Defect Energetics Research Articles

Vacancies in MgO at ultrahigh pressure: About mantle rheology of super-Earths

First-principles calculations are performed to investigate vacancy formation and migration in the B2 phase of MgO. Defect energetics suggest the importance of intrinsic non-interacting vacancy pairs, even though the extrinsic vacancy concentration might govern atomic diffusion in the B2 phase of MgO. The enthalpies of ionic vacancy migration are generally found to decrease across the B1-B2 phase transition around a pressure of 500 GPa. It is shown that this enthalpy change induces a substantial increase in the rate of vacancy diffusion in MgO of almost four orders of magnitude (∼104) when the B1 phase transforms into the B2 phase with increasing pressure. If plastic deformation is controlled by vacancy diffusion, mantle viscosity is expected to decrease in relation to this enhanced diffusion rate in MgO across the B1-B2 transition in the interior of Earth-like large exoplanets. Our results of atomic relaxations near the defects suggest that diffusion controlled creep viscosity may generally decrease across high-pressure phase transitions with increasing coordination number. Plastic flow and resulting mantle convection in the interior of these super-Earths may be therefore less sluggish than previously thought.

Study of point defects diffusion in nickel using kinetic activation-relaxation technique

Point defects play a central role in materials properties. Yet, details regarding their diffusion and aggregation are still largely lacking beyond the monomer and dimer. Using the kinetic Activation Relaxation Technique (k-ART), a recently proposed off-lattice kinetic Monte Carlo method, the energy landscape, kinetics and diffusion mechanisms of point defect in fcc nickel are characterized, providing an exhaustive picture of the motion of one to five vacancies and self-interstitials in this system. Starting with a comparison of the prediction of four empirical potentials — the embedded atom method (EAM), the original modified embedded atom method (MEAM1NN), the second nearest neighbor modified embedded atom method (MEAM2NN) and the Reactive Force Field (ReaxFF) —, it is shown that while both EAM and ReaxFF capture the right physics, EAM provides the overall best agreement with ab initio and molecular dynamics simulations and available experiments both for vacancies and interstitial defect energetics and kinetics. Extensive k-ART simulations using this potential provide complete details of the energy landscape associated with these defects, demonstrated a complex set of mechanisms available to both vacancies and self-interstitials even in a simple environment such as crystalline Ni. We find, in particular, that the diffusion barriers of both vacancies and interstitials do not change monotonically with the cluster size and that some clusters of vacancies diffuse more easily than single ones. As self-interstitial clusters grow, moreover, we show that the fast diffusion takes place from excited states but ground states can act as pinning centers, contrary to what could be expected.

Thermodynamic, electronic, and magnetic properties of intrinsic vacancy defects in antiperovskite Ca3SnO

The density functional theory based total energy calculations are performed to examine the effect of charge neutral and fully charged intrinsic vacancy defects on the thermodynamic, electronic, and magnetic properties of Ca3SnO antiperovskite. The chemical stability of Ca3SnO is evaluated with respect to binary compounds CaO, CaSn, and Ca2Sn, and the limits of atomic chemical potentials of Ca, Sn, and O atoms for stable synthesis of Ca3SnO are determined within the generalized gradient approximation parametrization scheme. The electronic properties of the pristine and the non-stoichiometric forms of this compound have been explored and the influence of isolated intrinsic vacancy defects (Ca, Sn, and O) on the structural, bonding, and electronic properties of non-stoichiometric Ca3SnO are analyzed. We also predict the possibility of achieving stable ferromagnetism in non-stoichiometric Ca3SnO by means of charge neutral tin vacancies. From the calculated total energies and the valid ranges of atomic chemical potentials, the formation energetics of intrinsic vacancy defects in Ca3SnO are evaluated for various growth conditions. Our results indicate that the fully charged calcium vacancies are thermodynamically stable under the permissible Sn-rich condition of stable synthesis of Ca3SnO, while tin and oxygen vacancies are found to be stable under the extreme Ca-rich condition.

