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At least 73 records · Page 4

Unconventional Pathways to Carbide Phase Synthesis via Thermal Decomposition of UI 4 (1,4-dioxane) 2

UI4(1,4-dioxane) 2 was subjected to laser-based heating-a method that enables localized, fast heating (T > 2000 °C) and rapid cooling under controlled conditions (scan rate, power, atmosphere, etc.)-to understand its thermal decomposition. A predictive computational thermodynamic technique estimated the decomposition temperature of UI 4 (1,4-dioxane) 2 to uranium (U) metal to be 2236 °C, a temperature achievable under laser irradiation. Dictated by the presence of reactive, gaseous byproducts, the thermal decomposition of UI 4 (1,4-dioxane) 2 under furnace conditions up to 600 °C revealed the formation of UO 2 , UI x , and U(C 1–x O x ) y , while under laser irradiation, UI 4 (1,4-dioxane) 2 decomposed to UO 2 , U(C 1–x O x ) y , UC 2–z O z , and UC. Despite the fast dynamics associated with laser irradiation, the central uranium atom reacted with the thermal decomposition products of the ligand (1,4-dioxane = C 4 H 8 O 2 ) instead of producing pure U metal. In conclusion, the results highlight the potential to co-develop uranium precursors with specific irradiation procedures to advance nuclear materials research by finding new pathways to produce uranium carbide.

36 MATERIALS SCIENCE↗

Facilities and experiment results of the NASA sounding rocket program

The NASA rocket program on reduced gravity materials experiments is reported, including experimental results obtained from the single-stage Black Brant VC sounding rockets first flight and the developed equipment. The first flight was made on 11 December 1975, and nine different experiments were done in the five min of weightlessness. All systems operated satisfactorily and each experiment generated interesting results and recorded phenomena that have been reported. Each of the experiments will be flown again in modified form to obtain additional data or check unexpected results on the multiple rocket launches planned each year. General-purpose apparatus and facilities are being developed and built to allow repeated experimentation of various materials by different investigators. For example, multiple-cavity furnaces with rapid heat-up and cool-down possibilities, providing isothermal and gradient thermal profiles, will accommodate a wide variety of solidification experiments. Special hardware satisfying specific individual requirements is also being developed.

Snyder, R. S.↗

Capillary Pumped Heat Transfer (CHT) Experiment

The operation of Capillary Pumped Loops (CPL's) in low gravity has generally been unable to match ground-based performance. The reason for this poorer performance has been elusive. In order to investigate the behavior of a CPL in low-gravity, an idealized, glass CPL experiment was constructed. This experiment, known as the Capillary-driven Heat Transfer (CHT) experiment, was flown on board the Space Shuttle Columbia in July 1997 during the Microgravity Science Laboratory mission. During the conduct of the CHT experiment an unexpected failure mode was observed. This failure mode was a result of liquid collecting and then eventually bridging the vapor return line. With the vapor return line blocked, the condensate was unable to return to the evaporator and dry-out subsequently followed. The mechanism for this collection and bridging has been associated with long wavelength instabilities of the liquid film forming in the vapor return line. Analysis has shown that vapor line blockage in present generation CPL devices is inevitable. Additionally, previous low-gravity CPL tests have reported the presence of relatively low frequency pressure oscillations during erratic system performance. Analysis reveals that these pressure oscillations are in part a result of long wavelength instabilities present in the evaporator pores, which likewise lead to liquid bridging and vapor entrapment in the porous media. Subsequent evaporation to the trapped vapor increases the vapor pressure. Eventually the vapor pressure causes ejection of the bridged liquid. Recoil stresses depress the meniscus, the vapor pressure rapidly increases, and the heated surface cools. The process then repeats with regularity.

