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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,459 records · Page 81
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Optimizing the accuracy of viscoelastic characterization with AFM force–distance experiments in the time and frequency domains

Atomic Force Microscopy (AFM) force-distance (FD) experiments have emerged as an attractive alternative to traditional micro-rheology measurement techniques owing to their versatility of use in materials of a wide range of mechanical properties. Here, we show that the range of time dependent behaviour which can reliably be resolved from the typical method of FD inversion (fitting constitutive FD relations to FD data) is inherently restricted by the experimental parameters: sampling frequency, experiment length, and strain rate. Specifically, we demonstrate that violating these restrictions can result in errors in the values of the parameters of the complex modulus. In the case of complex materials, such as cells, whose behaviour is not specifically understood a priori, the physical sensibility of these parameters cannot be assessed and may lead to falsely attributing a physical phenomenon to an artifact of the violation of these restrictions. We use arguments from information theory to understand the nature of these inconsistencies as well as devise limits on the range of mechanical parameters which can be reliably obtained from FD experiments. The results further demonstrate that the nature of these restrictions depends on the domain (time or frequency) used in the inversion process, with the time domain being far more restrictive than the frequency domain. Lastly, we demonstrate how to use these restrictions to better design FD experiments to target specific timescales of a material's behaviour through our analysis of a polydimethylsiloxane (PDMS) polymer sample.

information theory↗
DOE OSTI2024

Midgap state requirements for optically active quantum defects

Abstract Optically active quantum defects play an important role in quantum sensing, computing and communication. The electronic structure and the single-particle energy levels of these quantum defects in the semiconducting host have been used to understand their optoelectronic properties. Optical excitations that are central for their initialization and readout are linked to transitions between occupied and unoccupied single-particle states. It is commonly assumed that only quantum defects introducing levels well within the band gap and far from the band edges are of interest for quantum technologies as they mimic an isolated atom embedded in the host. In this perspective, we contradict this common assumption and show that optically active defects with energy levels close to the band edges can display similar properties. We highlight quantum defects that are excited through transitions to or from a band-like level (bound exciton) such as the T center and Se S i + in silicon. We also present how defects such as the silicon split-vacancy in diamond can involve transitions between localized levels that are above the conduction band or below the valence band. Loosening the commonly assumed requirement on the electronic structure of quantum defects offers opportunities in quantum defects design and discovery especially in smaller band gap hosts such as silicon. We discuss the challenges in terms of operating temperature for photoluminescence or radiative lifetime in this regime. We also highlight how these alternative type of defects bring their own needs in terms of theoretical developments and fundamental understanding. This perspective clarifies the electronic structure requirement for quantum defects and will facilitate the identification and design of new color centers for quantum applications especially driven by first principles computations.

Xiong, Yihuang (ORCID:0000000178096047)↗
DOE OSTI2020

Magnetic and transport properties of amorphous, B 2 and L 2 1 Co 2 MnGa thin films

We have studied the magnetic and transport properties of Co 2 MnGa (CMG) thin films grown on MgO(100) substrates in terms of their chemical evolution from amorphous to ordered L 2 1 phases at the substrate temperature T s during the thin film deposition. Interestingly, the chemical order and magnetic properties sharply change depending on T s . The CMG film deposited at T s = 550 °C exhibits the L 2 1 -ordered structure and the magnetization of 3.5 μ B /f.u., while the CMG film deposited at T s = 300 °C shows a B 2-ordered structure and a relatively lower magnetization of 3 μ B /f.u., possibly due to the Mn–Mn antiferromagnetic interactions. A metallic behavior of the electrical resistivity appeared in the CMG film deposited at T s = 550 °C, whereas the semiconducting behavior appeared in the CMG films deposited at 300 °C and room temperature. Moreover, we found that the absolute value of α = d(Δ ρ )/d( T 1/2 ) in the low-temperature range below about 20 K is a measure to evaluate the degree of the chemical disorder. In a Hall effect measurement, the L 2 1 -ordered CMG film obtained at T s = 550 °C shows a sizable anomalous Hall resistivity of 15 µ Ω cm. This study unveils the relation between T s and atomic ordering, providing a new pathway for optimizing the chemical order.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Anomalous size effect on yield strength enabled by compositional heterogeneity in high-entropy alloy nanoparticles

