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CeO2 superlattice
Applied Surface Science 130–132 Ž1998. 545–548
Molecular dynamics simulations on oxygen ion diffusion in strained YSZrCeO 2 superlattice Ken Suzuki, Akira Endou, Ryuji Miura, Yasunori Oumi, Hiromitsu Takaba, Momoji Kubo, Abhijit Chatterjee, Adil Fahmi, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba Aramaki, Aoba-ku, Sendai 980-77, Japan Received 16 September 1997; accepted 22 December 1997
Abstract Our earlier molecular dynamics results show that the construction of a strained yttria-stabilized zirconia ŽYSZ.rCeO 2 superlattice considerably enhances oxygen ion diffusion. In the present study, effect of several parameters Že.g., Y2 O 3 concentrations, stacking periodicity, and temperature. on oxygen ion diffusion in strained YSZrCeO2 superlattice were optimized to rationalize the understanding of the process mechanism. We found that self-diffusion coefficient of O ions reaches a maximum at around 9.1 mol% Y2 O 3 concentration, and the increment of CeO 2rYSZ ratio enhances oxygen ion diffusion. Moreover, activation energy for oxygen ion diffusion in the YSZrCeO2 superlattice Ž9 kcalrmol. was found to be lower than that observed in the bulk YSZ Ž15 kcalrmol.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: YSZ; CeO 2 ; Strained superlattice; Oxygen ion diffusion; Molecular dynamics
1. Introduction A cubic yttria-stabilized zirconia ŽYSZ. described as ŽY2 O 3 .c ŽZrO 2 .1yc has gained much attention because of its various industrial applications such as fuel cells, sensors, catalysts, ceramics etc. w1–3x. It is observed that the functionality of this material is based on high diffusion of oxygen ions. The increment of oxygen ion diffusion leads to the enhancement of the material performance. Many studies have been focused on the synthesis of novel YSZ-based materials which have high oxygen ion diffusion. Effects of yttria concentration and temperature on )
Corresponding author. Fax: q81-22-217-7235; e-mail: [email protected].
oxygen ion diffusion in YSZ were experimentally well studied, and the diffusion coefficient, a well established phenomenon of oxygen ions, reaches a maximum at yttria concentration of 0.08–0.10. Theoretical studies on oxygen ion diffusion in YSZ w4–6x using molecular dynamics ŽMD. method were also reported. We in our earlier communication w7x had reported a novel technique to enhance oxygen ion diffusion in YSZ and confirmed its validity by MD simulations. Fig. 1 shows our model to explain the enhancement of oxygen ion diffusion in YSZ. We proposed that the construction of a strained YSZ lattice sandwiched by CeO 2 ŽYSZrCeO2 superlattice. leads to an increase of oxygen ion diffusion in YSZ. Since CeO 2 has similar structure as YSZ ŽCaF2-like cubic
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 2 - 3
546
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
Fig. 1. Model of enhancement in oxygen ion diffusion in YSZ. Sandwiching YSZ between CeO 2 with larger lattice parameters lead to an increment of YSZ lattice parameters Žstrain.. Consequently, oxygen ion diffusion increases.
˚ which structure. with a lattice parameter of 5.411 A, is 5.17% larger than that of the YSZ Ž10 mol% ˚ the a- and b-axis parameters are Y2 O 3 . 5.145 A; expanded which result in the cation–cation distances elongation in the YSZ part of the YSZrCeO 2 superlattice. These structural changes result in the decrease of the barrier height followed by acceleration of the oxygen ion diffusion. However, the detailed processes of the above mentioned enhancement have not been discussed in the previous letter. Hence, in the present study in order to optimize several conditions of the strained YSZrCeO2 superlattice, we investigated the effects of Y2 O 3 concentration, stacking periodicity, and temperature on oxygen ion diffusion in the YSZrCeO 2 superlattice by MD simulations.
Eq. Ž1., the first and second terms refer to Coulomb and exchange repulsion interactions, respectively.