Hallinan, Kevin P.↗

Comments on the Operation of Capillary Pumped Loop Devices in Low Gravity

The operation of Capillary Pumped Loops (CPL's) in low gravity has generally been unable to match ground-based performance. The reason for this poorer performance has been elusive. In order to investigate the behavior of a CPL in low-gravity, an idealized, glass CPL experiment was constructed. This experiment, known as the Capillary-driven Heat Transfer (CHT) experiment, was flown on board the Space Shuttle Columbia in July 1997 during the Microgravity Science Laboratory mission. During the conduct of the CHT experiment an unexpected failure mode was observed. This failure mode was a result of liquid collecting and then eventually bridging the vapor return line. With the vapor return line blocked, the condensate was unable to return to the evaporator and dry-out subsequently followed. The mechanism for this collection and bridging has been associated with long wavelength instabilities of the liquid film forming in the vapor return line. Analysis has shown that vapor line blockage in present generation CPL devices is inevitable. Additionally, previous low-gravity CPL tests have reported the presence of relatively low frequency pressure oscillations during erratic system performance. Analysis reveals that these pressure oscillations are in part a result of long wavelength instabilities present in the evaporator pores, which likewise lead to liquid bridging and vapor entrapment in the porous media. Subsequent evaporation to the trapped vapor increases the vapor pressure. Eventually the vapor pressure causes ejection of the bridged liquid. Recoil stresses depress the meniscus, the vapor pressure rapidly increases, and the heated surface cools. The process then repeats with regularity.

Hallinan, K. P.↗

The energy balance of plasmoids in the solar atmosphere

The properties of an isolated magnetized plasmoid in a nonuniform magnetic field such as arises in stellar atmospheres are studied. The work of Pneuman and Cargill (1985) on the so-called melon-seed effect is extended to include an equation describing the energy balance, so giving a unified picture of the shape, motion, and energetics of the plasmoid. Three treatments of plasmoid energy balance are considered: (1) a polytropic law, (P = about N to the gamma); (2) one in which the plasmoid cools radiatively; and (3) one in which a heating function proportional to the local density balances the radiation. For a gamma = 4/3 polytrope the evolution is self-similar, so that the plasmoid maintains its shape as it moves out from the stellar surface. If gamma is less than 4/3, the final shape is a long thin cigar-shaped body, whereas if gamma is greater than or equal to 4/3, it ultimately becomes self-similar. In cases with radiation and also with heating, the ultimate shape of the plasmoid is determined by whether its gas or magnetic pressure dominate. The former is equivalent to the gamma-less-than-4/3 polytrope, and the latter to the gamma-greater-than-4/3 one. If radiation alone is present, the plasmoid cools rapidly and subsequently evolves self-similarly. If heating balances radiation initially, then the plasmoid heats up as it moves out, but, if the ratio of the transit of time of Alfven waves across it is much less than the radiative cooling time, it ultimately evolves as a gamma = 5/3 polytrope. In each case the plasmoid can be ejected to large distances (several radii) in a stellar atmosphere, for a reasonable choice of surface parameters.

Cargill, P. J.↗

Thermal Vacuum Testing of a Helium Loop Heat Pipe for Large Area Cryocooling

Future NASA space telescopes and exploration missions require cryocooling of large areas such as optics, detector arrays, and cryogenic propellant tanks. One device that can potentially be used to provide closed-loop cryocooling is the cryogenic loop heat pipe (CLHP). A CLHP has many advantages over other devices in terms of reduced mass, reduced vibration, high reliability, and long life. A helium CLHP has been tested extensively in a thermal vacuum chamber using a cryocooler as the heat sink to characterize its transient and steady performance and to verify its ability to cool large areas or components in the 3 degrees Kelvin temperature range. The helium CLHP thermal performance test included cool-down from the ambient temperature, startup, capillary limit, heat removal capability, rapid power changes, and long duration steady state operation. The helium CLHP demonstrated robust operation under steady state and transient conditions. The loop could be cooled from the ambient temperature to subcritical temperatures very effectively, and could start successfully by simply applying power to both the capillary pump and the evaporator plate without pre-conditioning. It could adapt to a rapid heat load change and quickly reach a new steady state. Heat removal between 10 megawatts and 140 megawatts was demonstrated, yielding a power turn down ratio of 14. When the CLHP capillary limit was exceeded, the loop could resume its normal function by reducing the power to the capillary pump. Steady state operations up to 17 hours at several heat loads were demonstrated. The ability of the helium CLHP to cool large areas was therefore successfully verified.

