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Grain boundary character dependence of oxygen grain boundary diffusion in α-Al2O3 bicrystals
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Scripta Materialia 65 (2011) 544–547 www.elsevier.com/locate/scriptamat
Grain boundary character dependence of oxygen grain boundary diffusion in a-Al2O3 bicrystals Tsubasa Nakagawa,a,b Hitoshi Nishimura,a Isao Sakaguchi,b Naoya Shibata,a Katsuyuki Matsunaga,c,d Takahisa Yamamotoa,c,d and Yuichi Ikuharaa,d,⇑ a
Institute of Engineering Innovation, The University of Tokyo, 2-11-16, Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan Optronic Materials Center, National Institute for Materials Science, 1-1, Namiki, Tsukuba, Ibaraki 305-0044, Japan c Department of Materials Science and Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan d Nanostructures Research Laboratory, Japan Fine Ceramics Center, Mutsuno, 2-4-1, Atsuta-ku, Nagoya 456-8587, Japan b
Received 13 May 2011; revised 11 June 2011; accepted 13 June 2011 Available online 22 June 2011
We measured oxygen diffusion coefficients (Dgb) along five grain boundaries (GBs) in alumina bicrystals by tracing 18O by secondary ion mass spectrometry. Although all boundaries are classified as coincident site lattice boundaries with relatively ordered structures, Dgb varied up to 103 times among them. On the other hand, the boundaries with identical boundary planes had relatively similar diffusivities as well as similar structures, regardless of R values. These results suggest that Dgb are related to GB atomic structures and hence the GB character, especially GB planes. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundary diffusion; Alumina; Bicrystal; HREM; SIMS
Alumina is one of the most important structural ceramics, and its diffusion behavior has been studied for several decades [1–13]. Extensive attention has been paid to its oxygen grain boundary (GB) diffusion behavior, because this is crucial for understanding and controlling many high-temperature properties and behavior, such as densification and grain growth during sintering and diffusional creep. For example, many researchers have studied the dopant effect on GB diffusion using a direct method (secondary ion mass spectrometry, SIMS [7–12]) or indirect methods (creep [14–16] and densification [17]). It is now widely known that small amounts of some elements, such as Y [14,15], La and Lu [15], and Zr [16], improve creep resistance and hence retard grain boundary diffusion, while other elements [16] promote GB diffusion in alumina. On the other hand, Sakaguchi et al. [12] estimated the oxygen diffusion coefficients along single GBs in undoped alumina polycrystalline ceramics using three-dimensional imaging of 18O tracers and found that the oxygen diffusion coefficients measured varied by up to three orders of magnitude from
⇑ Corresponding author. Present address: 2-11-16, Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan. Tel.: +81 3 5841 7689; fax: +81 5841 7694; e-mail: [email protected]
boundary to boundary. Their results indicate that the oxygen diffusion properties strongly depend on the GB characters and hence atomic structures of GBs. However, Sakaguchi et al. could not show any relationship between them, since they used polycrystalline materials in which the crystallographic and atomic structures were unknown. In the present study, we fabricated bicrystals, which enabled us to precisely control the crystallographic character of GBs, and measured the oxygen GB diffusion coefficients by the SIMS tracer method in order to find the dependence of the grain boundary character on oxygen GB diffusion. We fabricated five kinds of bicrystals. They were fabricated by joining two sapphire crystals (purity of 99.99 wt.%, from Shinkosha Co. Ltd., Yokohama, Japan) with desired geometrical configurations by diffusion bonding. Detailed procedures and results of ICP-AES analysis of impurities are provided in our previous paper [8]. A schematic illustration of the bicrystals used in this study and the geometrical parameters of the respective GBs are shown in Figure 1. All of them are symmetric tilt GBs with a common tilt axis of [0 0 0 1], but every boundary has a different character. Their GB geometries are classified using two different parameters (R value and GB plane), such as 7{2 3 1 0}, {4 5 1 0}, 4 5 1 0}, {2 3 1 0} and
1359-6462/$ - see front matter Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2011.06.024
T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
545
Figure 1. Schematic illustration of bicrystals fabricated in this study. Tilt angles, R values and grain boundary plane indices are also listed in the inset table.
