here, we demonstrate that top-down dimensional analysis of a densely packed porous nanostructure is a robust method for assessing extremely small differences in the lateral, chemical etch rate of doped Si to a degree of sensitivity that was previously unachievable. The minute, dense-packed nature of block copolymer self-assembled nanostructures is shown to be ideal for this application. This proposed method could be useful for designing fabrication processes for heterogeneous nanostructures, as slight dry etch rate variations that may be within process tolerance at the micrometer-scale appear to have nontrivial consequences at the nanometer scale.

42 ENGINEERING↗

Optical and microstructural studies of erbium-doped TiO 2 thin films on silicon, SrTiO 3 , and sapphire

Rare-earth ion doped oxide thin films integrated on silicon substrates provide a route toward scalable, chip-scale platforms for quantum coherent devices. Erbium-doped TiO 2 is an attractive candidate: the Er 3+ optical transition is compatible with C-band optical fiber communications, while TiO 2 is an insulating dielectric compatible with silicon process technology. Through structural and optical studies of Er-doped TiO 2 thin films grown via molecular beam deposition on silicon, SrTiO 3 , and sapphire substrates, we have explored the impact of polycrystallinity and microstructure on the optical properties of the Er emission. Comparing polycrystalline TiO 2 (rutile)/Si with single-crystalline TiO 2 (rutile)/r-sapphire and polycrystalline TiO 2 (anatase)/Si with single-crystalline TiO 2 (anatase)/SrTiO 3 , we observe that the inhomogeneous linewidth (Γ inh ) of the most prominent peak in the Er spectrum (the Y 1 –Z 1 transition, 1520 and 1533 nm in rutile and anatase TiO 2 ) is significantly narrower in the polycrystalline case. This implies a relative insensitivity to extended structural defects and grain boundaries in such films (as opposed to, e.g., point defects). We show that the growth of an undoped, underlying TiO 2 buffer on Si can reduce Γ inh by a factor of 4–5. Expectedly, Γ inh also reduces with decreasing Er concentrations: we observe a ∼2 order of magnitude reduction from ∼1000 ppm Er to ∼10 ppm Er. Γ inh then gets limited to a residual value of ∼5 GHz that is insensitive to further reduction in the Er concentration. Based upon the above results, we argue that the optical properties in these thin films are limited by the presence of high “grown-in” point defect concentrations.

Chemical elements↗

Charge carrier nonadiabatic dynamics in non-metal doped graphitic carbon nitride

Graphitic carbon nitride (GCN) has attracted significant attention due to its excellent performance in photocatalytic applications. Non-metal doping of GCN has been widely used to improve the efficiency of the material as a photocatalyst. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we study the charge carrier dynamics in oxygen and boron doped GCN systems. The reported simulations provide a detailed time-domain mechanistic description of the charge separation and recombination processes that are of fundamental importance while evaluating the photovoltaic and photocatalytic performance of the material. The appearance of smaller energy gaps due to the presence of dopant states improves the visible light absorption range of the doped systems. At the same time, the nonradiative lifetimes are shortened in the doped systems as compared to the pristine GCN. In the case of boron doped at a carbon (B–C–GCN), the charge recombination time is very long as compared to the other two doped systems owing to the smaller electron–phonon coupling strength between the valence band maximum and the trap state. The results suggest B–C–GCN as the most suitable candidate among three doped systems studied in this work for applications in photocatalysis. Finally, this work sheds light into the influence of dopants on quantum dynamics processes that govern GCN performance and, thus, guides toward building high-performance devices in photocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evolution of Structural Order and Magnetic Anisotropy in Yb 0.5 (Co 1– x Fe x ) 3 Ge 3 through Doping of a Kagome Lattice

