Energetics Of Point Defects Research Articles

Addressing accuracy by prescribing precision: Bayesian error estimation of point defect energetics

With density functional theory (DFT), it is possible to calculate the formation energy of charged point defects and in turn to predict a range of experimentally relevant quantities, such as defect concentrations, charge transition levels, or recombination rates. While prior efforts have led to marked improvements in the accuracy of such calculations, comparatively modest effort has been directed at quantifying their uncertainties. However, in the broader DFT research space, the development of Bayesian Error Estimation Functionals (BEEF) has enabled uncertainty quantification (UQ) for other properties. In this paper, we investigate the utility of BEEF as a tool for UQ of defect formation energies. We build a pipeline for propagating BEEF energies through a formation-energy calculation and test it on intrinsic defects in several materials systems spanning a variety of chemistries, bandgaps, and crystal structures, comparing to prior published results where available. We also assess the impact of aligning to a deep-level transition rather than to the VBM (valence band maximum). We observe negligible dependence of the estimated uncertainty upon a supercell size, though the relationship may be obfuscated by the fact that finite-size corrections cannot be computed separately for each member of the BEEF ensemble. Additionally, we find an increase in estimated uncertainty with respect to the absolute charge of a defect and the relaxation around the defect site without deep-level alignment, but this trend is absent when the alignment is applied. While further investigation is warranted, our results suggest that BEEF could be a useful method for UQ in defect calculations.

Influence of magnetic properties on elemental vacancy migration energy in Fe49.5Mn29.4Co10.1Cr10.1C0.9 high-entropy alloy

Randomly mixing ferromagnetic (FM) and antiferromagnetic (AFM) elements in high-entropy alloys (HEAs) can create fluctuating local magnetic moments that influence the energetics of point defects. In this study, we employed first-principles calculations to investigate the influence of magnetic properties on vacancy migration energy in Fe49.5Mn29.4Co10.1Cr10.1C0.9, alongside equiatomic NiCoFeCrMn alloy. By examining structures with paramagnetism, ferromagnetism, and no spin polarization, our study reveals significant impacts of magnetic interactions on vacancy migration barriers, potentially altering the sequence of elemental migration energies if overlooked. In Fe49.5Mn29.4Co10.1Cr10.1C0.9, the order of vacancy migration barriers is Co > Fe > Mn > Cr across all magnetic states, suggesting the dominant roles of atomic properties and inherent chemical bonding. Conversely, the NiCoFeCrMn HEA exhibits a pronounced magnetic state-dependent elemental migration energy order, indicating that magnetic interactions significantly influence vacancy migration behavior in this alloy. In addition, while FM elements generally exhibit higher migration barriers, AFM elements display lower barriers in the investigated Cantor alloys, with notable variations between the studied compositions. These findings underscore the critical role of magnetism in accurate migration energy calculations, which is important for studying chemically biased diffusion and radiation-induced segregation in HEAs.

Accelerating defect predictions in semiconductors using graph neural networks

First-principles computations reliably predict the energetics of point defects in semiconductors but are constrained by the expense of using large supercells and advanced levels of theory. Machine learning models trained on computational data, especially ones that sufficiently encode defect coordination environments, can be used to accelerate defect predictions. Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of group IV, III–V, and II–VI zinc blende semiconductors, powered by crystal Graph-based Neural Networks (GNNs) trained on high-throughput density functional theory (DFT) data. Using an innovative approach of sampling partially optimized defect configurations from DFT calculations, we generate one of the largest computational defect datasets to date, containing many types of vacancies, self-interstitials, anti-site substitutions, impurity interstitials and substitutions, as well as some defect complexes. We applied three types of established GNN techniques, namely crystal graph convolutional neural network, materials graph network, and Atomistic Line Graph Neural Network (ALIGNN), to rigorously train models for predicting defect formation energy (DFE) in multiple charge states and chemical potential conditions. We find that ALIGNN yields the best DFE predictions with root mean square errors around 0.3 eV, which represents a prediction accuracy of 98% given the range of values within the dataset, improving significantly on the state-of-the-art. We further show that GNN-based defective structure optimization can take us close to DFT-optimized geometries at a fraction of the cost of full DFT. The current models are based on the semi-local generalized gradient approximation-Perdew–Burke–Ernzerhof (PBE) functional but are highly promising because of the correlation of computed energetics and defect levels with higher levels of theory and experimental data, the accuracy and necessity of discovering novel metastable and low energy defect structures at the PBE level of theory before advanced methods could be applied, and the ability to train multi-fidelity models in the future with new data from non-local functionals. The DFT-GNN models enable prediction and screening across thousands of hypothetical defects based on both unoptimized and partially optimized defective structures, helping identify electronically active defects in technologically important semiconductors.

