Effect of Chemical Bonding State on High temperature Plastic Flow Behavior in Fine grained, Polycrystalline Cation doped Al2O3

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(1)Materials Transactions, Vol. 43, No. 7 (2002) pp. 1566 to 1572 Special Issue on Grain Boundaries, Interface, Defects and Localized Quantum Structures in Ceramics c 2002 The Japan Institute of Metals. Effect of Chemical Bonding State on High-temperature Plastic Flow Behavior in Fine-grained, Polycrystalline Cation-doped Al2 O3 Hidehiro Yoshida1, ∗ , Yorinobu Takigawa2 , Yuichi Ikuhara3 and Taketo Sakuma1 1. Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Tokyo 113-8656, Japan 2 Japan Fine Ceramics Center, Nagoya 456-8587, Japan 3 Engineering Research Institute, The University of Tokyo, Tokyo 113-8656, Japan High-temperature plastic deformation characteristics such as flow stress and elongation to failure in polycrystalline Al2 O3 with an average grain size of about 1 µm is remarkably changed by the doping of 0.1 mol% YO1.5 , SiO2 , TiO2 or ZrO2 at 1400◦ C under an initial strain rate of 1.2 × 10−4 s−1 . The difference in the flow stress and the tensile ductility is considered to be originated from change in the grain boundary chemistry in Al2 O3 due to segregation of the dopant cation in the vicinity of the grain boundary. A change in the chemical bonding state in the cations-doped Al2 O3 is examined by first-principle molecular orbital calculations using DV-Xα method based on [Al5 O21 ]27− cluster model. Chemical shift observed in electron energy-loss spectra (EELS) at the grain boundary due to the dopant segregation can be roughly reproduced by the molecular orbital calculations. A correlation is found between the flow stress and product of net charges of aluminum and oxygen ions. Moreover, the tensile elongation to failure seems to correlate with bond overlap population between Al and O. The change in the chemical bonding strength at the grain boundary must dominantly affect to the grain boundary diffusion and bond strength at the grain boundary, and thus seems to be an important factor to determine the plastic flow behavior in polycrystalline Al2 O3 . (Received January 25, 2002; Accepted March 11, 2002) Keywords: alumina ceramics, dopant, high-temperature deformation, grain boundary, transmission electron microscopy (TEM)-X-ray energy dispersive spectroscopy (EDS) technique, electron energy loss spectroscopy (EELS), molecular orbital calculation, chemical bonding state. 1. Introduction High-temperature plastic deformation in polycrystalline Al2 O3 has widely been studied for many years. One of the striking facts obtained in recent years for the high-temperature deformation in Al2 O3 is that the hightemperature plastic flow characteristics in fine-grained, polycrystalline Al2 O3 is sensitively affected by small amount of dopant cation.1–8) For example, it was found out that hightemperature creep strain rate in polycrystalline Al2 O3 with an average grain size of about 1 µm was reduced by the addition of 0.1 mass%ZrO2 by a factor of about 15 at 1250◦ C.5) It was also reported that the high-temperature creep strain rate in Al2 O3 with a grain size of 1 µm is about 200 times lowered by a doping of lanthanoid oxide such as Y2 O3 or Lu2 O3 even in the level of 0.05 mol%, and that the dopant effect attributes to grain boundary segregation of the dopant cations.6, 7) Similar effects of the segregated dopant cation on the flow stress or strain rate in Al2 O3 have been also reported in other oxides.3, 8) The tensile ductility in small amount of cation-doped Al2 O3 has also been examined so far from the viewpoint of superplastic deformation in ceramics. The tensile elongation to failure in Al2 O3 is generally very limited because of rapid grain growth during the deformation.2, 4) However, the tensile elongation of 54–70% has been obtained in 0.05–0.1 wt% MgO-doped Al2 O3 .1, 2) In the MgO-doped Al2 O3 , it is revealed that the enhancement in the tensile ductility can be reasonably explained in terms of inhibition of the concurrent grain growth during deformation.2) However, the mechanism of the effect of