2. Method
3. Results and discussion
MD simulations were carried out using MXDORTO program developed by Kawamura w8x. The Verlet algorithm was used for the calculation of the atomic motions, while the Ewald method was applied for the calculation of the electrostatic interactions under three-dimensional periodic boundary conditions. Temperature and pressure were controlled by scaling atom velocities and unit cell parameters, respectively. The calculations were performed for 50,000 steps with a time step of 2.0 = 10y1 5 s. The two-body interatomic potential, as shown in Eq. Ž1., was used for all calculations. In
3.1. Effect of Y2 O3 concentration in the YSZ part of the strained YSZ r CeO2 superlattice on the oxygen ion diffusion
U Ž ri j . s Zi Z j e 2rr i j q f 0 Ž bi q bj . = exp Ž a i q a j y ri j . r Ž bi q bj .
Ž 1.
where Zi is the atomic charge, e the elementary electric charge, ri j the interatomic distance, and f 0 a constant. The parameters a and b in Eq. Ž1. represent the size and stiffness, respectively. The potential parameters were determined, as reported in Ref. w7x. They reproduce the lattice constants and expansion coefficients of YSZ Ž10 mol% Y2 O 3 ., Y2 O 3 , and CeO 2 crystals. Dynamic features of the oxygen ion diffusion process were investigated by three-dimensional visualization programs MOMOVIE and RYUGA w9x developed in our group.
Y2 O 3 concentration in the YSZ part of the strained YSZrCeO 2 superlattice is one of the dominant parameters which affect the oxygen ion diffusion. MD simulations were carried out for four different concentrations of Y2 O 3 in the YSZ part of the YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells. superlattice: 4.3, 9.1, 14.3, and 20.0 mol% Y2 O 3 at 18008C. The mean square displacements ŽMSD. of the oxygen ion dif-
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
Fig. 2. MSD of oxygen ions in the YSZ part of four strained YSZrCeO2 superlattices with 4.3, 9.1, 14.3, and 20.0 mol% Y2 O 3 concentrations as a function of time at 18008C.
fusion as a function of time for all dopant concentrations were shown in Fig. 2. The self-diffusion coefficient Ž D . of O ions obtained from the slope of the MSD values shows a maximum at the concentration of 9.1 mol% Y2 O 3 . This tendency is similar to that observed in the bulk YSZ as obtained both by experiments w10x and previous MD simulations w4,5,7x. 3.2. Effect of stacking periodicity on the oxygen ion diffusion The stacking periodicity of the strained YSZrCeO 2 superlattice may greatly influence the oxygen ion diffusion. Hence, we constructed three YSZrCeO 2 superlattice models with different stacking combinations of YSZ, such as YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO 2 Ž1 unit cell., and the effect of stacking periodicity on the oxygen ion diffusion was investigated. The above models were constructed only for the YSZrCeO 2 superlattice with 9.1 mol% Y2 O 3 which has a maximum oxygen ion diffusion among all dopant concentrations as observed in Section 3.1. The cell parameTable 1 Induced strain Ž D ar a 0 . at the YSZ part in the three strained YSZrCeO2 superlattice models Ž9.1 mol% Y2 O 3 in YSZ.: YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO2 Ž1 unit cell. Models
Induced strain Ž D ar a 0 .
YSZŽ1 unit cell.rCeO 2 Ž3 unit cells. YSZŽ2 unit cells.rCeO 2 Ž2 unit cells. YSZŽ3 unit cells.rCeO 2 Ž1 unit cells.
