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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Robust Methodology to Elucidate Kinetics of Room Temperature Electrochemical Propane Adsorption on Platinum

Electrocatalytic activation of alkanes can further decarbonize chemical manufacturing by leveraging affordable renewable electricity and readily available shale gas reserves in the United States. Earlier works have identified the unique role of Pt in adsorbing and activating alkanes, like propane, at room temperature in acidic, aqueous electrolytes, revealing spontaneous formation of deeply dehydrogenated propane-derived surface species with an intact C 3 - backbone. Although an adsorption mechanism was hypothesized, it has not been explicitly investigated to date, preventing the quantification of kinetic rate parameters. A robust methodology to investigate and benchmark propane adsorption kinetics on Pt is critical for the rational design of electrocatalysts that exhibit higher selectivity toward desired partially oxidized products. Herein, we analyze an oxidative current transience that appears during the adsorption of propane on Pt in aqueous electrochemical conditions and develop a methodology that elucidates the adsorption mechanism and enables quantification of rate parameters such as order dependences and apparent activation barriers. This method yields an expected first-order dependence with respect to propane concentration at low coverage and reveals a second-order dependence with respect to the concentration of surface active sites. Additionally, the apparent activation barrier for propane adsorption was calculated using an Arrhenius analysis of the current transience under temperature control. The experimentally measured activation barrier of 35 kJ mol –1 is in excellent agreement with the theoretical barrier calculated by density functional theory (DFT). The kinetic analysis was extended, via the use of transition state theory, to extract entropy and enthalpy of activation, yielding consistent results with the proposed two-step adsorption mechanism and DFT calculations. These results demonstrate reliable quantification of kinetic parameters for electrocatalytic activation of C–H bonds in alkanes that can be employed for rational catalyst development for a versatile range of electrocatalytic conditions.

alkane activation↗
DOE OSTI2023

Nucleation kinetics model for primary crystallization in Al–Y–Fe metallic glass

The high density of aluminum nanocrystals (>10 21 m -3 ) that develop during the primary crystallization in Al-based metallic glasses indicates a high nucleation rate (~10 18 m -3 s -1 ). Several studies have been advanced to account for the primary crystallization behavior, but none have been developed to completely describe the reaction kinetics. Recently, structural analysis by fluctuation electron microscopy has demonstrated the presence of the Al-like medium range order (MRO) regions as a spatial heterogeneity in as-spun Al 88 Y 7 Fe 5 metallic glass that is representative for the class of Al-based amorphous alloys that develop Al nanocrystals during primary crystallization. From the structural characterization, an MRO seeded nucleation configuration is established, whereby the Al nanocrystals are catalyzed by the MRO core to decrease the nucleation barrier. The MRO seeded nucleation model and the kinetic data from the delay time (τ) measurement provide a full accounting of the evolution of the Al nanocrystal density (N v ) during the primary crystallization under isothermal annealing treatments. Moreover, the calculated values of the steady state nucleation rates (J ss ) predicted by the nucleation model agree with the experimental results. Moreover, the model satisfies constraints on the structural, thermodynamic, and kinetic parameters, such as the critical nucleus size, the interface energy, and the volume-free energy driving force that are essential for a fully self-consistent nucleation kinetics analysis. In conclusion, the nucleation kinetics model can be applied more broadly to materials that are characterized by the presence of spatial heterogeneities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Computational Predictions of the Hydrolysis of 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitroanisole (DNAN)

