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At least 127 records · Page 7

Adhesion, friction, and wear of binary alloys in contact with single-crystal silicon carbide

Sliding friction experiments, conducted with various iron base alloys (alloying elements are Ti, Cr, Mn, Ni, Rh and W) in contact with a single crystal silicon carbide /0001/ surface in vacuum are discussed. Results indicate atomic size misfit and concentration of alloying elements play a dominant role in controlling adhesion, friction, and wear properties of iron-base binary alloys. The controlling mechanism of the alloy properties is as an intrinsic effect involving the resistance to shear fracture of cohesive bonding in the alloy. The coefficient of friction generally increases with an increase in solute concentration. The coefficient of friction increases as the solute-to-iron atomic radius ratio increases or decreases from unity. Alloys having higher solute concentration produce more transfer to silicon carbide than do alloys having low solute concentrations. The chemical activity of the alloying element is also an important parameter in controlling adhesion and friction of alloys.

Miyoshi, K.↗

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

Composition dependence of atomic order in strain-relaxed, metastable GeSn alloys

Extended x-ray absorption fine structure (EXAFS) measurements of single-crystal Ge/GeSn radial heterostructure nanowires are used to examine the effects of composition on both short-range order (SRO) and longer-range disorder in GeSn alloys. GeSn has prompted significant interest because it can achieve a direct band gap for sufficient Sn concentrations beyond the equilibrium solid solubility limit in an all-group IV system. Short-range order in this material is particularly interesting as it has been predicted to affect the band gap independent of average composition or strain effects. By independently controlling the Sn composition and GeSn thickness during chemical vapor deposition of misfitting GeSn shells around ultrathin, elastically compliant, Ge core nanowires, the elastic misfit strain in the GeSn is minimized for Sn compositions over the studied range ≈Ge 0.96 Sn 0.04 to Ge 0.88 Sn 0.12 . The degree of SRO was found to decrease with increasing Sn composition. Additionally, damping of the EXAFS signal was observed as the Sn content increased, particularly for increasingly distant atomic shells about the absorbing atom, even for scattering paths not involving Sn atoms. This result is quantified as an increase in the mean-squared relative displacement parameters of the shells. These measurements reveal the accommodation of local strain due to the presence of the highly size-mismatched Sn atoms in the Ge diamond cubic lattice (≈14%), which may have effects on the band structure of the material in addition to the influence of short-range atomic order. Comparison among the nanowire samples allows for calculation of the topological rigidity parameter, a ∗∗ , for the first-neighbor bond lengths. Furthermore, these exhibit chemically distinct values for Ge-Ge, Ge-Sn, and Sn-Sn, and they are consistent with the value a ∗∗ = 0.75 ± 0.07 confirming the general applicability of the model to alloys with both large amounts of natural misfit strain and the potential for short-range order.

Crystal structure Semiconductors Transmission elec↗

Nano-enhanced solid-state hydrogen storage: Balancing discovery and pragmatism for future energy solutions

Nanomaterials have revolutionized the battery industry by enhancing energy storage capacities and charging speeds, and their application in hydrogen (H 2 ) storage likewise holds strong potential, though with distinct challenges and mechanisms. H 2 is a crucial future zero-carbon energy vector given its high gravimetric energy density, which far exceeds that of liquid hydrocarbons. However, its low volumetric energy density in gaseous form currently requires storage under high pressure or at low temperature. This review critically examines the current and prospective landscapes of solid-state H 2 storage technologies, with a focus on pragmatic integration of advanced materials such as metal-organic frameworks (MOFs), magnesium-based hybrids, and novel sorbents into future energy networks. These materials, enhanced by nanotechnology, could significantly improve the efficiency and capacity of H 2 storage systems by optimizing H 2 adsorption at the nanoscale and improving the kinetics of H 2 uptake and release. We discuss various H 2 storage mechanisms—physisorption, chemisorption, and the Kubas interaction—analyzing their impact on the energy efficiency and scalability of storage solutions. The review also addresses the potential of “smart MOFs”, single-atom catalyst-doped metal hydrides, MXenes and entropy-driven alloys to enhance the performance and broaden the application range of H 2 storage systems, stressing the need for innovative materials and system integration to satisfy future energy demands. High-throughput screening, combined with machine learning algorithms, is noted as a promising approach to identify patterns and predict the behavior of novel materials under various conditions, significantly reducing the time and cost associated with experimental trials. In closing, we discuss the increasing involvement of various companies in solid-state H 2 storage, particularly in prototype vehicles, from a techno-economic perspective. In conclusion, this forward-looking perspective underscores the necessity for ongoing material innovation and system optimization to meet the stringent energy demands and ambitious sustainability targets increasingly in demand.

