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We apply density functional theory to estimate the energetics and charge carrier concentrations and, in turn, the resistance across the (210)[001] and (111)[11¯0] grain boundaries (GBs) in proton conducting Y-doped BaZrO3, assessing four commonly used approximations in space charge modelling. The abrupt core approximation, which models the GB core as a single atomic plane rather than a set of multiple atomic planes, gives an underestimation of the GB resistance with around one order of magnitude for both GBs. The full depletion approximation, which assumes full depletion of effectively positive charge carriers in the space charge layers, has negligible effect on the GB resistance compared to a more accurate model with decaying depletion. Letting protons redistribute in the continuity between atomic planes gives a GB resistance up to 5 times higher than the case where protons are restricted to be located at atomic planes. Finally, neglecting trapping effects between the acceptor doping and the defect charge carriers gives a higher GB resistance with a factor of roughly 2. [ABSTRACT FROM AUTHOR]

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)[1̅10] 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 UGRAPHIC DISPLAY="INLINE" ID="UGT1" SRC="UGT1"/, protons UGRAPHIC DISPLAY="INLINE" ID="UGT2" SRC="UGT2"/ and the four trivalent acceptor dopants Sc, In, Y and Gd UGRAPHIC DISPLAY="INLINE" ID="UGT3" SRC="UGT3"/. The calculations reveal that the segregation free energy of UGRAPHIC DISPLAY="INLINE" ID="UGT4" SRC="UGT4"/ decreases with temperature while it remains fairly constant for UGRAPHIC DISPLAY="INLINE" ID="UGT5" SRC="UGT5"/, which increase the relative stability of UGRAPHIC DISPLAY="INLINE" ID="UGT6" SRC="UGT6"/ with respect to UGRAPHIC DISPLAY="INLINE" ID="UGT7" SRC="UGT7"/ 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. [ABSTRACT FROM AUTHOR]

Differentiating chemical and thermal expansion is virtually impossible to achieve experimentally. While thermal expansion stems from a softening of the phonon spectra, chemical expansion depends on the chemical composition of the material. In the present contribution, we, for the first time, completely decouple thermal and chemical expansion through first principles phonon calculations on BaCeO3, providing new fundamental insights to lattice expansion. We assess the influence of defects on thermal expansion, and how this in turn affects the interpretation of chemical expansion and defect thermodynamics. The calculations reveal that the linear thermal expansion coefficient is lowered by the introduction of oxygen vacancies being 10.6 × 10−6 K−1 at 300 K relative to 12.2 × 10−6 K−1 for both the protonated and defect-free bulk lattice. We further demonstrate that the chemical expansion coefficient upon hydration varies with temperature, ranging from 0.070 to 0.115 per mole oxygen vacancy. Ultimately, we find that, due to differences in the thermal expansion coefficients under dry and wet conditions, the chemical expansion coefficients determined experimentally are grossly underestimated – around 55% lower in the case of 10 mol% acceptor doped BaCeO3. Lastly, we evaluate the effect of these volume changes on the vibrational thermodynamics. [ABSTRACT FROM AUTHOR]

In the present contribution, we assess the efficiency of the alkali metals (Na, K, Rb and Cs) as A-site acceptor dopants in proton conducting BaZrO3 by first principles calculations. The calculated acceptor–proton complexes become weaker with increasing dopant size, with binding energies ranging from −0.33 eV for Na to −0.10 eV for Cs, which is in the range of, or even lower than, those found for B-site doped BaZrO3. By mapping out all relevant minimum energy pathways for the proton, we reveal that the highest migration energy barrier for most of the alkali metals is comparable or even lower than that of Y. Further, all A-site dopants display more exothermic hydration enthalpies compared to that of Y-doped BaZrO3, ranging from −131 kJ mol−1 to −83 kJ mol−1 for Na and Cs, respectively. The calculated dopant solubility increases in the order Na ＜ Cs ＜ Rb ＜ K, with the predicted solubilities of the two latter being in the range of that of e.g. Y. Although Cs would lead to the highest proton mobility, the higher solubility of K and Rb renders them more attractive A-site dopants for BaZrO3. Overall, our results suggest that alkali metals as A-site dopants may enhance the bulk proton conductivity of BaZrO3, compared to Y-doped BaZrO3. [ABSTRACT FROM AUTHOR]