Thermal Control Systems↗

Testing of a Helium Loop Heat Pipe for Large Area Cryocooling

Future NASA space telescopes and exploration missions require cryocooling of large areas such as optics, detector arrays, and cryogenic propellant tanks. One device that can potentially be used to provide closed-loop cryocooling is the cryogenic loop heat pipe (CLHP). A CLHP has many advantages over other devices in terms of reduced mass, reduced vibration, high reliability, and long life. A helium CLHP has been tested extensively in a thermal vacuum chamber using a cryocooler as the heat sink to characterize its transient and steady performance and verify its ability to cool large areas or components in the 3K temperature range. A copper plate with attached electrical heters was used to simulate the heat source, and heat was collected by the CLHP evaporator and transferred to the cryocooler for ultimate heat rejection. The helium CLHP thermal performance test included cool-down from the ambient temperature, startup, capillary limit, heat removal capability, rapid power changes, and long duration steady state operation. The helium CLHP demonstrated robust operation under steady state and transient conditions. The loop could be cooled from the ambient temperature to subcritical temperatures very effectively, and could start successfully without pre-conditioning by simply applying power to both the capillary pump and the evaporator plate. It could adapt to rapid changes in the heat load, and reach a new steady state very quickly. Heat removal between 10mW and 140mW was demonstrated, yielding a power turn down ratio of 14. When the CLHP capillary limit was exceeded, the loop could resume its normal function by reducing the power to the capillary pump. Steady state operations up to 17 hours at several heat loads were demonstrated. The ability of the helium CLHP to cool large areas was therefore successfully verified.

Crycooling↗

Testing of a Helium Loop Heat Pipe for Large Area Cryocooling

Future NASA space telescopes and exploration missions require cryocooling of large areas such as optics, detector arrays, and cryogenic propellant tanks. One device that can potentially be used to provide closed-loop cryocooling is the cryogenic loop heat pipe (CLHP). A CLHP has many advantages over other devices in terms of reduced mass, reduced vibration, high reliability, and long life. A helium CLHP has been tested extensively in a thermal vacuum chamber using a cryocooler as the heat sink to characterize its transient and steady performance and verify its ability to cool large areas or components in the 3K temperature range. A copper plate with attached electrical heaters was used to simulate the heat source, and heat was collected by the CLHP evaporator and transferred to the cryocooler for ultimate heat rejection. The helium CLHP thermal performance test included cool-down from the ambient temperature, startup, capillary limit, heat removal capability, rapid power changes, and long duration steady state operation. The helium CLHP demonstrated robust operation under steady state and transient conditions. The loop could be cooled from the ambient temperature to subcritical temperatures very effectively, and could start successfully without pre-conditioning by simply applying power to both the capillary pump and the evaporator plate. It could adapt to rapid changes in the heat load, and reach a new steady state very quickly. Heat removal between 10mW and 140mW was demonstrated, yielding a power turn down ratio of 14. When the CLHP capillary limit was exceeded, the loop could resume its normal function by reducing the power to the capillary pump. Steady state operations up to 17 hours at several heat loads were demonstrated. The ability of the helium CLHP to cool large areas was therefore successfully verified.

cryocooling↗

A technique for optimal temperature estimation for modeling sunrise/sunset thermal snap disturbance torque

A predictive temperature estimation technique which can be used to drive a model of the Sunrise/Sunset thermal 'snap' disturbance torque experienced by low Earth orbiting spacecraft is described. The twice per orbit impulsive disturbance torque is attributed to vehicle passage in and out of the Earth's shadow cone (umbra), during which large flexible appendages undergo rapidly changing thermal conditions. Flexible members, in particular solar arrays, experience rapid cooling during umbra entrance (Sunset) and rapid heating during exit (Sunrise). The thermal 'snap' phenomena has been observed during normal on-orbit operations of both the LANDSAT-4 satellite and the Communications Technology Satellite (CTS). Thermal 'snap' has also been predicted to be a dominant source of error for the TOPEX satellite. The fundamental equations used to model the Sunrise/Sunset thermal 'snap' disturbance torque for a typical solar array like structure will be described. For this derivation the array is assumed to be a thin, cantilevered beam. The time varying thermal gradient is shown to be the driving force behind predicting the thermal 'snap' disturbance torque and therefore motivates the need for accurate estimates of temperature. The development of a technique to optimally estimate appendage surface temperature is highlighted. The objective analysis method used is structured on the Gauss-Markov Theorem and provides an optimal temperature estimate at a prescribed location given data from a distributed thermal sensor network. The optimally estimated surface temperatures could then be used to compute the thermal gradient across the body. The estimation technique is demonstrated using a typical satellite solar array.