Stability of vacancy-type defect clusters in Ni based on first-principles and molecular dynamics simulations

Using first-principles calculations based on density-functional theory, the energetics of different vacancy-type defects, including voids, stacking fault tetrahedra (SFT) and vacancy loops, in Ni are investigated. It is found that voids are more stable than SFT at 0K, which is also the case after taking into account the volumetric strains. By carrying out ab initio molecular dynamics simulations at temperatures up to 1000K, direct transformations from vacancy loops and voids into SFT are observed. Our results suggest the importance of temperature effects in determining thermodynamic stability of vacancy clusters in face-centered cubic metals.

Insights into the radiation behavior of Ln2TiO5 (Ln = La-Y) from defect energetics

First-principles calculations have been performed to study the structural properties and defect energetics of orthorhombic Ln2TiO5 (Ln=La, Pr, Nd, Sm, Gd, Dy and Y). The lattice parameters decrease with increasing lanthanide cation radius. The mean 〈Ln1-O〉 and 〈Ln2-O〉 bond lengths increase systematically by respectively 1.16% and 1.19% from Dy2TiO5 to La2TiO5. Meanwhile, mean 〈Ti-O〉 bond length increases slightly with increasing Ln cation radius from Y2TiO5 to La2TiO5. The calculated results of point defect formation energies suggest that Ln2-Ti antisite defect is the most energetically favorable defect type for Ln2TiO5. The trend of Ln2-Ti antisite defect formation energy of Ln2TiO5 is precisely consistent with the radiation resistance, as demonstrates by the critical amorphization temperature, which indicates that the formation of Ln2-Ti antisite defect may has a significant influence on the radiation behavior of Ln2TiO5.

Heterogeneous Two‐Phase Pillars in Epitaxial NiFe2O4‐LaFeO3 Nanocomposites

Self‐assembled epitaxial oxide nanocomposites have been explored for a wide range of applications, including multiferroic and magnetoelectric properties, plasmonics, and catalysis. These so‐called “vertically aligned nanocomposites” form spontaneously during the deposition process when segregation into two phases is energetically favorable as compared to a solid solution. However, there has been surprisingly little work understanding the driving forces that govern the synthesis of these materials, which can include point defect energetics, surface diffusion, and interfacial energies. To explore these factors, La‐Ni‐Fe‐O films have been synthesized by molecular beam epitaxy and it is shown that these phase segregate into spinel‐perovskite nanocomposites. Using complementary scanning transmission electron microscopy and atom‐probe tomography, the elemental composition of each phase is examined and found that Ni ions are exclusively found in the spinel phase. From correlative analysis, a model for the relative favorability of the Ni2+ and Ni3+ valences under the growth conditions is developed. It is shown that multidimensional characterization techniques provide previously unobserved insight into the growth process and complex driving forces for phase segregation.

Density Functional Theory Modeling of A-site Cation Diffusion in Bulk LaMnO3 ±δ for Solid Oxide Fuel Cell Cathodes

Solid oxide fuel cells (SOFC)s performances and long term degradation are directly and indirectly influenced by cation diffusion in electrodes, electrolytes, and across their interfaces. For SOFC cathodes, due to the sluggish rates of cation diffusion and the complex coupling between the defect chemistry and cation diffusion pathways, the dependences of the cation diffusivities on temperature and O2 partial pressure in the state-of-the-art La1-xSrxMnO3±δ (LSM) remain insufficiently understood based on the available theoretical models. In this work, the interactions of the defect complexes for cation transport and the associated cation diffusion mechanisms in bulk LSM are investigated based on density functional theory simulations. While the active cation diffusion pathways in bulk LSM have been suggested to involve the transport of the cation defect clusters[3,4], this work assessed stability of a number of possible cation vacancy clusters as a function of temperature and P(O2) as well as the associated cation migration barriers, and unveiled new cation diffusion mechanisms with lower migration barriers than those proposed in the previous studies[1-2]. The temperature and P(O2) dependences of the cation self-diffusion coefficients in bulk LSM are further assessed, by incorporating the defect energetics and the transport carrier concentration obtained from the ab initio bulk defect model[5], and the migration barriers of the investigated cation diffusion pathways[6]. The predicted temperature and P(O2) dependences of the cation diffusivities obtained using this model were compared with the experimental tracer diffusion coefficients reported in the literature [2-3], and implications of the new cation diffusion mechanisms will be discussed. The trends in the migration barriers vs. various types of metal cations relevant to SOFC applications, including La3+, Sr2+, Zr4+, Y3+, etc,are also investigated, and the results obtained suggest that both the ionic charge and the ionic radius can correlate with the calculated cation migration barriers [6].

