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At least 55 records · Page 3

Smoother Surfaces Enhance Diffusion of Nanorods in Entangled Polymer Melts

Coarse-grained molecular dynamics simulations are used to study the diffusion of thin nanorods in entangled polymer melts for varying nanorod length and roughness. While prior studies observed a nanorod parallel diffusion constant scaling inversely with rod length D ∥ ~ l –1 , here, we show that this scaling is not universal and depends sensitively on the nanorod surface roughness. We observe D ∥ ~ l –k , where k < 1 and decreases with decreasing surface roughness. The weaker scaling is driven by the non-Gaussian diffusion of nanorods due to the emergence of an intermittent hopping process that becomes more pronounced with decreasing roughness at the monomer scale. Analysis shows that the mean hop size grows for smoother rods but shows little to no variation with rod length. The mean hopping frequency shows no dependence on either rod length or roughness, suggesting it originates from the polymer melt environment. Further, our results show that the small-scale features of the nanorod surface strongly influence the large-scale and long-time transport of nanorods in polymer matrices, creating new material design opportunities for precisely engineered nanocomposites.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Modification of Ni-20Cr corrosion dealloying behavior in molten fluorides via cold work induced plastic deformation

The corrosion dealloying behavior of cold-worked (CW) Ni20Cr alloy (wt%) was studied in molten LiF-NaF-KF (or FLiNaK) salts at 600 °C, equal to a homologous temperature (TH) of 0.52. Alloys were cold-rolled to achieve reductions of thickness of 10%, 30%, and 50% introducing plastic deformation and a high density of dislocations. Potentiostatic holds (Eapplied) were applied in two different electrode potential regimes. At 1.75VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, Cr dealloying to Cr(II) and Cr(III) is predominant, while at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, both Ni and Cr are oxidized in molten FLiNaK at 600 °C. In these potential regimes, dealloyed Ni20Cr displayed bicontinuous porosity within the grain interior and at grain boundaries, driven by the high driving force for Cr dissolution and sustained by defect mediated outward solid state diffusion of Cr in parallel with surface diffusion of Ni. The bicontinuous porous structure developed was observed to undergo further coarsening and densification of the Ni-rich ligaments at a higher electrode potential. The main effect of CW observed is the introduction of plastic deformation and dislocation substructures that serve as short-circuit paths for Cr solid state diffusion to surfaces exposed to FLiNaK. This modified the evolution of the bicontinuous porous structure which increased with CW substantially. Kinetic analysis reveals that the Cr dealloying at +1.75 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ and 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ is initially charge transfer controlled, except for the 50% CW condition at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, where the process becomes limited by slow Cr defect mediated bulk diffusion. The rate determining factors are explored and compared to experimental results.

Chan, Ho Lun↗

Surface coverage dynamics for reversible dissociative adsorption on finite linear lattices

Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N’s, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pore size effect on selective gas transport in shale nanopores

In shale gas production, gas composition may vary over time. To understand this phenomenon, we use molecular dynamics simulations to study the permeation of CH 4 , C 2 H 6 and their mixture from a source container through a pyrophyllite nanopore driven by a pressure gradient. For a pure gas, the flow rate of CH 4 is always higher than that of C 2 H 6 , regardless of pore size. For a 1:1 C 2 H 6 : CH 4 mixture, however, C 2 H 6 :CH 4 flow rate ratio is higher than the compositional ratio in the container (i.e., 1:1) when the pore size is smaller than ~1.8 nm. The selective transport is caused by the competitive adsorption of C 2 H 6 over CH 4 in the nanopore. The selectivity is also determined by the interplay between the surface diffusion of the adsorbed molecules and the viscous flow in the center of the pore, and it diminishes as the viscous flow becomes to dominate the surface diffusion when the pore size becomes larger than 1.8 nm. Our work shows that compositional differentiation of shale gas in production is a consequence of nanopore confinement and therefore a key characteristic of an unconventional reservoir. Finally, the related compositional information can potentially be used for monitoring the status of a production well such as its recovery rate.