31{7 1 1 4 0}, respectively. Note that four of them have a unique relationship to each other. Namely, there are two pairs with the same sigma values but with different GB planes (7{2 3 1 0} and {4 5 1 0}, {2 3 1 0} and {4 5 1 0}), while, at the same time, there are two pairs with the same GB planes but different sigma values (7{2 3 1 0} and {2 3 1 0}, {4 5 10} and {4 5 1 0}). This therefore enables us to estimate the effects of these parameters on GB diffusion. In our previous studies [18,19], the atomic structures of some boundaries were analyzed by high-resolution transmission electron microscopy (HRTEM) combined with static lattice calculations using empirical parameters. Figure 2 shows experimental HRTEM images and the most stable atomic structures obtained by static lattice calculations and their HRTEM simulation images for the respective boundaries. The HRTEM images were observed using an electron microscope operated at 400 kV (JEM4010, JEOL Co. Ltd., Tokyo, Japan), and were actually taken at defoci from 0 to 50 nm at steps of 5 nm. Under the conditions in which the images in Figure 2 were taken, the white dot contrast corresponds to Al columns along the [0 0 0 1] direction [18,19]. The GULP code was used for the static lattice calculations [20], and the Tempas program (Total Resolution, LLC, CA, USA) was used for the HRTEM image simulations. The detail of the calculation procedures have been described elsewhere [18,19]. As can be seen in Figure 2, the simulated HRTEM images based on the most stable computed structures show quite good agreement with the experi-
Figure 2. (Top) magnified HRTEM images, (middle) calculated stable structures and (bottom) simulated HRTEM images based on the calculated structures of a-Al2O3 grain boundaries.
Figure 3. Typical experimental 18O concentration profiles of bicrystals and single crystals after oxygen isotopic exchange annealing. Diffusion tails corresponding to “short-circuit diffusion” were observed only from those of bicrystals, indicating that such tails are due to the diffusion along each grain boundary.
mental images, indicating that the bicrystals had energetically stable GB structures. Matsunaga et al. [18] found that 7{2 3 1 0} and 21{2 3 1 0} have similar atomic structures, and suggested that the features of GB planes are more important for the GB structures than the R values. In the present study, we found that 7{4 5 1 0} and 21{4 5 1 0} also had similar atomic structures, which confirms Matsunaga et al.’s suggestion. For the oxygen diffusion study, the bicrystals were sliced normal to the common [0 0 0 1] direction. Subsequently, the polished samples were annealed in air for 3 h at 1400 °C to remove damage introduced during the polishing processes. Tracer diffusion annealing was then performed by means of a gas–solid exchange technique [21]. The samples were annealed in an 18O2 atmo-
Figure 4. Temperature dependence of dDgb (top) of each grain boundary and Dl (bottom). Lattice diffusion coefficients were deduced using all the data of five different bicrystals. All profiles can be expressed as an Arrhenius type relation, as shown in Table 1.
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T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
Table 1. Diffusion parameters of five grain boundaries and lattice diffusion coefficients, together with maximum and minimum values within a 95% confidence interval for each parameter. GB
dD0 (m3/s)
Maximum/minimum
E (eV)
R7{2 3 1 0}
1.4E 8
5.6 ± 0.4
R21{4 5 1 0}
4.7E 5
R7{4 5 1 0}
4.0E 2
R21{2 3 1 0}
9.2E 5
R31{7 1 1 4 0}
7.5E 8
Volume
6.8 10
1.6E 1.2E 8.4E 2.6E 3.8E 4.3E 6.9E 1.2E 2.8E 2.0E 1.1E 4.7E
6
(m2/s)
4 12 4 6 1 3 0 10 5 10 4 7
7.5 ± 0.4 8.8 ± 0.4 7.4 ± 2.1 5.8 ± 0.9 5.4 ± 0.4
(dDgb = dD0 exp ( E/kT)) (m3/s).
