Defect Energetics Research Articles

Surface doping of ZnO nanowires with Bi: Density-functional supercell calculations of defect energetics

Defect calculations using the density and hybrid functionals in combination with the supercell approach are employed to characterize the electrical properties of a number of ZnO nanowires of various thicknesses doped with Bi atoms occupying surface sites. The variation of the differences between the total energies of charged and neutral supercells with the supercell size is studied, which led the authors to devise an extrapolation procedure to obtain reliable defect energetics in the dilute defect limit. The calculated defect formation energies indicate that although the substitution of Bi into Zn or O sites can take place spontaneously under suitable thermodynamic conditions, the substitution into Zn sites is generally more likely. The defect (charge-state) transition energies are computed and parameterized as a function of the nanowire thickness. It is revealed that the substitution of Bi into O (Zn) sites on the surface of ZnO nanowires yields deep acceptor (shallow donor) levels (except for extremely thin nanowires). It is therefore concluded that the incorporation of Bi into the surface of ZnO nanowires results in $n$-type doping.

Tritium trapping and migration mechanisms in Li2O: a first-principles study.

The tritium recovery behaviors and related mechanisms in lithium-based breeding materials are the major concerns in fusion reactors. In the present work, the energetics of intrinsic point defects and H-related defects in Li2O has been investigated by the first-principles method. The results show that the formation energies, charge states and relative stability of the intrinsic point defects and H-related defects in Li2O under working conditions vary with the energy level. Based on the defect properties and migration process, a model of the tritium trapping and migration mechanisms in Li2O is proposed: (1) the bred tritium is first trapped by oxygen vacancies; (2) subsequently the tritium detrapped from oxygen vacancies is retrapped by lithium vacancies, forming T substituents; and (3) the T substituents hop along the Li lattice.

Ideal and real structures of different forms of carbon, with some remarks on their geological significance

Carbon is found in nature in a huge variety of allotropic forms and recent research in materials science has encouraged the development of technological materials based on nanocarbon. Carbon atoms with sp 2 or sp 3 hybridization can be thought of as building blocks. Following a bottom-up approach, we show how graphene and diamond molecules are built up and how their properties vary with size, reaching an upper limit with bulk graphite and diamond. Carbon atoms with sp 2 hybridization give rise to an impressive number of different materials, such as carbon nanotubes, graphene nanoribbons, porous carbon and fullerene. As in any crystalline phase, the crystal structures of natural carbon allotropes (i.e. graphite and diamond) contain various types of imperfections. These so-called lattice defects are classified by their dimensions into 0D (point), 1D (line), 2D (planar) and 3D (volume) defects. Lattice defects control the physical properties of crystals and are often a fingerprint of the geological environment in which they formed and were modified. Direct observations of lattice defects are commonly accomplished by transmission electron microscopy. We present and discuss the ideal and real structures of carbon allotropes, the energetics of lattice defects and their significance in understanding geological processes and conditions.

Helium irradiated cavity formation and defect energetics in Ni-based binary single-phase concentrated solid solution alloys

Binary single-phase concentrated solid solution alloys (SPCSAs), including Ni80Co20, Ni80Fe20, Ni80Cr20, Ni80Pd20, and Ni80Mn20 (in atomic percentage), were irradiated with 200 keV He+ ions at 500 °C. He cavity size and density distribution were systematically investigated using transmission electron microscope. Here we show that alloying elements have a clear impact on He cavity formation. Cavity size is the smallest in Ni80Mn20 but the largest in Ni80Co20. Alloying elements could also substantially affect cavity density profile. In-depth examination of cavities at peak damage region (∼500 nm) and at low damage region (∼300 nm) demonstrates that cavity size is depth (damage) dependent. Competition between consumption and production of vacancies and He atoms could lead to varied cavity size. Density functional theory (DFT) calculations were performed to obtain the formation and migration energies of interstitials and vacancies. Combined experimental and simulation results show that smaller energy gap between interstitial and vacancy migration energies may lead to smaller cavity size and narrower size distribution observed in Ni80Mn20, comparing with Ni80Co20. The results of this study call attention to alloying effects of specific element on cavity formation and defect energetics in SPCSAs, and could provide fundamental understanding to predict radiation effects in more complexed SPCSAs, such as high entropy alloys.

