Segregation energies of oxygen vacancies and protons near three symmetric tilt grain boundaries in BaZrO3 are determined using density functional theory. Two of the grain boundaries have the [110] direction as tilt axis with a (111) or (112) plane as grain boundary plane, while the third has the [001] direction as tilt axis and a (210) plane as grain boundary plane. Both defects are found to segregate to all three grain boundaries, with vacancy segregation energies of −0.5 eV and −1.5 eV and proton segregation energies of about −0.8 eV. The effects of the calculated segregation energies on defect concentrations and electrostatic potential in the grain boundary region are investigated using a thermodynamic space charge model. An increased concentration of defects is seen in all grain boundaries, giving electrostatic potential barriers around 0.6 V at 400-600 K. Protons are found to give important contributions to the space charge in all three grain boundaries.

Acceptor-doped BaZrO 3 (BZO) and BaCeO 3 (BCO) both exhibit considerable bulk proton conductivity, which makes them suitable as electrolytes in electrochemical devices. However, these materials display high grain-boundary (GB) resistance that severely limits the overall proton transport in polycrystalline samples. This effect has been attributed to the presence of space charges at the GBs, which form because of segregation of protons and charged oxygen vacancies. This blocking behavior is less prominent in BCO, but in contrast to BZO, BCO suffers from poor chemical stability. The aim with the present work is to elucidate why GBs in BZO are more resistive than GBs in BCO. We use density-functional theory (DFT) calculations to study proton and oxygen vacancy segregation to several GBs and find that the oxygen vacancy segregation energy is quite similar in both materials while the tendency for proton segregation is larger in BZO compared with that in BCO. This is not related to the GBs, which display similar proton formation energies in both materials, but because of different formation energies for protons in the bulk regions. This can be understood from a stronger hydrogen bond formation in bulk BCO compared with that in bulk BZO. Furthermore, segregation energies are evaluated in a space-charge model, and the resulting space-charge potentials provide a consistent explanation of the experimentally observed difference in GB conductivity.

We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaries are considered: one with a misorientation angle of 17.9• displaying an out-of-plane buckling 1.5 nm high and 5 nm wide, one with a misorientation angle of 9.4• and an out-of-plane buckling 0.6 nm high and 1.7 nm wide, and one with a misorientation angle of 32.2• and no out-of-plane buckling. At the flat grain boundary, the phonon transmission exceeds 95% for wavelengths above 1 nm. The buckled boundaries have a substantially lower transmission in this wavelength range, with a minimum transmission of 20% for the 17.9• boundary and 40% for the 9.4• boundary. At the buckled boundaries, coupling between flexural and longitudinal phonon modes is also observed. The results indicate that scattering of long-wavelength flexural phonons at grain boundaries in graphene is mainly due to out-of-plane buckling. A continuum mechanical model of the scattering process has been developed, providing a deeper understanding of the scattering process as well as a way to calculate the effect of a grain boundary on long-wavelength flexural phonons based on the buckling size.

Density-functional theory (DFT) has been used to determine the structure and interface energy of different rigid body translations (RBTs) of the (210)[001] grain boundary (GB) in BaZrO 3 . There exist several different stable structures with almost equally low interfacial energy. Segregation energies of protons and oxygen vacancies have been determined for the most stable (210)[001] grain boundary structure. The results suggest that both defect species favor segregation to the same site at the boundary interface with minimum segregation energies of −1.45 eV and −1.32 eV for vacancies and protons respectively. The segregation energies have been used in a thermodynamic space-charge model to obtain equilibrium defect concentrations and space-charge potentials at a 10 % dopant concentration. Space-charge potential barriers around 0.65 V were obtained at intermediate temperatures under hydrated conditions, where protons are the main contributor to the excess core charge. The potential is slightly lower under dry conditions.

We have used classical interatomic potentials to determine the structure, interface energy and oxygen vacancy segregation energies of eight different grain boundaries (GBs) in BaZrO 3 with tilt axis [110]. Two of these have been studied previously with density functional theory and the agreement is satisfactory. The results suggest that oxygen vacancies prefer to reside near the boundary interface for all these GBs. The minimum segregation energies range between −1.86 eV and −0.57 eV, and the typical core width is about 10Å. The resulting depletion layers have been evaluated using a thermodynamic space-charge model. Space-charge potential barriers between 0.2-0.8 eV were obtained with dopant concentrations of 5 % and 10 %.