High-entropy alloys (HEAs), although often presumed to be random solid solutions, have recently been shown to display nanometer-scale variations in the arrangements of their multiple chemical elements. Here, we study the effects of this compositional heterogeneity in HEAs on their mechanical properties using in situ compression testing in the transmission electron microscope (TEM), combined with molecular dynamics simulations. We report an anomalous size effect on the yield strength in HEAs, arising from such compositional heterogeneity. By progressively reducing the sample size, HEAs initially display the classical “smaller-is-stronger” phenomenon, similar to pure metals and conventional alloys. However, as the sample size is decreased below a critical characteristic length (~180 nm), influenced by the size-scale of compositional heterogeneity, a transition from homogeneous deformation to a heterogeneous distribution of planar slip is observed, coupled with an anomalous “smaller-is-weaker” size effect. Atomic-scale computational modeling shows these observations arise due to compositional fluctuations over a few nanometers. These results demonstrate the efficacy of influencing mechanical properties in HEAs through control of local compositional variations at the nanoscale.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Valence band electronic structure of the van der Waals ferromagnetic insulators: VI 3 and CrI 3

Ferromagnetic van der Waals (vdW) insulators are of great scientific interest for their promising applications in spintronics. It has been indicated that in the two materials within this class, CrI 3 and VI 3 , the magnetic ground state, the band gap, and the Fermi level could be manipulated by varying the layer thickness, strain or doping. To understand how these factors impact the properties, a detailed understanding of the electronic structure would be required. However, the experimental studies of the electronic structure of these materials are still very sparse. Here, we present the detailed electronic structure of CrI 3 and VI 3 measured by angle-resolved photoemission spectroscopy (ARPES). Our results show a band-gap of the order of 1 eV, sharply contrasting some theoretical predictions such as Dirac half-metallicity and metallic phases, indicating that the intra-atomic interaction parameter (U) and spin-orbit coupling (SOC) were not properly accounted for in the calculations. We also find significant differences in the electronic properties of these two materials, in spite of similarities in their crystal structure. In CrI 3 , the valence band maximum is dominated by the I 5p, whereas in VI 3 it is dominated by the V 3d derived states. Our results represent valuable input for further improvements in the theoretical modeling of these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Computational and experimental analysis of structural and Thermophysical properties of LiX-KX (X = chloride, iodide, or bromide) molten salts

Molten salts containing lithium (Li) and potassium (K) halides, including chlorides (Cl), bromides (Br), and iodides (I), are pivotal in advanced technological applications including nuclear reactor technologies, thermal batteries, and industrial pyrochemical processes. Despite their significance, the availability of the temperature-dependent structural and thermophysical properties of these molten salts remain scarce. Here, this study addresses this knowledge gap by predicting and measuring the key properties such as coordination number, radial distribution function, density, heat capacity, and volumetric thermal expansion of molten LiI-KI, LiBr-KBr and LiCl-KCl eutectic mixtures. Utilizing ab initio molecular dynamics (AIMD) simulations, we predict these properties of LiX-KX (X=Br,I, Cl) across various temperatures, with chlorides as a benchmark. Experimental measurements using Archimedes methods and Differential Scanning Calorimetry validate the densities and heat capacities of these molten salts. Our comprehensive analysis of the structural and thermophysical properties provides critical insights into the behavior of these molten salts at various temperatures, enhancing the understanding necessary for their application in advanced technologies.

