Defect Formation Enthalpies Research Articles

Thermodynamical stability of carbon-based defects in α boron from first principles

We report an exhaustive study of the formation enthalpy and charge states of carbon-based defects in rhombohedral α boron within the density functional theory (DFT) that enables us to derive rules about the formation of complex carbon defects. We have accounted for one and two interstitial carbon atoms, eventually combined with one substitutional carbon atom and/or one interstitial boron atom and varied several geometric parameters. We find that when positioned in the plane perpendicular to the [111] rhombohedral axis, two carbon atoms turn out to preferentially form a graphite-like hexagon with four boron atoms. When positioned instead along the [111] axis, the distance between them strongly affects the defect thermodynamic stability, and we find in particular that additional negative charges strongly stabilize the diatomic carbon–carbon chains.

Modulating Lattice Oxygen Activity of Iron-Based Triple-Conducting Nanoheterostructure Air Electrode via Sc-Substitution Strategy for Protonic Ceramic Cells.

Iron-based perovskite air electrodes for protonic ceramic cells (PCCs) offer broad application prospects owing to their reasonable thermomechanical compatibility and steam tolerance. However, their insufficient electrocatalytic activity has considerably limited further development. Herein, oxygen-vacancy-rich BaFe0.6Ce0.2Sc0.2O3-δ (BFCS) perovskite is rationally designed by a facile Sc-substitution strategy for BaFe0.6Ce0.4O3-δ (BFC) as efficient and stable air electrode for PCCs. The BFCS electrode with an optimized Fe 3d-eg orbital occupancy and more oxygen vacancies exhibits a polarization resistance of ≈ 0.175Ωcm2 at 600°C, ≈ 1/3 of the BFC electrode (≈0.64Ωcm2). Simultaneously, BFCS shows favorable proton uptake with a low proton defect formation enthalpy (- 81kJmol-1). By combining soft X-ray absorption spectroscopy and electrical conductivity relaxation studies, it is revealed that the enhancement of Fe4+-O2- interactions in BFCS promotes the activation and mobility of lattice oxygen, triggering the activity of BFCS in both oxygen reduction and evolution reactions (ORR/OER). The single cell achieves encouraging output performance in both fuel cell (1.55 Wcm-2) and electrolysis cell (-2.96Acm-2 at 1.3V) modes at 700°C. These results highlight the importance of activating lattice oxygen in air electrodes of PCCs.

Impact of alloying elements on generalized stacking fault energy and twinning of Ag-based alloys

The creep strength of Ag-based alloys can be remarkably enhanced through the formation of twin structures. In this study, the effects of alloying elements, including Sn, In, Zn, Cu, Zr, Ni, Ir, Cr, and W, on the formation enthalpy of point defects and the generalized stacking fault energy of Ag-based alloys were investigated using first-principles calculations. The formation enthalpy of point defects serves as a measure of the difficulty of alloying element doping in Ag-based alloys. Calculation results shows that the ability of alloying element doping to form point defects follows the order of Sn > In > Zn > Cu > Zr > Ni > Ir > Cr > W. The generalized stacking fault energy along the [112‾](111) slip direction in Ag-based alloys characterizes the competition between dislocation slip and twinning. As the formation enthalpy of point defects increases, the intrinsic stacking fault energy increases, leading to a decrease in twinning tendency. Once the formation enthalpy of point defects corresponding to the alloying element exceeds 1 eV, the intrinsic stacking fault energy and twinning tendency remain relatively unchanged. Comprehensive analysis shows that alloying elements Sn and In effectively reduce the intrinsic stacking fault energy and promote twinning, which aligns with the behavior observed in commonly used Ag–Sn–In electrical contact materials.

Defect graph neural networks for materials discovery in high-temperature clean-energy applications.