Zimbelman, D. F.↗

Durability of YSZ Coated Ti2AlC in 1300 °C Mach 0.3 Burner Rig Tests

A thermal barrier coating system survived burner rig testing at 1300 °C for 500 h. A 160 µm thick yttria stabilized zirconia (YSZ) coating was applied to a Ti2AlC MAX phase bar sample by plasma spray physical vapor deposition (PS-PVD) and tested face-on in an atmospheric Mach 0.3 jet fuel burner, using 5-h thermal cycles. No thermal barrier coating (TBC) spallation or recession was observed, only a 2.4 mg/cm2 mass gain. The modest weight gain precluded severe volatility losses under high velocity burner conditions. The coating surface exhibited colonies of (111)flourite fiber-textured columns separated by craze patterns, with no visible moisture attack. The metastable tetragonal t' YSZ phase was obtained initially, transitioning to equilibrium teq and cubic YSZ, but with little detrimental monoclinic. The thickness of the alumina TGO was ~21 to 23 μm under the heated YSZ face and ~13 to 15 μm on the uncoated, cooler backside. The backside exhibited removal of initial transient TiO2 nodules and partial etching of the underlying Al2O3 scale by volatile hydroxides formed in high temperature, high velocity water vapor. Aerodynamic forces produced some bending of the cantilevered sample via creep. The test indicated exceptional stability of YSZ coatings on Ti2AlC under turbine conditions, with thermal expansion matching playing a key role. The purpose of this study was to demonstrate long term durability of YSZ/MAX phase system in aggressive high temperature burner rig testing. MAX phases have been keenly studied because of their unique crystal structure and intriguing properties (Refs. 1 and 2). Having Mn+1(Al,Si)(C,N)n general composition, they are defined as ceramics, but possess unusual desirable attributes such as high conductivity, thermal shock resistance, easy machinability, and deformation tolerance. The mechanical properties derive from weak M-(Al,Si) bonding in the basal plane that leads to sliding and kinking in preference to catastrophic crack growth. Like most ceramics they are phase stable at high temperatures, generally up to 1500 °C. High temperature oxidation resistance is excellent for alumina-forming Ti3AlC2, Ti2AlC, and Cr2AlC, as reviewed by Tallman, et al. (Ref. 3). Compatibility with α-Al2O3 scales is further enhanced in cyclic exposures by a close matching of thermal expansion coefficients, (Ref. 4) i.e., (~9.3, 10.2, 11.3×10–6/K for Al2O3, Ti2AlC, and YSZ, to be discussed). Turbine environments generally contain 10 percent water vapor in the combustion gases, therefore moisture effects can be a concern for some materials (Ref. 5). Furnace tests of MAX phases in high temperature steam generally showed little effect on Al2O3 scale growth (Ref. 6). However, high velocity and high pressure gas can influence scale losses by the formation of volatile reaction products, such as TiO(OH)2 and Al(OH)3 (Refs. 7 to 10). This phenomenon had been discussed for 1100 to 1300 °C high pressure burner rig tests of Ti2AlC (Ref. 11). A single cubic growth rate parameter kcubic was measurably lower than comparable furnace TGA data, but it could be matched reasonably well if corrected for a slight volatility term. In general, a two-parameter cubic-linear growth-volatility law was believed to apply. Corresponding scale volatility loss rates, directly measured at 1300 °C on a pre-oxidized sample, were moderate (0.012 mg/cm2/h) and largely attributed to removal of the initial TiO2 transient scale. A related CH4 burner study of high purity Cr2AlC MAX phase demonstrated 1200 °C durability after 500 rapid (5 min. heat and 2 min. cool) thermal shock cycling (29 h hot time) (Ref. 12). Heating and cooling rates were ~1000 and 500 °C per minute, with a gas velocity of 5 m/s, producing a 75 °C/mm gradient. A 7 μm Al2O3 surface scale and a 13 μm Cr7C3 depletion zone formed with no signs of failure. No evidence of scale volatility was evident, although weight change was not provided, the velocity was moderate, and the total hot time was not extensive. The same high gradient BRT was used to produce 1400 °C surface temperatures for a YSZ/Cr2AlC/IN738 system in the first study of MAX phases used as bond coats for thermal barrier coatings (TBC) (Ref. 25). Here TBC failure was reported after 745 cycles, with only a 1.5 μm Al2O3 scale entrained within a porous, Cr7C3 bondcoat depletion phase. YSZ thermal barrier coatings have been considered to be a compatible complement to Al-MAX phases because of thermal expansion matching and extremely low volatility in water vapor. Initial studies showed superior oxidative stability up to 1300 °C, for long times (at least 500 h) for Ti2AlC substrates and less (268 h) for Cr2AlC, while withstanding large alumina TGO scale thickness (~35 to 40 μm) (Refs. 13 and 14). By comparison, typical superalloy systems can only survive 1150 °C maximum interface temperatures for extended periods, with a maximum sustained TGO below 10 μm (Ref. 15). High temperature SiC based systems are known to form slow-growing SiO2 scales. But these are subject to rate enhancement and volatile Si(OH)4 products in the presence of water vapor, as described comprehensively by Opila, et al. (Refs. 5, 16 to 19). Net weight losses are generally observed in high velocity, high pressure burner rig studies (e.g., 0.084 mg/cm2/h at 1300 °C) (Ref. 20). Furthermore, the loss rates have been shown from chemical physics to scale with v1/2 and pH2O 2 (Ref. 16). Low activity, moisture-resistant environmental barrier coatings (EBC), such as rare earth silicates, are needed to prevent substrate recession under turbine conditions (Refs. 21 to 23).