sphere using a radio frequency heating system in order to introduce 18O isotope into the polished surfaces. During the isotopic exchange annealing, the temperatures of the samples were monitored with a radiation thermometer and the oxygen partial pressure was set to be about 0.2 atm. 18O penetration depth profiles were measured for the present bicrystals by a secondary ion mass spectrometry (SIMS: CAMECA IMS-4F), with 133Cs+ as the primary ion at an accelerating voltage of 10 kV and a beam current of 5 nA. It should be noted that the sputter area was roughly 150 150 lm2, while the measurement area was 70 70 lm2. The detailed experimental procedures are described elsewhere [8]. Figure 3 shows typical experimental diffusion profiles of 18O along the tilt axis ([0 0 0 1]) of the bicrystals. A 18 O diffusion profile in a grain interior region is also shown for comparison. Diffusion tails, which indicate the existence of a short-circuit diffusion path, can clearly be seen in the profiles of specimens with GBs, while there is no such tail in the profile from the grain interior. This result strongly suggests that the diffusion tails in deeper regions are related to the GBs of the bicrystals, not to sub-boundaries, dislocations or any other defects that may be introduced during the sample preparation [5]. In the present case, the diffusion behavior of our specimen can be classified as type B diffusion according to the Harrison classification [22] and the GB diffusivities (dDgb) can be computed using the Le Claire equation [23]. Lattice diffusion coefficients were calculated using the near-surface region profiles, which have an error function shape. Arrhenius diagrams of oxygen grain boundary diffusion and their parameters are shown in Figure 4 and Table 1, respectively. Although it was reported that there was significant variation in the values of the oxygen lattice diffusion coefficients [7], the present results showed a good agreement with our previous studies [7,8]. This means that our results for oxygen lattice diffusion are reproducible and internally consistent. On the other hand, the results show that differences in the diffusion coefficients of these five boundaries can be up to three orders of magnitude, although all boundaries are classified as coincident site lattice boundaries, which have relatively ordered structures. The activation energies of GB diffusion ranged from 5.8 to 8.8 eV. All of them were comparable to or higher than the value for
lattice diffusion, 5.4 eV. Similar results were reported by Monty’s group [9–11] and attributed to segregated impurities increasing activation enthalpies. In the present study, the difference in activation enthalpies between lattice diffusion and GB diffusion is much smaller than that in their report. We think this is because our samples were much purer, which decreased the interaction between the segregated impurities and mobile defects in the vicinity of GBs. Concerning the relationship between the diffusivities and geometrical characters of GBs, the diffusivities of the respective boundaries followed the order 31{7 1 1 4 0} P 7{2 3 1 0} > 21{2 3 1 0} > 21 {4 5 1 0} > 7{4 5 1 0}. There seems to be only a slight correlation between R values and diffusivities, e.g. one R7 boundary had higher diffusivities than the R21 boundaries and one had lower diffusivities. On the other hand, there is a tendency for boundaries with a {4 5 1 0} GB plane to have lower diffusivities than those with {2 3 1 0} GB planes. Taking into account the fact that boundaries with the same GB plane had similar atomic structures, as mentioned above, this indicates that atomic structures in GB cores have some correlation to oxygen diffusion parameters. However, their relationship is not easily understood, inasmuch as boundaries with higher index planes had lower