the general dopant cation has not been clarified in detail yet. For instance, the doping of YO1.5 is effective to ∗ Corresponding. author: E-mail: [email protected]. suppress the grain growth during deformation, but the flow stress is twice as large as that in undoped-Al2 O3 and the tensile ductility is very limited.9) In contrast, the doping of ZrO2 enhances both the flow stress and tensile ductility, though it has an effect of inhibiting the grain growth.4) In our previous works, we have systematically investigated the high-temperature creep resistance in various kinds of lanthanoid-doped Al2 O3 in order to make clear the origin of the dopant effect.6, 10, 11) As a result, it has been found out that the dopant effect depends on the type of lanthanoid cation, and that the high-temperature creep resistance in the lanthanoid cation-segregated Al2 O3 is correlated well with a change in ionic bonding strength between aluminum and oxygen ions at the grain boundaries, rather than the dopant cations’ ionic size.6, 10, 11) In order to generally confirm the correlation between the chemical bonding strength and the high-temperature plastic flow behavior in cation doped Al2 O3 , we need to examine high-temperature tensile plastic flow characteristics such as the flow stress and the elongation to failure and electronic structures in various kinds of cationdoped Al2 O3 . In the case of tetravalent dopant cations such as Zr4+ , it is supposed that aluminum vacancy should be introduced to maintain the electronic neutrality, on the contrary to trivalent cations such as Y3+ cation. This paper aims to examine the high-temperature flow stress and the tensile ductility and the chemical bonding state in Y3+ , Si4+ , Ti4+ or Zr4+ iondoped fine-grained, polycrystalline Al2 O3 ; the dopant cations are expected to segregate at Al2 O3 grain boundaries because of the limited solubility into Al2 O3 .12–15) In the present study, a first-principle molecular orbital calculation using DV-Xα method16) was conducted to argue the effect of the presence of dopant cations and accompanying vacancy on the chemical.

(2) Effect of Chemical Bonding State on High-temperature Plastic Flow Behavior in Fine-grained Table 1 Sintering conditions and grain size of undoped- and oxide-doped Al2 O3 . The dopant level is constant, 0.1 mol%. Sample. Sintering conditions. Average grain size/µm. undoped-Al2 O3 YO1.5 -doped Al2 O3 SiO2 -doped Al2 O3 TiO2 -doped Al2 O3 ZrO2 -doped Al2 O3. 1300◦ C-2 h 1400◦ C-2 h 1400◦ C-2 h 1285◦ C-2 h 1400◦ C-2 h. 0.9 0.9 0.9 0.9 1.0. bonding state. 2. Experimental Procedure The materials used in this study were undoped, high-purity Al2 O3 and Al2 O3 with 0.1 mol% of YO1.5 , SiO2 , TiO2 and ZrO2 . The sintering conditions and average grain size of the present materials are shown in Table 1. High-purity alumina powders with 99.99% purity (TM-DAR, Taimei Chemicals, Japan), yttrium acetate (99.99%, Rare Metallic, Japan), colloidal silica (high-purity grade, Nissan Chemical Industry, Japan), titanium oxide powder (Ultra-fine grade, Sumitomo Osaka Cement, Japan) and colloidal zirconia particles dispersed in water (99.9%, NZS-30B, Nissan Chemical Industry, Japan) were used for starting materials. The powders were mixed, ball-milled in ethanol together with 5 mm diameter high-purity (> 99.9%) alumina balls for 24 h, dried and shifted through a 60 mesh sieve for granulation. The green compacts were prepared by pressing the mixed powders into bars with a cemented carbide die under a pressure of 33 MPa, and then isostatically-pressed under a pressure of 100 MPa. The green compacts were sintered at a temperature in the range 1285–1400◦ C for 2 h in air to obtain an average grain size of about 1 µm in all samples as shown in Table 1. The bulk density of sintered bodies was measured by Archimedes technique. High-temperature mechanical experiments were carried out under uniaxial tension in air at a constant cross-head speed using an Instrontype testing machine equipped with a resistance-heated furnace (Shimazu AG-5000C). The initial strain rate and temperature were 1.2 × 10−4 s−1 and 1400◦ C, respectively. The test