First-principles calculations were utilized to elucidate the complete defect equilibria of surfaces of proton conducting BaZrO3, encompassing charged species adsorbed to the surface, defects in the surface layer as well as in the subsurface space-charge region and bulk. Defect calculations were performed for the BaZrO3 (0 0 1) surface with focus on protons, oxygen vacancies and Y-acceptor dopants as well as adsorbed hydroxide and oxide adions. Protons were found to exhibit a particularly strong tendency to segregate to the surface with a segregation energy of −1.3 eV. While the concentration of negatively charged Y-acceptors and hydroxide species on the outer surface can be quite high, they do not fully charge compensate the protons, yielding a net positive charge of the surface. The resulting surface potential can exceed 1 V, resulting in significant depletion of charge carriers in the subsurface space-charge region. Moreover, the results are discussed in relation to surface adsorption of water, and computational approaches for treating charged point defects in periodic slab cells are evaluated with respect to symmetry and charge compensation. [ABSTRACT FROM AUTHOR]

In this contribution, we determine the compositional dependence of the chemical expansion and entropy of hydration of the proton conducting perovskites BaZrO3, BaSnO3, BaCeO3, and SrZrO3 by first principles phonon calculations. The calculations reveal that the cubic BaZrO3 and BaSnO3, which display the least favourable hydration enthalpies, −72 and −65 kJ mol−1, respectively, exhibit the most favourable entropies, −108 and −132 J mol−1 K−1, respectively. The strong compositional dependency of the hydration entropy primarily originates from the entropy gain upon filling the oxygen vacancy, which is closely related to the chemical expansion coefficient of oxygen vacancies, and thus the chemical expansion upon hydration. The chemical expansion coefficient of oxygen vacancies is more negative for the cubic than the orthorhombic perovskites, leading to a considerably larger chemical expansion upon hydration of the former. The calculations therefore suggest that challenges associated with chemical expansion upon hydration of BaZrO3 proton conducting electrolytes to some extent can be avoided, or reduced, by partial substitution of Zr by Ce. [ABSTRACT FROM AUTHOR]

In this contribution, we study possible confinement effects on the atomic and electronic structure, and phonon properties of neutral UGRAPHIC DISPLAY="INLINE" ID="UGT3" SRC="UGT3"/ and fully charged UGRAPHIC DISPLAY="INLINE" ID="UGT4" SRC="UGT4"/ oxygen vacancies in BaZrO3 (001) ultra-thin films. First principles phonon calculations were performed as a function of film thickness (from 3 to 7 atomic planes) with two complementary DFT methods. The calculations reveal that for both types of vacancies the confinement effect is very short-range; for films containing 5 planes or more, the oxygen vacancy properties are predicted to be similar to those observed in the bulk material. [ABSTRACT FROM AUTHOR]

The impact of phonons on the hydration and defect thermodynamics of undoped and acceptor (Sc, In, Y and Gd) doped BaZrO3 is addressed by means of first principles supercell calculations. In contrast to previous, similar investigations, we evaluate contributions from all phonon modes, and also pressure/volume effects on the phonon properties. The calculations are performed at the GGA-level with the PBE and RPBE functionals, both of which predict for BaZrO3 a stable cubic perovskite structure. For all dopants, the vibrational formation entropy of the doubly positively charged oxygen vacancy UGRAPHIC DISPLAY="INLINE" ID="UGT1" SRC="UGT1"/ is significantly lower than that of the protonic defect UGRAPHIC DISPLAY="INLINE" ID="UGT2" SRC="UGT2"/, which therefore also is the dominant contribution to the entropy of hydration, in addition to loss of H2O(g). The large, negative contribution from phonons to the formation entropy of UGRAPHIC DISPLAY="INLINE" ID="UGT3" SRC="UGT3"/ stems both from large local structural relaxations, and contraction of the entire supercell and corresponding blue-shift of the phonon spectrum. Neglect of the phonon contribution to the vacancy free formation energy leads to a considerable error (100 kJ mol−1 at 1000 K). For the acceptor doped systems, the calculated hydration entropy becomes more negative in the order Y ＜ Gd ＜ In ＜ Sc, which stems from that both the formation volume and vibrational formation entropy of UGRAPHIC DISPLAY="INLINE" ID="UGT4" SRC="UGT4"/ and UGRAPHIC DISPLAY="INLINE" ID="UGT5" SRC="UGT5"/ become more negative with increasing dopant ion size. Both functionals also give similar defect entropies for undoped, and Sc- and In-doped BaZrO3. However, for the larger Y- and Gd-ions, PBE underestimates (too negative) the vibrational formation entropies due to a poor representation of low frequency modes at the R point of the Brillouin zone. The calculated hydration entropies are in good agreement with experimental results, lending support to the applicability of the adopted method. [ABSTRACT FROM AUTHOR]