36 - MATERIALS SCIENCE↗
DOE OSTI2022

Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics

Conventional machine-learning (ML) models in computational chemistry learn to directly predict molecular properties using quantum chemistry only for reference data. While these heuristic ML methods show quantum-level accuracy with speeds several orders of magnitude faster than traditional quantum chemistry methods, they suffer from poor extensibility and transferability; i.e., their accuracy degrades on large or new chemical systems. Incorporating quantum chemistry frameworks into the ML models directly solves this problem. Here we take the structure of semiempirical quantum mechanics (SEQM) methods to construct dynamically responsive Hamiltonians. SEQM methods use empirical parameters fitted to experimental properties to construct reduced-order Hamiltonians, facilitating much faster calculations than ab initio methods but with compromised accuracy. By replacing these static parameters with machine-learned dynamic values inferred from the local environment, we greatly improve the accuracy of the SEQM methods. Trained on molecular energies and atomic forces, these dynamically generated Hamiltonian parameters show a strong correlation with atomic hybridization and bonding. Trained with only about 60,000 small organic molecular conformers, the resulting model retains interpretability, extensibility, and transferability when testing on much larger chemical systems and predicting various molecular properties. Overall, this work demonstrates the virtues of incorporating physics-based descriptions with ML to develop models that are simultaneously accurate, transferable, and interpretable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Experimental Study of the Fundamental Properties of Warm Dense Mixtures

The aim of the proposed research was to provide a multi-scale study of the properties of warm dense hydrocarbons, by studying the thermodynamic properties through the equation of state and the microscopic properties by x-ray scattering. Understanding the fundamental properties of warm dense mixtures is an intellectual challenge due to the complexity of the system. Unlike liquids or gases, where constituent particle interactions occur through collisions or bonding between valence electrons, in these strongly coupled systems the atoms will be partially ionized and compressed so tightly together that interactions between the inner core electrons can play a role in the systems chemistry. Advances in computational capabilities and development of new theoretical models have been used to predict the properties of mixtures but there is currently no experimental data of the fundamental interaction between the particles in mixtures to test these predictions against. The proposed research was to experimentally investigate the interaction of the different species in hydrocarbons by measuring the compressibility of substances with different carbon and hydrogen ratios and the complexity of the microscopic interactions through elastic and inelastic x-ray scattering. To study the bulk properties of warm dense hydrocarbons we established the Warm Dense Matter Research Laboratory (WDMRL) in the Institute for Shock Physics at Washington State University. The goal was for experiments in the WDMRL to determine shock loading conditions of interest in the hydrocarbon mixtures. We planned on using Hugoniot EOS measurements and a range of carbon and hydrogen concentrations to determine conditions when the EOS of the mixture varied significantly from that of the classical mixing model. Even though shock transit measurements through aluminum foils suggested pressures upto 400GPa, the experiments in the WDMRL were unsuccessful in getting usable shockwave compression data above 100GPa in polystyrene which was below the pressure of interest for hydrocarbon mixtures (>200GPa). To complete the project, we tested a technique using x-ray phase contrast imaging to map the location of tracer layers in a test sample of polycarbonate to record the material motion in dynamically compressed samples. A technique that will be useful for future warm dense matter experiments. These experiments used <200nm gold layers in polycarbonate samples to measure the material velocity and shock speed using x-ray phase contrast imaging. These results were compared to continuum surface measurements performed at ISP and show that the tracer layer technique can measure hydrodynamic properties accurately in dynamically compressed materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Calculation and interpretation of classical turning surfaces in solids

Abstract Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs). They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. They can also appear at a monovacancy in a metal. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. Nonetheless, a strong correlation with insulating behavior can still be inferred. Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.

Chemistry↗
DOE OSTI2022

Copper Single Atom-Triggered Niobia–Ceria Catalyst for Efficient Low-Temperature Reduction of Nitrogen Oxides

To reduce nitrogen oxide (NO x ) emission from diesel engines in the cold-start process benefitting the atmospheric environment, catalysts with superior low-temperature NO x removal efficiency are highly demanded. Herein, we report an efficient Nb 2 O 5 /CuO/CeO 2 (NbCuCe) oxide catalyst for the selective catalytic reduction (SCR) of NO x , showing much higher DeNO x activity below 200 °C, superior sulfur resistance, faster response, and much less NH 3 slip than the state-of-the-art Cu-CHA zeolite catalyst. Additionally, atomically dispersed Cu species facilitate the strong interaction between Cu and the Nb/Ce base catalyst, which significantly improves the low-temperature redox properties at Cu–O–Ce sites and NH 3 adsorption/activation at Nb–O–Cu sites, thus contributing to the superior SCR performance of NbCuCe at low temperatures. The developed NbCuCe catalyst is highly promising for efficient DeNO x from cold-start diesel engines and can be coupled with Cu-CHA to achieve a broad operation temperature window.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Reactivity descriptors in acid catalysis: acid strength, proton affinity and host–guest interactions