25 ENERGY STORAGE↗

Characterizing the surface compositions of supported bimetallic PtSn clusters: Effects of cluster-support interactions and surface adsorbates

PtSn bimetallic clusters on TiO2(110) and highly oriented pyrolytic graphite (HOPG) surfaces have been characterized by scanning tunneling microscopy, low energy ion scattering (LEIS), Xray photoelectron spectroscopy, and temperature programmed desorption (TPD); density functional theory (DFT) calculations have also been performed to better understand adsorption of CO and D2 on the PtSn surfaces. On TiO2 at coverages of 2 ML of Pt and 2 ML of Sn, exclusively bimetallic clusters are formed for both orders of deposition because clusters of the first metal completely cover the surface such that all atoms of the second metal are incorporated into the existing clusters. In contrast, on HOPG, the high mobility and weak cluster-support interactions on HOPG result in much larger 2 ML monometallic clusters (~30 Å high) that do not completely cover the surface, and deposition of the second metal produces larger clusters as well as smaller ones. Despite the difference in cluster morphologies for the different orders of deposition and supports, the LEIS experiments demonstrate that in all cases, the PtSn clusters are rich in Sn at the surface, as expected based on the lower surface free energy for Sn compared to Pt. Furthermore, the +0.2 eV shift in the Sn(3d5/2) binding energy observed on all surfaces in the presence of Pt is consistent with PtSn alloy formation. Deposition of 2 ML of Sn on TiO2 produces two-dimensional clusters with oxidation of Sn and reduction of titania at the clustersupport interface, but addition of Pt to the Sn clusters causes Sn to diffuse away from this interface, leaving Sn in the metallic state. TPD experiments on 2 ML Pt/TiO2 with increasing coverages of Sn show that the number of adsorption sites for D2 sharply decreases to nearly zero at 0.5 ML, while CO adsorption decreases to zero only at much higher Sn coverages of 2 ML. DFT studies for Sn modified Pt surfaces and bulk structures demonstrate that for CO adsorption at low Sn coverages (<0.25 ML), the strong Pt-CO interactions induce diffusion of Pt to the cluster surface and the formation of a bulk Pt3Sn alloy, whereas D2 adsorption does not lead to interactions with the Pt surface that are strong enough to induce alloy formation. A single Sn adatom prevents D2 adsorption on four neighboring Pt atoms via site-blocking and the donation of electron density to Pt.

Li, Fangliang↗

Minimizing the diffusivity difference between vacancies and interstitials in multi-principal element alloys

Interstitial atoms usually diffuse much faster than vacancies, which is often the root cause for the ineffective recombination of point defects in metals under irradiation. Here, via ab initio modeling of single-defect diffusion behavior in the equiatomic NiCoCrFe(Pd) alloy, we demonstrate an alloy design strategy that can reduce the diffusivity difference between the two types of point defects. The two diffusivities become almost equal after substituting the NiCoCrFe base alloy with Pd. The underlying mechanism is that Pd, with a much larger atomic size (hence larger compressibility) than the rest of the constituents, not only heightens the activation energy barrier ( E a ) for interstitial motion by narrowing the diffusion channels but simultaneously also reduces E a for vacancies due to less energy penalty required for bond length change between the initial and the saddle states. Our findings have a broad implication that the dynamics of point defects can be manipulated by taking advantage of the atomic size disparity, to facilitate point-defect annihilation that suppresses void formation and swelling, thereby improving radiation tolerance.