temperature was measured by a Pt-PtRh thermocouple attached to each specimen and kept to within ±1◦ C. The size of the specimens was 2 × 2 mm2 in cross-section and 13.5 mm in gauge length for tensile tests. Microstructures were examined with a scanning electron microscope (JSM5200, JEOL, Japan). The grain size was measured by a linear intercept method using SEM photographs. TEM specimens were prepared using standard technique involving mechanical grinding to a thickness of 0.1 mm, dimpled to a thickness of 20 µm and ion beam milling to electron transparency at about 4 kV. High-resolution electron microscopy (HREM) observations were performed to analyze the grain-boundary structure using Hitachi H-9000NAR (300 kV), JEOL-2010 (200 kV) and Topcon EM-002BF (200 kV) transmission electron microscopes. Chemical analysis was carried out by an Xray energy dispersive spectrometer (EDS: Noran Voyager system) attached to the field-emission type microscope (Topcon-. 1567. 002BF) with a probe size of less than 1 nm. Change in chemical bonding state in alumina grain boundaries was examined by electron energy loss spectroscopy (EELS) with a Gatan PEELS spectrometer in a field-emission microscope with an energy resolution of 0.7 eV and with a probe size of less than 1 nm. 3. Method of Calculations Figure 1 shows model clusters of undoped- and cationdoped Al2 O3 used in this study. Figure 1(a) shows a model cluster for undoped-Al2 O3 , [Al5 O21 ]27− , which represents a part of the corundum structure; O ions form a close-packed structure and all Al ions take the octahedral coordination. An Al ion at the center of the cluster (Al(1) ) is surrounded by three Al ions (Al(2) ) with the atomic distance of 0.279 nm and one Al ion (Al(3) ) with the atomic distance of 0.266 nm in [0001] direction. The model cluster is rather simple one, but the electronic structure and chemical bonding state in Al2 O3 can be fairly reproduced by the [Al5 O21 ]27− cluster, because the major interaction between cation and anion (Al–O) or between cations (Al–Al) is involved in the model cluster;17, 18) density of states of conduction band and band gap energy of about 10 eV in Al2 O3 can be obtained by using the model cluster. In Al2 O3 ceramics, aluminum ions’ vacancies are introduced by an addition of tetravalent cations to maintain local electrical neutrality. Figure 1(b) shows model cluster of [Al4 O21 ]30− , which contains Al3+ ion vacancy (V Al ). In order to estimate an effect of the vacancy, the vacancy is introduced at Al(1) site as shown in Fig. 1(b). Figure 1(c) shows a model cluster of [Al2 M3 O21 ]27− , in which M is trivalent cation (Y3+ ) and the ions are substituted at Al(2) sites. Figure 1(d) shows [AlM3 O21 ]27− cluster, which include tetravalent (Si4+ , Ti4+ , Zr4+ ) cations and accompanying Al3+ vacancies for electronic neutrality, respectively. A first-principle molecular orbital calculation was performed by solving the Hartree-Fock-Slater equations selfconsistently using discrete-variational (DV)-Xα method developed by Adachi et al.16) In the DV-Xα method, numerical atomic orbitals obtained by solving the Schrödinger equation for atoms was used as the basic function. Therefore, the Hamiltonian and overlap matrices can be evaluated as weighted sums of integrated values at an arbitrary point in a cluster for all kinds of elements, instead of the conventional Rayleigh-Ritz method. The Mulliken population analysis provides an orbital population, the sum of which is regarded as an effective net charge (NC), and also gives bond overlap population between atoms (BOP), a measure of the strength of covalent bonding.17, 19) 4. Results and Discussion The stress-strain curves for undoped, high-purity Al2 O3 and 0.1 mol% YO1.5 , SiO2 , TiO2 , or ZrO2 -doped Al2 O3 deformed at 1400◦ C and an initial strain rate of 1.2 × 10−4 s−1 are shown in Fig. 2. The stress-strain curve in undoped Al2 O3 is characterized by extensively large strain-hardening at the nominal strain up to 10% followed by stress decreasing after reaching a peak stress. The elongation to failure is less than 20% in the undoped Al2 O3 . The deformation charac-.