High-throughput calculations of charged point defect properties with semi-local density functional theory—performance benchmarks for materials screening applications

Calculations of point defect energetics with Density Functional Theory (DFT) can provide valuable insight into several optoelectronic, thermodynamic, and kinetic properties. These calculations commonly use methods ranging from semi-local functionals with a-posteriori corrections to more computationally intensive hybrid functional approaches. For applications of DFT-based high-throughput computation for data-driven materials discovery, point defect properties are of interest, yet are currently excluded from available materials databases. This work presents a benchmark analysis of automated, semi-local point defect calculations with a-posteriori corrections, compared to 245 “gold standard” hybrid calculations previously published. We consider three different a-posteriori correction sets implemented in an automated workflow, and evaluate the qualitative and quantitative differences among four different categories of defect information: thermodynamic transition levels, formation energies, Fermi levels, and dopability limits. We highlight qualitative information that can be extracted from high-throughput calculations based on semi-local DFT methods, while also demonstrating the limits of quantitative accuracy.

Ab initio investigations of a CoBiS monolayer with and without point defects.

Through density functional theory (DFT) calculations, a new triclinic monolayer, namely CoBiS, with higher stability than that of penta-CoBiS, is predicted. Our results show that this monolayer is a nonmagnetic metallic compound. To tune its magnetic properties, we systematically investigated the formation and energetics of different point defects in the CoBiS monolayer, such as VBi, VS and VCo. We find that the monolayer becomes magnetic with the different points defects. Our calculated magnetic anisotropy energy (MAE) indicated that VBi and VS exhibit out-of-plane MAE, while the MAE is in-plane for VCo. By solving the Heisenberg model using the Monte Carlo simulation method, we obtain transition temperatures for VS and VCo systems much larger than room temperature, implying potential applications in spintronic devices.

A first-principles investigation of point defect structure and energetics in ThO2

The structure and energetics of charged point defects in thorium dioxide (ThO2) have been investigated using the density functional theory (DFT) and phonon simulations. DFT simulations were performed under both zero-pressure and constant volume conditions. Termed as the free volume change of the point defects, the change in volume of the supercell has been computed in the zero-pressure case. Supercell expansion was observed with the increase of the (nominal) charge state of anion (O) interstitials and cation (Th) vacancies from neutral to its maximum. On the contrary, contraction of the supercell has been observed with anion vacancies and cation interstitials as the defect charge increases. The supercell volume change with respect to the charge state has been correlated with the resulting defect energetics. It has been observed that, as the defect charge increased, the internal energy and entropy of defect formation of the cation vacancies and anion interstitials were found to increase, while that of the cation interstitials and anion vacancies decreased. The temperature dependence of internal energy and entropy has also been examined. It was found that, as the temperature increases, the internal energies of the formation of cation vacancies and anion interstitials decrease, while those of the cation interstitials and anion vacancies increase. An opposite observation is seen for the entropies of formation defects when above room temperatures.

Phenomenological potentials for the refractory metals Cr, Mo and W

Cohesion in the refractory metals Cr, Mo, and W is phenomenologically described in this work via a n-body energy functional with a set of physically motivated parameters that were optimized to reproduce selected experimental properties characteristic of perfect and defective crystals. The functional contains four terms accounting for the hard-core repulsion, the Thomas–Fermi kinetic energy repulsion and for contributions to the binding energy of s and d valence electrons. Lattice dynamics, molecular statics, and molecular dynamics calculations show that this model describes satisfactorily thermodynamic properties of the studied metals whereas, unlike other empirical approaches from the literature, predictions of phonon dispersion relations and of surface and point defect energetics reveal in fair good agreement with experiments. These results suggest that the present model is well adapted to large-scale simulations and whenever total energy calculations of thermodynamic properties are unfeasible.

Energetics of intrinsic point defects and hydrogen in tungsten borides: a first-principles study

To understand the irradiation resistance and hydrogen (H) behavior in tungsten borides (W x B y ) in a burning plasma fusion environment, the energetics of intrinsic point defects and H in six stable ground state W borides, including W2B, WB, WB2, W2B5, WB3 and WB4, have been investigated using first-principles density functional theory calculations. The results show that the formation energies of interstitials and vacancies do not directly depend on the W and B content in W borides. However, the interaction between vacancies of a stoichiometric vacancy (SV) cluster in W x B y is related to the atomic ratio of B to W (y/x). The vacancies of a minimum-size SV cluster in W x B y are energetically repulsive for y/x ⩽ 1, while the vacancies energetically bind together for y/x larger than 1. The formation energy of B Frenkel pairs in each W boride is lower than that of W Frenkel pairs. Among the six evaluated W x B y compositions, WB has the highest and the lowest formation energy of H interstitials and H-vacancy complexes, respectively; however, these two energies in WB2 are in reverse order. The average H binding energies to single vacancies in WB and WB4 are comparable with that in W, while this binding energy in WB3 and WB2 is obviously higher or lower than in W, respectively. The diffusion activation energy of H in W borides is anisotropic. One dimensional (1D) diffusion of H in W2B, as well as 1D/2D diffusion in WB, W2B5, WB3 and WB4 are preferred at relatively low temperatures; however, three-dimensional diffusion of H is predicted in WB2. The diffusion activation energy of H generally increases with B content in W borides due to the increasing local charge deficit caused by strong B–B covalent bonds. This study is useful for evaluating the performance of W borides in a fusion environment.

Computational design of thermoelectric alloys through optimization of transport and dopability.