Hydrolysis is a common transformation reaction that can affect the environmental fate of many organic compounds. In this study, three proposed mechanisms of alkaline hydrolysis of 2,4,6-trinitrotoluene (TNT) and 2,4-dinitroaniline (DNAN) were investigated with plane-wave density functional theory (DFT) combined with ab initio and classical molecular dynamics (AIMD/MM) free energy simulations, Gaussian basis set DFT calculations, and correlated molecular orbital theory calculations. Most of the computations in this study were carried out using the Arrows web based tools. For each mechanism: Meisenheimer complex formation, nucleophilic aromatic substitution, and proton abstraction reaction energies and activation barriers were calculated for the reaction at each relevant site. For TNT, it was found that the most kinetically favorable first hydrolysis steps involve Meisenheimer complex formation by attachment of OH$^{-}$ at the C1 and C3 arene carbons and proton abstraction from the methyl group. The nucleophilic aromatic substitution reactions at the C2 and C4 arene carbons were found to be thermodynamically favorable. However, the calculated activation barriers were slightly lower than previous studies, but still found to be $\Delta$G$^{\ddagger} \approx 18$ kcal/mol using PBEo AIMD/MM free energy simulations, suggesting the reactions are not kinetically significant. For DNAN, the barriers of nucleophilic aromatic substitution were even greater ($\Delta$G$^{\ddagger} > 29$ kcal/mol PBEo AIMD/MM). Further, the most favorable hydrolysis reaction for DNAN was found to be a two-step process in which the hydroxyl first attacks the C1 carbon to form a Meisenheimer complex at the C1 arene carbon C1-(OCH$_3$)OH$^{-}$, subsequently, the methoxy anion (-OCH$_3$) at the C1 arene carbon dissociates and the proton shuttles from the C1-OH to the dissociated methoxy group, resulting in methanol and an aryloxy anion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

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↗
NASA NTRS2014

Sintering Characteristics of Multilayered Thermal Barrier Coatings Under Thermal Gradient and Isothermal High Temperature Annealing Conditions

Pyrochlore oxides have most of the relevant attributes for use as next generation thermal barrier coatings such as phase stability, low sintering kinetics and low thermal conductivity. One of the issues with the pyrochlore oxides is their lower toughness and therefore higher erosion rate compared to the current state-of-the-art TBC material, yttria (6 to 8 wt%) stabilized zirconia (YSZ). In this work, sintering characteristics were investigated for novel multilayered coating consisted of alternating layers of pyrochlore oxide viz Gd2Zr2O7 and t' low k (rare earth oxide doped YSZ). Thermal gradient and isothermal high temperature (1316 C) annealing conditions were used to investigate sintering and cracking in these coatings. The results are then compared with that of relevant monolayered coatings and a baseline YSZ coating.

Thermal Barrier Coatings↗
DOE OSTI2024

Electrochemical leaching of spent LIBs: Kinetics, novel reactor, and modeling

The use of electrons as main reagent for the recovery and recycling of critical metals from spent lithium-ion batteries (LIBs) is a process electrification strategy that can be used to close the life-cycle loop of LIBs through more sustainable methods. Electrochemical leaching, a process that uses a reductant that is constantly regenerated electrochemically for the leaching of lithium-ion battery black mass (LIBBM), has shown high extraction efficiencies and sustainable scores. However, slow kinetics, reactor design challenges and lack of deeper understanding of the underlying processes are barriers to the optimization, scale-up, and market adoption of this technology. In this paper, a kinetic study and mathematical model for dissolving LIBBM is presented to better understand the underlying mechanisms aiming to reduce the processing time and make predictions for future design and scale-up. The effect of acid and electrochemically mediated reductant concentrations, LIBBM loading, and cathode/reactor designs were explored. As a result, the leaching time was reduced from 7h to under 1h at a pulp density of 73 g/L, without external heating. A novel reactor with parallel baffle electrodes (PBE) was developed, which significantly reduced the leaching time by improving convection in a stirred slurry electrochemical reactor. Dimensionless numbers were deduced from an unsteady state model, which can be used in dimensional analysis for future process design and scale-up.