diffusivities. In addition, if one compares boundaries of identical GB planes by assessing the diffusivity rations as a function of temperature from 1400 to 1700 °C using the data in Table 1, one get roughly 9.7–52.0 for {2 3 1 0} boundaries, while the ratio for {4 5 1 0} boundaries is much smaller, 2.3– 8.2. This suggests that the R value and the GB plane could be important, and that the relative importance could vary with the specific R value and GB plane. We think this is because each boundary has a relaxed structure, not a rigid one, and the conventional approach, like atomic densities in lattice planes, in not sufficient to describe the atomic structures of high-angle GBs. Therefore, a more detailed analysis of atomic structures will be a desirable next step. Also, measurements in which diffusion occurs along different directions in the grain boundary plane may be necessary or useful since diffusivities along GBs should have direction dependence. In summary, we examined oxygen GB diffusion behavior of single GBs with controlled geometric characters and found that oxygen diffusivities can vary
T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
by a factor of 103, depending on the grain boundary character. While there was a small relationship between diffusivities and R values, boundaries with {2 3 1 0} GB plane had lower diffusivities than those with {4 5 1 0} and {7 1 1 4 0} planes. Moreover, we found that boundaries with the same boundary planes ({2 3 1 0} and {4 5 1 0}) had similar atomic structures regardless of their R values. This strongly indicates that the atomic structures themselves are crucial for the oxygen diffusivities. A part of this study was supported by a Grantin-Aid for Scientific Research on Priority Areas “Nano Materials Science for Atomic Scale Modification 474” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The authors wish to thank Prof. A.H. Heuer of Case Western Reserve University for his careful reading of this manuscript and useful comments. [1] Y. Oishi, K. Ando, N. Suga, W.D. Kingery, J. Am. Ceram. Soc. 66 (1983) C130. [2] Y. Oishi, K. Ando, Y. Kubota, J. Chem. Phys 73 (1980) 1410. [3] D.J. Reed, B.J. Wuensch, J. Am. Ceram. Soc. 63 (1988) 88. [4] J.D. Cawley, J.W. Halloran, A.R. Cooper, J. Am. Ceram. Soc. 74 (1991) 2086. [5] A.H. Heuer, K.P.D. Lagerlo¨f, Phil. Mag. Lett. 79 (1999) 619.
547
[6] J.H. Harding, K.J.W. Atkinson, R.W. Grimes, J. Am. Ceram. Soc. 86 (2003) 554. [7] T. Nakagawa, A. Nakamura, I. Sakaguchi, N. Shibata, K.P.D. Lagerlo¨f, T. Yamamoto, H. Haneda, Y. Ikuhara, J. Ceram. Soc. Jpn. 114 (2006) 1013. [8] T. Nakagawa, I. Sakaguchi, N. Shibata, K. Matsunaga, T. Mizoguchi, T. Yamamoto, H. Haneda, Y. Ikuhara, Acta Mater. 55 (2007) 6627. [9] D. Prot, C. Monty, Phil. Mag. A 73 (1996) 899. [10] M. Le Gall, A.M. Huntz, C. Monty, Phil. Mag. A 73 (1996) 919. [11] D. Prot, M. Le Gall, B. Lesage, A.M. Huntz, C. Monty, Phil. Mag. A 73 (1996) 935. [12] I. Sakaguchi, V. Srikanth, T. Ikegami, H. Haneda, J. Am. Ceram. Soc. 78 (1995) 2557. [13] A.H. Heuer, J. Eur. Ceram. Soc. 28 (2008) 1498. [14] J. Cho, M.P. Harmer, H.M. Chan, J.M. Rickman, A.M. Thompson, J. Am. Ceram. Soc. 80 (1997) 1013. [15] H. Yoshida, Y. Ikuhara, T. Sakuma, J. Mater. Res. 13 (1997) 2597. [16] H. Yoshida, Y. Ikuhara, T. Sakuma, Acta Mater. 50 (2009) 2955. [17] H. Yoshida, S. Hashimoto, T. Yamamoto, Acta Mater. 53 (2005) 433. [18] K. Matsunaga, H. Nishimura, T. Saito, T. Yamamoto, Y. Ikuhara, Phil. Mag. 83 (2003) 4071. [19] H. Nishimura, K. Matsunaga, T. Saito, T. Yamamoto, Y. Ikuhara, J. Am. Ceram. Soc. 86 (2003) 574. [20] J.D. Gale, A.L. Rohl, Mol. Simulat. 29 (1993) 291. [21] H. Haneda, I. Sakaguchi, A. Watanabe, T. Ishigaki, J. Tanaka, J. Electroceram. 4 (1999) 41. [22] L.G. Harrison, Trans. Faraday Soc. 57 (1961) 1191. [23] A.D. Le Claire, Br. J. Appl. Phys. 14 (1963) 351.
