Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Vacancies”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Modeling kinetic effects of charged vacancies on electromechanical responses of ferroelectrics: Rayleighian approach

Understanding the time-dependent effects of charged vacancies on the electromechanical responses of materials is at the forefront of research for designing materials exhibiting metal-insulator transitions and memristive behavior. A Rayleighian approach is used to develop a model for studying the nonlinear kinetics of the reaction leading to generation of vacancies and electrons via the dissociation of vacancy-electron pairs. Also, diffusion and elastic effects of charged vacancies are considered to model polarization-electric potential and strain-electric potential hysteresis loops. The model captures multiphysics phenomena by introducing couplings among polarization, the electric potential, stress, strain, and concentrations of charged (multivalent) vacancies and electrons (treated as classical negatively charged particles), where the concentrations can vary due to association-dissociation reactions. A derivation of coupled time-dependent equations based on the Rayleighian approach is presented. Three limiting cases of the governing equations are considered, highlighting the effects of (1) nonlinear reaction kinetics on the generation of charged vacancies and electrons, (2) Vegard's law (i.e., the concentration-dependent local strain) on asymmetric strain-electric potential relations, and (3) coupling between a fast component and the slow component of the net polarization on the polarization-electric-field relations. The Rayleighian approach discussed in this work should pave the way for developing a multiscale modeling framework in a thermodynamically consistent manner while capturing multiphysics phenomena in ferroelectric materials. Published by the American Physical Society 2025

Kumar, Rajeev (ORCID:0000000194943488)↗
DOE OSTI2024

Oxygen vacancy migration and impact on high voltage DC polarization in 0.8BaTiO 3 –0.2BiZn 0.5 Ti 0.5 O 3

Electrical polarization and defect transport are examined in 0.8BaTiO 3 –0.2BiZn 0.5 Ti 0.5 O 3 , an attractive capacitor material for high power electronics. Oxygen vacancies are suggested to be the majority charge carrier at or below 250°C with a grain conduction hopping activation energy of 0.97 eV and 0.92 eV for thermally stimulated depolarization current (TSDC) and impedance spectroscopy measurements, respectively. At higher temperature, thermally generated electronic conduction with an activation energy of 1.6 eV is dominant. Significant oxygen vacancy concentration is indicated (up to ~1%) due to cation vacancy formation (i.e., acceptor defects) from observed Bi (and likely Zn) volatility. Oxygen vacancy diffusivity is estimated to be 10 -12.8 cm 2 /s at 250°C. Low diffusivity and high activation energies are indicative of significant defect interactions. Dipolar oxygen vacancy defects are also indicated, with an activation energy of 0.59 eV from TSDC measurements. In conclusion, the large oxygen vacancy content leads to a short lifetime during high voltage (30 kV/cm), high temperature (250°C) direct current (DC) electrical measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Cobalt-free and high-rate stable 5V lithium nickel manganese oxide spinel cathodes enabled via surface oxygen vacancies

Spinel LiNi 0.5 Mn 1.5 O 4 offers both the high-rate, low-cost and safety advantages of LiFePO 4 and the high energy density of LiNiₓMnᵧCo₁₋ₓ₋ᵧO₂ and LiNiₓCoᵧAlzO₂ cathodes. However, the large operating voltage of these materials induces electrolyte oxidation, which degrades the interface and drives Mn dissolution. These reactions are further exacerbated at high rates due to temperature rise. In this study, we discover that ammoniacal treatment followed by annealing introduces a high density of oxygen vacancies in the “near-surface region” of LiNi 0.5 Mn 1.5 O 4 particles. These vacancies release electrons changing the oxidation state of Mn and suppressing its tendency to oxidize the electrolyte. Further, these vacancies enhance the electrode’s electronic conductivity (by ∼3-fold) and Li + diffusivity (by ∼2-fold) greatly improving charge transport, especially when operated at high rates. This results in an across-the-board improvement in self-discharge, specific capacity, energy density, rate capability, coulombic efficiency and cycling stability. When cycled at ∼200 mA g −1 , the capacity fade averaged over 3000 cycles for the surface vacancy-enriched material is ∼0.0167% per cycle compared to an order of magnitude higher fade rate for the baseline material. In conclusion, these findings reveal the potential of targeted surface oxygen vacancy doping to develop cobalt-free and high energy density cathodes that tolerate fast charging and deliver improved cycle life.

