Search

We calculate the stability of the MAX-phase materials ${\mathrm{Zr}}_{n+1}{\mathrm{AlC}}_{n}$ and ${\mathrm{Ti}}_{n+1}{\mathrm{AlC}}_{n}$ in the context of the M-A-X ternary phase diagrams and competing binary and ternary compounds, as a function of temperature, by applying density functional theory (DFT) within the quasiharmonic approximation. By examining the convex hull of free energy we find that the Zr-based MAX phases are thermodynamically unstable at room temperature and below with respect to decomposition to carbide and intermetallics, although with increasing temperature the ${\mathrm{Zr}}_{3}{\mathrm{AlC}}_{2}$ phase becomes stable. On the other hand, the pure ${\mathrm{Ti}}_{2}\mathrm{AlC}$ phase is thermodynamically stable at room temperature, consistent with the success in its synthesis.

Vacancies in iron are hydrogen traps, important in the understanding of hydrogen embrittlement of steel. We present a grand canonical approach to computing the trap occupancy as a function of both temperature and hydrogen concentration from practically zero to super-saturation. Our method couples a purpose-made machine-learned H-Fe potential, which enables rapid sampling with near density functional theory accuracy, with a statistical mechanical calculation of the trap occu- pancy using the technique of nested sampling. In contrast to the conventional assumption (based on Oriani theory) that at industrially relevant hydrogen concentrations and ambient conditions vacancy traps are are fully occupied, we find that vacancy traps are less than fully occupied under these conditions, necessitating a reevaluation of how we think about “mobile hydrogen” in iron and steel.

We present an approach that enables an efficient and accurate study of dynamically unstable crystals over the full temperature range. The approach is based on an interatomic potential fitted to ab initio molecular dynamics energies for both the high- and low-temperature stable phases. We verify by comparison to explicit ab initio simulations that such a bespoke potential, for which we use here the functional form of the embedded atom method, provides accurate transformation temperatures and atomistic features of the transformation. The accuracy of the potential makes it an ideal tool to study the important impact of finite size and finite time effects. We apply our approach to the dynamically unstable $\ensuremath{\beta}$ (bcc) titanium phase and study in detail the transformation to the low-temperature stable hexagonal $\ensuremath{\omega}$ phase. We find a large set of previously unreported linear-chain disordered (LCD) structures made up of three types of ${[111]}_{\ensuremath{\beta}}$ linear-chain defects that exhibit randomly disordered arrangements in the ${(111)}_{\ensuremath{\beta}}$ plane.

Thermodynamic properties of ZrC are calculated up to the melting point (${T}^{\mathrm{melt}}\ensuremath{\approx}3700\phantom{\rule{0.28em}{0ex}}\text{K}$), using density functional theory (DFT) to obtain the fully anharmonic vibrational contribution, and including electronic excitations. A significant improvement is found in comparison to results calculated within the quasiharmonic approximation. The calculated thermal expansion is in better agreement with experiment and the heat capacity reproduces rather closely a CALPHAD estimate. The calculations are presented as an application of a development of the upsampled thermodynamic integration using Langevin dynamics (UP-TILD) approach. This development, referred to here as two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD), is the inclusion of tailored interatomic potentials to characterize an intermediate reference state of anharmonic vibrations on a two-stage path of thermodynamic integration between the original DFT quasiharmonic free energy and the fully anharmonic DFT free energy. This approach greatly accelerates the convergence of the calculation, giving a factor of improvement in efficiency of $\ensuremath{\sim}50$ in the present case compared to the original UP-TILD approach, and it can be applied to a wide range of materials.

The electron energy-loss near-edge structure ~ELNES! at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia ~YSZ! materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method ~NFP-LMTO! as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater’s transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr 2Y2O7 are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

We derive a formula, useful for first-principles calculations, which relates the free energy of an oxide/metal interface to the free energies of surfaces and the work of separation of the interface. We distinguish the latter mechanical quantity from the thermodynamic work of adhesion, and we describe explicitly how both may be calculated. Our formulas for interfacial and surface energies are cast in terms of quantities which can be calculated or looked up in tables, and include as additional parameters the ambient temperature and partial pressure of oxygen ${P}_{{\mathrm{O}}_{2}}.$ From total-energy calculations for the $\mathrm{Nb}(111)/\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ (0001) interface, free Nb and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ surfaces, we obtain firstly numerical estimates of the works of separation, which are independent of ${P}_{{\mathrm{O}}_{2}}.$ We then obtain surface energies, interfacial energies, and the equilibrium work of adhesion as a function of ${P}_{{\mathrm{O}}_{2}}.$

We predict the existence of an isostructural first-order phase transition in high-pressure Al-rich NiAl alloys, between vacancy-rich and antisite-rich phases. A critical point terminates the region of phase coexistence. The driving force for this phase transition is the positive defect mixing enthalpy originating from elastic interaction between vacancies and antisites on the Ni sublattice. We highlight the similarity between the critical behavior of Al-rich alloys and that of binary liquid mixtures. Analogous isostructural phase transitions are expected in other compounds with constitutional defects.