We present a graph neural network approach that fully automates the prediction of defect formation enthalpies for any crystallographic site from the ideal crystal structure, without the need to create defected atomic structure models as input. Here we used density functional theory reference data for vacancy defects in oxides, to train a defect graph neural network (dGNN) model that replaces the density functional theory supercell relaxations otherwise required for each symmetrically unique crystal site. Interfaced with thermodynamic calculations of reduction entropies and associated free energies, the dGNN model is applied to the screening of oxides in the Materials Project database, connecting the zero-kelvin defect enthalpies to high-temperature process conditions relevant for solar thermochemical hydrogen production and other energy applications. The dGNN approach is applicable to arbitrary structures with an accuracy limited principally by the amount and diversity of the training data, and it is generalizable to other defect types and advanced graph convolution architectures. It will help to tackle future materials discovery problems in clean energy and beyond.

Effects of alloying elements on the super-lattice intrinsic stacking fault energy and ideal shear strength of Ni3Al crystals

The effects of alloying elements (Re,W,Ti,Ta,andMo) on the super-lattice intrinsic stacking fault energy and ideal shear strength (σmax) of Ni3Al crystals at 0 K was studied through first-principles calculation. The calculated formation enthalpy of point defects reveals that single solute atoms (i.e., Re,W,Ti,Ta,andMo) tend to occupy the Al site, while solute–solute complex defects (i.e., Re-Re, Re-W, Re-Mo, Re-Ta, Re-Ti, W-Mo, W-Ta, W-Ti, Mo-Ta, Mo-Ti, and Ta-Ti) tend to occupy the Al-Al site. The addition of single solute atom can increase the unstable stacking fault energy and ideal shear strength (σmax) of perfect Ni3Al crystals. Therefore, the doping of a single solute atom is beneficial for the creep strengthening of Ni3Al crystals. Compared with the doping of W,Ti,Ta,andMo, the doping of Re can more effectively impede the nucleation and movement of dislocations of Ni3Al crystals. Through the careful comparison of the creep properties of Ni3Al crystals with solute–solute complex defects, a conclusion can be drawn that the doping of alloy elements W and Re exhibit similar strengthening effects on the creep properties of Ni3Al crystals. W can be preliminarily predicted to replace part of Re in Ni3Al crystals without affecting creep properties. In addition, comprehensive evaluation reveals that the weak interaction between solute–solute complex defects should improve the strengths of Ni3Al crystals to a certain extent.

The N-body interatomic potentials for molecular dynamics simulations of diffusion in C15 Cr[formula omitted]Ta Laves phase

In this work, the interatomic potentials for modeling diffusion in the C15 Cr2Ta Laves phase were constructed within the N-body approach. The potential for Ta–Ta interactions reproduces the lattice parameter, cohesive energy, elastic constants, equation of state, thermal expansion, point defect energies, and phonon dispersion of body-centered cubic Ta in qualitative agreement with density functional theory (DFT) data and almost quantitative agreement with available experimental data in the temperature range of stability of C15 Cr2Ta Laves phase. The potential for Cr–Ta interactions reproduces the elastic constants, point defect properties, equilibrium volumes, and formation enthalpies of Cr–Ta structures in qualitative agreement with DFT data. Also, it reproduces the lattice stability and high-temperature formation enthalpy of C15 Cr2Ta Laves phase in very close agreement with the available experimental data. The calculations of diffusion coefficients with constructed potentials showed that diffusion in C15 Cr2Ta lattice is governed by Cr atoms which cannot move without creation of vacancies. The constructed potentials can be used in further investigations of diffusion processes in Cr–Ta phases at temperatures up to 2000 K, while the obtained results on diffusion coefficients in C15 Cr2Ta Laves phase would be useful in the rational design of Cr–Ta based alloys.