03 NATURAL GAS↗

Thermal Shape Stability of fcc Metal Nanocrystals Synthesized with Faceted Nonequilibrium Shapes

Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Twin Proliferation and Prolongation under Kinetic Control: Pd–Au Janus Icosahedra versus Pd@Au Core–Shell Starfishes

Heterogeneous bimetallic nanocrystals featuring explicit spatial configurations and abundant twin defects can simultaneously enable geometric and ligand effects to enhance catalytic and photonic applications. Herein, we report two growth patterns of Au atoms on penta-twinned Pd decahedra, involving twin proliferation to generate asymmetric Pd–Au Janus icosahedra and twin elongation to produce anisotropic Pd@Au core–shell starfishes, respectively. Mechanistic analysis indicates that the injection rate determines the lower-limit number (n low ) of Au(III) ions in the steady state and thus controls the growth pattern. When n low ≤ 5.5, the kinetic rate is slow enough to initiate asymmetrical one-side growth but fast enough to outpace surface diffusion; Au tetrahedral subunits are successively proliferated along the axial $\langle$110$\rangle$ direction of Pd decahedra to form Pd–Au Janus icosahedra. Composed of five Pd and 15 Au tetrahedral subunits, such a heterogeneous icosahedron supports high (2.2 GPa) tensile strain and high strain difference up to +21.9%. In contrast, when n low > 5.5, the fast reduction kinetics promotes symmetric growth with inadequate surface diffusion. As such, Au atoms are laterally deposited along five high-indexed $\langle$211$\rangle$ ridges of Pd decahedra to generate concave Pd@Au core–shell starfishes with tunable sizes (28–40 nm), twin elongation ratios (33.82–162.08%), and lattice expansion ratios (8.82–20.10%).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evolution of PTCDA-derived seeds prior to graphene nanoribbon growth on Ge(001)

The synthesis of graphene nanoribbons (GNRs) can be realized via CH4 chemical vapor deposition (CVD) on substrates such as Ge(001) that promote highly anisotropic growth kinetics. Small polycyclic aromatic hydrocarbons (PAHs) are first sublimed onto Ge near room temperature to form graphene-like seeds that subsequently initiate GNR growth with CH4 exposure at 1173 K. The behaviors of PAHs in the time in between their sublimation onto Ge and GNR growth are unclear. Here, we study an archetypical PAH, perylene-3,4,9,10-tetracarboxyl acid dianhydride (PTCDA), on Ge(001) using both scanning tunneling microscopy (STM) and density functional theory (DFT) to characterize PAH conformation, surface diffusivity, and clustering, versus temperature. PTCDA becomes mobile above 673 K (consistent with a DFT calculated diffusion barrier of 2.01 eV). The mobile PTCDA molecules meet, cluster, and fuse at Ge step edges. These clusters have an apparent height of 0.4 nm, similar to small graphene islands, and grow laterally with increasing temperature – reaching 1.2 – 2.1 nm in width at 1173 K, consistent with the seed size extrapolated from CVD experiments. These results provide a plausible picture for how PTCDA forms seeds for anisotropic GNR CVD and show that PAHs with reduced surface diffusivity and inter-molecular reactivity are needed to enable more monodisperse PAH-seeded GNR synthesis.

36 MATERIALS SCIENCE↗

Shape Stability of Truncated Octahedral fcc Metal Nanocrystals

Metallic nanocrystals (NCs) can be synthesized with tailored nonequilibrium shapes to enhance desired properties, e.g., octahedral fcc metal NCs optimize catalytic activity associated with {111} facets. However, maintenance of optimized properties requires stability against thermal reshaping. Thus, we analyze the reshaping of truncated fcc metal octahedra mediated by surface diffusion using a stochastic atomistic-level model with energetic input parameters for Pd. Furthermore, the model describes NC thermodynamics by an effective nearest-neighbor interaction and includes a realistic treatment of diffusive hopping for undercoordinated surface atoms. Kinetic Monte Carlo simulation reveals that the effective barrier, E eff , for the initial stage of reshaping is strongly tied to the degree of truncation of the vertices in the synthesized initial octahedral shapes. This feature is elucidated via exact analytic determination of the energy variation along the optimal reshaping pathway at low-temperature (T), which involves transfer of atoms from truncated {100} vertex facets to form new layers on {111} side facets. Deviations from predictions of the low-T analysis due to entropic effects are more prominent for higher T and larger NC sizes.

