Grain Boundary Strengthening in Alumina by Rare Earth Impurities

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Science  13 Jan 2006:
Vol. 311, Issue 5758, pp. 212-215
DOI: 10.1126/science.1119839


Impurity doping often alters or improves the properties of materials. In alumina, grain boundaries play a key role in deformation mechanisms, particularly in the phenomenon of grain boundary sliding during creep at high temperatures. We elucidated the atomic-scale structure in alumina grain boundaries and its relationship to the suppression of creep upon doping with yttrium by using atomic resolution microscopy and high-precision calculations. We find that the yttrium segregates to very localized regions along the grain boundary and alters the local bonding environment, thereby strengthening the boundary against mechanical creep.

Structural ceramics have a large range of applications for engines and turbines. To avoid failure, the material needs to have a high resistance to deformations at the very high operating temperatures. Deformations almost always nucleate at atomic-scale defects, particularly grain boundaries (GBs). A commonly used and well-studied structural ceramic is alumina (Al2O3). However, GBs in Al2O3 are known for having a weak resistance to deformations via sliding because of creep (15) at high temperatures. One method to improve the resistance to sliding due to creep is through the addition of small amounts of rare earth elements (4, 5). These additives (i.e., dopants) are known to segregate to the GBs and are expected to retard GB sliding. Systematic measurements of GB sliding by creep tests were investigated by using a pair of bicrystals (6). One was pristine and the other was Y-doped, with a tilt angle about the [0001] axis of ∼18°, corresponding to a Σ value of 31 (7). Here, the Σ value represents the degree of geometrical coincidence at GB. These results showed that Y doping increased the creep resistance for even a single GB by two orders of magnitude. Several simple models to explain the increase in GB creep resistance due to rare earth impurity doping have been proposed (4, 5), but the atomic-scale mechanism of how these dopants actually strengthen grain boundaries is still very unclear and controversial. This is mainly because of poor understanding of the atomic structure of alumina GBs and how it is affected by rare earth doping.

We describe the results of our investigation of the atomic mechanism of Y doping and of the increase in grain boundary mechanical strength with the use of Z-contrast images obtained by scanning transmission electron microscopy (STEM), performed on the same bicrystal pair used in the creep tests in (6), to determine the GB structure. STEM used in the present study is JEM2100F (200 kV, JEOL, Limited, Tokyo, Japan. We follow with a theoretical analysis of the GB structure and bonding using a combination of first principles and static lattice calculations.

A number of previous studies have used high-resolution TEM (HRTEM) to characterize the structure of pristine and Y-doped alumina GBs (814). Although much information on the atomic structure can be obtained through HRTEM, finding the specific atomic-scale location of dopants remains a very difficult task. However, because the image intensity in the STEM is roughly proportional to the square of the atomic number Z (i.e., the heaviest elements appear the brightest) (15), the Z-contrast technique is especially well suited for understanding the role of heavy impurities in a crystal of lighter atoms (16, 17). Figure 1A shows a Z-contrast image of an undoped Σ31 GB in Al2O3 (18). Bright spots in the image correspond to atomic columns of Al (columns of oxygen do not scatter strong enough to be seen in the image). The schematic overlay (Fig. 1B) illustrates the presence of periodic structural units along the boundary plane. A notable feature of the GB structure is the presence of a seven-member ring of Al ions leading to a large open structure.

Fig. 1.

Z-contrastimagesofundopedand Y-doped alumnia GBs. (A) Z-contrast STEM image of pristine Σ31 [0001] tilt GB in alumina. (B) Same image with overlay to illustrate the aluminum atomic column arrangement of the structural units. Note the large open structure of the seven-member ring unit, which is nearly periodic along the GB. (C) Z-contrast STEM image of Y-doped Σ31 [0001] tilt GB in alumina. (D) Same image with overlay to illustrate the atomic column arrangement. The two brightest columns indicate the presence of the heavy Y ions. These Y-containing columns are found right at the center of the seven-member ring unit. Images were processed by Gaussian smoothing.

For the Y-doped Σ31 GB, the Z-contrast image is shown in Fig. 1C. The most striking features are the unusually bright columns that lie periodically along the boundary plane, indicating the presence of Y. By using nanoprobe energy dispersive spectroscopy (EDS) in the STEM, we confirmed Y to be confined to the boundary plane, consistent with the direct observation. Figure 1D shows a structural schematic of the Y-doped Al2O3 GB superimposed on the image. Here, the structural units observed at the Y-doped boundary closely resemble the units found in the undoped case, suggesting that Y does not alter the basic GB structure on length scales greater than ∼0.1 nm. Instead it appears that Y3+ simply replaces Al3+ at the specific site on the cation sublattice. The Y-containing columns are only found at the center of the seven-membered ring and periodically along the GB, suggesting that Y preferentially segregates to special cation sites. Furthermore, the amount of Y present at the GB is very small and is much less than a monolayer.

