Figure 1

(Color) Atomic-resolution scanning transmission electron microscope (STEM) Z-contrast images of intergranular films (IGF) in (a) Lu-, (b) Gd-, and (c) La-doped $\beta \text{−}{\mathrm{Si}}_3{\mathrm{N}}_4$ samples, respectively. The right-hand crystals are aligned with the [0001] projection so that the $\left(10\overline{1}0\right)$ prismatic plane is set at an “edge-on” condition. The bright band seen at the center of each image corresponds to the IGF, and the brightest spots indicate the location of rare-earth dopants. By superimposing the crystal structure of $\beta \text{−}{\mathrm{Si}}_3{\mathrm{N}}_4$, it is determined that the surface of the right-hand crystal is terminated by nitrogen in all the cases, and each rare earth clearly segregates to the surface as the first cation layer of the IGF, indicated by red arrows. This indicates that anion crystal termination is the universal lowest-energy structure in the presence of rare-earth dopants in the IGF. On the other hand, the density of the occupied surface attachment sites clearly differs for each of the dopants; the density increases from Lu to La. Thus, surface site occupancy is dependent on the specific rare earth.Reuse & Permissions

Figure 2

(Color) Magnified STEM Z-contrast images of the interfacial structure between IGF and the prismatic surface of $\beta \text{−}{\mathrm{Si}}_3{\mathrm{N}}_4$ grain in (a) Lu-, (b) Gd-, and (c) La-doped $\beta \text{−}{\mathrm{Si}}_3{\mathrm{N}}_4$ samples, respectively. The red arrows indicate the surface attachment sites of the dopants. The segregation sites predicted from first-principles calculations are shown by the open circles in each case. In the Gd and La cases, the predicted position and number of stable sites agree with the experimental STEM images. The slight shift between the calculated and observed sites is likely a result of the absence of the IGF in the calculations. On the other hand, in the case of Lu, one of the two calculated attachment sites (X site) agrees very well with the STEM observations, while the Y site appears to be largely vacant. The theoretical calculations show that the REs are more energetically stable in the X site than the Y site, with the Z site having very low stability.Reuse & Permissions