Cobalt-free cathodes↗
DOE OSTI2022

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

Here, we develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch. We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Engineering the fracture resistance of 2H-transition metal dichalcogenides using vacancies: An in-silico investigation based on HRTEM images

Vacancy engineering of 2H-transition metal dichalcogenides (2H-TMDs) has recently attracted great attention due to its potential to fine-tune the phonon and opto-electric properties of these materials. From a mechanical perspective, this symmetry-breaking process typically reduces the overall crack resistance of the material and adversely affects its reliability. However, vacancies can trigger the formation of heterogeneous phases that synergistically improve fracture properties. In this study, using MoSe2 as an example, we characterize the types and density of vacancies that can emerge under electron irradiation and quantify their effect on fracture. Molecular dynamic (MD) simulations, employing a re-parameterized Tersoff potential capable of accurately capturing bond dissociation and structural phase changes, reveal that isolated transition metal monovacancies or chalcogenide divacancies tend to arrest the crack tip and hence enhance the monolayer toughness. In contrast, isolated chalcogenide monovacancies do not significantly affect toughness. The investigation further reveals that selenium vacancy lines, formed by high electron dose rates, alter the crack propagating direction and lead to multiple crack kinking. Using atomic displacements and virial stresses together with a continuum mapping, displacement, strain, and stress fields are computed to extract mechanistic information, e.g., conditions for crack kinking and size effects in fracture events. The study also reveals the potential of specific defect patterns, “vacancy engineering,” to improve the toughness of 2H-TMDs materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The deep-acceptor nature of the chalcogen vacancies in 2D transition-metal dichalcogenides

Abstract Chalcogen vacancies in the semiconducting monolayer transition-metal dichalcogenides (TMDs) have frequently been invoked to explain a wide range of phenomena, including both unintentional p-type and n-type conductivity, as well as sub-band gap defect levels measured via tunneling or optical spectroscopy. These conflicting interpretations of the deep versus shallow nature of the chalcogen vacancies are due in part to shortcomings in prior first-principles calculations of defects in the semiconducting two-dimensional TMDs that have been used to explain experimental observations. Here we report results of hybrid density functional calculations for the chalcogen vacancy in a series of monolayer TMDs, correctly referencing the thermodynamic charge transition levels to the fundamental band gap (as opposed to the optical band gap). We find that the chalcogen vacancies are deep acceptors and cannot lead to n-type or p-type conductivity. Both the (0/−1) and (−1/−2) transition levels occur in the gap, leading to paramagnetic charge states S = 1 / 2 and S = 1, respectively, in a collinear-spin representation. We discuss trends in terms of the band alignments between the TMDs, which can serve as a guide to future experimental studies of vacancy behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Vacancy-mediated transport and segregation tendencies of solutes in fcc nickel under diffusional creep: A density functional theory study

The Nabarro-Herring (NH) diffusional creep theory postulates the vacancy-mediated transport of atoms under a stress gradient as the creep mechanism under low-stress and high-temperature conditions. In multicomponent alloys, we premise that this stress-assisted flow of vacancies to and from grain boundaries will produce elemental segregation. An observation of such segregation, validated with theoretical predictions, can provide the necessary experimental evidence for the occurrence of NH creep. Theoretical calculations of the segregation tendencies via analyzing the dominant solute diffusion mechanisms and the difference in diffusivities of the elements are therefore essential. To this end, this study applies density functional theory calculations of migration barriers and solute-vacancy binding energies as input to the self-consistent mean-field theory to assess the vacancy-mediated diffusion mechanisms, transport coefficients, and segregation tendencies of Co, Cr, Mo, Re, Ta, and W solutes in face-centered-cubic Ni. We find Co, Re, and W to be slow diffusers at high temperatures and Cr, Mo, and Ta to be fast diffusers. Further analysis shows that the slow diffusers tend to always enrich at vacancy sinks over a wide range of temperatures. In contrast, the fast diffusers show a transition from depletion to enrichment as the temperature lowers. Furthermore, our analysis of the segregation tendencies under tensile hydrostatic strains shows that slow diffusers are largely unaffected by the strain and favor enrichment. On the other hand, the fast diffusers exhibit high sensitivity to strain and their segregation tendency can transition from depletion to enrichment at a given temperature. Finally, the transport coefficients calculated in this work are expected to serve as input to mesoscale microstructure models to provide a more rigorous assessment of solute segregation under NH creep conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

In Situ Scattering Studies of Superconducting Vacancy‐Ordered Monoclinic TiO Thin Films