(3) 1568. H. Yoshida, Y. Takigawa, Y. Ikuhara and T. Sakuma. Fig. 1 Atomic structure of cluster models (a) [Al5 O21 ]27− , (b) [Al4 O21 ]30− , (c) [Al2 M3 O21 ]27− (M: Y3+ ) and (f) [AlM3 O21 ]27− (M: Si4+ , Ti4+ , Zr4+ ) used for the first-principle molecular orbital calculation by DV-Xα method. 100. / MPa. +0.1mol YO1.5 80 60 Flow Stress,. Table 2 Average grain size of undoped- and 0.1 mol% of oxide-doped Al2 O3 after failure.. 1400 . 0 =1.2x10 s. +ZrO2. undopedAl 2 O 3. 20 +TiO2 5. 10. undopedAl2 O3. +YO1.5. +SiO2. +TiO2. +ZrO2. Grain size/µm. 2.1. 1.5. 1.5. 4.1. 1.6. +SiO2. 40. 0 0. Sample. 15. 20. 25. 30. 35. Nominal Strain ( ). Fig. 2 Stress-strain curves in undoped, high-purity Al2 O3 and 0.1 mol% of YO1.5 , SiO2 , TiO2 or ZrO2 -doped Al2 O3 at 1400◦ C for an initial strain rate of 1.2 × 10−4 s−1 .. teristics such as flow stress and elongation to failure are affected by the addition of the oxide, even in the doping level of 0.1 mol%. The flow stress increases by the doping of YO1.5 or ZrO2 , but decreases by the doping of TiO2 . The increasing of the flow stress by Y3+ or Zr4+ doping corresponds to the previous results on high-temperature creep experiments. in fine-grained Al2 O3 .5, 6) On the other hand, the elongation to failure in Al2 O3 is enhanced by the doping of SiO2 , TiO2 or ZrO2 , but is suppressed by YO1.5 doping. It is well known that grain growth occurs during the hightemperature deformation in Al2 O3 . Table 2 shows the grain size of the present materials after the failure. The average grain size in undoped-Al2 O3 becomes to be about 2.1 µm at the failure with the nominal strain of about 19%. The large strain-hardening in undoped-Al2 O3 is understood in terms of the rapid grain growth during deformation.2) The grain growth during deformation is slightly suppressed by the addition of SiO2 , ZrO2 or YO1.5 . In contrast, the grain growth rate in Al2 O3 is enhanced by TiO2 doping. Generally, the flow stress in polycrystalline Al2 O3 increases with coarsening the grain size. However, the difference in the flow stress in the present.

(4) Effect of Chemical Bonding State on High-temperature Plastic Flow Behavior in Fine-grained. 1569. Fig. 3 A bright field image of an as-sintered (a) YO1.5 , (b) SiO2 , (c) TiO2 and (d) ZrO2 -doped Al2 O3 .. materials cannot be explained from the grain size effect; the flow stress in TiO2 -doped Al2 O3 is lower than that in YO1.5 or ZrO2 -doped Al2 O3 , though the grain size after the failure is more than two times larger than that in other materials. Moreover, the concurrent grain growth in Al2 O3 is fairly suppressed by YO1.5 doping, but the ductility in YO1.5 -doped Al2 O3 is lower than that in undoped-one. Figure 3 shows a bright field image of an as-sintered (a) YO1.5 , (b) SiO2 , (c) TiO2 and (d) ZrO2 -doped Al2 O3 . In the conventional TEM micrographs, small cation doped Al2 O3 seems to be a single phase material as well as the undopedone. By HREM observation, it is confirmed that the present materials are essentially single phase materials. Figure 4 shows an example of a high-resolution electron micrograph of an as-sintered ZrO2 -doped Al2 O3 . The HREM image is taken for the grain boundary at the edge-on view. No second phase or amorphous phase was observed along the grain boundary. The chemical composition around the grain boundary was examined by EDS analysis using the probe size of less than 1 nm. Figure 5 shows (a) scanning transmission electron microscopy (STEM) image and (b) Zr-Kα image obtained by STEM-EDS method for the grain boundary in the ZrO2 doped Al2 O3 . The dopant atoms present uniformly along the grain boundaries. This result suggests that ZrO2 -doped Al2 O3 is a single-phase material, and that the doped atoms segregate at the grain boundary, not to form the second phase. The microstructure in other oxide-doped Al2 O3 is essentially similar to that in ZrO2 -doped Al2 O3 . In polycrystalline Al2 O3 , the high-temperature plastic deformation often occurs by diffusional process.20–27) The predominant deformation mechanism in Al2 O3 with a grain size of less than about 10 µm is grain boundary diffusion creep at temperatures of 1100–1400◦ C and the applied stress of less than 100 MPa,20–23) and the grain boundary sliding contributes dominantly to the plastic flow in polycrystalline Al2 O3 with a grain size of less than about 2 µm.24–27) In our previous study, it has been revealed that a stress exponent n (inverse strain rate sensitivity) in fine-grained, single-phase Al2 O3 for high-temperature creep deformation is about 2, which indicates the creep deformation mechanism of interface reaction28) or grain boundary sliding.29–32) Since no dislocation activity was observed in deformed samples, and since the estimated activation energy for high-purity Al2 O3 is in good agreement with that for Al3+ grain boundary diffusion. Fig. 4 A high-resolution electron micrograph of an as-sintered ZrO2 -doped Al2 O3 at the grain boundary.. of 418 kJ/mol,33) it is safe to say that high-temperature plastic deformation in undoped-Al2 O3 takes place by the grain boundary sliding accommodated by the grain boundary diffusion.2, 4, 10, 11) It is possible to speculate that the high-temperature plastic flow characteristics such as the flow stress and the tensile ductility in polycrystalline Al2 O3 is changed by the grain boundary segregation of the dopant cations. Since the ratecontrolling process in undoped, fine-grained Al2 O3 is considered to be the grain boundary diffusion, and since the hightemperature fracture in fine-grained Al2 O3 is occurred by intergranular failure,2, 34, 35) the segregation of the dopant cation at the vicinity of the grain boundary is expected to change chemistry of the grain boundary and results in the difference in the plastic flow behavior in Al2 O3 . For example, TiO2.