Scripta Materialia 65 (2011) 544–547 www.elsevier.com/locate/scriptamat
Grain boundary character dependence of oxygen grain boundary diffusion in a-Al2O3 bicrystals Tsubasa Nakagawa,a,b Hitoshi Nishimura,a Isao Sakaguchi,b Naoya Shibata,a Katsuyuki Matsunaga,c,d Takahisa Yamamotoa,c,d and Yuichi Ikuharaa,d,⇑ a
Institute of Engineering Innovation, The University of Tokyo, 2-11-16, Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan Optronic Materials Center, National Institute for Materials Science, 1-1, Namiki, Tsukuba, Ibaraki 305-0044, Japan c Department of Materials Science and Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan d Nanostructures Research Laboratory, Japan Fine Ceramics Center, Mutsuno, 2-4-1, Atsuta-ku, Nagoya 456-8587, Japan b
Received 13 May 2011; revised 11 June 2011; accepted 13 June 2011 Available online 22 June 2011
We measured oxygen diffusion coefficients (Dgb) along five grain boundaries (GBs) in alumina bicrystals by tracing 18O by secondary ion mass spectrometry. Although all boundaries are classified as coincident site lattice boundaries with relatively ordered structures, Dgb varied up to 103 times among them. On the other hand, the boundaries with identical boundary planes had relatively similar diffusivities as well as similar structures, regardless of R values. These results suggest that Dgb are related to GB atomic structures and hence the GB character, especially GB planes. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundary diffusion; Alumina; Bicrystal; HREM; SIMS
Alumina is one of the most important structural ceramics, and its diffusion behavior has been studied for several decades [1–13]. Extensive attention has been paid to its oxygen grain boundary (GB) diffusion behavior, because this is crucial for understanding and controlling many high-temperature properties and behavior, such as densification and grain growth during sintering and diffusional creep. For example, many researchers have studied the dopant effect on GB diffusion using a direct method (secondary ion mass spectrometry, SIMS [7–12]) or indirect methods (creep [14–16] and densification [17]). It is now widely known that small amounts of some elements, such as Y [14,15], La and Lu [15], and Zr [16], improve creep resistance and hence retard grain boundary diffusion, while other elements [16] promote GB diffusion in alumina. On the other hand, Sakaguchi et al. [12] estimated the oxygen diffusion coefficients along single GBs in undoped alumina polycrystalline ceramics using three-dimensional imaging of 18O tracers and found that the oxygen diffusion coefficients measured varied by up to three orders of magnitude from
⇑ Corresponding author. Present address: 2-11-16, Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan. Tel.: +81 3 5841 7689; fax: +81 5841 7694; e-mail: [email protected]
boundary to boundary. Their results indicate that the oxygen diffusion properties strongly depend on the GB characters and hence atomic structures of GBs. However, Sakaguchi et al. could not show any relationship between them, since they used polycrystalline materials in which the crystallographic and atomic structures were unknown. In the present study, we fabricated bicrystals, which enabled us to precisely control the crystallographic character of GBs, and measured the oxygen GB diffusion coefficients by the SIMS tracer method in order to find the dependence of the grain boundary character on oxygen GB diffusion. We fabricated five kinds of bicrystals. They were fabricated by joining two sapphire crystals (purity of 99.99 wt.%, from Shinkosha Co. Ltd., Yokohama, Japan) with desired geometrical configurations by diffusion bonding. Detailed procedures and results of ICP-AES analysis of impurities are provided in our previous paper [8]. A schematic illustration of the bicrystals used in this study and the geometrical parameters of the respective GBs are shown in Figure 1. All of them are symmetric tilt GBs with a common tilt axis of [0 0 0 1], but every boundary has a different character. Their GB geometries are classified using two different parameters (R value and GB plane), such as 7{2 3 1 0}, {4 5 1 0}, 4 5 1 0}, {2 3 1 0} and
1359-6462/$ - see front matter Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2011.06.024
T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
545
Figure 1. Schematic illustration of bicrystals fabricated in this study. Tilt angles, R values and grain boundary plane indices are also listed in the inset table.