Abstract The structural and transport properties of vacancy‐ordered monoclinic superconducting titanium oxide (TiO) thin films grown by molecular beam epitaxy are investigated. The evolution of the crystal structure during growth is monitored by in situ synchrotron X‐ray diffraction. Long‐range ordering of Ti and O vacancies in the disordered cubic phase stabilizes the vacancy‐ordered monoclinic TiO phase. The reduced structural disorder arising from vacancy‐ordering is correlated with a superconductor‐metal transition (SMT) in contrast to the superconductor‐insulator transition (SIT) observed in cubic TiO, orthorhombic Ti 2 O 3 , and the Magneli γ − Ti 3 O 5 and γ − Ti 4 O 7 phase. Magnetoresistance measurements for the SIT phases indicate superconducting fluctuations persisting in the normal phase. These results confirm the role of disorder related to Ti and O vacancies and structural inhomogeneity in determining the electronic properties of the normal state of titanium oxide‐based superconductors.

Baksi, Merve↗
DOE OSTI2024

Te Vacancy‐Driven Anomalous Transport in ZrTe 5 and HfTe 5

Abstract The strongly sample‐dependent anomalous transport properties observed in the layered Dirac materials ZrTe 5 and HfTe 5 are known to strongly correlate with the presence of Te vacancies. One phenomenon, a negative longitudinal magnetoresistance (NLMR), is widely speculated to be a signature of broken chiral symmetry. However, the role of electronic structure in the sample dependence of the transport properties of these materials is poorly understood. This prompts the question as to whether the NLMR is a genuine signature of the chiral anomaly in ZrTe 5 and HfTe 5 . In this work, the effect of Te vacancies on the electronic structure of ZrTe 5 and HfTe 5 is investigated via first‐principles calculations. Te vacancies serve two purposes: modification of the cell volume via effective compressive strain and production of local changes to the electronic structure. The reorganization of the electronic structure near the Fermi energy indicates that Te vacancies can rationalize conflicting reports in spectroscopic and transport measurements that have remained elusive in prior first‐principles studies. These results show that Te vacancies contribute, in part, to the anomalous transport properties of ZrTe 5 and HfTe 5 but, critically, do not eliminate the possibility of a genuine manifestation of the chiral anomaly in these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Vacancy-mediated complex phase selection in high entropy alloys

Phase selection in Ti-Zr-Hf-Al high-entropy alloys was investigated by in-situ high-energy x-ray diffraction, single-crystal x-ray diffraction, and KKR-CPA electronic-structure methods that address disorder and vacancies, predicting formation enthalpy and chemical short-range order (SRO). Samples with varying Al content were synthesized, characterized, and computationally assessed to ascertain the composition-dependent phase selection, as increased Al content often acts as a stabilizer of a body-centered-cubic structure. Equiatomic TiZrHfAl was especially interesting due to its observed bcc superstructure – a variant of γ-brass with 4 vacancies per cell (not 2 as in γ-brass). We highlight how vacancy ordering mediates selection of this variant of γ-brass, which is driven by vacancy-atom SRO that dramatically suppress all atomic SRO. As vacancies are inherent in processing refractory systems, we expect that similar discoveries await in other high entropy alloys or in revisiting older experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Predicting displacement damage for ion irradiation: Origin of the overestimation of vacancy production in SRIM full-cascade calculations

Ion irradiation and implantation have wide applications that demand accurate determination of displacement damage profile and distribution of implanted ion concentration. The prediction of vacancies is especially important to determine displacements per atom (dpa), the standard parameter of primary radiation damage in materials. However, significant discrepancies exist in estimations of vacancies between full-cascade (F-C) and quick calculation (Q-C) options in the popular computer code SRIM. This study inspected the SRIM code and a relatively new code called Iradina, which uses a similar methodology, to develop an understanding of the origin of vacancy overestimation in the F-C options for SRIM and Iradina. Here, we found that the default values of thresholds (namely final energy in SRIM and replacement energy in Iradina) in displacement production calculations results in excessively large number of calculated vacancies and very few replacements. After conducting multiple calculations using SRIM, Iradina, and MARLOWE (all based on the binary collision approximation), a comparison of the results indicates that there is a shortcoming in the SRIM and Iradina F-C methodology for treating near-threshold collisions. This issue is responsible for the deficiency of replacements and excess of calculated vacancies in the SRIM and Iradina F-C results. Drawing on the principles of collision physics, we propose recommendations for modifying the source codes to address these issues.