Static lattice calculations (11, 12, 18, 19) were performed to determine the lowest energy structure of the Al2O3 GB. A simulation cell of the Σ31 boundary (1240 atoms) was used to systematically calculate various rigid body translation states of the adjacent crystal across the boundary to find the most stable GB structure, using two-body Buckingham-type ionic potentials (20, 21) for atomic relaxations. Figure 2A displays a schematic of the theoretically predicted lowest energy structure for the undoped case. This structure agrees well with the experimentally observed GB structure shown in Fig. 1, and the seven-membered ring structure with a large open space is clearly reproduced.

Fig. 2.

Theoretical GB structure and segregation energies. (A) Schematic of the lowest energy GB structure obtained by static lattice calculations. Bold lines mark the GB structure that the structure observed in the Z-contrast image (Fig. 1). Columns labeled a through p mark the location of the Al columns where the Y-segregation energies were investigated. Column m in the middle of the seven-membered ring shows the lowest segregation energy. (B) Plot of the average Y-segregation energies for each column marked as a function of distance from the GB plane. Dashed line corresponds to the formation energy of Y substitution for Al in the bulk.

To locate the most energetically stable site for Y segregation, a single Y ion was substituted at various columns (marked a through p in Fig. 2A) at and near the boundary plane. The Y-containing atomic structure was allowed to relax by using the Buckingham ionic potentials. Each Al column contains four distinct Al sites, and the segregation energy for each distinct site was calculated. An additional calculation was performed to evaluate the bulk Y-segregation energy by introducing Y at the middle (far from the GB) of the Al2O3 crystal slab in the Σ31 simulation cell. Lastly, the Y-segregation energy for each particular ionic site along the grain boundary was obtained from the total energy difference between the energy of the supercell for Y substituted in the bulk and the energy of the supercell where the cation site in question is occupied by a single Y ion.

The segregation energy for each column was averaged over the four Al sites along the [0001] axis (Fig. 2B). The Y-segregation energies for sites more than 5 Å away from the boundary approximate the bulk value. On the other hand, Y segregation becomes energetically favorable near the grain boundary plane. In particular, the site right in the middle of the seven-membered ring shows the lowest segregation energy, which is consistent with the experimental results. Because both Y and Al ions are isovalent, the main difference between the two ions is the ionic radius. For comparison, the ionic radius for Al is 67.5 pm, whereas Y is 104 pm. Thus, the preferential segregation of Y to the center of the large seven-membered ring must be due to the facility of an expanded region to accommodate the larger ion.

Static lattice calculations are useful to qualitatively investigate candidates for stable GB structures when they can be verified experimentally. However, they have their basis in empirical interatomic potentials and thus are not suitable for a quantitative evaluation of the energetics, chemical, or bonding environment of the GB. Because the valence shell of Y contains a d electron, changes in the bonding environment at the GB are expected after doping with Y. Ab initio calculations can provide accurate information on the local atomic bonding and charge distributions, and we performed high precision ab initio calculations with the use of the Vienna Ab Intitio Simulation Package (VASP) (18). A large periodic supercell with 700 atoms containing two oppositely oriented GBs was constructed by using the structure obtained from static lattice calculations described above. First, the supercell was fully relaxed to obtain the most accurate GB structure for the undoped case. The results showed that further relaxations occurred. However, these relaxations were relatively small (less than 0.1 nm), yielding a GB structure that still matched the structure observed in the STEM image. The calculated GB energy, obtained from the difference between the total energy of the model and that of a perfect crystal model of same size, is 3.93 J/m2. The fairly large GB energy reflects the complexity of the Σ31 GB. Next, assuming that all four distinct Al sites were substituted with Y ions in the column at the center of the seven-membered ring (the location that was observed in the STEM image), the structure was fully relaxed, and again the final structure matched well with the corresponding experimental image. The calculated GB energy for the Y-doped case is found to be 3.48 J/m2, which is smaller than the pristine one and indicates that the GB is energetically stabilized upon Y doping [see (18) for more details].

Changes in the bonding character between the Y-O bonds and the Al-O bonds can be best illustrated by plotting the charge density maps. Figure 3, A and B, shows the charge density maps along the (0001) plane for the undoped and the Y-doped cases, respectively. Because of the complexity of the GB structure in Al2O3, cations and anions do not lie on the same (0001) plane. Therefore, we have carefully selected appropriate (0001) planes, which are close to a cation belonging to the center column of the seven-membered ring such that the charge densities of the neighboring oxygen ions can also be clearly seen. To facilitate visualization, we indicated schematically the locations of the cation columns. The charge density map for the undoped GB (Fig. 3A) shows the presence of sharp nodes between the oxygen charge densities and the charge density from the Al ion in the center of the seven-membered ring. In contrast, the Y-doped GB charge density map (Fig. 3B) shows that the oxygen electron densities are elongated toward the Y ion, indicating a stronger covalency for the Y-O bonds. It can be seen that Y at the center column interacts considerably with the surrounding oxygen ions. An increase in covalent character of Y-O bonds in bulk Al2O3 has also been theoretically suggested in previous studies (22, 23).