(5) 1570. H. Yoshida, Y. Takigawa, Y. Ikuhara and T. Sakuma. 0.24. Bond Overlap Population in Al-O. +Si. 0.22. 0.20 +Ti. 0.18. +Zr. undopedAl 2 O 3. +Y. 0.16 3.4 3.6 3.8 4.0 4.2 Product of Al and O Net Charge Fig. 6 A plot of an average value of bond overlap population in Al(3) –O against product of net charges in O and Al(3) ions obtained using the cluster models shown in Fig. 1.. Fig. 5 (a) A scanning transmission electron microscopy (STEM) image and (b) Zr-Kα image obtained by STEM-X-ray energy dispersive spectrometer (EDS) for the grain boundary in ZrO2 -doped Al2 O3 .. is effective to promote the densification of Al2 O3 probably due to the acceleration of the grain boundary diffusivity.36) On the other hand, the doping of ZrO2 is considered to suppress the grain boundary diffusion in Al2 O3 from the results of grain growth behavior.37) The grain boundary segregation of the dopant cations must affect the grain boundary diffusion, which seems to determine the flow stress in the present materials. In our previous study, chemical shift on core-loss peaks in the electron energy loss spectroscopy (EELS) spectrum in O K-edge or Al L-edges has been detected at the grain boundaries in Al2 O3 due to the segregation of dopant such as Zr4+ , Mg2+ and lanthanoid cations with a probe size of less than 1 nm and an energy resolution of 0.7 eV.4, 7, 11) Since near edge structure of core-loss peaks in the EELS spectrum (ELNES) is sensitive to the chemical environment of the atoms,38) the chemical shift suggests that the chemical bond-. ing state is changed by the segregation of the dopant at the grain boundary. In this study, the model cluster for perfect crystal shown in Fig. 1 was used for the calculation as a first approximation in order to estimate the chemical bonding state at the grain boundary in cation-doped Al2 O3 . The net charge (NC) and the bond overlap population (BOP) for the clusters are important parameters to argue the chemical bonding state represented by ionic and covalent bond strength. Figure 6 shows a plot of an average value of BOP in Al(3) –O against absolute value of product of net charges in O and Al(3) ions obtained from each cluster model shown in Fig. 1. The product of NC in Al and O ions is supposed to correspond to the Coulomb’s attractive force between the anion and cation. As shown in Fig. 7, the value of BOP is increased by the tetravalent cation doping. BOP of Al(3) –O in Si-doped clusters shows the highest value in the present cluster models. In contrast, the BOP in Y-doped Al2 O3 is lower than that in undoped-one. This result indicates that the covalent bonding strength around O ions is increased by the doping of tetravalent cations, especially by Si-doping, but is decreased by Y-doping. On the other hand, the product of NC in Y-doped Al2 O3 is the largest in the present cluster. The value of the product of NC is also increased by Zr doping. This fact suggests that the ionic bond strength in Al2 O3 is enhanced by Y3+ or Zr4+ doping, but is reduced by Ti4+ or Si4+ doping. The present results of Fig. 7 in the value of BOP and NC seem to be correlated with the tensile ductility and the flow stress, respectively. Figure 7 shows a plot of (a) the flow stress at 5% nominal strain against the absolute value of the product of NC in Al(3) and O and (b) the tensile elongation to failure against the BOP between Al(3) and O for the presents materials at 1400◦ C under the initial strain rate of 1.2 × 10−4 s−1 . As shown in Fig. 7(a), the flow stress tends to decrease with increasing the value of the product of net charges. Since the product.