Smialek, James L.↗

A rapid heating and high magnetic field thermal analysis technique

Abstract A new thermal analysis technique is described that allows measurements to be performed on bulk samples at extreme heating and cooling rates and in high magnetic fields. High heating rates, up to 1000 °C min −1 , are achieved through electromagnetic induction heating of a custom-built apparatus fitted with commercial thermal analysis heads and sensor. Rapid cooling rates, up to 100 °C min −1 , are enabled by gas quenching and the small thermal mass of the induction furnace. The custom apparatus is designed to fit inside a superconducting magnet capable of fields up to 9 Tesla. This study demonstrates that the instrument is capable of collecting accurate thermal analysis data in high magnetic fields and rapidly acquiring data for dynamic processes. While the full potential of the technique is still unrealized, currently, it can provide insight into phenomena at time scales relevant to heat treatment in many industrial processes and into little understood effects of high magnetic field processing.

47 OTHER INSTRUMENTATION↗

High-Temperature, High-Flux Multifoil Shield Developed for Space Applications

Spacecraft employing solar dynamic power systems typically use parabolic, point focus concentrators to collect solar power and direct it to the aperture of a heat receiver. Solar fluxes several thousand times the intensity of one solar constant are typically produced in the focal plane of such concentrators. Under heat loading this severe, passively cooled surfaces constructed of most engineering materials would rapidly melt. Therefore, high-temperature shielding is required to protect heat receiver surfaces and other spacecraft surfaces that may be exposed to high flux. To meet this challenge for the joint U.S./Russian Solar Dynamic Flight Demonstration Program, AlliedSignal Aerospace and the NASA Lewis Research Center developed a high-temperature, high-flux multifoil shield tolerant of extreme heat loading conditions in a vacuum environment. The shield is passively cooled, obviating the need for pumped fluid loops and/or heat pipe cooling systems with their attendant cost, mass, complexity, and reliability issues.

Kerslake, Thomas W.↗

Comparison of experimental and theoretical thermal fatigue lives for five nickel base alloys

The alloys Nimonic 90, IN 100, coated IN 100, B 1900, coated B 1900, MAR M200, and MAR M200DS (directionally solidified) were studied. Maximum temperatures ranged from 770 C to 1120 C (1420 F to 2050 F). Specimen geometries included tapered disks, double-edged wedges, and cambered airfoils. The disks and wedges were heated and cooled in fluidized beds. The airfoil specimens were heated by a Mach 1 natural gas burner and rapid-air-cooled, with and without spanwise loading. Life calculations included two distinct failure modes: conventional low cycle fatigue and cyclic creep. Required material properties were limited to conventional thermal, tensile, and creep rupture data. The complete life calculation system included the calculation of transient temperature distributions, thermal strains, stresses, creep damage, fatigue damage, and cycles to first crack. Calculated lives were within a factor of two for 76 of the 86 data points analyzed. Cyclic creep accounted for 81% of all the calculated damage.