40 years of mineral elasticity: a critical review and a new parameterisation of equations of state for mantle olivines and diamond inclusions

Elasticity is a key property of materials, not only for predicting volumes and densities of minerals at the pressures and temperatures in the interior of the Earth, but also because it is a major factor in the energetics of structural phase transitions, surface energies, and defects within minerals. Over the 40 years of publication of Physics and Chemistry of Minerals, great progress has been made in the accuracy and precision of the measurements of both volumes and elastic tensors of minerals and in the pressures and temperatures at which the measurements are made. As an illustration of the state of the art, all available single-crystal data that constrain the elastic properties and pressure–volume–temperature equation of state (EoS) of mantle-composition olivine are reviewed. Single-crystal elasticity measurements clearly distinguish the Reuss and Voigt bulk moduli of olivine at all conditions. The consistency of volume and bulk modulus data is tested by fitting them simultaneously. Data collected at ambient pressure and data collected at ambient temperature up to 15 GPa are consistent with a Mie–Grunesien–Debye thermal-pressure EoS in combination with a third-order Birch–Murnaghan (BM) compressional EoS, the parameter V 0 = 43.89 cm3 mol−1, isothermal Reuss bulk modulus $$K_{\text{TR,0}} = 126.3(2){\text{ GPa}}$$ , $$K^{\prime}_{\text{TR,0}} = 4.54(6)$$ , a Debye temperature $$\theta_{\text{D}} = 644(9)\;{\text{K}}$$ , and a Gruneisen parameter γ 0 = 1.044(4), whose volume dependence is described by q = 1.9(2). High-pressure softening of the bulk modulus at room temperature, relative to this EoS, can be fit with a fourth-order BM EoS. However, recent high-P, T Brillouin measurements are incompatible with these EoS and the intrinsic physics implied by it, especially that $$\left( {\frac{{\partial K^{\prime}_{\text{TR}} }}{\partial T}} \right)_{P} > 0$$ . We introduce a new parameterisation for isothermal-type EoS that scales both the Reuss isothermal bulk modulus and its pressure derivative at temperature by the volume, $$K_{\text{TR}} (T,P = 0) = K_{\text{TR,0}} \left[ {\frac{{V_{0} }}{V(T)}} \right]^{{\delta_{\text{T}} }}$$ and $$K^{\prime}_{\text{TR}} (T,P = 0) = K^{\prime}_{\text{TR,0}} \left[ {\frac{V(T)}{{V_{0} }}} \right]^{{\delta^{\prime}}}$$ , to ensure thermodynamic correctness at low temperatures. This allows the elastic softening implied by the high-P, T Brillouin data for mantle olivine to be fit simultaneously and consistently with the same bulk moduli and pressure derivatives (at room temperature) as the MGD EoS, and with the additional parameters of α V0 = 2.666(9) × 10−5 K−1, $$\theta_{\text{E}} = 484(6)$$ , $$\delta_{\text{T}}$$ = 5.77(8), and $$\delta^{\prime}$$ = −3.5(1.1). The effects of the differences between the two EoS on the calculated density, volume, and elastic properties of olivine at mantle conditions and on the calculation of entrapment conditions of olivine inclusions in diamonds are discussed, and approaches to resolve the current uncertainties are proposed.

Energetics of intrinsic point defects in aluminium via orbital-free density functional theory

The formation and migration energies for various point defects, including vacancies and self-interstitials, in aluminium are systematically reinvestigated using the supercell approximation in the framework of orbital-free density functional theory. In particular, the finite-size effects and the accuracy of various kinetic energy density functionals are examined. It is demonstrated that as the supercell size increases, the finite-size errors asymptotically decrease as . Notably, the formation energies of self-interstitials converge much more slowly than that of vacancies. With carefully chosen kinetic energy density functionals, the calculated results agree quite well with the available experimental data and those obtained through Kohn–Sham density functional theory, which has an exact kinetic term.

