Anders Lindman

Size and shape of oxygen vacancies and protons in acceptor-doped barium zirconate

The defect induced chemical expansion in acceptor-doped barium zirconate is investigated using density-functional theory (DFT) calculations. The two defect species involved in the hydration reaction, the +2 charged oxygen vacancy and the proton interstitial forming a hydroxide ion, are considered both as free defects and in association with the dopants Y, In, Sc and Ga. The defect induced strain tensor lambda is introduced, which provides a natural generalisation of the ordinary chemical expansion to three dimensions and to anisotropic distortions. Both the addition of a vacancy and a proton cause anisotropic distortions and a net contraction of the lattice, indicating that both the vacancy and the hydroxide ion are smaller than the oxygen ion. The contraction is considerably larger for the vacancy and the net effect in hydration, when a vacancy is filled and two protons are added, is an expansion, consistent with the experimental findings. The effect of the dopants on the chemical expansion in hydration is found to be quite small, even if it is assumed that both the vacancy and the proton are fully associated with a dopant atom in the lattice.

Implications of the band gap problem on oxidation and hydration in acceptor-doped barium zirconate

Charge carrier concentrations in acceptor-doped proton-conducting perovskites are to a large extent determined by the hydration and oxidation of oxygen vacancies, which introduce protons and holes, respectively. First-principles modeling of these reactions involves calculation of formation energies of charged defects, which requires an accurate description of the band gap and the position of the band edges. Since density-functional theory (DFT) with local and semilocal exchange-correlation functionals (LDA and GGA) systematically fails to predict these quantities this can have serious implications on the modeling of defect reactions. In this study we investigate how the description of band gap and band-edge positions affects the hydration and oxidation in acceptor-doped BaZrO3. First-principles calculations are performed in combination with thermodynamic modeling in order to obtain equilibrium charge carrier concentrations at different temperatures and partial pressures. Three different methods have been considered: DFT with both semilocal (PBE) and hybrid (PBE0) exchange-correlation functionals, and many-body perturbation theory within the G(0)W(0) approximation. All three methods yield similar results for the hydration reaction, which are consistent with experimental findings. For the oxidation reaction, on the other hand, there is a qualitative difference. PBE predicts the reaction to be exothermic, while the two others predict an endothermic behavior. Results from thermodynamic modeling are compared with available experimental data, such as enthalpies, concentrations, and conductivities, and only the results obtained with PBE0 and G(0)W(0), with an endothermic oxidation behavior, give a satisfactory agreement with experiments.

Defect segregation to grain boundaries in BaZrO3 from first-principles free energy calculations

Acceptor-doped BaZrO3 is currently the most promising ceramic proton conductor for application in electrolyzers and reactor membranes. Its overall proton conductivity is, however, limited by space-charge formation due to defect segregation to grain boundaries (GBs). In this contribution, we determine the vibrational contribution to the free energy of GB formation and defect segregation in the symmetric Σ3 (112)[10] tilt GB in BaZrO3 in order to elaborate on the high temperature GB defect chemistry. We consider segregation of several different defect species: oxygen vacancies , protons and the four trivalent acceptor dopants Sc, In, Y and Gd . The calculations reveal that the segregation free energy of decreases with temperature while it remains fairly constant for , which increase the relative stability of with respect to with increasing temperature. As a consequence the onset for hydration of the GB core is shifted towards lower temperatures. For the dopants we find that both the segregation energy and entropy correlate with the ionic radius, where they are positive for the smaller dopants (Sc and In) while negative for the larger (Y, Gd). In turn, this leads to similar segregation free energies for all species, which are close to zero, at high temperatures where dopants are mobile, implying that dopant segregation is almost entirely driven by segregated positively charged defects. Neglecting the phonon contribution erroneously leads to the conclusion that the thermodynamic driving force for dopant segregation increases with increasing dopant radii, and it is therefore important to consider free energies when predicting the high temperature defect chemistry of BaZrO3 GBs.

Polaronic contributions to oxidation and hole conductivity in acceptor-doped BaZrO3

Acceptor-doped perovskite oxides like BaZrO3 are showing great potential as materials for renewable energy technologies where hydrogen acts an energy carrier, such as solid oxide fuel cells and hydrogen separation membranes. While ionic transport in these materials has been investigated intensively, the electronic counterpart has received much less attention and further exploration in this field is required. Here, we use density functional theory (DFT) to study hole polarons and their impact on hole conductivity in Y-doped BaZrO3. Three different approaches have been used to remedy the self-interaction error of local and semilocal exchange-correlation functionals: DFT + U, pSIC-DFT, and hybrid functionals. Self-trapped holes are found to be energetically favorable by about -0.1 eV and the presence of yttrium results in further stabilization. Polaron migration is predicted to occur through intraoctahedral transfer and polaron rotational processes, which are associated with adiabatic barriers of about 0.1 eV. However, the rather small energies associated with polaron formation and migration suggest that the hole becomes delocalized and bandlike at elevated temperatures. These results together with an endothermic oxidation reaction [A. Lindman, P. Erhart, and G. Wahnstrom, Phys. Rev. B 91, 245114 (2015)] yield a picture that is consistent with experimental data for the hole conductivity. The results we present here provide new insight into hole transport in acceptor-doped BaZrO3 and similar materials, which will be of value in the future development of sustainable technologies.

A Unifying Perspective on Oxygen Vacancies in Wide Band Gap Oxides

Wide band gap oxides are versatile materials with numerous applications in research and technology. Many properties of these materials are intimately related to defects, with the most important defect being the oxygen vacancy. Here, using electronic structure calculations, we show that the charge transition level (CTL) and eigenstates associated with oxygen vacancies, which to a large extent determine their electronic properties, are confined to a rather narrow energy range, even while band gap and the electronic structure of the conduction band vary substantially. Vacancies are classified according to their character (deep versus shallow), which shows that the alignment of electronic eigenenergies and CTL can be understood in terms of the transition between cavity-like localized levels in the large band gap limit and strong coupling between conduction band and vacancy states for small to medium band gaps. We consider both conventional and hybrid functionals and demonstrate that the former yields results in very good agreement with the latter provided that band edge alignment is taken into account.