Density functional theory study of the point defect energetics in γ-LiAlO2, Li2ZrO3 and Li2TiO3 materials

The defect energetics in γ-LiAlO2, Li2TiO3, and Li2ZrO3 materials used in tritium-producing burnable absorber rods and fusion solid breeder applications was investigated using density functional theory calculations. A comprehensive analysis of the charged defects was performed for cation and anion vacancies, interstitials, antisite defects, and 3H interstitial and substitutional defects to understand the defect structures at different charge states and their stability as a function of the electron chemical potential across the electronic band gap of crystals at operating temperature and oxygen partial pressure conditions. Through investigation of the local bonding configurations and projected electronic density of states of the 3H related charged defects, including 3H interstitial (3Hint), 3Hint bound with an oxygen interstitial, and substitutional 3H defects on the Li, O, and M (M = Al, Ti, and Zr) sites (3HLi, 3HO, and 3HM), the 3H states of these defects were distinguished, i.e. triton (3H+), neutral 3H (3H0), and tritide (3H−). The two stable 3H related defects under the Li2O-LiOH rich condition at T = 1000 K, between P(O2) = 10−5 and 10−25 atm were found to be 3H interstitial (3Hint) with charge of +1 and neutral 3HLi (substitutional 3H on the Li site) in γ-LiAlO2, Li2ZrO3, and Li2TiO3 materials. For Li2TiO3, the stability of the 3HO with charge of +1 and 3HM with charge of −3 becomes comparable to that of 3Hint atm at P(O2) = 10−25 atm. Overall, our results indicate the energy cost to form the stable 3H defect species (3Hint with charge of +1 and neutral 3HLi) in γ-LiAlO2 material are higher than those of Li2TiO3 and Li2ZrO3 materials at T = 1000 K, between P(O2) = 10−5 and 10−25 atm. Interactions between the point defects and the 3H species as a function of the electron chemical potential across the band gap of the materials were also examined. All the three materials exhibit strong interactions between the 3Hint and the O vacancy, Li vacancy, and O interstitial defects with the strongest interactions found in the case of γ-LiAlO2 phase, indicating a higher tendency to trap 3H at such point defects in γ-LiAlO2.

Energetics of defect production in fluorite-structured CeO2 induced by highly ionizing radiation

Understanding the energetics of radiation-induced defects is critical to the development of next-generation materials for nuclear and other energy systems and for aerospace applications. However, it remains a challenge to experimentally characterize defect morphologies and energies, especially in regard to anion defects in irradiated oxides. Here, using a combination of advanced structural and calorimetric characterization techniques, we show that the energetic response of defects in ${\mathrm{CeO}}_{2}$ is strongly coupled to atomic disordering on the oxygen sublattice induced by energetic heavy ions. Fitting of calorimetric data yields an estimate of stored energy in the form of defects and microstrain. These results provide a means to calculate the efficiency of structural destabilization and aid in a better understanding of defect formation and annealing mechanisms in fluorite-structured materials subject to extreme conditions.

Energetics of point defects in rocksalt structure transition metal nitrides: Thermodynamic reasons for deviations from stoichiometry