Brønsted acids mediate chemical transformations via proton transfer to bound species and interactions between the conjugate anion and bound cationic intermediates and transition states that are also stabilized by van der Waals forces within voids of molecular dimensions in inorganic hosts. This Feature Article describes the relevant descriptors of reactivity in terms of the properties of acids and molecules that determine their ability to donate and accept protons and to reorganize their respective charges to optimize their interactions at bound states. The deprotonation energy (DPE) of the acids and the protonation energy (Eprot) of the gaseous analogs of bound intermediates and transition states reflect their respective properties as species present at non-interacting distances. These properties accurately describe the reactivity of acids of a given type, such as polyoxometalates (POM) with a given type of addenda atom but different central atoms and heterosilicates, for different families of reactions. They do not fully capture, however, differences among acid types (e.g., Mo and W POM, heterosilicates, mineral acids) for diverse types of chemical transformations (e.g., elimination, isomerization, dimerization, condensation). The incompleteness of such descriptors reflects their inability to describe how protonated molecular species and conjugate anions restructure their respective charges when present as a binding pair at interacting distances. Such interaction energies represent electrostatic forces that depend on charge distributions in the cations and anions and the ability to reorganize the distributions to maximize the interactions. In the case of deprotonation, the electrostatic and charge reorganization components of DPE for various acids solely reflect the ability of the conjugate anion to accept and distribute the negative charge, a characteristic unique of each type of solid acid and specifically of the composition of its extended conjugate anion framework. The energy required to accept and rearrange the positive charge in bound intermediates and transition states reflects, in turn, their respective ability to recover the ionic and covalent components of DPE, the energy required to detach proton from conjugate anions. The DPE components and the recovery fractions together lead to a modified DPE, which captures only the part of DPE that remains unrecovered by the ion-pair interactions at bound intermediates and transition states, as the unifying descriptor for broad families of acids and reactions. The electrostatic and charge reorganization energies involved in these general descriptors are placed in historical context by assessing their connections to the heuristics of hard–soft acid–base displacements. Further development of these concepts requires benchmarking and extension of electrostatic and reorganization components of energies for a more diverse set of reaction types and acid families and advancement of methods for more efficient calculations of electrostatic interactions. Reactivity descriptors must also account for dispersive interactions between host cavities and guest molecules, requiring a framework analogous to the one described here for ion-pair interactions; these dispersive interactions depend on the fit between their shapes and sizes as well as their ‘‘structural stiffness’’ that determines the ability to modify the shapes of molecules and voids to minimize free energy. Entropy considerations and estimates of their dependence on properties of catalysts and molecules are also required for accurately determining Gibbs free energies that ultimately determine reaction rates.

Deshlahra, Prashant↗
DOE OSTI2024

Manufacturing Oxide Dispersion Strengthened (ODS) steel plate via cold spray and friction stir processing

Oxide dispersion strengthened (ODS) steels, traditionally fabricated by ball milling and conventional powder metallurgy techniques to achieve bulk form, followed by intricate rolling and thermal treatment steps to achieve plate or sheet form. Here, we present a novel processing route that combines cold spray (CS) with friction stir processing (FSP) to manufacture ODS steel plate directly from gas atomization reaction synthesis (GARS)-prepared powder, thus no rolling steps involved. Microstructural and mechanical characterizations were performed to assess the quality and properties of the resulting ODS steel plate. Our findings demonstrate that the slightly porous CS deposited layer was fully consolidated after FSP, yielding a fully dense ODS steel plate that exhibited a favorable tradeoff between strength and ductility upon extraction from the substrate. Furthermore, through microstructural analysis, we revealed the presence of an appreciable density (∼10 22 /m 3 ) of nano-sized oxide particles, with the majority being smaller than 5 nm via the combined CS + FSP fabrication route. This work serves as a first proof-of-concept demonstration of the manufacturing approach described herein, offering a possible alternative route for producing ODS steel plates.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Preparation of Ultrathin Gold Films with Subatomic Surface Roughness

