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Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths. 

Ceria has proven to be an excellent ion-transport and ion-exchange material when used in polycrystalline form and with a high-concentration of aliovalent doped cations. Despite its widespread application, the impact of atomic-scale defects in this material are scarcely studied and poorly understood. In this article, using first-principles simulations, we provide a fundamental understanding of the atomic-structure, thermodynamic stability and electronic properties of undoped grain-boundaries (GBs) and alkaline-earth metal (AEM) doped GBs in ceria. Using density-functional theory simulations, with a GGA+U functional, we find the 3 (111)/[101] GB is thermodynamically more stable than the 3 (121)/[101] GB due to the larger atomic coherency in the 3 (111)/[101] GB plane. We dope the GBs with 20% [M]GB (M=Be, Mg, Ca, Sr, and Ba) and find that the GB energies have a parabolic dependence on the size of solutes,the interfacial strain and the packing density of the GB. We see a stabilization of the GBs upon Ca, Sr and Ba doping whereas Be and Mg render them thermodynamically unstable. The electronic density of states reveal that no defect states are present in or above the band gap of the AEM doped ceria, which is highly conducive to maintain low electronic mobility in this ionic conductor. The electronic properties, unlike the thermodynamic stability, exhibit complex inter-dependence on the structure and chemistry of the host and the solutes. This work makes advances in the atomic-scale understanding of aliovalent cation doped ceria GBs serving as an anchor to future studies that can focus on understanding and improving ionic-transport.