First principle calculations of point defect formation energies in group 3–6 transition metal (Me) nitrides MeNx are employed to explain the thermodynamic reasons for the large reported compositional range (typically x = 0.7–1.3) in the rocksalt structure. Both under-stoichiometric (x < 1) and over-stoichiometric (x > 1) compositions are due to relatively low vacancy formation energies that decrease from an average of 2.7 and 4.5 eV for nitrogen and cation vacancies in group 3 nitrides (ScN, YN, LaN) to −1.8 and −0.8 eV in group 6 nitrides (CrN, MoN, WN), indicating that they become thermodynamically stable at zero temperature for group 6 and for group 4–6 nitrides, respectively. Similarly, nitrogen and cation interstitials in tetragonal and 111- or 110-split configurations are unstable for groups 3–5 but become thermodynamically stable for group 6 nitrides, consistent with the mechanical instability of the latter compounds. All antisite defects possess high formation energies and are unlikely to form. The nitrogen chemical potential at finite temperatures and in equilibrium with a N2 gas is strongly affected by the vapor phase entropy, leading to shifts in the defect free energy of, for example, 1.2 eV at 1 Pa N2 at 800 K, causing an increasing likelihood for nitrogen vacancies and cation interstitials at elevated temperatures. In addition, the configurational entropy of point defects causes a correction of e.g. 0.4 eV for a 1% vacancy defect concentration at 800 K. Considering these entropy contributions leads to predicted temperature windows for stoichiometry of e.g. 200–1100 K for TiN, 500–1400 K for ZrN, and 1200–1400 K for HfN, while considerable cation and nitrogen vacancy concentrations are expected for temperatures below and above these ranges, respectively. Schottky pair defects are predicted in VN for T > 200 K and in NbN, TaN, and group 6 nitrides at all temperatures, independent of the N2 partial pressure. The overall results show that thermodynamic arguments (even in the absence of kinetic barriers) can explain many of the reported composition vs temperature and pressure relationships in rocksalt structure nitrides.

Classical interatomic potential for quaternary Ni–Fe–Cr–Pd solid solution alloys

In this paper, we present a new quaternary interatomic potential for the NiFeCrPd system, which is an extension on the previous NiFeCr potential. Density functional theory is used to calculate the quantities to be fitted, with particular focus on the energetics of point defects with solutes, for the potential to be used towards understanding radiation damage properties. The potential thus will enable the modeling of multi-elemental solid solution alloys consisting of up to four elements. To test the potential, we have performed atomistic kinetic Monte Carlo simulations to investigate the effect of configurational entropy on the self-diffusion coefficients. The self-diffusion coefficients are found to increase with chemical complexity, contrary to the common postulation of sluggish diffusion in high entropy alloys (HEAs). In addition, we have performed molecular dynamics simulations to elucidate the effect of Pd on vacancy diffusion and clustering in pure Ni and binary alloys. In agreement with recent irradiation experiments, our simulations show that while large vacancy clusters, such as stacking fault tetrahedra, are formed in pure Ni, Ni–Fe and Ni–Cr systems, negligible vacancy clustering is observed in Ni–Pd systems, indicating a possible effect of Pd in reducing cluster sizes. We suggest that this potential will be useful for studying the defect evolution in multi-component HEAs.

Beryllium, tungsten and their alloys Be2W and Be12W: Surface defect energetics from density functional theory calculations

The binding, adsorption and removal energies of atoms on the surfaces of Be with the major orientations (112¯0) and (112¯1), and of W and Be/W alloys with (110) and (111) orientations have been obtained from density functional theory calculations. An analysis of adatom formation on viable surfaces and of adsorption and step formation processes is provided as well. Possible surface changes at conditions occurring during plasma-wall interactions are discussed. The large differences of the energetic parameters for various surface orientations and terminations mean that atomistic modeling is indeed essential for understanding the behavior of PFMs in a fusion environment.

Distribution of defect clusters in the primary damage of ion irradiated 3C-SiC

We report a statistical analysis of sizes and compositions of clusters produced in cascades during irradiation of SiC. The results are obtained using molecular dynamics (MD) simulations of cascades caused by primary knock-on atoms (PKAs) with energies between 10 eV and 50 keV. The results are averaged over six crystallographic directions of the PKA and integrated over PKA energy spectrum derived from the Stopping and Range of Ions in Matter (SRIM) code. Specific results are presented for 1 MeV Kr ion as an example of an impinging particle. We find that distributions of cluster size n for both vacancies and interstitials obey a power law f=A/nS and these clusters are dominated by carbons defects. The fitted values of A and S are different than values reported for metals, which can be explained through different defect energetics and cascade morphology between the two classes of materials. In SiC, the average carbon ratio for interstitial clusters is 91.5%, which is higher than the ratio of C in vacancy clusters, which is 85.3%. Size and composition distribution of in-cascade clusters provide a critical input for long-term defect evolution models.