Oxygen Defect Formation Thermodynamics of CaMnO3: A Closer Look

Sustainable hydrogen production is one of the most important topics in modern energy economics. Of technological relevance are, for example, electrochemical and thermal splitting of water. For such processes anode materials with a variable concentration of oxygen defects are required. Herein, the oxygen defect thermochemistry of a possible anode material, the perovskite CaMnO3, is investigated theoretically. The aim of this work is to identify reliable quantum chemical methods for the calculation of oxygen defect formation enthalpies and entropies, including configuration entropy, which is usually neglected. All possible defect configurations in a supercell are computed to obtain the configuration entropy using Boltzmann statistics. Various generalized gradient approximation (GGA), meta‐GGA, and hybrid functionals as implemented in the solid‐state programs CRYSTAL and VASP are evaluated for the calculation of structure parameters, electronic and magnetic properties, and reaction energies of CaMnO3. The global hybrid functional PW1PW gives the most accurate overall description of CaMnO3 and is therefore recommended for future theoretical studies of more efficient water‐splitting catalysts based on calcium manganate.

Charge Compensation by Iodine Covalent Bonding in Lead Iodide Perovskite Materials

Metal halide perovskite materials (MHPs) are a family of next-generation semiconductors that are enabling low-cost, high-performance solar cells and optoelectronic devices. The most-used halogen in MHPs, iodine, can supplement its octet by covalent bonding resulting in atomic charges intermediate to I− and I0. Here, we examine theoretically stabilized defects of iodine using density functional theory (DFT); defect formation enthalpies and iodine Bader charges which illustrate how MHPs adapt to stoichiometry changes. Experimentally, X-ray photoelectron spectroscopy (XPS) is used to identify perovskite defects and their relative binding energies, and validate the predicted chemical environments of iodine defects. Examining MHP samples with excess iodine compared with near stoichiometric samples, we discern additional spectral intensity in the I 3d5/2 XPS data arising from defects, and support the presence of iodine trimers. I 3d5/2 defect peak areas reveal a ratio of 2:1, matching the number of atoms at the ends and middle of the trimer, whereas their binding energies agree with calculated Bader charges. Results suggest the iodine trimer is the preferred structural motif for incorporation of excess iodine into the perovskite lattice. Understanding these easily formed photoactive defects and how to identify their presence is essential for stabilizing MHPs against photodecomposition.

Ion transport mechanism in anhydrous lithium thiocyanate LiSCN Part I: ionic conductivity and defect chemistry.

This work reports on the ion transport properties and defect chemistry in anhydrous lithium thiocyanate Li(SCN), which is a pseudo-halide Li+ cation conductor. An extensive doping study was conducted, employing magnesium, zinc and cobalt thiocyanate as donor dopants to systematically vary the conductivity and derive a defect model. The investigations are based on impedance measurements and supported by other analytical techniques such as X-ray powder diffraction (XRPD), infrared (IR) spectroscopy, and density functional theory (DFT) calculations. The material was identified as Schottky disordered with lithium vacancies being the majority mobile charge carriers. In the case of Mg2+ as dopant, defect association with lithium vacancies was observed at low temperatures. Despite a comparably low Schottky defect formation enthalpy of (0.6 ± 0.3) eV, the unexpectedly high lithium vacancy migration enthalpy of (0.89 ± 0.08) eV distinguishes Li(SCN) from the chemically related lithium halides. A detailed defect model of Li(SCN) is presented and respective thermodynamic and kinetic data are given. The thiocyanate anion (SCN)- has a significant impact on ion mobility due to its anisotropic structure and bifunctionality in forming both Li-N and Li-S bonds. More details about the impact on ion dynamics at local and global scale, and on the defect chemical analysis of the premelting regime at high temperatures are given in separate publications (Part II and Part III).

N -type electrical conduction in SnS thin films

Tin monosulfide (SnS) usually exhibits p-type conduction due to the low formation enthalpy of acceptor-type defects, and as a result n-type SnS thin films have never been obtained. This study realizes n-type conduction in SnS thin films for the first time by using RF-magnetron sputtering with Cl doping and sulfur plasma source during deposition. N-type SnS thin films are obtained at all the substrate temperatures employed in this study (221-341 C), exhibiting carrier concentrations and Hall mobilities of ~2 x 10 18 cm-3 and 0.1-1 cm V-1s-1, respectively. The films prepared without sulfur plasma source, on the other hand, exhibit p-type conduction despite containing a comparable amount of Cl donors. This is likely due to a significant amount of acceptor-type defects originating from sulfur deficiency in p-type films, which appears as a broad optical absorption within the band gap. The demonstration of n-type SnS thin films in this study is a breakthrough for the realization of SnS homojunction solar cells, which are expected to have a higher conversion efficiency than the conventional heterojunction SnS solar cells.