31{7 1 1 4 0}, respectively. Note that four of them have a unique relationship to each other. Namely, there are two pairs with the same sigma values but with different GB planes (7{2 3 1 0} and {4 5 1 0}, {2 3 1 0} and {4 5 1 0}), while, at the same time, there are two pairs with the same GB planes but different sigma values (7{2 3 1 0} and {2 3 1 0}, {4 5 10} and {4 5 1 0}). This therefore enables us to estimate the effects of these parameters on GB diffusion. In our previous studies [18,19], the atomic structures of some boundaries were analyzed by high-resolution transmission electron microscopy (HRTEM) combined with static lattice calculations using empirical parameters. Figure 2 shows experimental HRTEM images and the most stable atomic structures obtained by static lattice calculations and their HRTEM simulation images for the respective boundaries. The HRTEM images were observed using an electron microscope operated at 400 kV (JEM4010, JEOL Co. Ltd., Tokyo, Japan), and were actually taken at defoci from 0 to 50 nm at steps of 5 nm. Under the conditions in which the images in Figure 2 were taken, the white dot contrast corresponds to Al columns along the [0 0 0 1] direction [18,19]. The GULP code was used for the static lattice calculations [20], and the Tempas program (Total Resolution, LLC, CA, USA) was used for the HRTEM image simulations. The detail of the calculation procedures have been described elsewhere [18,19]. As can be seen in Figure 2, the simulated HRTEM images based on the most stable computed structures show quite good agreement with the experi-
Figure 2. (Top) magnified HRTEM images, (middle) calculated stable structures and (bottom) simulated HRTEM images based on the calculated structures of a-Al2O3 grain boundaries.
Figure 3. Typical experimental 18O concentration profiles of bicrystals and single crystals after oxygen isotopic exchange annealing. Diffusion tails corresponding to “short-circuit diffusion” were observed only from those of bicrystals, indicating that such tails are due to the diffusion along each grain boundary.
mental images, indicating that the bicrystals had energetically stable GB structures. Matsunaga et al. [18] found that 7{2 3 1 0} and 21{2 3 1 0} have similar atomic structures, and suggested that the features of GB planes are more important for the GB structures than the R values. In the present study, we found that 7{4 5 1 0} and 21{4 5 1 0} also had similar atomic structures, which confirms Matsunaga et al.’s suggestion. For the oxygen diffusion study, the bicrystals were sliced normal to the common [0 0 0 1] direction. Subsequently, the polished samples were annealed in air for 3 h at 1400 °C to remove damage introduced during the polishing processes. Tracer diffusion annealing was then performed by means of a gas–solid exchange technique [21]. The samples were annealed in an 18O2 atmo-
Figure 4. Temperature dependence of dDgb (top) of each grain boundary and Dl (bottom). Lattice diffusion coefficients were deduced using all the data of five different bicrystals. All profiles can be expressed as an Arrhenius type relation, as shown in Table 1.
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T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
Table 1. Diffusion parameters of five grain boundaries and lattice diffusion coefficients, together with maximum and minimum values within a 95% confidence interval for each parameter. GB
dD0 (m3/s)
Maximum/minimum
E (eV)
R7{2 3 1 0}
1.4E 8
5.6 ± 0.4
R21{4 5 1 0}
4.7E 5
R7{4 5 1 0}
4.0E 2
R21{2 3 1 0}
9.2E 5
R31{7 1 1 4 0}
7.5E 8
Volume
6.8 10
1.6E 1.2E 8.4E 2.6E 3.8E 4.3E 6.9E 1.2E 2.8E 2.0E 1.1E 4.7E
6
(m2/s)
4 12 4 6 1 3 0 10 5 10 4 7
7.5 ± 0.4 8.8 ± 0.4 7.4 ± 2.1 5.8 ± 0.9 5.4 ± 0.4
(dDgb = dD0 exp ( E/kT)) (m3/s).