Kagome materials provide fruitful grounds for exploring the intersection of topology and magnetism. In this article, the single crystal growth of Yb 0.5 (Co 1–x Fe x ) 3 Ge 3 (x = 0.00, 0.25, 0.50, 0.75, and 1.00) is reported. As Fe is substituted into the Co-containing kagome net, the structure transforms from the disordered Y 0.5 Co 3 Ge 3 /CoSn-type hybrid structure to the ordered HfFe 6 Ge 6 -type structure. Diffusive scattering is observed in all doped concentrations that eventually converge to a single reflection in the Fe end member, ultimately doubling the unit cell along the c-axis. Anisotropic magnetic measurements were performed to evaluate how the magnetism of the kagome lattice is influenced by Fe substitution. Magnetic interactions are primarily observed along the c-axis. Additionally, a reorientation of the magnetic easy axis is observed with increasing Fe incorporation, highlighting how the magnetism of this material can be chemically tuned. Resistivity with unusual behavior observed in the doped compositions is also reported. Furthermore, the rationale behind the structural evolution from disordered to ordered is discussed.

36 MATERIALS SCIENCE↗

Magnetic Switching in Monolayer 2D Diluted Magnetic Semiconductors via Spin‐to‐Spin Conversion

Abstract The integration of 2D van der Waals (vdW) magnets with topological insulators or heavy metals holds great potential for realizing next‐generation spintronic memory devices. However, achieving high‐efficiency spin–orbit torque (SOT) switching of monolayer vdW magnets at room temperature poses a significant challenge, particularly without an external magnetic field. Here, it is shown field‐free, deterministic, and nonvolatile SOT switching of perpendicular magnetization in the monolayer, diluted magnetic semiconductor (DMS), Fe‐doped MoS 2 (Fe:MoS 2 ) at up to 380 K with a current density of ≈7 × 10 4 A cm −2 . The in situ doping of Fe into monolayer MoS 2 via chemical vapor deposition and the geometry‐induced strain in the crystal break the rotational switching symmetry in Fe:MoS 2 , promoting field‐free SOT switching by generating out‐of‐plane spins via spin‐to‐spin conversion. An apparent anomalous Hall effect (AHE) loop shift at a zero in‐plane magnetic field verifies the existence of z spins in Fe:MoS 2 , inducing an antidamping‐like torque that facilitates field‐free SOT switching. This field‐free SOT application using a 2D ferromagnetic monolayer provides a new pathway for developing highly power‐efficient spintronic memory devices.

Chen, Siwei [Department of Mechanical Engineering ↗

Advancing the Performance of Lithium-Rich Oxides in Concert with Inherent Complexities: Domain-Selective Substitutions

Historically, modifications to Li- and Mn-rich (LMR) cathodes have been studied in relation to their efficacy in solving challenges such as oxygen loss and voltage fade, which are inherent to the activation process of these electrodes. However, even in the presence of these phenomena, well-optimized LMR cathodes show considerable promise as earth-abundant options, particularly if other barriers to implementation can be overcome or mitigated. As the complex mechanisms of LMR electrodes are known to stem from the local, chemical inhomogeneities that define the nanocomposite domain nature of these oxides, strategies aimed at manipulating the performance of activated electrodes, irrespective of voltage fade, through domain-selective modifications, could prove instructive. In this work, we use a novel synthesis process aimed at influencing the site occupancy of substituted Sn 4+ , as an example 4+ cation, into a Co-free Li 1.13 Mn 0.57(1–x) Sn 0.57x Ni 0.3 O 2 LMR oxide. We show that Sn 4+ can be selectively substituted into Li-rich environments. The consequences are revealed to be both chemical and morphological, and the domain-selective doping strategy provides a knob for directed control of the low state-of-charge impedance behavior. In conclusion, these results reveal new clues and insights with respect to further advancing the practical relevance of LMR cathode particles and electrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fermiology of a topological line-nodal compound CaSb 2 and its implication to superconductivity: Angle-resolved photoemission study