(6) 80 (a). Flow Stress at 5. Strain,. +ZrO 2. +YO1.5. 60. 40. 1571. (b). +SiO2 undopedAl 2 O 3. Elongation to Failure ( ). / MPa. Effect of Chemical Bonding State on High-temperature Plastic Flow Behavior in Fine-grained. +SiO 2. 30 +ZrO2. +TiO2. 20. undopedAl 2 O 3. +YO1.5. +TiO2 20. 10 3.4. 3.6 3.8 4.0 Product of Net Charges in Al and O. 4.2. 0.16 0.18 0.20 0.22 0.24 Bond Overlap Population in Al-O. Fig. 7 A plot of (a) 5% flow stress against product of Al(3) and O net charges and (b) elongation to failure against bond overlap population between Al(3) and O in the present materials at 1400◦ C under an initial strain rate of 1.2 × 10−4 s−1 .. of NC is supposed to correspond to the Coulomb’s attractive force between anion and cation, this result suggests that the ionic bonding strength between Al and O ions is related to the grain boundary diffusion; as the ionic bond strength increases, the diffusion may retarded and hence the flow stress is reduced. On the other hand, the effect of dopant cations on the tensile ductility is correlated with the BOP values; the elongation to failure increases with increasing the BOP value. The enhancement of tensile ductility by the segregation of Si, Ti or Zr in the vicinity of the grain boundaries may be caused by the generation of strong covalent bonds. Usually the diffusion is considered to be a thermally activated process corresponding to the energy maximum intermediate between the initial and final atom positions. As an atom immigrates, the potential energy experienced by the atom changes periodically because of the atomic configuration as the atom translates from one normal site to a neighboring one. The configuration of the transition state is expected to correspond to a higher potential energy than the normal configuration. In polar bonding crystal such as alumina,39) the ionic bonding must have major role to the longrange atomic interaction and may form the periodical energy potential. Moreover, contribution of the covalent bonding to the high potential energy at the transition site is expected to be relatively small because of the strong directional nature and rather short-range interaction of the covalent bonding.39, 40) It may be possible to speculate that the diffusivity is thus expected to be determined mainly by the Coulomb’s interaction. The result of the correlation between the product of net charges and flow stress in Fig. 7(a) is consistent with the expectation. On the other hand, the tensile ductility must be related to resistance to intergranular failure at high-temperatures. However, the intergranular failure at high temperatures is strongly influenced by various factors such as stress condition, nucleation and growth behavior of cavities,. vacancy flow along grain boundaries, etc. and is difficult to establish an atomistic model of failure at high-temperature. In spite of such uncertainties, a simple relationship can be found between elongation and BOP values of Fig. 7(b). Such a relationship between the elongation to failure and covalent bonding strength in superplastic tetragonal zirconia polycrystal with silica glass was also found out in the previous report of our group.41) The covalency must be an important factor relating with the high-temperature fracture at the grain boundaries. Further study on the role of chemical bonding strength on the diffusion or the fracture phenomena will allow one to expect the high-temperature plastic flow behavior in Al2 O3 more quantitatively. 5. Conclusion High-temperature plastic flow behavior in polycrystalline Al2 O3 with an average grain size of 1 µm is very sensitive to the doping of 0.1 mol% YO1.5 , SiO2 , TiO2 or ZrO2 at 1400◦ C under an initial strain rate of 1.2 × 10−4 s−1 . The high-temperature plastic deformation in the present materials is likely to take place mainly by grain boundary sliding accommodated by grain boundary diffusion, and that difference in flow stress and tensile elongation to failure is attributed to change in chemistry of the grain boundary in Al2 O3 due to segregation of the dopant cations at the vicinity of the grain boundaries. By a first-principle molecular orbital calculation using DV-Xα method based on [Al5 O21 ]27− model cluster, a correlation is found between the flow stress and the product of net charges of aluminum and oxygen ions. The grain boundary diffusion in the present materials is supposed to be affected mainly by the change in the ionic bonding strength between Al and O ions. On the other hand, the tensile elongation is correlated well with values of bond overlap population between Al and O. Strengthening of the covalent bonding at the.

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