36 MATERIALS SCIENCE↗
DOE OSTI2025

First-principles investigation of cerium and neodymium diffusion in BCC chromium and vanadium via vacancy-mediated transport

Lanthanide transport plays a crucial role in the performance and longevity of metallic nuclear fuels. This study examines the diffusion behavior of Ce and Nd—two major fission products—in body-centered cubic (BCC) Cr and V, which are potential liner or coating materials for mitigating fuel-cladding chemical interactions (FCCI). Using density functional theory (DFT) calculations and self-consistent mean-field (SCMF) analysis, the vacancy-mediated diffusion coefficients are evaluated. Our findings reveal that Ce and Nd act as oversized solutes and are strongly bound to vacancies in BCC Cr and V, with diffusivities in Cr significantly lower than in V and in hexagonal closed-packed (HCP) Zr, as investigated in our previous work. The activation energies for Ce and Nd diffusion are 3.39 and 3.32 eV, respectively, in BCC Cr, and 2.56 and 2.33 eV, respectively, in BCC V. Analysis of vacancy drag and partial diffusion coefficient ratios indicates a strong tendency for lanthanide enrichment at vacancy sinks in BCC Cr, and to a lesser extent in BCC V, with this effect persisting up to the melting point in Cr and remaining substantial for Nd in V at high temperatures. Under irradiation, the increase in vacancy concentration is expected to enhance lanthanide transport, potentially accelerating interactions at liner-cladding interfaces. Although BCC Cr exhibits relatively low lanthanide diffusivities under equilibrium conditions, the expected segregation tendencies under irradiation suggest that Zr liners may be a more favorable option. Further investigations using rate theory, cluster dynamics, and phase-field modeling are required to quantitatively assess the performance of these materials in reactor environments.

36 - MATERIALS SCIENCE↗
DOE OSTI2020

The Role of Surface Oxygen Vacancies in BiVO 4

Bismuth vanadate (BiVO 4 ) is a widely studied oxide in solar water splitting, known for its ease of synthesis, high charge extraction yields, and advantageous band alignment with water. We present a combined first-principles and experimental study of the electronic structure of the (010) surface of BiVO 4 aimed at disentangling the impact of the surface and bulk oxygen vacancies on the electronic structure and transport properties. We found that oxygen vacancies are deep donors at the surface as they are in the bulk; our calculations on defect and polaron formation energies suggest that, while polarons formed from oxygen vacancies in the bulk can contribute to conductivity, those at the surface likely do not. Our results also show that out-of-plane structural relaxations at the surface contribute to the relatively immobile nature of electron polarons derived from surface oxygen vacancies. The structural model derived from first-principles calculation was validated by comparing computed results with experimental measurements of single-crystal and epitaxially grown single-crystalline BiVO 4 samples. Finally, we also found a reasonably good agreement between our calculated and measured work functions for BiVO 4 samples with and without oxygen vacancies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Colossal oxygen vacancy formation at a fluorite-bixbyite interface

Oxygen vacancies in complex oxides are indispensable for information and energy technologies. There are several means to create oxygen vacancies in bulk materials. However, the use of ionic interfaces to create oxygen vacancies has not been fully explored. As such, we report an oxide nanobrush architecture designed to create high-density interfacial oxygen vacancies. An atomically well-defined (111) heterointerface between the fluorite CeO 2 and the bixbyite Y 2 O 3 is found to induce a charge modulation between Y 3+ and Ce 4+ ions enabled by the chemical valence mismatch between the two elements. Local structure and chemical analyses, along with theoretical calculations, suggest that more than 10% of oxygen atoms are spontaneously removed without deteriorating the lattice structure. Our fluorite–bixbyite nanobrush provides an excellent platform for the rational design of interfacial oxide architectures to precisely create, control, and transport oxygen vacancies critical for developing ionotronic and memristive devices for advanced energy and neuromorphic computing technologies.

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

Effects of local compositional and structural disorder on vacancy formation in entropy-stabilized oxides from first-principles

Entropic stabilization has evolved into a strategy to create new oxide materials and realize novel functional properties engineered through the alloy composition. Achieving an atomistic understanding of these properties to enable their design, however, has been challenging due to the local compositional and structural disorder that underlies their fundamental structure-property relationships. Here, we combine high-throughput atomistic calculations and linear regression algorithms to investigate the role of local configurational and structural disorder on the thermodynamics of vacancy formation in (MgCoNiCuZn)O-based entropy-stabilized oxides (ESOs) and their influence on the electrical properties. We find that the cation-vacancy formation energies decrease with increasing local tensile strain caused by the deviation of the bond lengths in ESOs from the equilibrium bond length in the binary oxides. The oxygen-vacancy formation strongly depends on structural distortions associated with the local configuration of chemical species. Vacancies in ESOs exhibit deep thermodynamic transition levels that inhibit electrical conduction. By applying the charge-neutrality condition, we determine that the equilibrium concentrations of both oxygen and cation vacancies increase with increasing Cu mole fraction. Our results demonstrate that tuning the local chemistry and associated structural distortions by varying alloy composition acts an engineering principle that enables controlled defect formation in multi-component alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Unveiling the role of structural vacancies in Mn-based Prussian blue analogues for energy storage applications