The behaviour of hydrogen in both defect free and acceptor doped bulk rutile TiO2is investigated through defect calculations performed within the density functional theory formalism. Both interstitial and substitutional hydrogen defects are shown to behave as shallow donors in the material, thereby existing as effectively positive hydroxide defects, , and substitutional hydrogen defects, . Of the investigated isolated hydrogen defects, the defect is shown to have the lowest formation energy over the whole Fermi level range under both oxidising and reducing conditions. However, the formation energy of is only 0.35 eV higher under conditions where TiO2is in equilibrium with Ti2O3, indicating that it exists as a minority defect in rutile TiO2under highly reducing conditions such as under growth of TiO2on a Ti metal surface. The enthalpy of hydration of oxygen vacancies is calculated to be −1.64 and −1.60 eV for the 2 × 2 × 3 and 3 × 3 × 3 supercells, indicating that defects will prevail in wet atmospheres, even at high temperatures. Hydrogen incorporated in the material can furthermore be expected to associate significantly with various acceptor centres (e.g., substitutional N and Al acceptors and Ti vacancies). The binding energies of the substitutional NH×O(imide) defect and of the association complexes between H and fully ionised substitutional Al, , and Ti vacancies, and (i.e., Ruetschi type defects), are calculated to be −0.36, −0.12, −0.47 and −0.82 eV, respectively. [ABSTRACT FROM AUTHOR]

We apply density functional theory to estimate the energetics and charge carrier concentrations and, in turn, the resistance across the (210)[001] and (111)[11[combining macron]0] grain boundaries (GBs) in proton conducting Y-doped BaZrO 3 , assessing four commonly used approximations in space charge modelling. The abrupt core approximation, which models the GB core as a single atomic plane rather than a set of multiple atomic planes, gives an underestimation of the GB resistance with around one order of magnitude for both GBs. The full depletion approximation, which assumes full depletion of effectively positive charge carriers in the space charge layers, has negligible effect on the GB resistance compared to a more accurate model with decaying depletion. Letting protons redistribute in the continuity between atomic planes gives a GB resistance up to 5 times higher than the case where protons are restricted to be located at atomic planes. Finally, neglecting trapping effects between the acceptor doping and the defect charge carriers gives a higher GB resistance with a factor of roughly 2.

Differentiating chemical and thermal expansion is virtually impossible to achieve experimentally. While thermal expansion stems from a softening of the phonon spectra, chemical expansion depends on the chemical composition of the material. In the present contribution, we, for the first time, completely decouple thermal and chemical expansion through first principles phonon calculations on BaCeO 3 , providing new fundamental insights to lattice expansion. We assess the influence of defects on thermal expansion, and how this in turn affects the interpretation of chemical expansion and defect thermodynamics. The calculations reveal that the linear thermal expansion coefficient is lowered by the introduction of oxygen vacancies being 10.6 × 10 -6 K -1 at 300 K relative to 12.2 × 10 -6 K -1 for both the protonated and defect-free bulk lattice. We further demonstrate that the chemical expansion coefficient upon hydration varies with temperature, ranging from 0.070 to 0.115 per mole oxygen vacancy. Ultimately, we find that, due to differences in the thermal expansion coefficients under dry and wet conditions, the chemical expansion coefficients determined experimentally are grossly underestimated - around 55% lower in the case of 10 mol% acceptor doped BaCeO 3 . Lastly, we evaluate the effect of these volume changes on the vibrational thermodynamics.

In this contribution, we study possible confinement effects on the atomic and electronic structure, and phonon properties of neutral (V(O)(x) and fully charged (V(O)oxygen vacancies in BaZrO3 (001) ultra-thin films. First principles phonon calculations were performed as a function of film thickness (from 3 to 7 atomic planes) with two complementary DFT methods. The calculations reveal that for both types of vacancies the confinement effect is very short-range; for films containing 5 planes or more, the oxygen vacancy properties are predicted to be similar to those observed in the bulk material.