The strontium titanate $\ensuremath{\Sigma}3\phantom{\rule{0.3em}{0ex}}(112)\phantom{\rule{0.3em}{0ex}}[\overline{1}10]$ grain boundary has been investigated using aberration-corrected high-resolution transmission electron microscopy and exit wave-function reconstruction. By quantitatively comparing the experimental exit wave phase with that expected from relaxed model structures obtained by density-functional theory, it has been possible to differentiate between two proposed structures not significantly different in their calculated energies, and to deduce information about three-dimensional atomic arrangements near the boundary using the reconstructed exit wave-function phase.

We address the calculation within density functional theory (DFT) of defect formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calculated defect formation energies, especially those of charged defects, are independent of the principal approximations of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calculation must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell containing a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chemical potentials of the atomic species. Our results for formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.

A method for calculating free-energy differences based on a free-energy perturbation (FEP) formalism in an alloy system described by two different Hamiltonians is reported. The intended application is the calculation of solid-liquid phase equilibria in alloys with the accuracy of first-principles electronic density-functional theory (DFT). For this purpose free energies are derived with a classical interatomic potential, and FEP calculations are used to compute corrections to these reference values. For practical applications of this approach, due to the relatively high computational cost of DFT calculations, it is critical that the FEP calculations converge rapidly in terms of the number of samples used to estimate relevant ensemble averages. This issue is investigated in the current study employing two classical interatomic-potential models for Ni-Cu. These models yield differences in predicted phase-boundary temperatures of approximately 100 K, comparable to those that might be expected between a DFT Hamiltonian and a well-fit classical potential. We show that for pure elements the FEP calculations converge rapidly with the number of samples, yielding free-energy differences converged to within a fraction of a meV/atom in a few dozen energy calculations. For a concentrated equiatomic alloy similar precision requires roughly a hundred samples. The results suggest that the proposed methodology could provide a computationally tractable framework for calculating solid-liquid phase equilibria in concentrated alloys with DFT accuracy.

The technological importance of polycrystalline strontium titanate $({\text{SrTiO}}_{3})$ is directly linked to its interfacial and grain boundary properties, which are at present poorly understood. A complete understanding (including links with experiment) requires information from many length scales, including electronic and atomistic, up to microstructural and macroscopic. In addition, the size and complexity of many general grain boundaries makes first-principles simulations prohibitively expensive. We have tested the ability of a number of interatomic potentials from the literature to accurately describe at least the structures of some simple grain boundaries in ${\text{SrTiO}}_{3}$. The potentials we have tested are of three types: rigid ion model with either fixed formal or partial charges and shell model. We have also performed a detailed density functional theory (DFT) study of the same boundaries and used this data (interface structures and energies) to validate the interatomic potentials. Our conclusion is that none of the potentials can reproduce the energy ordering of the boundaries predicted by the DFT calculations. The boundary structures produced by some of the potentials do however agree reasonably well with the DFT structures. We discuss the implications of our findings for ionic oxide grain boundary research and critically examine the rigid ion and shell model approximations.

The surface structure of magnetite ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ in contact with oxygen and water is investigated using spin-density functional theory plus on-site Coulomb interactions. The present results unravel apparent contradictions in the experimental data regarding the equilibrium stoichiometry of the bare surface termination. Both for 298 and $1200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the equilibrium structure is terminated by $\frac{1}{4}$ monolayer (ML) of iron (Fe) on top of a full oxygen layer, consistent with an earlier low-energy electron diffraction analysis. Nonetheless, the calculated negative slope of the surface energies vs oxygen partial pressure shows that a $\frac{1}{2}$ ML Fe termination would become stable under oxygen-poor conditions at high temperatures, in agreement to interpretation of scanning tunneling microscopy experiments. Initial water adsorption is dissociative and saturates when all Fe sites are occupied by OH groups, while the H atoms bind to surface oxygen. Further, water bridges the OH and H groups resulting in a unique type of H-bonded molecular water with its oxygen forming a hydronium-ion-like structure $\mathrm{O}{\mathrm{H}}_{3}^{+}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}$. This water structure is different from the water dimeric structures found as yet on oxide and metal surfaces for partially dissociated $({\mathrm{H}}_{2}\mathrm{O}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}\text{\ensuremath{-}}\mathrm{H})$ overlayers.