36 MATERIALS SCIENCE↗

Solution-Phase Growth of Cu Nanowires with Aspect Ratios Greater Than 1000: Multiscale Theory

Penta-twinned metal nanowires are finding widespread application in existing and emerging technologies. However, little is known about their growth mechanisms. Here, we probe the origins of chloride- and alkylamine-mediated, solution-phase growth of penta-twinned Cu nanowires from first principles using multi-scale theory. Using quantum density functional theory (DFT) calculations, we characterize the binding and surface diffusion of Cu atoms on chlorine-covered Cu(100) and Cu(111) surfaces. We find stronger binding and slower diffusion of Cu atoms on chlorinated Cu(111) than on chlorinated Cu(100) – a reversal of the trend for bare Cu surfaces. We also probe inter-facet diffusion and find this proceeds faster from Cu(100) to Cu(111) than the reverse. Using the DFT rates for hopping between individual sites at Ångstrom scales, we calculate coarse-grained, inter-facet rates for nanowires of various lengths – up to hundreds of μm – and diameters in the 10-nm range. We predict nanowires with aspect ratios around 100 based on surface diffusion, alone. We also account for the influence of a self-assembled alkylamine layer that covers most of the {100} facets, but is absent or thin and disordered on the {111} facets and in an “end zone” near the {100}-{111} boundary. With an end zone, we predict a wide range of nanowire aspect ratios in the experimental ranges. Our work reveals the mechanisms by which a halide – chloride – promotes the growth of high-aspect-ratio nanowires.

36 MATERIALS SCIENCE↗

Emergence of Subsurface Oxygen on Rh(111)

Oxygen atoms on transition metal surfaces are highly mobile under the demanding pressures and temperatures typically employed for heterogeneously catalyzed oxidation reactions. This mobility allows for rapid surface diffusion of oxygen atoms, as well as absorption into the subsurface and reemergence to the surface, resulting in variable reactivity. Subsurface oxygen atoms play a unique role in the chemistry of oxidized metal catalysts, yet little is known about how subsurface oxygen is formed or returns to the surface. Furthermore, if oxygen diffusion between the surface and subsurface is mediated by defects, there will be localized changes in the surface chemistry due to the elevated oxygen concentration near the emergence sites. We observed that oxygen atoms emerge preferentially along the boundary between surface phases and that subsurface oxygen is depleted before the surface oxide decomposes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Examining Ni Coarsening in Solid Oxide Electrolysis Cells by Characterizing NiH on Ni (111) Using a Combined Theoretical Approach

Ni coarsening in the fuel electrode of solid oxide cells (SOCs) is an important degradation mechanism. In this talk, density-functional theory and kinetic Monte Carlo methods are used to explore the hypothesis that the surface diffusion of NiH on Ni may promote Ni coarsening in the SOC operated in electrolysis cell mode. Using both methods and defining the diffusivity as the product of the surface coverage and single-molecule diffusivity, the diffusivity of NiH on Ni (111) is found to be sufficiently large under a significant overpotential to support the above hypothesis. Also, the time between the formation and dissociation of NiH on Ni (111) is predicted to be short at low coverages of H on Ni (111). Thus, significant progress is made toward developing a model of Ni coarsening considering both molecular and dissociated forms of NiH on Ni (111).

density functional theory (DFT)↗

Assessment of the literature about Be-W mixed material layer formation in the fusion reactor environment