25 ENERGY STORAGE↗
DOE OSTI2024

Kinetic Modeling Analysis of Ar Addition to Atmospheric Pressure N 2 –H 2 Plasma for Plasma-Assisted Catalytic Synthesis of NH 3

Zero-dimensional kinetic modeling of atmospheric pressure Ar–N 2 –H 2 nonthermal plasma was carried out to gain mechanistic insights into plasma-assisted catalytic synthesis of ammonia. Ar dilution is a common technique for tailoring plasma discharge properties and has been shown to enhance NH 3 formation when added to N 2 –H 2 plasma. The kinetic model was developed for a coaxial dielectric barrier discharge quartz wool-packed bed reactor operating at near room temperature using a kHz-frequency plasma source. With 30% Ar mixed in a 1:1 N 2 –H 2 plasma at 760 Torr, we find that NH 3 production is dominated by Eley–Rideal (E-R) surface reactions, which heavily involve surface NH x species derived from N and H radicals in the gas phase, while the influence of excited N 2 molecules is negligible. This is contrary to the commonly proposed mechanism that excited N 2 molecules created by Penning excitation of N 2 by Ar(4s) and Ar(4p) play a significant role in assisting NH 3 formation. Our model shows that the enhanced NH 3 formation upon Ar dilution is unlikely due to the interactions between Ar and H species, as excited Ar atoms have a weak effect on H radical formation through H 2 dissociation compared to electrons. We find that excited Ar atoms contribute to 28% of the N radical production in the gas phase via N 2 dissociation, while the rest are dominated by electron-impact dissociation. Furthermore, Ar species play a negligible role in the product NH 3 dissociation. N 2 conversion sensitivity analyses were carried out for electron number density (ne) and reduced electric field (E/N), and contributions from Ar to gas-phase N radical production were quantified. Finally, the model can provide guidance on potential reasons for observing enhanced NH 3 formation upon Ar dilution in N 2 –H 2 plasma beyond changes in the discharge characteristics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the violation of the zeroth law of turbulence in space plasmas

The zeroth law of turbulence states that, for fixed energy input into large-scale motions, the statistical steady state of a turbulent system is independent of microphysical dissipation properties. This behaviour, which is fundamental to nearly all fluid-like systems from industrial processes to galaxies, occurs because nonlinear processes generate smaller and smaller scales in the flow, until the dissipation – no matter how small – can thermalise the energy input. Using direct numerical simulations and theoretical arguments, we show that in strongly magnetised plasma turbulence such as that recently observed by the Parker Solar Probe spacecraft, the zeroth law is routinely violated. Namely, when such turbulence is ‘imbalanced’ – when the large-scale energy input is dominated by Alfvénic perturbations propagating in one direction (the most common situation in space plasmas) – nonlinear conservation laws imply the existence of a ‘barrier’ at scales near the ion gyroradius. This causes energy to build up over time at large scales. The resulting magnetic-energy spectra bear a strong resemblance to those observed in situ , exhibiting a sharp, steep kinetic transition range above and around the ion-Larmor scale, with flattening at yet smaller scales. The effect thus offers a possible solution to the decade-long puzzle of the position and variability of ion-kinetic spectral breaks in plasma turbulence. The existence of the ‘barrier’ also suggests that, how a plasma is forced at large scales (the imbalance) may have a crucial influence on thermodynamic properties such as the ion-to-electron heating ratio.

Physics↗
DOE OSTI2025

PFSA-Ionomer Adsorption to C and Pt/C Particles in Fuel-Cell Inks

Catalyst inks used to make fuel-cell electrodes consist of Pt/C catalyst particles and a perfluorosulfonic acid (PFSA) ionomer dispersed in water/alcohol solvent mixtures. PFSA ionomer in the ink adsorbs to the surface of the catalyst particles, dictating the dispersion colloid properties. Following adsorption, the subsequent distribution of excess nonadsorbed ionomer in the ink then governs the final structure of the electrode. Here, we characterize the adsorption of the PFSA ionomer onto Pt/C catalyst particles. PFSA adsorption is largely irreversible. Adsorbed sulfonic-acid moieties impart a negative charge on the catalyst surface, causing electrostatic repulsion between the free ionomer in solution and the ionomer-covered Pt/C particle surface. The amount of adsorption is limited by the resulting electrostatic charge that grows as more ionomer adsorbs, and the catalyst surface becomes more negatively charged. Attenuating electrostatic repulsion by increasing the ink ionic strength promotes ionomer adsorption. Electrostatically limited adsorption is observed, irrespective of the solvent water/n-propanol ratio or the catalyst particle porosity and Pt loading. Experimentally measured ionomer adsorption isotherms are well predicted by a Smoluchowski-based kinetic adsorption model, in which the electrostatic energy barrier for adsorption is predicted from DLVO theory. These findings help to unravel the complex phenomena within these colloidal dispersions, allowing for subsequent tailoring of inks to optimize fuel-cell electrode structure and performance.