Role of oxygen diffusion in the dislocation reduction of epitaxial AlN on sapphire during high-temperature annealing

Recovery of epitaxial AlN films on sapphire at high temperatures is now an established process to produce pseudo-substrates with high crystalline perfection, which can be used to grow epitaxial structures for UV-light-emitting devices. To elucidate the elementary mechanisms taking place during the thermal treatment of MOVPE-grown films, we studied as-grown and annealed samples combining transmission electron microscopy techniques and secondary ion mass spectrometry (SIMS). By using SIMS, we find a temperature-dependent increase in the overall oxygen content of the films, which cannot be explained quantitatively with either simple bulk or pure pipe-diffusion from the sapphire substrate. Instead, we propose a lateral outdiffusion from the dislocation cores to explain qualitatively and quantitatively the presence of observed oxygen concentration plateaus. Based on the formation enthalpy of various atomic defects and complexes found in literature, we conclude that the di-oxygen/aluminum vacancy complex (VAl–2ON) is the dominant point defect controlling the annealing process. The formation of this defect at high temperatures promotes a dislocation core climb process, which causes the annihilation/fusion of the threading dislocation segments.

Determination of the thermodynamic potentials of metallic glasses and their relation to the defect structure

We performed calorimetric and shear modulus measurements on four bulk metallic glasses upon heating up to the temperature of the complete crystallization as well as in the fully crystallized state. On the basis of calorimetric experiments, we calculated the excess thermodynamic potentials with respect to the crystalline state—the enthalpy ΔH, entropy ΔS and Gibbs free energy ΔΦ—as functions of temperature. Using high-frequency shear modulus measurements we show that calorimetric determination of ΔH, ΔS and ΔΦ is consistent with the calculation of these potentials within the framework of the interstitialcy theory (IT) within a 15% uncertainty in the worst case for all MGs under investigation. It is concluded that the physical origin of the excess thermodynamic potentials in MGs can be related to a system of interstitial-type defects frozen-in from the liquid state upon melt quenching as suggested by the IT. The estimates of the defect formation enthalpy H f and entropy S f show that H f scales with the shear modulus while S f is quite large (10 k B to 20 k B), in line with the basic assumptions of the IT.

Impact of point defects on the electrical properties of selenium: A density functional theory investigation with discussion of the entropic term

Selenium in ambient conditions exhibits two crystalline allotropic forms. The thermodynamically stable phase is the pseudo-1D trigonal form with ${}^{1}{/}_{\ensuremath{\infty}}$[Se] chains. A metastable phase composed of $[{\mathrm{Se}}_{8}]$ rings also coexists. Both are studied herein by means of density functional theory. The recent SCAN functional offers a fair description of both phases. The Birch-Murnaghan equation of states is fitted onto ab initio results to obtain the energy-volume and pressure-energy relationships. Phonon properties (bands and DOS) are computed and a pressure-temperature phase diagram is derived. Intrinsic and extrinsic defect formation enthalpies are also computed using SCAN functional and HSE06-GD3 for the band shifts. The low $p$-type conductivity of the trigonal phase can be attributed to Se self-interstitials while the very low conductivity of the metastable phase is related to very deep native defects. Antimony, and bromine extrinsic defects are tested as potential dopants. Of those three, only antimony in the trigonal phase seems to possibly have a positive impact on the conductivity. Finally, the configurational entropy linked to defect creation is computed. Our calculations clearly show that the usual assumption that defect entropy is negligible compared to the enthalpy seems relevant.

