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(Left) Atomistic representation of the CSL grain boundary in cubic , with atomic coordinates optimized and particular sites numbered. Big, green balls stand for hafnium while small, red balls stand for oxygen. The shaded square indicates the grain boundary region. (Right) Schematic non-optimized geometry of the Σ5 36.87° (310)/ CSL and Kingery grain boundary models. z = 0 is the topmost plane of atoms in the unit cell.
Total DOS and site-projected partial DOS for the CSL grain boundary model. The DOS for single crystal cubic is shown for comparison. The highest occupied molecular orbitals (HOMOs) are indicated by vertical lines. Atom numbers follow the convention introduced in Fig. 1 .
c-direction view of various grain boundary models with their atomic positions optimized. Big (small) hollow balls stand for hafnium (oxygen). In (a) the two arrows indicate the two O atoms (the lower one is hidden by the upper one in this perspective) removed to generate the configuration shown in (d); in (e) and (f) the circle and the cross indicate the locations of the O and Hf interstitials, respectively; in (g) and (h) foreign interstitial Ti and Pt atoms, respectively, are represented by solid balls.
DOS for the models shown in Fig. 3 . In (d), the band marked by #1 is created by one O vacancy per GB, while two vacancies per GB result in the two bands marked by #1 and #2. Vertical red lines indicate the Fermi level [for (f) and (g)] or HOMO (for the rest).
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