Understanding the Effects of Cd and Ag Doping in Cu2ZnSnS4 Solar Cells

Cu2ZnSnS4-based solar cells, which constitute an inexpensive, beyond-Si photovoltaic technology, often suffer from low open-circuit voltage and efficiency. This drawback is often attributed to disorder in the Cu–Zn sublattice of the kesterite structure. While previous experiments have reported improved performances with isovalent substitution of Cd and Ag for Cu and Zn, respectively, the fundamental driving force for such improvements remains unclear. Here, we use density functional theory to study bulk stability, defect, and surface energetics, as well as the electronic structure of these dopants in Cu2ZnSnS4. We find that Cd and Ag can increase efficiencies, depending on the dopant concentration and Cu content used during synthesis. Most importantly, we find that a low level of Cd doping can suppress disorder in the kesterite phase across all Cu concentrations, while a low level of Ag doping can do so only when Zn- and Sn-rich conditions are employed. A higher Ag content is beneficial as it stabilizes t...

Nanoscale Control of Oxygen Defects and Metal–Insulator Transition in Epitaxial Vanadium Dioxides

Strongly correlated vanadium dioxide (VO2) is one of the most promising materials that exhibits a temperature-driven, metal-insulator transition (MIT) near room temperature. The ability to manipulate the MIT at nanoscale offers both insight into understanding the energetics of phase transition and a promising potential for nanoelectronic devices. In this work, we study nanoscale electrochemical modifications of the MIT in epitaxial VO2 thin films using a combined approach with scanning probe microscopy (SPM) and theoretical calculations. We find that applying electric voltages of different polarity through an SPM tip locally changes the contact potential difference and conductivity on the surface of VO2 by modulating the oxygen stoichiometry. We observed nearly 2 orders of magnitude change in resistance between positive and negative biased-tip written areas of the film, demonstrating the electric field modulated MIT behavior at the nanoscale. Density functional theory calculations, benchmarked against more accurate many-body quantum Monte Carlo calculations, provide information on the formation energetics of oxygen defects that can be further manipulated by strain. This study highlights the crucial role of oxygen vacancies in controlling the MIT in epitaxial VO2 thin films, useful for developing advanced electronic and iontronic devices.

Energetics of native defects, solute partitioning, and interfacial energy of Q precipitate in Al-Cu-Mg-Si alloys

The compound Al3Cu2Mg9Si7, is known as the Q-phase and forms as a thermodynamically stable precipitate during aging in the quaternary Al-Cu-Mg-Si system. We perform atomic-scale density functional theory (DFT) calculations of defect properties, solute partitioning, and interfacial stability of the Al3Cu2Mg9Si7 (Q) precipitate. We find: (i) simple native point defect (i.e., vacancies and anti-sites) thermodynamics can partially explain the experimentally observed off-stoichiometry, such as the observed variation of compositions, Al3+δCu2Mg9-δSi7 (Mg-deficient and Al-rich) in experiment. (ii) Calculated solute-partitioning energies of common solutes allow us to define general rules for site-preference in the Q-phase in terms of electronic structure and atomic radius. To validate our DFT predictions, we perform atom-probe tomography (APT) experiments for six-different elements (Zn, Ni, Mn, Ti, V, and Zr). The results show that the partitioning behavior of solutes Ni, Zn, and Mn are consistent with DFT predictions, but the transition elements (Ti, V, and Zr), which are anomalously slow diffusers in Al, partition to the Q-phase in constrast to DFT partitioning energies. (iii) For the low energy interface (112¯0)Q//(510)Al observed in needle shaped Q-precipitate, we survey various terminations and orientations and derive a low-energy interfacial structure. We find this low-energy interfacial model has Cu atoms nearest to the interface, which is in agreement with previous literature on Cu interfacial segregation at the Q′//α-Al interface. The computed interfacial energy (0.52 J/m2) and the corresponding structure will be useful input to future multi-scale modeling of microstructural evolution.