Possibility of interstitial Na as electron donor in Yb14MgSb11

Here, we investigate Na-doping Yb14MgSb11 as a potential route to increase carrier concentration based on an improved multiband model. Experimental transport data were collected on Yb14-xNaxMgSb11 samples prepared by ball milling and hot pressing. We show that Na increases the Seebeck coefficient and resistivity, suggesting that it behaves not as a substituent but as an interstitial electron donor under this synthesis and processing conditions, decreasing hole carrier concentration. Density functional theory (DFT) calculations of equilibrium phases, defect formation enthalpies, and band diagrams shed light on the defect-modified carrier concentrations. Depending on the equilibrium phase, Na can behave as a substitutional or interstitial defect.

One-to-one correlation between the kinetics of the enthalpy changes and the number of defects assumed responsible for structural relaxation in metallic glasses

Parallel measurements of the enthalpy and high-frequency shear modulus changes occurring upon structural relaxation of five bulk metallic glasses are performed. An analysis showed that there exists a one-to-one correlation between the change of the molar enthalpy and the alteration of the number of defects calculated within the framework of the Interstitialcy theory on the basis of shear modulus relaxation data. The defect formation enthalpy derived using this correlation agrees quite well with this quantity accepted in the Interstitialcy theory.

Visualizing defect energetics

Defect energetics impact most thermal, electrical and ionic transport phenomena in crystalline compounds. The key to chemically controlling these properties through defect engineering is understanding the stability of (a) the defect and (b) the compound itself relative to competing phases at other compositions in the system. The stability of a compound is already widely understood in the community using intuitive diagrams of formation enthalpy (ΔHf) vs. composition, in which the stable phases form the 'convex-hull'. In this work, we re-write the expression of defect formation enthalpy (ΔHdef) in terms of the ΔHf of the compound and its defective structure. We show that ΔHdef for a point defect can be simply visualized as intercepts in a two-dimensional convex-hull plot regardless of the number of components in the system and choice of chemical conditions. By plotting ΔHf of the compound and its defects all together, this visualization scheme directly links defect energetics to the compositional phase stability of the compound. Hence, we simplify application level defect thermodynamics within a widely used visual tool understandable from basic materials science knowledge. Our work will be beneficial to a wide community of experimental chemists seeking to build an intuition for appropriate choice of chemical conditions for defect engineering.

Correlation between the Enthalpy of Melting and the Enthalpy of Anti-Frenkel Defect Formation in Homologous MF2 Fluorite Crystals

The homologous series of MF2 (M = Ca2+, Sr2+, Ba2+, Cd2+, Pb2+, Sm2+, Eu2+, Yb2+, Ra2+, and Hg2+) crystals having the fluorite structure (CaF2, space group $$Fm\bar {3}m,$$ Z = 4) holds an important place in fluoride materials science. A correlation between the enthalpy of anti-Frenkel defect formation (Hf) and the enthalpy of melting (Hm) was elucidated for CaF2, SrF2, BaF2, and PbF2 based on the most reliable experimental data set: Hf (kJ/mol) = 8.6Hm (kJ/mol) or Hf (eV) = 0.089Hm (kJ/mol). Experimentally determined Hm values were used to calculate the enthalpies of defect formation Hf = 2.0 and 2.6 eV for CdF2 and EuF2 crystals, respectively. The correlation is prognostic for the whole series of homologous MF2 fluorite crystals and for SrCl2.

Simulation of Intrinsic Defects and Cd Site Occupation in LaIn<sub>3</sub> and LuIn<sub>3</sub>

In previous work, perturbed angular correlation spectroscopy (PAC) was used to determine jump rates of 111Cd, the daughter of the 111In radiotracer, in the series of phases RIn3 (R = rare-earth element) through nuclear quadrupole relaxation. Greater relaxation, indicating faster Cd jump rates, was observed in heavy rare-earths for compositions more deficient in indium, as would be expected for diffusion mediated by vacancies on the In sublattice. On the other hand, greater relaxation was observed for light rare-earths (R = La, Ce, and Pr) for compositions with excess indium, suggesting Cd diffusion is mediated there by a different mechanism. In this work, computer simulations were carried out to better understand the nature of the relaxation observed for the light rare-earths and the origin of the change in behavior across the rare-earth series. As a first step, formation enthalpies of intrinsic defects were calculated using density functional theory (DFT) for series end-members LaIn3 and LuIn3. Both compounds were found to exhibit Schottky thermal disorder. Additional DFT simulations show that the binding enthalpy between In-and R-vacancies is larger in LaIn3 than in LuIn3, suggesting that diffusion in LaIn3 might be mediated by divacancies. Site enthalpies of Cd also were calculated, and it was found more favorable energetically for Cd to occupy the In sublattice than the R sublattice in both end-member phases.

Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy

A concise procedure to determine the self-consistent Fermi energy and defect and carrier concentrations in an extended crystalline system is presented. It is assumed that the formation enthalpies of a set of variously charged point defects in thermodynamic equilibrium are known, as well as the density of electronic states in the defect-free system. By applying the constraint of overall charge neutrality, the self-consistent Fermi energy is determined using an iterative searching routine. The procedure is incorporated within a Fortran code ‘SC-FERMI’: the input consists of the defect formation energies, density of sites where they can form, and the degeneracy of each charge state; the material band gap; and the calculated density of states of the pristine system. The output is the self-consistent Fermi energy, the total concentrations of each defect as well as the concentration of its individual charge states, and the free carrier concentrations. Furthermore, the procedure facilitates fixing the concentration of one or more defects and determining the resulting self-consistent Fermi energy and concentrations of other defects (performed using the related code ‘FROZEN-SC-FERMI’), thus modelling ‘frozen-in’ defects which may form by kinetic, rather than thermodynamic, processes. One can fix the total concentration or the concentration of a particular charge state; it is also possible to introduce new defects with a fixed concentration, but here the charge state must be specified. The background theory is discussed in some detail, and the operation of the program is demonstrated by some examples. Program summaryProgram Title:SC-FERMIProgram Files doi:http://dx.doi.org/10.17632/dh3hjdf4fc.1Licensing provisions: MIT licenseProgramming language:FORTRAN 90Nature of problem: To determine the self-consistent Fermi energy and equilibrium defect and carrier concentrations given a set of point defect formation energies in a crystalline system, assuming the constraint of charge neutrality.Solution method: The concentrations of each defect in each charge state are calculated, as are the free carrier concentrations. These concentrations are functions of the Fermi energy. The code, using an iterative search algorithm, determines the Fermi energy that satisfies the charge neutrality constraint (the self-consistent Fermi energy). The defect and carrier concentrations at that Fermi energy are then reported, as well as the Fermi energy itself.Restrictions: Thermodynamic equilibrium is assumed. The defect formation enthalpies and electronic density of states of the pristine system must be known.Additional comments: The concentrations of defects can be fixed to a particular value, thus modelling ‘frozen-in’ defects formed by e.g. kinetic processes. This procedure is facilitated by the related program, FROZEN-SC-FERMI, which is identical to SC-FERMI apart from the additional defect concentration fixing routine.

Effect of stress on vacancy formation and migration in body-centered-cubic metals

Vacancy formation and migration control self-diffusion in pure crystalline materials, whereas irradiation produces high concentrations of vacancy and self-interstitial atom defects, exceeding by many orders of magnitude the thermal equilibrium concentrations. The defects themselves, and the extended dislocation microstructure formed under irradiation, generate strongly spatially fluctuating strain and stress fields. These fields alter the local formation and migration enthalpies of defects, and give rise to the anisotropy of diffusion even if in the absence of stress the diffusion tensor is isotropic. We have performed ab initio calculations of formation and migration energies of vacancies in all the commonly occurring body-centered-cubic (bcc) metals, including alkaline, alkaline-earth and transition metals, and computed elastic dipole and relaxation volume tensors of vacancies at the equilibrium lattice positions and along the vacancy migration pathways. We find that in all the bcc metals the dipole tensor of a migrating vacancy at a saddle point exhibits an anticrowdion character. Applied external stresses or the local stresses generated by dislocations may enhance or suppress anisotropic diffusion by altering the energy barriers with respect to the direction of migration of a defect.