Adsorption↗
DOE OSTI2020

Calcium-triggered fusion of lipid membranes is enabled by amphiphilic nanoparticles

Significance Lipid membrane fusion is a critical component of biological transport, communication, and developmental processes. The fusion reaction is kinetically constrained since it contains multiple large energy barriers, so proteins and ions are used by natural systems to intervene and catalyze the reaction toward biologically relevant timescales. Here, we demonstrate how amphiphilic nanoparticles can prime lipid membranes for fusion so that complete fusion proceeds only upon exposure to an excess of calcium or other stimulus that would stress the outer leaflet. This is a major advance in the nascent field of controlled fusion and may unlock new avenues of research on how nanomaterials can be designed from first principles to perform targeted functional roles in biological systems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Nonperturbative and perturbative dynamics of a light QCD axion: Dark matter and the strong 𝐶⁢𝑃 problem

Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The 𝑍 𝒩 QCD axion model reduces the QCD axion mass naturally, by invoking a discrete 𝑍 𝒩 symmetry through which the axion field is coupled to 𝒩 copies of the Standard Model. Before the QCD phase transition at temperature 𝑇 QCD , the 𝑍 𝒩 potential has a minimum at misalignment angle 𝜃 = 𝜋. At 𝑇 QCD , 𝜃 = 𝜋 becomes a maximum; the axion potential becomes exponentially suppressed and develops 𝒩 minima—only one of which actually solves the strong 𝐶⁢𝑃 problem. Before 𝑇 QCD , 𝜃 relaxes toward 𝜋. After 𝑇 QCD , the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the 𝑍 𝒩 QCD axion using 𝒞osmoℒattice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong 𝐶⁢𝑃 problem tends to diverge considerably from the naïve expectation of 1/𝒩.

Axions↗
NASA NTRS1974

Instrument to measure energy and charge of low energy interplanetary particles

An experiment to measure the charge composition and energy spectra of ultra low energy charged particles in interplanetary space has been developed and launched on the IMP 8 (Explorer 50) satellite on Oct. 26, 1973. The instrument consists of two separate sensors sharing common electronics. One of these sensors uses a thin window gas proportional counter to measure the rate of energy loss and a totally depleted silicon surface barrier detector to measure total energy of incoming particles. The energy range for two dimensional analysis extends from 300 KeV to 2.5 MeV for protons and 60 KeV/nucleon to 25 MeV/nucleon for iron with excellent resolution of individual chemical elements. The other sensor combines electrostatic deflection with total energy measurements in silicon surface barrier detectors to give the ionic charge and kinetic energy of the particle.

Tums, E.↗
NASA NTRS1994

The Materials Chemistry of Atomic Oxygen with Applications to Anisotropic Etching of Submicron Structures in Microelectronics and the Surface Chemistry Engineering of Porous Solids

Neutral atomic oxygen is the most abundant component of the ionospheric plasma in the low Earth orbit environment (LEO; 200 to 700 kilometers altitude) and can produce significant degradation of some spacecraft materials. In order to produce a more complete understanding of the materials chemistry of atomic oxygen, the chemistry and physics of O-atom interactions with materials were determined in three radically different environments: (1) The Space Shuttle cargo bay in low Earth orbit (the EOIM-3 space flight experiment), (2) a high-velocity neutral atom beam system (HVAB) at Los Alamos National Laboratory (LANL), and (3) a microwave-plasma flowing-discharge system at JSC. The Space Shuttle and the high velocity atom beam systems produce atom-surface collision energies ranging from 0.1 to 7 eV (hyperthermal atoms) under high-vacuum conditions, while the flowing discharge system produces a 0.065 eV surface collision energy at a total pressure of 2 Torr. Data obtained in the three different O-atom environments referred to above show that the rate of O-atom reaction with polymeric materials is strongly dependent on atom kinetic energy, obeying a reactive scattering law which suggests that atom kinetic energy is directly available for overcoming activation barriers in the reaction. General relationships between polymer reactivity with O atoms and polymer composition and molecular structure have been determined. In addition, vacuum ultraviolet photochemical effects have been shown to dominate the reaction of O atoms with fluorocarbon polymers. Finally, studies of the materials chemistry of O atoms have produced results which may be of interest to technologists outside the aerospace industry. Atomic oxygen 'spin-off' or 'dual use' technologies in the areas of anisotropic etching in microelectronic materials and device processing, as well as surface chemistry engineering of porous solid materials are described.