Nanoscale device fabrication requires control over film growth at the atomic scale. Growth conditions must be tuned in consideration of interface parameters like chemical bonding, surface free energy, and lattice matching. In metals, electronic properties may also be utilized for control of physical parameters. Quantum size effects can induce metals to spontaneously form specific shapes and sizes according to their electronic structure. Unfortunately, such electronic growth is generally known only for a few systems and is typically only stable under cryogenic conditions. In this work, we explore a recently discovered class of electronic growth systems in which metal films are grown upon the relatively inert surfaces of van der Waals crystals. In this class of materials, the electronic growth is highly stable at room temperature and actually requires higher temperature annealing to achieve proper equilibrium. We work with the Au/MoS 2 system, which shows excellent stability and can readily form discrete and atomically flat nanostructures. Here, we show how the electronic growth modes facilitate the formation of atomically flat films with nanometer scale thickness. Here, the surface roughness of these films was found to be less than a single atom over several square microns, creating nearly perfect surfaces for studies of self-assembled monolayers or other applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Correlating microstructure and mechanical properties of harvested high dose Zorita light water reactor internals

Here, in this study, microstructural studies and micro-mechanical testing of an ex-plant material harvested from the decommissioned pressurized water reactor (PWR) is carried out. Irradiated 304 stainless steel (SS) components were harvested by the Electric Power Research Institute, U.S. Nuclear Regulatory Commission, and members of the José Cabrera Nuclear Power Station (Zorita) in Spain. The bi-crystalline micro-tensile specimens, atom probe tomography (APT) tips, and transmission electron microscopy (TEM) lamellae were fabricated from the baffle plate materials irradiated to 0.05, 15 and 50 dpa to elucidate microstructural, microchemical, and local mechanical properties changes as a function of dose. TEM and APT studies reveal radiation induced Ni, Cr, and Si rich precipitates in the 15 dpa sample that become smaller and partially redissolve into the matrix of the 50 dpa sample (decreasing size and number density). Dislocation loop and cavity number density and size were quantified as a function of dose as well as swelling. Intergranular Ni and Si enrichments with concomitant Fe and Cr depletion were observed in the 15 dpa sample and were more pronounced in the 50 dpa sample. Micro-tensile testing performed in the scanning electron microscope (SEM) at room temperature and 300 °C shows that the material's local yield strength and ultimate tensile strength decreases with increased dose and elevated test temperature and provides further insights via localized strain mapping. Current and previous mechanical data was compared with calculated values using the dispersed barrier hardening model with inputs of dislocation loops, precipitates, and cavities from microstructural characterization.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Impact of controlled prewetting on part formation in binder jet additive manufacturing

Binder jetting is an additive manufacturing process that bonds powder through selectively depositing binder by inkjet printing. The part is then extracted and densified by sintering and/or infiltration. The process offers low costs and fast build rates, but properties can be poor due to residual porosity after sintering. The inkjet printing process may contribute to this residual porosity by creating large pores. The droplet kinetic energy ejects some powder particles from the bed and rearranges others. Particle ejection and rearrangement are theorized to create porous regions in binder-jetted parts. In this work, small amounts of moisture are added to the spread powder before printing and the impact on part formation, part properties, and printing parameters measured with varied droplet spacing, droplet velocity, and print frequency. Moisture is added by applying an atomized fluid mixture to the powder between layer spreading and binder printing. The fluid mixture partially evaporates but leaves a stable residue to increase cohesion and enhance imbibition. Moisture addition to the powder increases the range of droplet spacings for line formation while reducing particle ejection, powder rearrangement, and balling in layer and multilayer parts. Excessive moisture addition decreases the effective saturation of printed lines, but saturation in 3D parts is less impacted. Increased surface roughness in the first few layers of a print was also mitigated with prewetting. Finally, high-speed X-ray imaging verified prewetting reduction in particle ejection and rearrangement.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Atomistic modeling of energy band alignment in CdSeTe surfaces