Fig. 3.

Charge density map. A charge density map for the undoped GB (A) is shown for a (0001) plane near an Al ion in the middle of the seven-membered ring, where the charge density from the neighboring O ions (appearing as graduated blue spots) can be easily seen. (Insets) The nodes between the charge density of the O ions with the Al ion are typical of ionic bonding. A charge density map for the Y-doped GB (B) is displayed with a similar (0001) plane. The elongation of the O charge density toward the Y ion in the center of the seven-membered ring indicates covalent-type bonding. White circles indicate the location of Al ions, and the yellow circle indicates the location of the Y columns.

Differences between the local atomic environments at the seven-membered ring were also found from the results of the ab initio calculations. In particular, we find that the coordination of the cation site in the middle of the seven-membered ring changes notably depending on whether the site is occupied by Al or by Y. The coordination numbers can be determined by simply counting the number of nearest neighbors of a particular ion that lie within a distance of a maximum bond-length cutoff. Here, we used a cutoff of 0.22 nm for the Al-O bonds and 0.29 nm for the Y-O bonds, which were determined in a previous study (24). By using the relaxed structures from the ab initio calculations, we exemplify (Fig. 4, A and B) the coordination changes through ball and stick illustrations of the seven-membered rings for the undoped and the Y-doped, respectively. Because the illustrations are two-dimensional projections of three-dimensional structures, it may be difficult to determine the coordination number from these figures alone. The reported coordination numbers were thus obtained from the numerical data. Additional illustrations (fig. S1) show the bonding from a different perspective. In the undoped case, for the four distinct Al ions that are found along the central column in the center of the seven-member ring, we find that one Al site is only fourfold coordinated and the remaining three sites are only fivefold coordinated with neighboring O ions according to the cutoff criteria, less than the sixfold coordination in the bulk. The central Al ions do not lie at the exact center of the seven-membered ring but are attracted toward the region that contains a higher concentration of oxygen ions, preventing some oxygen ions on the opposite side of the seven-membered ring from forming bonds. However, when these undercoordinated Al ions are all replaced by Y ions, the larger Y ions remain near the center of the seven-membered ring, forming more bonds and thus allowing the coordination to increase to sixfold for one of the ions and to sevenfold for the remaining three ions. Such increases in the coordination numbers of Y in the center of the seven-membered ring contribute to lowering the GB energy.

Fig. 4.

Coordination changes illustrated by VASP. Here, the bonds, represented by sticks, are drawn in accordance with the bond length cutoffs mentioned in the text. (A) A ball-and-stick model for the seven-membered ring found along the GB in the undoped case. The column of Al ions is shifted from the center of the seven-membered ring, causing the coordination for these Al to be reduced to fivefold, whereas Al ions in the bulk are sixfold coordinated. (B) A similar ball-and-stick model when Y ions replace the Al ions in the middle of the seven-membered ring. The Y ions form a column near the center of the seven-membered ring, which allows bonds to be formed with a larger number of O anions, thereby increasing the coordination number up to 7. Bold dashed lines indicate the approximate perimeter of the seven-membered rings for comparison with previous figures.

The actual mechanism for GB creep is still not well understood, although a number of models have been proposed (25, 26). However, no matter which mechanism is correct, atomic bonds must continuously be broken and reformed as the two grains move with respect to each other. Therefore, GBs containing a larger number of bonds and higher bond strength should exhibit a higher creep resistance than that for a boundary with fewer and/or weaker bonds. Looking at the structure of the pristine GB, we find that the seven-membered rings have fewer bonds (lower coordination number) than the grain interior, implying that these seven-membered rings are mechanically weak points along the GB.

However, upon Y doping our results show that the large Y ions are energetically more stable at the expanded regions (in this case, the seven-membered rings). These are the same locations where, in the pristine boundary, the bonds are less in number and weaker than in the bulk. The presence of Y at these seven-membered rings increases the number of bonds, and the bond strength is increased because of the higher covalency of the Y-O bonds. This should result in a much stronger GB, which explains why the Y-doped GBs can have such a large increase to creep resistance despite the fact that only a small amount of Y is present. Similar effects are expected for other rare earth elements (e.g., La and Zr), although the degree of bond strength enhancement in the expanded regions along the GB and the increase in bonding coordination for each specific element may depend on the ion size and should play a large factor in how much the creep resistance can be increased. This mechanical strengthening of grain boundaries via rare earth doping should also be applicable to other ceramic oxides.

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