Structures and energetics of point defects with charge states in zircon: A first-principles study

The fundamental problem of point defects under different phase equilibrium conditions in zircon (ZrSiO4) is carried out by first-principles calculation. The formation energies with the structural deformation of various native defects, i.e., single vacancy, interstitial, Frenkel and Schottky pairs at different charge states are calculated, which agree well with the available results. We identify VO2+ shows an important role in non-stoichiometric regime of ZrSiO4−x (x < 1). When Fermi level (εF) locates close to the CBM, the VZr4− becomes more easily observed than VO2+ in O-rich environment. In turn, the most abundant interstitial defects are IZr4+ and ISi4+. The non-interacting Si Frenkel-pair, made of the association of quadruply charged defect in energy of 5.947 eV, is more likely to form than other type of Frenkel-pairs. By formation the complex defects associating partial and full Schottky defects requires higher formation energy. These results provide a good reference to understand storage state as well as disposal of excess weapons-grade Pu and high-actinide wastes.

Random telegraph noise in 2D hexagonal boron nitride dielectric films

This study reports the observation of low frequency random telegraph noise (RTN) in a 2D layered hexagonal boron nitride dielectric film in the pre- and post-soft breakdown phases using conductive atomic force microscopy as a nanoscale spectroscopy tool. The RTN traces of the virgin and electrically stressed dielectric (after percolation breakdown) were compared, and the signal features were statistically analyzed using the Factorial Hidden Markov Model technique. We observe a combination of both two-level and multi-level RTN signals in h-BN, akin to the trends commonly observed for bulk oxides such as SiO2 and HfO2. Experimental evidence suggests frequent occurrence of unstable and anomalous RTN traces in 2D dielectrics which makes extraction of defect energetics challenging.

Design and analysis of forward and reverse models for predicting defect accumulation, defect energetics, and irradiation conditions

The complexity of radiation effects in a material’s microstructure makes developing predictive models a difficult task. In principle, a complete list of all possible reactions between defect species being considered can be used to elucidate damage evolution mechanisms and its associated impact on microstructure evolution. However, a central limitation is that many models use a limited and incomplete catalog of defect energetics and associated reactions. Even for a given model, estimating its input parameters remains a challenge, especially for complex material systems. Here, we present a computational analysis to identify the extent to which defect accumulation, energetics, and irradiation conditions can be determined via forward and reverse regression models constructed and trained from large data sets produced by cluster dynamics simulations. A global sensitivity analysis, via Sobol’ indices, concisely characterizes parameter sensitivity and demonstrates how this can be connected to variability in defect evolution. Based on this analysis and depending on the definition of what constitutes the input and output spaces, forward and reverse regression models are constructed and allow for the direct calculation of defect accumulation, defect energetics, and irradiation conditions. This computational analysis, exercised on a simplified cluster dynamics model, demonstrates the ability to design predictive surrogate and reduced-order models, and provides guidelines for improving model predictions within the context of forward and reverse engineering of mathematical models for radiation effects in a materials’ microstructure.

Vacancy assisted He-interstitial clustering and their elemental interaction at fcc-bcc semicoherent metallic interface

Cu-Nb layered nanocomposite system can be considered as a prototype system to investigate stability of the fcc-bcc semicoherent metallic interfaces. Theoretical simulations based on density functional theory have been performed in order to investigate the stability of different defects in such interfaces. The calculations find the interfacial misfit dislocation intersections as the preferred site for defects including a vacancy, He-interstitial, and a vacancy-He complex in good agreement with previous works. Our results suggest that the presence of a metallic vacancy may act as a sink for defect and favour the migration of He interstitials leading to their aggregation at the interface. The potential capability of the vacancy to accommodate He atoms was also predicted with a higher affinity towards Nb. This aggregation of He atoms is driven by local density of electron and strain in a region in the neighbourhood of Nb. Finally, we propose a plausible picture of defect energetics in the vicinity of the interface based on the Voronoi volume and Bader’s charge analysis. This analysis may replace the conventional methods used for surface energetics mapping which are extremely tedious for such large systems.