Exact mean field concept to compute defect energetics in random alloys on rigid lattices

In modern materials science modeling, the evolution of the energetics of random alloys with composition are desirable input parameters for several meso-scale and continuum scale models. When using atomistic methods to parameterize the above mentioned concentration dependent function, a mean field theory can significantly reduce the computational burden associated to obtaining the desired statistics in a random alloy. In this work, a mean field concept is developed to obtain the energetics of point-defect clusters in perfect random alloys. It is demonstrated that for a rigid lattice the concept is mathematically exact. In addition to the accuracy of the presented method, it is also computationally efficient as a small box can be used and perfect statistics are obtained in a single run. The method is illustrated by computing the formation and binding energy of solute and vacancy pairs in FeCr and FeW binaries. Also, the dissociation energy of small vacancy clusters was computed in FeCr and FeCr-2%W alloys, which are considered model alloys for Eurofer steels. As a result, it was concluded that the dissociation energy is not expected to vary by more than 0.1eV in the 0–10% Cr and 0–2% W composition range. The present mean field concept can be directly applied to parameterize meso-scale models, such as cluster dynamics and object kinetic Monte Carlo models.

Antimony Diffusion in CdTe

Group V dopants may be used for next-generation high-voltage cadmium telluride (CdTe) solar photovoltaics, but fundamental defect energetics and kinetics need to be understood. Here, antimony (Sb) diffusion is studied in single-crystal and polycrystalline CdTe under Cd-rich conditions. Diffusion profiles are determined by dynamic secondary ion mass spectroscopy and analyzed with analytical bulk and grain-boundary diffusion models. Slow bulk and fast grain-boundary diffusion are found. Density functional theory is used to understand formation energy and mechanisms. The theory and experimental results create new understanding of group V defect kinetics in CdTe.

X-ray absorption investigation of local structural disorder in Ni1-xFex (x = 0.10, 0.20, 0.35, and 0.50) alloys

Defect energetics in structural materials has long been recognized to be affected by specific alloy compositions. Local structural distortion greatly affects the physical properties and performance of alloys. To reveal the atomic-level lattice distortion, the local structures of Ni and Fe in Ni1-xFex (x = 0.10, 0.20, 0.35 and 0.50) solid solution alloys were measured with extended X-ray absorption fine structure (EXAFS) technique. The EXAFS measurements have revealed that the bond length of Fe with surrounding atoms is 0.01–0.02 Å larger than that of Ni with its neighbors in the alloys. Both the lattice constant and the interatomic distance of the nearest neighbors increase with the addition of Fe content in the solid solutions. The local bonding environments in Ni1-xFex alloys were also calculated from ab initio and compared with the experimental results.

Evolution pattern of collision cascades in bcc V with different grain boundary structures: an atomic scale study

In this paper, by means of atomic-scale simulations, we investigate modifications of the evolution pattern of collision cascades in bcc vanadium (V) with different grain boundary (GB) structures on picosecond (ps) timescale. In primary damage state, in agreement with previous results of bcc and fcc bi-crystals, we find that the GBs in V are biased towards interstitials. The biased absorption of interstitials over vacancies reduces the in-cascade annihilation of vacancy-interstitial pairs and leads to aggregation of more number of vacancies in the grains interiors. The sessile vacancies accumulate in the bulk and form immobile vacancy clusters; in contrast, the glissile interstitials disperse in the damage zone and mostly diffuse in the form of single self-interstitial atoms (SIAs)/di-interstitials towards the GB region. Moreover, meanwhile, as we discuss the mechanisms that reduce (or increase) the concentration of defects in bi-crystal structures on picosecond timescale, we study the energetics of defects in close vicinity of pristine GBs, as an alternative driving force that facilitates formation and accumulation of defects in the GB regions. Finally, in a prolonged irradiation, we examine stability and sink properties of the damaged GBs. The results reveal that, irrespective of GB structure, the presence of grain boundaries leads to aggregation of more number of vacancies in the grain interiors in continuous bombardment. Overall, based on the results obtained in the primary damage event and the prolonged irradiation, we conclude that the GBs in bcc V act as efficient defect sinks on the simulated time frame.