Atomistic modeling based on Desnity Functional Theory (DFT)- 1/2 method coupled with surface Green’s function has been employed to investigate the energy band alignment results in cadmium selenium telluride (CdSeTe) surfaces. The structural and electronic properties of the bulk ternary alloy were established before cleaving the CdSeTe low index surface facets. The dependency of atomic-scale electronic features on different plane orientations was explored by studying the energy band alignment diagrams in the unreconstructed and reconstructed surfaces. While the low index CdSeTe surface geometry reconstructions replicate the CdTe surface geometries, the energy band alignment features of the unreconstructed and reconstructed CdSeTe surfaces differ from those observed in CdTe low index surfaces. The structurally relaxed reconstructed CdSeTe surface results in purely flat bands as opposed to an internal cusp feature observed in CdTe surfaces. The presence of an internal energy cusp in CdTe(111) surfaces is expected to play a key role in enhancing the hole charge transport towards the back of CdTe-only solar cell device and the absence of such feature in CdSeTe surface may explain one of the reason for the lower performance of CdSeTe-only solar cell seen experimentally.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Structural evolution and magnetic hardness of (Sm,Zr)(Fe,Co,Ti) 12 alloy particles via reduction-diffusion

The quest for achieving high coercivity in Sm(Fe,Co,Ti) 12 alloys, despite their inherent strong magnetocrystalline anisotropy, has posed significant challenges. Recently, (Sm,Zr)(Fe,Co,Ti) 12 monocrystalline particles have exhibited coercivity μ 0 H c > 1.2 T, showcasing promising prospects and significant potential for both manufacturing and research endeavors. This study delves into the structural evolution of (Sm,Zr)(Fe,Co,Ti) 12 (1:12) alloy particles made via the calciothermic reduction-diffusion synthesis process as influenced by the molar ratios of Ca atoms to O 2- ions (Ca/O), annealing time and annealing temperature. Critical insight that informs conditions to optimize the magnetic response is gained via systematic experimentation and advanced electron microscopy. Complex structural features, including core-shell morphologies and intricate multiphase compositions within individual particles, are unveiled. An optimal Ca/O ratio of 1.30 produces particles with a coercivity up to μ 0 H c = 1.63 T, while higher Ca/O ratios induce the formation of a Sm-rich TbCu 7 -type (1: 7 ) phase, which only partially transforms into the desired 1:12 phase during annealing. Persistent remnants of the 1:7 phase locally impact atomic structure, particle morphology, and coercivity. Furthermore, these findings underscore the complex interplay between synthesis parameters, resulting structures, and magnetic properties, informing the design and optimization of high-performance permanent magnets comprised of the (1:12) compound.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Teaching Nonradiative Transitions with MATLAB and Python

Nonradiative transitions are changes in energy states of atoms, ions, or molecules that do not involve the emission or absorption of photons. Despite their importance in understanding luminescent properties and photochemical reaction mechanisms, nonradiative transitions are rarely given more than a qualitative overview in undergraduate and even graduate physical chemistry curricula. To supplement the coverage of nonradiative transition topics, we provide here a set of active learning exercises to help students develop an intuitive understanding of the factors that determine the rate of nonradiative transitions. Here, we start by outlining the theoretical background through the formulations of the Franck–Condon factor and its relation to the rate of nonradiative transition. We then introduce three teaching modules, with associated MATLAB and Python codes, to explore how (1) the excited state nuclear displacement, (2) the electronic energy gap between excited and ground state and (3) the excited/ground state vibrational mode frequencies affect the magnitude of the Franck–Condon factor and thereby the rate of nonradiative transitions. The wave function overlap plots that accompany all teaching modules provide direct visualization of the effect of input parameters on the magnitude of Franck–Condon overlap integral.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