Here, we performed angle-resolved photoemission spectroscopy with microfocused beam on a topological line-nodal compound CaSb 2 which undergoes a superconducting transition at the onset T c ~ 1.8 K, to clarify the Fermi-surface topology relevant to the occurrence of superconductivity. We found that a three-dimensional hole pocket at the Γ point is commonly seen for two types of single-crystalline samples fabricated by different growth conditions. On the other hand, the carrier-doping level estimated from the position of the chemical potential was found to be sensitive to the sample fabrication condition. The cylindrical electron pocket at the Y(C) point predicted by the calculations is absent in one of the two samples, despite the fact that both samples commonly show superconductivity with similar T c 's. This suggests a key role of the three-dimensional hole pocket to the occurrence of superconductivity, and further points to an intriguing possibility to control the topological nature of superconductivity by carrier tuning in CaSb 2 .

36 MATERIALS SCIENCE↗

A theoretical investigation of the effect of Ga alloying on thermodynamic stability, electronic-structure, and oxidation resistance of Ti 2 AlC MAX phase

We present a systematic investigation of thermodynamic stability, phase-reaction, and chemical activity of Al containing disordered Ti 2 (Al-Ga)C MAX phases using machine-learning driven high-throughput framework to understand the oxidation resistance behavior with increasing temperature and exposure to static oxygen. The A-site (at Al) disordering of Ti 2 AlC with Ga shows significant change in the chemical activity of Al with increasing temperature and exposure to static oxygen, which is expected to enable surface segregation of Al, thereby, the formation of Al 2 O 3 and improved oxidation resistance. We performed in-depth convex hull analysis of ternary Ti-Al-C, Ti-Ga-C, and Ti-Al-Ga-C based MAX phase, and provide detailed contribution arising from electronic, chemical and vibrational entropies. The thermodynamic analysis shows change in the Gibbs formation enthalpy (ΔG form ) at higher temperatures, which implies an interplay of temperature-dependent enthalpy and entropic contributions in oxidation resistance Ga doped Ti 2 AlC MAX phases. A detailed electronic structure and chemical bonding analysis using crystal orbital Hamilton population method reveal the origin of change in phases stability and in oxidation resistance in disorder Ti2(Al 1-x Ga x )C MAX phases. Our electronic structure analysis correlate well with the change in oxidation resistance of Ga doped MAX phases. We believe our study provides a useful guideline to understand to role of alloying on electronic, thermodynamic, and oxidation related mechanisms of bulk MAX phases, which can work as a precursor to understand oxidation behavior of twodimensional MAX phases, i.e., MXenes (transition metal carbides, carbonitrides and nitrides).

36 MATERIALS SCIENCE↗

Tuning the surface energy of fluorinated diamond-like carbon coatings via plasma immersion ion implantation plasma-enhanced chemical vapor deposition with 1,1,1,2-tetrafluoroethane

Here, we demonstrate an environmentally friendly and scalable method to create fluorine-doped diamond-like carbon (F-DLC) coatings using plasma immersion ion implantation plasma-enhanced chemical vapor deposition (PIII-PECVD) with 1,1,1,2-tetrafluoroethane. F-DLC films tend to have low wettability and good mechanical flexibility, which make them suitable for applications in biomedical devices and antibiofouling surfaces. We report on the effects of fluorine incorporation on the surface chemistry, surface energy, and morphology of these coatings, showing that our method is effective in increasing the fluorine content in the F-DLC up to 40%. We show that the addition of fluorine leads to a decrease in surface energy, which is consistent with a reduction in surface wettability.