Oxygen DX center in In0.17Al0.83N: Nonradiative recombination and persistent photoconductivity

Using a hybrid density-functional scheme, we address the O impurity substitutional to N (ON) in In0.17Al0.83N. Our modelling supports In clustering to account for the strong band-gap bowing observed in InxAl1−xN alloys. To study the ON defect in In0.17Al0.83N alloys, we therefore consider a model containing an In cluster and find that the most stable configuration shows four In nearest neighbors. We show that such a ON defect forms a DX center and gives rise to two defect levels at 0.70 and 0.41 eV below the conduction band edge, in good agreement with experiment. The calculated defect energetics entail a fast nonradiative recombination upon photoexcitation at room temperature and account for the observation of persistent photoconductivity at low temperature.

Fission gas in thoria

The fission gases Xe and Kr, formed during normal reactor operation, are known to degrade fuel performance, particularly at high burn-up. Using first-principles density functional theory together with a dispersion correction (DFT + D), in ThO2 we calculate the energetics of neutral and charged point defects, the di-vacancy (DV), different neutral tri-vacancies (NTV), the charged tetravacancy (CTV) defect cluster geometries and their interaction with Xe and Kr. The most favourable incorporation point defect site for Xe or Kr in defective ThO2 is the fully charged thorium vacancy. The lowest energy NTV in larger supercells of ThO2 is NTV3, however, a single Xe atom is most stable when accommodated within a NTV1. The di-vacancy (DV) is a significantly less favoured incorporation site than the NTV1 but the CTV offers about the same incorporation energy. Incorporation of a second gas atom in a NTV is a high energy process and more unfavourable than accommodation within an existing Th vacancy. The bi-NTV (BNTV) cluster geometry studied will accommodate one or two gas atoms with low incorporation energies but the addition of a third gas atom incurs a high energy penalty. The tri-NTV cluster (TNTV) forms a larger space which accommodates three gas atoms but again there is a penalty to accommodate a fourth gas atom. By considering the energy to form the defect sites, solution energies were generated showing that in ThO2−x the most favourable solution equilibrium site is the NTV1 while in ThO2 it is the DV.

A multi-state modified embedded atom method potential for titanium

The continuing search for broadly applicable, predictive, and unique potential functions led to the invention of the multi-state modified embedded atom method (MS-MEAM) (Baskes et al 2007 Phys. Rev. B 75 094113). MS-MEAM replaced almost all of the prior arbitrary choices of the MEAM electron densities, embedding energy, pair potential, and angular screening functions by using first-principles computations of energy/volume relationships for multiple reference crystal structures and transformation paths connecting those reference structures. This strategy reasonably captured diverse interactions between atoms with variable coordinations in a face-centered-cubic (fcc)-stable copper system. However, a straightforward application of the original MS-MEAM framework to model technologically useful hexagonal-close-packed (hcp) metals proved elusive. This work describes the development of an hcp-stable/fcc-metastable MS-MEAM to model titanium by introducing a new angular function within the background electron density description. This critical insight enables the titanium MS-MEAM potential to reproduce first principles computations of reference structures and transformation paths extremely well. Importantly, it predicts lattice and elastic constants, defect energetics, and dynamics of non-ideal hcp and liquid titanium in good agreement with first principles computations and corresponding experiments, and often better than the three well-known literature models used as a benchmark. The titanium MS-MEAM has been made available in the Knowledgebase of Interatomic Models (https://openkim.org/) (Tadmor et al 2011 JOM 63 17).

First-principles investigation of the energetics of point defects at a grain boundary in tungsten

Tungsten (W) and W alloys are considered as the most promising candidates for plasma facing materials in future fusion reactor. Grain boundaries (GBs) play an important role in the self-healing of irradiation defects in W. Here, we investigate the stability of point defects [vacancy and self-interstitial atoms (SIA’s)] in a Σ5(310) [001] tilt W GB by calculating the energetics using a first-principles method. It is found that both the vacancy and SIA are energetically favorable to locate at neighboring sites of the GB, suggesting the vacancy and SIA can easily segregate to the GB region with the segregation energy of 1.53eV and 7.5eV, respectively. This can be attributed to the special atomic configuration and large available space of the GB. The effective interaction distance between the GB and the SIA is ∼6.19Å, which is ∼2Å larger than that of the vacancy-GB, indicating the SIA are more preferable to locate at the GB in comparison with the vacancy. Further, the binding energy of di-vacancies in the W GB are much larger than that in bulk W, suggesting that the vacancy energetically prefers to congregate in the GB.