We describe a self consistent magnetic tight-binding theory based in an expansion of the Hohenberg-Kohn density functional to second order, about a non spin polarised reference density. We show how a first order expansion about a density having a trial input magnetic moment leads to the Stoner--Slater rigid band model. We employ a simple set of tight-binding parameters that accurately describes electronic structure and energetics, and show these to be transferable between first row transition metals and their alloys. We make a number of calculations of the electronic structure of dilute Cr impurities in Fe which we compare with results using the local spin density approximation. The rigid band model provides a powerful means for interpreting complex magnetic configurations in alloys; using this approach we are able to advance a simple and readily understood explanation for the observed anomaly in the enthalpy of mixing., Comment: Submitted to Phys Rev B

Density functional theory calculations have been used to study relaxed interstitial configurations in FeCr alloys. The ionic and electronic ground states of 69 interstitial structures have been determined. Interstitials were placed in alloys with up to 14 at. % Cr. Cr atoms were either monatomically dispersed or clustered together within a periodically repeated supercell consisting of 4x4x4 cubes of bcc unit cells. The distance between the interstitials and Cr atoms was varied within the supercells. It is shown that Cr atoms beyond third-nearest-neighbor distance from the interstitial can still have an interaction with it of up to 0.9 eV. The multibody nature of the Cr-Cr interactions causes the Cr-interstitial interaction to be strongly concentration dependent. The Cr-Cr interaction in defect-free alloys is also dependent on the overall Cr concentration. The effective Cr-Cr repulsion is weaker in alloys than in an environment of pure Fe. Apart from the Cr concentration, the Cr-interstitial interaction also depends on the dispersion level of Cr atoms beyond third-nearest-neighbor distance from the interstitial. The formation energy differences between dumbbell interstitials with different orientations are independent of the Cr concentration. We show that the long-range influence of Cr atoms on the interstitial is not due to the interstitial strain field protruding into Cr-rich parts of the supercells. The Fermi-level and band energies were found not to be the sole governing parameter in determining the formation energies. Implications for the construction of empirical potentials are discussed.

First principles calculations of the Sigma 5 (310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect., Comment: 13 pages, 5 figures; Accepted in Phys. Rev. B

Density functional theory calculations have been used to study the mixing behavior of Fe-Cr alloys. The heats of formation $\ensuremath{\Delta}{E}_{f}$ of 65 Fe-Cr structures in their magnetic ground states have been determined. A positive $\ensuremath{\Delta}{E}_{f}$ is found over most of the concentration range. From 0--12 % Cr a small negative $\ensuremath{\Delta}{E}_{f}$ down to $\ensuremath{-}8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom is found. The origin of the negative $\ensuremath{\Delta}{E}_{f}$ in Fe-rich structures is traced to the solution energy of single Cr atoms. At low concentration, Cr atoms in Fe repel each other, causing ordering. The Cr-Cr interactions are well reproduced even without the self-consistent relaxation of the electron density and the positions of atoms. Multi-ion (or concentration-dependent) interactions are indispensable in order to describe the whole phase diagram. The interesting magnetic situation that arises when ferromagnetic and antiferromagnetic metals are mixed in different ratios is discussed with reference to nearest- and next-nearest-neighbor clusters of Cr in Fe. Magnetic frustration leads to a strong dependence of the Cr moment on the number of Cr neighbors. The ``normal'' chemical-mixing energy and the influence of magnetism are distinguished by comparing magnetic and nonmagnetic calculations for similar systems.

Density-functional theory calculations, within the plane-wave-ultrasoft pseudopotential framework, were performed in the ⟨110⟩ projection for MgO and for the coherent {111} $\mathrm{Ag}\ensuremath{-}\mathrm{Mg}\mathrm{O}$ polar interface. First-principles calculations were incorporated in high-resolution transmission electron microscopy (HRTEM) simulations by converting the charge density into electron scattering factors to examine the influence of charge transfer, charge redistribution at the interface, and ionicity on the dynamical electron scattering and on calculated HRTEM images. It is concluded that the ionicity of oxides and the charge redistribution at interfaces play a significant role in HRTEM image simulations. In particular, the calculations show that at oxygen-terminated {111} $\mathrm{Ag}\mathrm{Mg}\mathrm{O}$ interfaces the first oxygen layer at the interface is much brighter than that in calculations with neutral atoms, in agreement with experimental observations.

s131d and s231d reconstructions of the (001) SrTiO3 surface were studied using the first-principles fullpotential linear muffin-tin orbital method. Surface energies were calculated as a function of TiO2 chemical potential, oxygen partial pressure and temperature. The s131d unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the s231d Ti2O3 reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the s131d surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the s231d reconstructions would be easier to image than the s131d surfaces. The possibility that the presence of oxygen vacancies would destabilise the s131d surfaces was also investigated. If the s131d surfaces are unstable then there exists the further possibility that the s2 31d DL-TiO2 reconstruction [Natasha Erdman et al. Nature (London) 419, 55 (2002)] is stable in a TiO2-rich environment and for pO2 .10−18 atm.

The electron energy-loss near-edge structure ~ELNES! at the O K edge has been studied in yttria-stabilized zirconia ~YSZ!. The electronic structure of YSZ for compositions between 3 and 15 mol % Y2O3 has been computed using a pseudopotential-based technique to calculate the local relaxations near the O vacancies. The results showed phase transition from the tetragonal to cubic YSZ at 10 mol % of Y2O3, reproducing experimental observations. Using the relaxed defect geometry, calculation of the ELNES was carried out using the full-potential linear muffin-tin orbital method. The results show very good agreement with the experimental O K-edge signal, demonstrating the power of using ELNES to probe the stabilization mechanism in doped metal oxides.