Effect of atomic order/disorder on vacancy clustering in concentrated NiFe alloys

Using molecular dynamics simulations, we elucidate the effect of atomic structure on vacancy clustering in ordered (L10) and random NiFe. Based on our simulations, we predict the vacancy evolution to be in complete contrast between the two systems. While large vacancy clusters, i.e., stacking fault tetrahedra (SFT) are formed in the random structure, no clustering is observed in the ordered-L10 structure. Similar simulations are performed on L10-CuAu and L10-TiAl to understand whether SFT formation is generic in L10 structures, or is specific to NiFe. Both materials show SFT formation, thereby highlighting specific defect energetics in L10 NiFe that lead to the lack of vacancy clustering. We elucidate that L10-NiFe has unique thermodynamic and kinetic defect energetics, i.e., antisite energies, vacancy sublattice preference, and directional migration energy barriers that collectively lead to the lack of vacancy clustering. Understanding such defect energetics could open avenues to prevent defect clustering in the vision towards development of radiation-tolerant concentrated alloys for nuclear reactor applications.

Effect of d electrons on defect properties in equiatomic NiCoCr and NiCoFeCr concentrated solid solution alloys

The role of $d$ electrons in determining distributions of formation and migration energies for point defects in equiatomic NiCoCr and NiCoFeCr concentrated solid solution alloys (CSAs) are studied regarding electron density deformation flexibility based on first-principles calculations. The disordered state is taken into account by constructing special quasirandom structures. The migration barriers are determined by directly optimizing the saddle point. It is found that the formation energies of interstitials in CSAs are lower than those in pure Ni, whereas the formation energies of vacancies are higher. In both NiCoCr and NiCoFeCr, Co-related dumbbell interstitials exhibit lower formation energies. Notably, the distributions of migration energies for Cr interstitials and vacancies exhibit a remarkable overlap region. A detailed analysis of electronic properties reveals that the electronic charge deformation flexibility regarding ${e}_{g}$ to ${t}_{2}$g transition has a dominant effect on defect energetics for different elements in CSAs. Thus the electron deformation ability is suggested as a key factor in understanding the peculiar defect behavior in CSAs.

Experimental and computational phase boundary mapping of Co4Sn6Te6.

Binary Co4Sb12 skutterudite (also known as CoSb3) has been extensively studied; however, its mixed-anion counterparts remain largely unexplored in terms of their phase stability and thermoelectric properties. In the search for complex anionic analogs of the binary skutterudite, we begin by investigating the Co4Sb12-Co4Sn6Te6 pseudo-binary phase diagram. We observe no quaternary skutterudite phases and as such, focus our investigations on the ternary Co4Sn6Te6 via experimental phase boundary mapping, transport measurements, and first-principles calculations. Phase boundary mapping using traditional bulk syntheses reveals that the Co4Sn6Te6 exhibits electronic properties ranging from a degenerate p-type behavior to an intrinsic behavior. Under Sn-rich conditions, Hall measurements indicate degenerate p-type carrier concentrations and high hole mobility. The acceptor defect SnTe, and donor defects TeSn and Coi are the predominant defects and rationally correspond to regions of high Sn, Te, and Co, respectively. Consideration of the defect energetics indicates that p-type extrinsic doping is plausible; however, SnTe is likely a killer defect that limits n-type dopability. We find that the hole carrier concentration in Co4Sn6Te6 can be further optimized by extrinsic p-type doping under Sn-rich growth conditions.