Self-diffusion measurements in isotopic heterostructures of undoped andin situdoped ZnO: Zinc vacancy energetics

It is well established that formation energies of point defects depend on the chemical potential (\ensuremath{\mu}) and Fermi level position $({E}_{F})$, which is widely used when modeling diffusion phenomena in semiconductors. In return, Arrhenius analysis of self-diffusion can be exploited for the investigation of point defect energetics since self-diffusion is mediated by intrinsic point defects. Specifically, the energetics of Zn vacancies (${V}_{\mathrm{Zn}}$) and/or Zn interstitials in ZnO can be potentially revealed via Zn self-diffusion measurements. In this study we have measured Zn self-diffusion varying \ensuremath{\mu} (by shifting from Zn- to O-rich conditions during the sample synthesis) and ${E}_{F}$ (by Ga, F, and Cu in situ doping). Corresponding diffusion activation energies were deduced and are discussed in terms of the vacancy diffusion mechanism. This results in an upper limit estimate for the ${V}_{\mathrm{Zn}}$ migration energy of $\ensuremath{\sim}1.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and prominent trends for the ${V}_{\mathrm{Zn}}$ formation energy as a function of \ensuremath{\mu} and ${E}_{F}$ are revealed. Concurrently, it is argued that dopant-${V}_{\mathrm{Zn}}$ clustering and ${E}_{F}$ pinning at deep donor traps should be taken into account when generalizing the interpretation of diffusion data for impurities in ZnO.

A Combined Theoretical-Experimental Study of Energy Storage Behavior of Reduced Graphene Oxide/Manganese Oxide Supercapacitor

Miniaturized electrochemical capacitors, such as micro-supercapacitors, have emerged as a new class of micro-power sources. However, they have limited uses in micro-energy storage because of their low volumetric energy densities. Here, compact structured Birnessite (MnO2)/reduced graphene oxide (RGO) hybrid films (Fig.1) consisting of multi-valent Mn ions were prepared via a two-step fabrication process involving a simple chemical redox reaction and post-thermal annealing to form a multi-layer structured film. With this versatile method, GO sheets can act as either a growth template for the highly capacitive MnO2 nanosheets or as a mechanical support for the production of compact hybrid films. Enhanced electrochemical characterization of the MnO2/RGO hybrid film revealed a remarkable ultrahigh volumetric capacitance (493 F/cm3 at 10 mV/s), ultrahigh energy and power density (13.3 mWh/cm3 at 2.5 A/cm3 and 22.6 W/cm3 at 58 A/cm3, respectively) and a semi-permanent cycle life (97% capacitance retention) in an aqueous electrolyte system. We also elucidated operating mechanisms of MnO2/RGO capacitor using state-of-the-art density-functional theory calculations with MnO2 nanoparticle/RGO sheet models. Various materials properties of MnO2/RGO systems including stoichiometric deviation, defect energetics, electron transfer, and kinetic behavior of cations and their contributions to their capacitance have been explored in atomic level. Figure 1

Point defects stabilise cubic Mo-N and Ta-N

We employ ab initio calculations to investigate energetics of point defects in metastable rocksalt cubic Ta-N and Mo-N. Our results reveal a strong tendency to off-stoichiometry, i.e. defected structures are surprisingly predicted to be more stable than perfect ones with metal-to-nitrogen stoichiometry. Despite the similarity of Ta-N and Mo-N systems in exhibiting this unusual behaviour, we also point out their crucial differences. While Ta-N significantly favours metal vacancies, Mo-N exhibits similar energies of formation regardless of the vacancy type (VMo, VN) as long as their concentration is below . The overall lowest energies of formation were obtained for and , which are hence predicted to be the most stable compositions. To account for various experimental conditions during synthesis, we further evaluated the phase stability as a function of chemical potential of individual species. The proposed phase diagrams reveal four stable compositions, , , and , in the case of Mo-N and nine stable compositions in the case of Ta-N indicating the important role of metal under-stoichiometry, since and significantly dominate the diagram. This is particularly important for understanding and designing experiments using non-equilibrium deposition techniques. Finally, we discuss the role of defect ordering and estimate a cubic lattice parameter as a function of defect contents and put them in the context of existing literature theoretical and experimental data.