Contact angle↗

Controlling thermoelectric transport via native defects in the diamond-like semiconductors Cu 2 HgGeTe 4 and Hg 2 GeTe 4

Diamond like semiconductors (DLS) have emerged as candidates for thermoelectric energy conversion. Towards understanding and optimizing performance, we present a comprehensive investigation of the electronic properties of two DLS phases, quaternary Cu 2 HgGeTe 4 and related ordered vacancy compound Hg 2 GeTe 4 , including thermodynamic stability, defect chemistry, and transport properties. To establish the thermodynamic link between the related but distinct phases, the stability region for both is visualized in chemical potential space. In spite of their similar structure and bonding, we show that the two materials exhibit reciprocal behaviors for dopability. Cu 2 HgGeTe 4 is degenerately p-type in all environments despite its wide stability region, due to the presence of low-energy acceptor defects V Cu and Cu Hg and is resistant to extrinsic n-type doping. Meanwhile Hg 2 GeTe 4 has a narrow stability region and intrinsic behavior due to the relatively high formation energy of native defects, but presents an opportunity for bi-polar doping. While these two compounds have similar structure, bonding, and chemical constituents, the reciprocal nature of their dopability emerges from significant differences in band edge positions. A Brouwer band diagram approach is utilized to visualize the role of native defects on carrier concentrations, dopability, and transport properties. Here this study elucidates the doping asymmetry between two solid-solution forming DLS phases Cu 2 HgGeTe 4 and Hg 2 GeTe 4 by revealing the defect chemistry of each compound, and suggests design strategies for defect engineering of DLS phases.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Doping as a tuning mechanism for magnetothermoelectric effects to improve z T in polycrystalline NbP

Weyl semimetals combine topological and semimetallic effects, making them candidates for interesting and effective thermoelectric transport properties. Here, we present experimental results on polycrystalline NbP, demonstrating the simultaneous existence of a large Nernst effect and a large magneto-Seebeck effect, which is typically not observed in a single material at the same temperature. We compare transport results from two polycrystalline samples of NbP with previously published work, observing a shift in the temperature at which the maximum Nernst and magneto-Seebeck thermopowers occur, while still maintaining thermopowers of similar magnitude. Theoretical modeling shows how doping strongly alters both the Seebeck and Nernst magneto-thermopowers by shifting the temperature-dependent chemical potential, and the corresponding calculations provide a consistent interpretation of our results. Thus, we offer doping as a tuning mechanism for shifting magneto-thermoelectric effects to temperatures appropriate for device applications, improving zT at desirable operating temperatures. Furthermore, the simultaneous presence of both a large Nernst and magneto-Seebeck thermopower is uncommon and offers unique device advantages if the thermopowers are used additively. Finally, we also propose a unique thermoelectric device which would collectively harness the large Nernst and magneto-Seebeck thermopowers to greatly enhance the output and zT of conventional thermoelectric devices.

30 DIRECT ENERGY CONVERSION↗

Spatial BCS-BEC crossover in superconducting $\textit{p–n}$ junctions

Here, we present a theory of superconducting $\textit{p–n}$ junctions. To this end, we consider a two band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states, and the chemical potential as a function of the semiconductor gap $Δ_0$ and the doping level ε. We verify previous results for the quantum phase diagram for a system with constant density of states in the conduction and valence band, which show BCS-superconductor to Bose-Einstein-condensation (BEC) and BEC-to-insulator transitions as a function of doping level and the size of the band gap. Then, we extend this formalism to a density of states which is more realistic for 3D systems and derive the corresponding quantum phase diagram, where we find that a BEC phase can only exist for small band gaps $Δ_0 < Δ ^{\ast}_0$. For larger band gaps, we find rather a direct transition from an insulator to a BCS phase. Next, we apply this theory to study the properties of superconducting $\textit{p–n}$ junctions. We derive the spatial variation of the superconducting order parameter along the $\textit{p–n}$ junction. As the potential difference across the junction leads to energy band bending, we find a spatial crossover between a BCS and BEC condensate, as the density of charge carriers changes across the $\textit{p–n}$ junction. For the two-dimensional system, we find two possible regimes, when the bulk is in a BCS phase, a BCS-BEC-BCS junction with a single BEC layer in the space charge region, and a BCS-BEC-I-BEC-BCS junction with two layers of BEC condensates separated by an insulating layer. In three dimensions we find that there can also be a conventional BCS-I-BCS junction for semiconductors with band gaps exceeding $Δ^{\ast}_0$. Thus, we find that there can be BEC layers in the well controlled setting of doped semiconductors, where the doping level can be varied to change and control the thickness of BEC and insulator layers, making Bose-Einstein condensates thereby possibly accessible to experimental transport and optical studies in solid-state materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling the performance and faradaic efficiency of solid oxide electrolysis cells using doped barium zirconate perovskite electrolytes