The structural, electronic and thermodynamic properties of neutral and positively doubly charged oxygen vacancies in BaZrO3 are addressed by first principles phonon calculations. The calculations are performed using two complementary first principles approaches and functionals; the linear combination of atomic orbitals (LCAO) within the hybrid Hartree-Fock and density functional theory formalism (HF-DFT), and the projector augmented plane wave approach (PAW) within DFT. Phonons are shown to contribute significantly to the formation energy of the charged oxygen vacancy at high temperatures (∼1 eV at 1000 K), due to both its large distortion of the local structure, and its large negative formation volume. For the neutral vacancy, the resulting lattice distortions, and thus the contributions from phonons to the free formation energy, are significantly smaller. As a result, phonons affect the relative stability of the two defects at finite temperatures and the charge transition level for oxygen vacancies (+2/0) changes from 0.42 to 0.83 eV below the conduction band bottom from 0 K to 1000 K.

In this contribution we investigate trends in the defect chemistry and hydration thermodynamics of rare-earth pyrochlore structured oxides, RE(2)X(2)O(7) (RE = La-Lu and X = Ti, Sn, Zr and Ce). First principles density functional theory (DFT) calculations have been performed to elucidate trends in the general defect chemistry and hydration enthalpy for the above-mentioned series. Further, to justify the use of such theoretical methods, the hydration properties of selected compositions were studied by means of thermogravimetric measurements. Both DFT calculations and TG measurements indicate that the hydration enthalpy becomes less exothermic with decreasing radii of RE ions within the RE(2)X(2)O(7) series (X = Ti, Sn, Zr and Ce), while it is less dependent on the X site ion. The observed hydration trends are discussed in connection with trends in the stability of both protons and oxygen vacancies and changes in the electronic density of states and bonding environment through the series. Finally, the findings are discussed with respect to existing correlations for other binary and ternary oxides.

The nitrogen related defect chemistry and electronic structure of wide band gap oxides are investigated by density functional theory defect calculations of N(O)(q), NH(O)(×), and (NH2)(O)(·) as well as V(O)(··) and OH(O)(·) in MgO, CaO, SrO, Al(2)O(3), In(2)O(3), Sc(2)O(3), Y(2)O(3), La(2)O(3), TiO(2), SnO(2), ZrO(2), BaZrO(3), and SrZrO(3). The N(O)(q) acceptor level is found to be deep and the binding energy of NH(O)(×) with respect to N(O)' and (OH(O)(·) is found to be significantly negative, i.e. binding, in all of the investigated oxides. The defect structure of the oxides was found to be remarkably similar under reducing and nitriding conditions (1 bar N(2), 1 bar H(2) and 1 × 10(-7) bar H(2)O): NH(O)(×) predominates at low temperatures and [N(O)'] = 2[V(O)(··) predominates at higher temperatures (>900 K for most of the oxides). Furthermore, we evaluate how the defect structure is affected by non-equilibrium conditions such as doping and quenching. In terms of electronic structure, N(O)' is found to introduce isolated N-2p states within the band gap, while the N-2p states of NH(O)(×) are shifted towards, or overlap with the VBM. Finally, we assess the effect of nitrogen incorporation on the proton conducting properties of oxides and comment on their corrosion resistance in nitriding atmospheres in light of the calculated defect structures.

The behaviour of hydrogen in both defect free and acceptor doped bulk rutile TiO2 is investigated through defect calculations performed within the density functional theory formalism. Both interstitial and substitutional hydrogen defects are shown to behave as shallow donors in the material, thereby existing as effectively positive hydroxide defects, OH*(O), and substitutional hydrogen defects, H*O. Of the investigated isolated hydrogen defects, the OH*(O) defect is shown to have the lowest formation energy over the whole Fermi level range under both oxidising and reducing conditions. However, the formation energy of H*O is only 0.35 eV higher under conditions where TiO2 is in equilibrium with Ti2O3, indicating that it exists as a minority defect in rutile TiO2 under highly reducing conditions such as under growth of TiO2 on a Ti metal surface. The enthalpy of hydration of oxygen vacancies is calculated to be -1.64 and -1.60 eV for the 2 x 2 x 3 and 3 x 3 x 3 supercells, indicating that OH*(O) defects will prevail in wet atmospheres, even at high temperatures. Hydrogen incorporated in the material can furthermore be expected to associate significantly with various acceptor centres (e.g., substitutional N and Al acceptors and Ti vacancies). The binding energies of the substitutional NH(x)O (imide) defect and of the association complexes between H and fully ionised substitutional Al, (Al'Ti x OH*(O)), and Ti vacancies, (V(Ti)x OH*(O)and (V(Ti) x 4OH*(O)) (i.e., Ruetschi type defects), are calculated to be -0.36, -0.12, -0.47 and -0.82 eV, respectively.