Alloying is a common technique to optimize the functional properties of materials for thermoelectrics, photovoltaics, energy storage etc. Designing thermoelectric (TE) alloys is especially challenging because it is a multi-property optimization problem, where the properties that contribute to high TE performance are interdependent. In this work, we develop a computational framework that combines first-principles calculations with alloy and point defect modeling to identify alloy compositions that optimize the electronic, thermal, and defect properties. We apply this framework to design n-type Ba2(1-x)Sr2xCdP2 Zintl thermoelectric alloys. Our predictions of the crystallographic properties such as lattice parameters and site disorder are validated with experiments. To optimize the conduction band electronic structure, we perform band unfolding to sketch the effective band structures of alloys and find a range of compositions that facilitate band convergence and minimize alloy scattering of electrons. We assess the n-type dopability of the alloys by extending the standard approach for computing point defect energetics in ordered structures. Through the application of this framework, we identify an optimal alloy composition range with the desired electronic and thermal transport properties, and n-type dopability. Such a computational framework can also be used to design alloys for other functional applications beyond TE.

Interactions of oxygen with intrinsic defects in L1[formula omitted][formula omitted]-TiAl in presence of substitutional solutes: Influence on diffusion kinetics

This work reexamines the insertion of O atoms in the L10γ-TiAl system using first-principles calculations and thermodynamic modeling in the independent point defect approximation. It includes a study of intrinsic point defects, the insertion of many alloying elements (more than twenty were considered), as well as a study of their interaction with oxygen. The formation of complex defects composed of either vacancies, anti-sites or solute elements is then studied. Results at the atomic scale show a high segregation of oxygen in titanium-rich environments: oxygen easily segregates onto Ti anti-sites (TiAl) and alloying elements are located in the vicinity of Al sub-lattices. DFT point-defect energetics shows that there is a clear correlation between the nature and site preference of an alloying element, and the oxygen segregation energy in the vicinity of this solute. The thermodynamic model shows that at equilibrium, oxygen does not occupy isolated interstitial sites but prefers to be located in the vicinity of Ti anti-sites or alloying elements. The effect of this strong segregation on oxygen diffusivity is discussed hereinafter. Results show a strong slowdown in oxygen diffusivity due to intrinsic defects. For Ti/Al >0.5 ratios, the traps for O diffusion are mainly constituted by Ti anti-sites, and the addition of solutes does not contribute much to the trapping of diffusing O atoms. For Ti/Al < 0.5 ratios however, the contribution of solutes to trapping phenomena can be very important, and a decrease by 1–2 orders of magnitude of effective O diffusion coefficients can be observed for temperatures around 800–1100 K.

Lattice stability and point defect energetics of TiSi2 and TiGe2 allotropes from first-principles calculations

This work determines the phase stabilities and point defect energetics of TiSi2 and TiGe2 allotropes using density functional theory. The primary focus is on the C49 and C54 allotropes, which compete during TiSi2 phase formation. It is found that the ground state structure for TiGe2 is the C54 allotrope, desirable for its low sheet resistance, while the less desirable, higher resistance C49 allotrope forms the ground state structure of TiSi2. A first attempt to understand the Ge atom's role in lowering the enthalpy of formation for the C54 structure is made from the perspective of the extended Born model. Charge density differences, the density of states, and Bader charge analysis show that these systems are predominantly ionically bonded, with the Ge atoms introducing additional covalent bond stability for the C54 allotrope. It is known that higher temperatures favor C54 formation in TiSi2. Helmholtz free energy calculations for TiSi2 suggest that the vibrational free energy does not drive the system to the C54 phase. The formation energies of certain point defects within the C49 structure of TiSi2 are less than 1 eV, which is consistent with experiments that show high defect concentrations. Thus, the driving force for C54 formation at higher temperatures may be related to the high defect concentration in the C49 allotrope.

Effect of different point-defect energetics in Ni80X20 (X=Fe, Pd) on contrasting vacancy cluster formation from atomistic simulations

Recent irradiation experiments have shown that smaller vacancy clusters are observed in Ni80Pd20 compared to Ni80Fe20. Using atomistic calculations, we find that the vacancy energetics are significantly different between the two alloys. Ni80Pd20 has lower vacancy migration barriers and lower vacancy-vacancy binding energies than Ni80Fe20. The consequence of these energetic differences is observed in molecular dynamics (MD) simulations, where despite higher vacancy diffusivity that would help in cluster formation, significantly reduced vacancy clusters are observed in Ni80Pd20 than Ni80Fe20. Calculations show that binding energy decreases and formation energy increases with increasing Ni-Ni bond lengths, and larger Ni-Ni bond lengths are observed in Ni80Pd20 than Ni80Fe20. Thus, the reduced vacancy-vacancy binding and higher formation energy due to longer Ni-Ni bonds in Ni80Pd20 are possibly the underlying reasons for smaller vacancy clusters in Ni80-Pd20 than Ni80Fe20. This study illustrates the unique effects of alloying elements on defect energetics and microstructural evolution in random alloys.

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.

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 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.

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.

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.

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.

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.