sphere using a radio frequency heating system in order to introduce 18O isotope into the polished surfaces. During the isotopic exchange annealing, the temperatures of the samples were monitored with a radiation thermometer and the oxygen partial pressure was set to be about 0.2 atm. 18O penetration depth profiles were measured for the present bicrystals by a secondary ion mass spectrometry (SIMS: CAMECA IMS-4F), with 133Cs+ as the primary ion at an accelerating voltage of 10 kV and a beam current of 5 nA. It should be noted that the sputter area was roughly 150 150 lm2, while the measurement area was 70 70 lm2. The detailed experimental procedures are described elsewhere [8]. Figure 3 shows typical experimental diffusion profiles of 18O along the tilt axis ([0 0 0 1]) of the bicrystals. A 18 O diffusion profile in a grain interior region is also shown for comparison. Diffusion tails, which indicate the existence of a short-circuit diffusion path, can clearly be seen in the profiles of specimens with GBs, while there is no such tail in the profile from the grain interior. This result strongly suggests that the diffusion tails in deeper regions are related to the GBs of the bicrystals, not to sub-boundaries, dislocations or any other defects that may be introduced during the sample preparation [5]. In the present case, the diffusion behavior of our specimen can be classified as type B diffusion according to the Harrison classification [22] and the GB diffusivities (dDgb) can be computed using the Le Claire equation [23]. Lattice diffusion coefficients were calculated using the near-surface region profiles, which have an error function shape. Arrhenius diagrams of oxygen grain boundary diffusion and their parameters are shown in Figure 4 and Table 1, respectively. Although it was reported that there was significant variation in the values of the oxygen lattice diffusion coefficients [7], the present results showed a good agreement with our previous studies [7,8]. This means that our results for oxygen lattice diffusion are reproducible and internally consistent. On the other hand, the results show that differences in the diffusion coefficients of these five boundaries can be up to three orders of magnitude, although all boundaries are classified as coincident site lattice boundaries, which have relatively ordered structures. The activation energies of GB diffusion ranged from 5.8 to 8.8 eV. All of them were comparable to or higher than the value for
lattice diffusion, 5.4 eV. Similar results were reported by Monty’s group [9–11] and attributed to segregated impurities increasing activation enthalpies. In the present study, the difference in activation enthalpies between lattice diffusion and GB diffusion is much smaller than that in their report. We think this is because our samples were much purer, which decreased the interaction between the segregated impurities and mobile defects in the vicinity of GBs. Concerning the relationship between the diffusivities and geometrical characters of GBs, the diffusivities of the respective boundaries followed the order 31{7 1 1 4 0} P 7{2 3 1 0} > 21{2 3 1 0} > 21 {4 5 1 0} > 7{4 5 1 0}. There seems to be only a slight correlation between R values and diffusivities, e.g. one R7 boundary had higher diffusivities than the R21 boundaries and one had lower diffusivities. On the other hand, there is a tendency for boundaries with a {4 5 1 0} GB plane to have lower diffusivities than those with {2 3 1 0} GB planes. Taking into account the fact that boundaries with the same GB plane had similar atomic structures, as mentioned above, this indicates that atomic structures in GB cores have some correlation to oxygen diffusion parameters. However, their relationship is not easily understood, inasmuch as boundaries with higher index planes had lower diffusivities. In addition, if