Spera, D. A.↗

Comparison of experimental and theoretical thermal fatigue lives for five nickel-base alloys.

Alloys investigated were Nimonic 90, IN 100, coated IN 100, B 1900, coated B 1900, MAR M200, and MAR M200DS (directionally solidified). Maximum temperatures ranged from 770 to 1120 C. Specimen geometries included tapered disks, double-edged wedges, and cambered airfoils. The disks and wedges were heated and cooled in fluidized beds. The airfoil specimens were heated by a Mach 1 natural gas burner and rapid-air cooled, with and without spanwise loading. Life calculations included two distinct failure modes: conventional low-cycle fatigue and cyclic creep. The complete life calculation system included the calculation of transient temperature distributions, thermal strains, stresses, creep damage, fatigue damage, and finally cycles to first crack. Calculated lives were within a factor of two for 76 of the 86 data points analyzed.

Spera, D. A.↗

Switching of Hybrid Improper Ferroelectricity in Oxide Double Perovskites

In ABO 3 -type perovskite oxides with Pnma symmetry, rotation (Q R+ , a 0 a 0 c + ) and tilt (Q T , a – a – c 0 ) of BO 6 octahedra are the two primary order parameters. These order parameters establish an inherent trilinear coupling with anti-ferroelectric A-site displacement (Q AFE ) to form the low-symmetry phase. The symmetry is further lowered in double perovskite oxides (DPOs) due to A/A' cation ordering. It in turn makes these systems polar via hybrid improper ferroelectric mechanism, primarily driven by Q R+ and Q T . Naturally, it has been believed that functionalities such as polarization can also be switched by tuning these primary order parameters. However, mystery around finding switching mechanism still remains. Our study based on density functional theory calculations combined with finite-temperature molecular dynamics simulations shows that the polarization switching is a two-step process, driven by out-of-phase rotation (Q R– , a 0 a 0 c – when Q T = 0 or, a – a – b – when Q T ≠ 0). A series of polar DPOs such as KLnFeOsO 6 [Ln = Sm, Gd, Dy, Tm (lanthanides) and Y (rare earth)], all belonging to P2 1 symmetry, are considered in this investigation. The polarization switching P ($\overrightarrow{P}$) occurs at a very high temperature of ~1150 K through a phase transition, from a polar (P2 1 ) phase with $\overrightarrow{P}$(+) to $\overrightarrow{P}$(-) via a non-polar P4/n phase. The switching itself is metastable in nature. The switching (both polarization and spin state) is only observed for a very short period of time (~23 ps) that poses limitation on using such a mechanism in memory device realization. We demonstrate a concurrent heating–cooling procedure to overcome such shortcoming. In conclusion, simulations conducted at 600 K further imply that long lasting switching can be achieved, at least for 1.2 ns for 600 K, and ideally for an infinite time, if the material is heated just above the T c followed by rapid cooling to a temperature below T c .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Laser-Induced Thermal Decomposition of Uranium Coordination Compounds with Non-oxidic Ligands to Produce Nitride and Carbide Materials

The production of ceramics from uranium coordination compounds can be achieved through thermal processing if an excess amount of the desired atoms (i.e., C or N), or reactive gaseous products (e.g., methane or nitrogen oxide) is made available to the reactive uranium metal core via decomposition/fragmentation of the surrounding ligand groups. Here, computational thermodynamic approaches were utilized to identify the temperatures necessary to produce uranium metal from some starting compounds—UI 4 (TMEDA) 2 , UCl 4 (TMEDA) 2 , UCl 3 (pyridine) x , and UI 3 (pyridine) 4 . Experimentally, precursors were irradiated by a laser under various gaseous environments (argon, nitrogen, and methane) creating extreme reaction conditions (i.e., fast heating, high temperature profile >2000 °C, and rapid cooling). Despite the fast dynamics associated with laser irradiation, the central uranium atom reacted with the thermal decomposition products of the ligands yielding uranium ceramics. Residual gas analysis identified vaporized products from the laser irradiation, and the final ceramic products were characterized by powder X-ray diffraction. The composition of the uranium precursor as well as the gaseous environment had a direct impact on the production of the final phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