36 MATERIALS SCIENCE↗

Across the Board: Sheng Dai on Catalyst Design by Entropic Factors

In this series of articles, the board members of ChemSusChem discuss recent research articles that they consider of exceptional quality and importance for sustainability. This entry features Dr. S. Dai, who discusses high-entropy materials (HEMs) as new materials in catalysis. In this viewpoint, two types of HEMs (alloy and non-alloy HEMs), their synthesis, and their application in various catalytic reactions are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrocatalyst advances for hydrogen oxidation in phosphoric acid fuel cells

The important considerations that presently exist for achieving commercial acceptance of fuel cells are centered on cost (which translates to efficiency) and lifetime. This paper addresses the questions of electrocatalyst utilization within porous electrode structures and the preparation of low-cost noble metal electrocatalyst combinations with extreme dispersions of the metal. Now that electrocatalyst particles can be prepared with dimensions of 10 A, either singly or in alloy combinations, a very large percentage of the noble metal atoms in a crystallite are available for reaction. The cost savings for such electrocatalysts in the present commercially driven environment are considerable.

Stonehart, P.↗

Lattice-Distortion-Enhanced Yield Strength in a Refractory High-Entropy Alloy

Severe distortion is one of the four core effects in single-phase high-entropy alloys (HEAs) and contributes significantly to the yield strength. However, the connection between the atomic-scale lattice distortion and macro-scale mechanical properties through experimental verification has yet to be fully achieved, owing to two critical challenges: 1) the difficulty in the development of homogeneous single-phase solid-solution HEAs and 2) the ambiguity in describing the lattice distortion and related measurements and calculations. Here, a single-phase body-centered-cubic (BCC) refractory HEA, NbTaTiVZr, using thermodynamic modeling coupled with experimental verifications, is developed. Compared to the previously developed single-phase NbTaTiV HEA, the NbTaTiVZr HEA shows a higher yield strength and comparable plasticity. The increase in yield strength is systematically and quantitatively studied in terms of lattice distortion using a theoretical model, first-principles calculations, synchrotron X-ray/neutron diffraction, atom-probe tomography, and scanning transmission electron microscopy techniques. These results demonstrate that severe lattice distortion is a core factor for developing high strengths in refractory HEAs.

36 MATERIALS SCIENCE↗

Uncovering the role of nanoscale precipitates on martensitic transformation and superelasticity

Here we characterize the role of coherent nanoscale B2 Ni 50 Al 50 precipitates on the temperature- and stress-induced martensitic phase transformation in nanocrystalline Ni 63 Al 37 shape memory alloys using multi-million-atoms molecular dynamics (MD) simulations. We studied two types of precipitates: one with single crystal precipitates (SXP) and a second where grain boundaries cut through precipitates (PXP). Simulations reveal that the presence of B2 precipitates stabilizes the cyclic flag-shaped stress-strain response, characteristic of superelasticity, and reduces remnant strain. In contrast, single-phase nanocrystalline Ni 63 Al 37 exhibits degradation of the reverse transformation during cyclic loading and, eventually, incomplete reversible transformation within a few cycles. This is consistent with previous experimental findings of ultra-low fatigue in Ni-Ti-Cu alloys with Ti 2 Cu precipitates. The simulations reveal that the presence of precipitates significantly improves the reversibility of the transformation by acting as elastic zones that partially shield the martensitic transformation and drive the reverse transformation. A detailed analysis of the MD trajectories reveals that the martensitic transformation of the matrix induces ultra-large elastic deformation in some of the B2 precipitates (approximately 12%) to the point of resulting in a martensite-like atomic structure.

36 MATERIALS SCIENCE↗

Utilizing local phase transformation strengthening for nickel-based superalloys

Almost 75 years of research has been devoted to producing superalloys capable of higher operating temperatures in jet turbine engines, and there is an ongoing need to increase operating temperature further. Here, a new disk Nickel-base superalloy is designed to take advantage of strengthening atomic-scale dynamic complexions. This local phase transformation strengthening provides the alloy with a three times improvement in creep strength over similar disk superalloys and comparable strength to a single crystal blade alloy at 760 °C. Ultra-high-resolution chemical mapping reveals that the improvement in creep strength is a result of atomic-scale η (D024) and χ (D019) formation along superlattice stacking faults. To understand these results, the energy differences between the L12 and competing D024 and D019 stacking fault structures and their dependence on composition are computed by density functional theory. This study can help guide researchers to further optimize local phase transformation strengthening mechanisms for alloy development.