Abstract All plasma facing surfaces in a fusion reactor, whether initially pure or an alloy, will rapidly evolve into a mixed material due to plasma-induced erosion, migration and redeposition. Beryllium (Be) erosion from the main chamber, and its transport and deposition on to a tungsten (W) divertor results in the growth of mixed Be-W layers, which can evolve to form beryllides. These Be-W mixed materials exhibit generally less desirable properties than pure tungsten or pure beryllium, such as lower melting points. In order to better understand the parameter space for growth of these alloys, this paper reviews the literature on Be-W mixed material formation experiments—in magnetically confined fusion reactors, in linear plasma test stands, and during thin-film deposition—and on computational modeling of Be-W interactions, as well as briefly assesses the Be-W growth kinetics. We conclude that the following kinetic steps drive the material mixing: adsorption of the implanted/deposited ion on the metal surface; diffusion of the implanted/deposited ion from surface into the bulk, which is accelerated by defects; and loss of deposited material through erosion. Adsorption dominates (or prevents) material mixing in thin-film deposition experiments, whereas diffusion drives material mixing in plasma exposures due to the energetic ion implantation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessment of the literature about Be-W mixed material layer formation in the fusion reactor environment

All plasma facing surfaces in a fusion reactor, whether initially pure or an alloy, will rapidly evolve into a mixed material due to plasma-induced erosion, migration and redeposition. Beryllium (Be) erosion from the main chamber, and its transport and deposition on to a tungsten (W) divertor results in the growth of mixed Be-W layers, which can evolve to form beryllides. These Be-W mixed materials exhibit generally less desirable properties than pure tungsten or pure beryllium, such as lower melting points. In order to better understand the parameter space for growth of these alloys, this paper reviews the literature on Be-W mixed material formation experiments—in magnetically confined fusion reactors, in linear plasma test stands, and during thin-film deposition—and on computational modeling of Be-W interactions, as well as briefly assesses the Be-W growth kinetics. We conclude that the following kinetic steps drive the material mixing: adsorption of the implanted/deposited ion on the metal surface; diffusion of the implanted/deposited ion from surface into the bulk, which is accelerated by defects; and loss of deposited material through erosion. Adsorption dominates (or prevents) material mixing in thin-film deposition experiments, whereas diffusion drives material mixing in plasma exposures due to the energetic ion implantation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mapping the Temperature-dependent and network site-specific onset of spectral diffusion at the surface of a water cluster cage

We explore the kinetic processes that sustain equilibrium in a microscopic, finite system. This is accomplished by monitoring the spontaneous, time-dependent frequency evolution (the frequency autocorrelation) of a single OH oscillator, embedded in a water cluster held in a temperature-controlled ion trap. The measurements are carried out by applying two-color, IR-IR photodissociation mass spectrometry to the D3O+?(HDO)(D2O)19 isotopologue of the “magic number” protonated water cluster, H+?(H2O)21. The OH group can occupy any one of the five spectroscopically distinct sites in the distorted pentagonal dodecahedron cage structure. The OH frequency is observed to evolve over tens of milliseconds in the temperature range (90-120 K). Starting at 100 K, large “jumps” are observed between two OH frequencies separated by ~300 cm-1 indicating migration of the OH group from the bound OH site at 3350 cm-1 to the free position at 3686 cm-1. Increasing the temperature to 110 K leads to partial interconversion among many sites. All sites are observed to interconvert at 120 K such that the distribution of the unique OH group among them adopts the form one would expect for a canonical ensemble. The spectral dynamics displayed by the clusters thus offer an unprecedented view into the molecular-level processes that drive spectral diffusion in an extended network of water molecules.

Yang, Nan↗

Oxidation of NiCr and NiCrMo Alloys at Low Temperatures

Oxidation of Ni-Cr and Ni-Cr-Mo was studied in operando with near ambient pressure x-ray photoelectron spectroscopy in the Cabrera-Mott regime. The oxidation temperature was 200 °C - a severely diffusion limited regime. The near-surface alloy is Cr-enriched after reduction of natives oxide in vacuum, and especially so for Ni-15Cr-6Mo. Mo-cations are integrated in the oxide and Mo(VI) dominates at the surface. The surface chemistry driven promotion of chromia by Mo predicted by theory is negated by the limited surface diffusion of reactants. Furthermore, pre-oxidation processing is proposed to control the oxide properties for use of Ni-Cr superalloys at low temperatures.

36 MATERIALS SCIENCE↗

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells (Final Report)

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co2O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

30 DIRECT ENERGY CONVERSION↗