one compares boundaries of identical GB planes by assessing the diffusivity rations as a function of temperature from 1400 to 1700 °C using the data in Table 1, one get roughly 9.7–52.0 for {2 3 1 0} boundaries, while the ratio for {4 5 1 0} boundaries is much smaller, 2.3– 8.2. This suggests that the R value and the GB plane could be important, and that the relative importance could vary with the specific R value and GB plane. We think this is because each boundary has a relaxed structure, not a rigid one, and the conventional approach, like atomic densities in lattice planes, in not sufficient to describe the atomic structures of high-angle GBs. Therefore, a more detailed analysis of atomic structures will be a desirable next step. Also, measurements in which diffusion occurs along different directions in the grain boundary plane may be necessary or useful since diffusivities along GBs should have direction dependence. In summary, we examined oxygen GB diffusion behavior of single GBs with controlled geometric characters and found that oxygen diffusivities can vary
T. Nakagawa et al. / Scripta Materialia 65 (2011) 544–547
by a factor of 103, depending on the grain boundary character. While there was a small relationship between diffusivities and R values, boundaries with {2 3 1 0} GB plane had lower diffusivities than those with {4 5 1 0} and {7 1 1 4 0} planes. Moreover, we found that boundaries with the same boundary planes ({2 3 1 0} and {4 5 1 0}) had similar atomic structures regardless of their R values. This strongly indicates that the atomic structures themselves are crucial for the oxygen diffusivities. A part of this study was supported by a Grantin-Aid for Scientific Research on Priority Areas “Nano Materials Science for Atomic Scale Modification 474” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The authors wish to thank Prof. A.H. Heuer of Case Western Reserve University for his careful reading of this manuscript and useful comments. [1] Y. Oishi, K. Ando, N. Suga, W.D. Kingery, J. Am. Ceram. Soc. 66 (1983) C130. [2] Y. Oishi, K. Ando, Y. Kubota, J. Chem. Phys 73 (1980) 1410. [3] D.J. Reed, B.J. Wuensch, J. Am. Ceram. Soc. 63 (1988) 88. [4] J.D. Cawley, J.W. Halloran, A.R. Cooper, J. Am. Ceram. Soc. 74 (1991) 2086. [5] A.H. Heuer, K.P.D. Lagerlo¨f, Phil. Mag. Lett. 79 (1999) 619.
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[6] J.H. Harding, K.J.W. Atkinson, R.W. Grimes, J. Am. Ceram. Soc. 86 (2003) 554. [7] T. Nakagawa, A. Nakamura, I. Sakaguchi, N. Shibata, K.P.D. Lagerlo¨f, T. Yamamoto, H. Haneda, Y. Ikuhara, J. Ceram. Soc. Jpn. 114 (2006) 1013. [8] T. Nakagawa, I. Sakaguchi, N. Shibata, K. Matsunaga, T. Mizoguchi, T. Yamamoto, H. Haneda, Y. Ikuhara, Acta Mater. 55 (2007) 6627. [9] D. Prot, C. Monty, Phil. Mag. A 73 (1996) 899. [10] M. Le Gall, A.M. Huntz, C. Monty, Phil. Mag. A 73 (1996) 919. [11] D. Prot, M. Le Gall, B. Lesage, A.M. Huntz, C. Monty, Phil. Mag. A 73 (1996) 935. [12] I. Sakaguchi, V. Srikanth, T. Ikegami, H. Haneda, J. Am. Ceram. Soc. 78 (1995) 2557. [13] A.H. Heuer, J. Eur. Ceram. Soc. 28 (2008) 1498. [14] J. Cho, M.P. Harmer, H.M. Chan, J.M. Rickman, A.M. Thompson, J. Am. Ceram. Soc. 80 (1997) 1013. [15] H. Yoshida, Y. Ikuhara, T. Sakuma, J. Mater. Res. 13 (1997) 2597. [16] H. Yoshida, Y. Ikuhara, T. Sakuma, Acta Mater. 50 (2009) 2955. [17] H. Yoshida, S. Hashimoto, T. Yamamoto, Acta Mater. 53 (2005) 433. [18] K. Matsunaga, H. Nishimura, T. Saito, T. Yamamoto, Y. Ikuhara, Phil. Mag. 83 (2003) 4071. [19] H. Nishimura, K. Matsunaga, T. Saito, T. Yamamoto, Y. Ikuhara, J. Am. Ceram. Soc. 86 (2003) 574. [20] J.D. Gale, A.L. Rohl, Mol. Simulat. 29 (1993) 291. [21] H. Haneda, I. Sakaguchi, A. Watanabe, T. Ishigaki, J. Tanaka, J. Electroceram. 4 (1999) 41. [22] L.G. Harrison, Trans. Faraday Soc. 57 (1961) 1191. [23] A.D. Le Claire, Br. J. Appl. Phys. 14 (1963) 351.