Timothy M. Smith↗

Alloying–realloying enabled high durability for Pt–Pd-3d-transition metal nanoparticle fuel cell catalysts

Abstract Alloying noble metals with non-noble metals enables high activity while reducing the cost of electrocatalysts in fuel cells. However, under fuel cell operating conditions, state-of-the-art oxygen reduction reaction alloy catalysts either feature high atomic percentages of noble metals (>70%) with limited durability or show poor durability when lower percentages of noble metals (<50%) are used. Here, we demonstrate a highly-durable alloy catalyst derived by alloying PtPd (<50%) with 3d-transition metals (Cu, Ni or Co) in ternary compositions. The origin of the high durability is probed by in-situ/operando high-energy synchrotron X-ray diffraction coupled with pair distribution function analysis of atomic phase structures and strains, revealing an important role of realloying in the compressively-strained single-phase alloy state despite the occurrence of dealloying. The implication of the finding, a striking departure from previous perceptions of phase-segregated noble metal skin or complete dealloying of non-noble metals, is the fulfilling of the promise of alloy catalysts for mass commercialization of fuel cells.

25 ENERGY STORAGE↗

Role of chemical disorder on radiation-induced defect production and damage evolution in NiFeCoCr

Understanding chemical disorder in many concentrated solid solution alloys (CSAs) at the levels of electrons and atoms has attracted increasing attention as a path forward to reveal and identify underlying mechanisms for extraordinary mechanical properties and improved radiation tolerance. Single-phase NiFeCoCr CSA is a common base for many high-entropy alloys (HEAs) that have shown improved mechanical strength and radiation tolerance. In this study, defect production and damage evolution in NiFeCoCr under ion irradiation at room temperature to dose over 20 dpa are determined using ion channeling technique along both <100> and <110> directions utilizing multiple probing beam energies. The results obtained from the multi-axial and multi-energy channeling analysis are compared with those previously obtained for Ni crystals irradiated under similar conditions. The influence of chemical complexity on defect production and clustering at early-stage under room temperature irradiation up to dose of 1 dpa is discussed based on positron annihilation spectroscopy results. Defect structure evaluation in Ni and NiFeCoCr is also discussed based on transmission electron microscopy results over a prolonged irradiation at both room and elevated temperatures. Compared with chemically complex NiFeCoCr, larger dislocation loops thus less lattice strain are expected to form in pure Ni. Moreover, the role of chemical disorder in this CSA is also investigated based on ab initio calculations using large supercells. Finally, to understand the impact of chemical complexity effect on defect structure evolution, this integrated research effort attempts to link the relatively large charge redistribution due to difference in valence electron counts resulting from alloying different 3d transition metal elements, moderate lattice distortion arising from similar adaptable atomic size, and notable suppressed or delayed damage evolution in NiFeCoCr.

36 MATERIALS SCIENCE↗

Durable hybrid electrocatalysts for proton exchange membrane fuel cells

The low durability of carbon-based non-precious metal electrocatalysts hinders their practical applications in proton exchange membrane fuel cells (PEMFCs). In this study, we rationally design a hybrid Pt-Fe-N-C electrocatalyst with unprecedented durability. It consists of abundant Pt and Fe single atoms homogeneously dispersed on the nitrogen-doped carbon support and a small amount of Pt-Fe alloy nanoparticles. A PEMFC with Pt-Fe-N-C as the cathode shows a larger peak power density (0.75 W cm -2 ) than that with Fe-N-C as the cathode (0.50 W cm -2 ). The remarkable durability of Pt-Fe-N-C is reflected from no noticeable drop in the half-wave potential after 70000 potential cycles between 0.6 and 1.0 V in the liquid cell, and 80% current retention after 85 h of potential hold at 0.4 V in the fuel cell. This work demonstrates the feasibility of improving the durability of Fe-N-C material via ultra-low Pt doping and makes non-precious metal electrocatalysts be close to achieving commercial metrics.