Y-doped BaZrO 3 (BaZr 1 x Y x O 3 δ , or “BZY”), a proton-conducting ceramic featuring high bulk conductivity and good chemical stability, is a promising electrolyte material for solid oxide electrolysis cells. Further doping with Ce and/or Yb (creating materials “BCZY” and “BCZYYb”) can improve conductivity and sintering properties, but at significant penalty to cells’ faradaic efficiency (FE). Studies have proposed that reduction of lattice Ce can occur in the hydrogen electrode, which consumes some hydrogen produced by the hydrogen evolution reaction, leading to decreased FE. Despite studies suggesting this phenomenon, the mechanism is largely unknown. In this work, we developed a multiphysics model to study the transport of multiple defect species and the performance of BZY, BCZY, and BCZYYb, capturing the tradeoff between enhanced performance at the cost of FE for BCZY and BCZYYb electrolytes compared to BZY. We also found that increasing the water content of the anode gas supply lowers the current output of the cell but results in better FE. The model, which uses several parameters previously unavailable in the literature, was validated to experiments varying temperature, steam water content, and electrolyte material, as well as two performance metrics (performance curves and FE). Results verify and explain observed trends, informing future work on Ce-doped BZY electrolytes.

08 HYDROGEN↗

Nanopinhole Passivating Contact Si Solar Cells Fabricated with Metal-Assisted Chemical Etching

Monocrystalline Si (c-Si) solar cells with passivating contacts based on doped polycrystalline Si (poly-Si) on ≈2.0 nm silicon oxide (SiO x ) require >1000 °C thermal processing to create conducting pinholes in the SiO x layer. However, this high thermal budget can induce bulk defects in the Czochralski c-Si wafers used as the cell absorber layer. We demonstrate that pinholes can instead be created using metal-assisted chemical etching on planar or textured morphologies, at room temperature. This wet process creates up to 200 nm wide conducting pinholes that are directly observed with transmission electron and atomic force microscopies. High-performance hole-selective poly-Si/SiN y /SiO x and electron-selective poly-Si/SiO x passivating contacts are fabricated and implemented in laboratory-scale solar cells. This process development significantly broadens the range of passivation layer materials, their thicknesses, and surface morphologies, which enables the design of poly-Si contacts with superior passivating quality.

14 SOLAR ENERGY↗

First-Principles Insights into the Thermodynamics of Variable-Temperature Ammonia Synthesis on Transition-Metal-Doped Cu (100) and (111)

Ammonia (NH 3 ) is one of the most produced chemicals worldwide. NH 3 synthesis predominantly utilizes the Haber–Bosch (HB) process, requiring high temperatures and pressures. Despite significant process advances, ample opportunity remains for improving the rate, selectivity, catalyst stability, and energy efficiency. Inspired by a recently developed programmable heating and quenching (PHQ) technique, we present in this paper a first-principles screening of candidate single-atom alloy catalysts generated from doping (111) and (100) surfaces of copper (Cu), an ineffective HB catalyst in its pure form. We predict the thermodynamics of two rate-limiting reactions, N 2 dissociative adsorption and the final hydrogenation step leading up to NH 3 release, at 400 and 900 K. Thermodynamically, the former reaction is favored at low temperatures, while the latter is favored at high temperatures. Vanadium-, chromium-, and molybdenum-doped Cu surfaces, due to intermediate M–N covalent bonding character, emerge as appealing candidate catalysts for PHQ NH 3 synthesis, as they balance the thermodynamics of the above-mentioned reaction steps at their respective optimal temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