Koontz, Steve L.↗
NASA NTRS2002

Theoretical Study of Decomposition Pathways for HArF and HKrF

To provide theoretical insights into the stability and dynamics of the new rare gas compounds HArF and HKrF, reaction paths for decomposition processes HRgF to Rg + HF and HRgF to H + Rg + F (Rg = Ar, Kr) are calculated using ab initio electronic structure methods. The bending channels, HRgF to Rg + HF, are described by single-configurational MP2 and CCSD(T) electronic structure methods, while the linear decomposition paths, HRgF to H + Rg + F, require the use of multi-configurational wave functions that include dynamic correlation and are size extensive. HArF and HKrF molecules are found to be energetically stable with respect to atomic dissociation products (H + Rg + F) and separated by substantial energy barriers from Rg + HF products, which ensure their kinetic stability. The results are compatible with experimental data on these systems.

Chaban, Galina M.↗
DOE OSTI2025

Tailoring Na⁺ Chelation Dynamics for Expedient Sulfur Redox Kinetics in Low‐Temperature Sodium–Sulfur Batteries

Sodium–sulfur (Na–S) batteries have attracted considerable attention due to their high theoretical energy density and the abundant natural availability of sodium and sulfur. However, sluggish kinetics of sulfur conversion, slow Na⁺ transport, and interfacial instability at low temperatures pose significant challenges for their operation and limit their practical application. Herein, three solvents with well-designed molecular configurations are examined. We systematically investigate the impact of chelation effect on the desolvation behavior, sulfur conversion process, ion dynamics, and Na⁺ plating/stripping behavior. Compared with conventional linear ether solvents, the incorporation of methyl groups not only weaken the chelation capability and tailors the inner solvation sheath, but also reduces the energy barrier for Na⁺ transport, thus promoting enhanced sulfur conversion kinetics under low temperature conditions. This work elucidates the relationship among solvent molecules, Na⁺ desolvation behavior, and sulfur reaction kinetics, and offers a strategy for rational design of electrolytes for low-temperature metal–sulfur batteries.

25 ENERGY STORAGE↗
DOE OSTI2025

Mechanistic Studies of Ligand Substitution, Linkage Isomerism, and Insertion Reactions in Electron Rich Pd(II) Complexes of a Zwitterionic Diimine Ligand