25 ENERGY STORAGE↗

Manufacture aluminum alloy tube from powder with a single-step extrusion via ShAPE

Mechanical performance of aluminum in terms of strength, wear and corrosion resistance, especially high-temperature strength has been shown to improve with the addition of transition metal (TM) elements of Fe, Cr, and Ti. However, these feedstock materials occur as powders. As such, the traditional fabrication process is complex and expensive because it requires multiple procedures and consumes considerable energy. This study developed Shear Assisted Processing and Extrusion (ShAPE) as a single-step process that manufactures tubes directly from Al-TM powders obtained via gas atomization. Meter-long Al-TM alloy tubes are extruded from powders with different processing conditions. The ShAPE tubes have very low porosity and the average density is 2.94 kg/cm 3 , which is equal to or higher than parts fabricated by hot extrusion and sintering. The powder-to-tube fabrication process was revealed and discussed by examining the microstructural evolution. The Vickers hardness of ShAPE tubes ranges from 110 to 140 HV through wall thickness and at different extrusion speeds. The variation in hardness was correlated with the extent of refinement of intermetallics and attributed to the shear deformation per unit extrusion length. Energy cost analysis shows that ShAPE save ~60% energy compared to the conventional sintering and extrusion processes. Results indicate ShAPE is a low-cost, high-efficiency manufacturing process for producing tubes from metallic powders.

36 MATERIALS SCIENCE↗

Interface velocity dependent solute trapping and phase selection during rapid solidification of laser melted hypo-eutectic Al-11at.%Cu alloy

Microstructure formation of a hypo-eutectic Al-11Cu (atom percent) alloy during solidification after laser melting has been studied by transmission electron microscopy (TEM). The evolution of the solid-liquid-interface velocity, V SL , during the solidification process has been determined from direct observation by in-situ TEM. This enabled correlating V SL with development of four distinct microstructure zones. Crystal growth mode transitions from planar to cellular, cellular to dendritic, dendritic to cellular, and cellular to planar, have been observed for the accelerating solid-liquid-interface. The transition from coupled two-phase growth to the single-phase growth occurred for V SL = V a = (0.80±0.05) m/s, where V a is the velocity of absolute stability, at the onset of banded morphology grain formation. The in-situ and post-mortem TEM uniquely permitted determination of the non-equilibrium solidus for the rapidly solidifying Al-11Cu alloy. Experimental evidence for solute clustering and chemical ordering tendencies at length scales on the order of ≤ 5nm has been detected in the single-phase regions of the banded grains. The structural features of the single-phase bands have been interpreted as signatures of ‘frozen in’ configurations present in the liquid boundary layer adjacent to the growing crystal, which has a width of about 3nm. Finally, the nano-scale spatiotemporal resolution experimental TEM studies performed here provided quantitative metrics, e.g. the solidification interface velocity dependent solute concentration of the α-Al phase and the near-atomic scale structure in the single-phase bands, that are uniquely suitable for comparison with theory and model predictions for solidification microstructure development in multicomponent alloys after laser melting.

36 MATERIALS SCIENCE↗

Hyperthermal atomic oxygen generator

Characterization of the transport properties of oxygen through silver was continued. Specifically, experiments measuring the transport through Ag(111), Ag(110), Ag(100) single crystals and through Ag0.05 Zr alloy were completed. In addition, experiments using glow discharge excitation of oxygen to assist in the transport were completed. It was found that the permeability through the different orientations of single crystal Ag was the same, but significant differences existed in the diffusivity. The experimental ratio of diffusivities, however, was in reasonable agreement with theoretical estimates. Since the solubilities of orientations must be the same, this suggests some problems with the assumption K = DS. The glow discharge experiments show that there is a substantial increase in transport (factor of six) when the upstream pressure is dissociated to some fraction of atoms (which have a much higher sticking coefficient). These results indicate that there is a significant surface limitation because of dissociative adsorption of the molecules. Experiments with the Ag0.05 Zr alloy and its high-grain boundary and defect density show a permeability of greater than a factor of two over ordinary polycrystalline Ag, but it is unclear as to whether this is because of enhanced transport through these defects or whether the Zr and defects on the surface increased the sticking coefficient and therefore the transport.

Khandelwal, Govind S.↗