Prussian blue analogues (PBAs) are promising cathode materials for monovalent- and multivalent-ion batteries due to their large framework structures. Nevertheless, the influence of lattice vacancies on their electrochemical performance has not been thoroughly clarified, hindering the further development of PBAs. Here we identify two types of functional vacancies, i.e., structural vacancies (SVs) and incidental vacancies (IVs), in manganese hexacyanoferrate (MnHCF) through synchrotron-based X-ray absorption spectroscopy and density functional theory calculations. Unlike structurally disordered IVs, the introduction of structurally ordered SVs promotes ion transport and reduces the interaction between host ions and the framework, enabling improved cycling and rate performance. The controllable adjustment of SVs in K-rich MnHCF is achieved through a co-reactant method. Furthermore, the partial introduction of SVs in K-rich MnHCF is demonstrated to favor both a milder structural evolution by alleviating the Jahn–Teller distortion of Mn 3+ and a stable dynamic process of interface reaction. As a result, this study unveils the potential importance of incorporating structural vacancies into MnHCF for advanced energy storage applications.

Gao, Chongwei↗
DOE OSTI2020

Influence of tungsten doping on nonradiative electron–hole recombination in monolayer MoSe 2 with Se vacancies

Two-dimensional transition metal dichalcogenides (TMDs) are receiving significant attention due to their excellent electronic and optoelectronic properties. The material quality is greatly affected by defects that are inevitably generated during material synthesis. Focusing on chalcogenide vacancies, which constitute the most common defect, we use the state-of-the-art simulation methodology developed in our group to demonstrate that W doping of MoSe 2 with Se vacancies reduces charge carrier losses by two mechanisms. First, W doping makes the formation of double Se vacancies unfavorable, while it is favorable in undoped MoSe 2 . Second, if a Se vacancy is present, the charge carrier lifetimes are extended in the W-doped MoSe 2 . Combining ab initio real-time time-dependent density functional theory with nonadiabatic molecular dynamics, the simulations show that the nonradiative carrier losses in the presence of Se vacancies proceed by sub-10 ps electron trapping and relaxation down the manifold of trap states, followed by a 100 ps recombination of trapped electrons with free holes. The electron–vibrational energy exchange is driven by both in-plane and out-of-plane vibrational motions of the MoSe 2 layer. Additionally, the atomistic studies advance our understanding of the influence of defects on charge carrier properties in TMDs and guide improvements of material quality and development of TMD applications.

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

Prediction of vacancy defect diffusion paths in high entropy alloys via machine learning on molecular dynamics data

Identifying the diffusion path of point defects is a critical step in understanding their evolution and the mechanisms of related phenomena. Defect diffusion occurs at small length and time scales, with impacts on material properties that may continue to evolve over ns to μs, ms, and the continuum scale (s, min, etc., and cm, m, etc.). The time scale accessible to molecular dynamics (MD) simulations is limited by small step sizes, typically in the fs range. Thus, surrogate models of MD simulations through machine learning (ML)-based algorithms are of great interest, especially for complex systems such as high entropy alloys (HEAs). In this work, dynamics governing vacancy migration in HEA were approximated with graph convolutional network (GCN) models as ansatzes for kinetic Monte Carlo (KMC) rate catalogs. Network design considered that diffusion in crystalline solids generally depends on interactions between defects and their immediate neighbor atoms. Graphs represented the vacancy surroundings, MD-generated trajectories provided training and comparison datasets, and unsupervised GCN models approximated interatomic dynamics governing vacancy migration in HEAs as ansatzes for KMC. A proof-of-concept model trained on MD data for the Fe, Ni, Cr, Co, and Cu HEA environment was used with two different neighbor interactions to assess the feasibility of training a GCN to predict vacancy defect transition rates in the HEA environment. The resulting setup rapidly generated MD-formatted synthetic trajectories based on dynamics learned from the MD training set, with a time acceleration of roughly two orders of magnitude and a similar diffusion coefficient to MD observations. Additionally, Nudged Elastic Band (NEB) calculations were performed on randomly generated FeNiCrCoCu HEA structures to determine vacancy migration barriers across nearest-neighbor sites. Transition probabilities for each jump, categorized by atomic type, were extracted from these calculations. NEB-based and GCN-based approaches led to similar outcomes.

Reimer, C↗