We have prepared cationic palladium complexes possessing a new zwitterionic ligand bis-N,N’–1-(2,4,6-triphenylpyridyl) oxalamide [(N ^ N)Pd(Me)(L)] + [BArF] - , (BArF=3,5-(CF 3 ) 2 C 6 H 3 , L=NCMe, CO). The structure of [(N ^ N)Pd(Me)(CO)] + [BArF] - was determined by X-ray diffraction analysis. Energy Decomposition Analysis (EDA) indi-cates this N ^ N zwitterionic ligand is more electron-donating relative to bidentate diimine ligands. Low temperature NMR analysis shows the existence of linkage isomers with the N ^ N isomer the most stable. Structures were assigned using NMR and DFT analysis. Barriers to interconversion of isomers are ΔG ‡ = 10-12 kcal/mol. Kinetics of acetoni-trile displacement from [(N ^ N)Pd(Me)(NCCH 3 )] + [BArF] - by CD 3 CN, ethylene and t Bu 3 P were measured and mechanisms of exchange determined. The ethylene complex, [(N ^ N)Pd(Me)(C 2 H 4 )] + was generated at -45 °C, and the barrier of migrato-ry insertion determined at 0 °C (ΔG ‡ = 23.4 kcal/mol) and compared to related diimine complexes. The methyl carbonyl complex undergoes migratory insertion in the presence of CO at -70 to -55 °C (ΔG ‡ = ca. 15.7 kcal/mol) to yield the acyl carbonyl complex. Furthermore, the neutral bis-trimethylsilylmethyl complex [(N ^ N)Pd(CH 2 SiMe 3 ) 2 was prepared and characterized by X-ray diffraction analysis. It displays dynamic behavior at very low temperatures in the NMR spectrum (-90 °C, ΔG ‡ =7.9 kcal/mol) which, supported by DFT analysis, is ascribed to rotation of the bulky -CH 2 SiMe 3 groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Delineating the kinetic limitations of Mn 2+/3+ redox in LiMn x Fe 1−x PO 4 cathodes for lithium-ion batteries

LiMn x Fe 1−x PO 4 (LMFP) cathodes offer higher energy density than LiFePO 4 due to a higher operating voltage. However, the kinetic limitations of the Mn 2+/3+ redox couple in LMFP restrict its practically achievable capacity and hinder the ability to achieve high energy density. While the shortcomings of Mn 2+/3+ redox are recognized, its behavior and the factors that impact it remain to be fully understood. We present here an in-depth kinetics study of LMFP by utilizing novel techniques, such as chronoamperometry and galvanostatic electrochemical impedance spectroscopy. Compared to moderate-Mn LMFP (40–60% Mn), high-Mn LMFP (80% Mn) experiences reduced capacity, poor rate capability, and heightened impedance during Mn 2+/3+ redox. The oxidation of Mn 2+ to Mn 3+ becomes more resistive during charge due to the formation of Jahn–Teller active Mn 3+ and the increasing charge-transfer insulating behavior of Mn x Fe 1−x PO 4 . However, the impedance associated with Mn 3+ to Mn 2+ reduction remains constant during discharge in the entire region. The protracted Mn2+ oxidation in high-Mn LMFP results in excessive impedance compared to that in moderate-Mn LMFP, even at low C-rates and high cycling temperatures. Despite the promise of high energy density, the extreme kinetic limitations inherent to high-Mn LMFP present a barrier.

25 ENERGY STORAGE↗
DOE OSTI2023

Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

Atomic-precision advanced manufacturing enables unique silicon quantum electronics built on quantum dots fabricated from small numbers of phosphorus dopants. The number of dopant atoms comprising a dot plays a central role in determining the behavior of charge and spin confined to the dots and thus overall device performance. Here in this work, we use both theoretical and experimental techniques to explore the combined impact of lithographic variation and stochastic kinetics on the number of P incorporations in quantum dots made using these techniques and how this variation changes as a function of the size of the dot. Using a kinetic model of PH3 dissociation augmented with novel reaction barriers, we demonstrate that for a 2 × 3 silicon dimer window the probability that no donor incorporates goes to zero, allowing for certainty in the placement of at least one donor. However, this still comes with some uncertainty in the precise number of incorporated donors (either one or two), and this variability may still impact certain applications. We also examine the impact of the size of the initial lithographic window, finding that the incorporation fraction saturates to δ-layer-like coverage as the circumference-to-area ratio decreases. We predict that this incorporation fraction depends strongly on the dosage of the precursor and that the standard deviation of the number of incorporations scales as ~√n, as would be expected for a sequence of largely independent incorporation events. Finally, we characterize an array of 36 experimentally prepared multidonor 3 × 3 nm lithographic windows with scanning tunneling microscopy, measuring the fidelity of the lithography to the desired array and the final location of PH x fragments within these lithographic windows. We use our kinetic model to examine the expected variability due to the observed lithographic error, predicting a negligible impact on incorporation statistics. We find good agreement between our model and the inferred incorporation locations in these windows from scanning tunneling microscope measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