4.5% 3.2% 1.7%
547
Fig. 3. MSD of oxygen ions in the YSZ part of the three strained YSZrCeO2 superlattice models Ž9.1 mol% Y2 O 3 in YSZ. as a function of time at 18008C: YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO 2 Ž1 unit cell.. MSD of oxygen ions in the bulk YSZ Ž9.1 mol% Y2 O 3 . is also shown.
ters were optimized, and the induced strain D ara0 ˚ . was calculated ŽTable 1.. It is obŽ a 0 s 5.243 A served that the stacking combination, YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. model has the highest strain. It indicates that the stacking periodicity has influences the strain value which further shows that higher strain in the superlattice is induced with increase in the CeO 2rYSZ ratio. MSDŽ t . values of the O ions in the YSZ part of the above three superlattice models are presented as a function time in Fig. 3. The diffusion coefficient of the oxygen ions in all three YSZrCeO 2 superlattice was more than 1.3 times larger than that observed in the bulk YSZ. Especially, YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. model has the maximum oxygen ion diffusion among all the three models Ž2.0 times larger than that in the bulk YSZ., which is due to the maximum induced strain. We conclude from the current data set that the stacking periodicity is one of the important factors which influences the oxygen ion diffusion in the YSZrCeO 2 superlattice and the increase of the CeO 2rYSZ ratio enhances oxygen ion diffusion. 3.3. Effect of temperature on the oxygen ion diffusion Experimentally, temperature also plays a key role in controlling oxygen ion diffusion in YSZ. Hence, we simulated the oxygen ion diffusion in the YSZ part of the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice Ž9.1 mol% Y2 O 3 in YSZ., which has a maximum oxygen ion diffusion among three models employed in Section 3.2 in the temperature range of
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
548
Table 2 Temperature-dependency of the self-diffusion coefficients of the oxygen ion diffusion in the bulk YSZ and YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. Ž9.1 mol% Y2 O 3 in YSZ. superlattice Temperature ŽC8.
800 1000 1200 1500 1800
Self-diffusion coefficient Ž=10y6 cm2 rs. Bulk YSZ
YSZ Ž1 unit cell.r CeO 2 Ž3 unit cells.
0.11 0.18 0.36 0.80 1.76
0.47 0.67 1.65 1.97 3.75
8008C–18008C. The oxygen ion diffusion in the bulk YSZ was also simulated, as a reference to compare. Table 2 shows the temperature-dependency of the self-diffusion coefficients of oxygen ions in the bulk YSZ and in the above YSZrCeO2 superlattice. It was found that the temperature greatly influences the oxygen ion diffusion and high temperature enhances the oxygen ion diffusion in the YSZrCeO 2 superlattice. Following Arrhenius law for temperature-dependency of the diffusion coefficient, we derive the value of activation energy for oxygen ion diffusion in the YSZ part of the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice. Fig. 4 shows the Arrhenius plot which gives an activation energy of 15 kcalrmol for the bulk YSZ and 9 kcalrmol for YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice, respectively. The activation energy for the bulk YSZ as obtained by MD simulations, matches with the experimental value of 18 kcalrmol w11x. The activation energy for oxygen ion diffusion in the above YSZrCeO 2 super-
Fig. 4. Arrhenius plots for oxygen ion diffusion in the bulk YSZ and the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice Ž9.1 mol% Y2 O 3 in YSZ..
lattice was less than that in the bulk YSZ. According to results w4,5x, the barrier for oxygen ion diffusion is located at the center of two cations ŽZr–Zr, Zr–Y and Y–Y.. Hence, the above results indicate that the oxygen ions can easily cross the center of two cations and migrate towards a neighboring tetrahedron in the YSZrCeO 2 superlattice, which is due to the elongation of the cation–cation distance and also due to the reduction of the activation barrier. Finally, we established that the construction of a strained YSZrCeO 2 superlattice decreases the activation energy barrier for the oxygen ion diffusion in the YSZ. 4. Conclusion In the present study, we successfully simulated the oxygen ion diffusion in several YSZrCeO 2 superlattices with different Y2 O 3 concentration and stacking periodicity using MD simulation. We optimized several conditions of the YSZrCeO 2 superlattice structure and identified YSZrCeO 2 superionic conductor model with higher oxygen ion diffusion Ž2.0 times. than that in the bulk YSZ. Moreover, we found that the activation energy barrier for oxygen ion diffusion in the above YSZrCeO 2 superlattice is much lower than that observed for the bulk YSZ. References w1x S. Somiya, N. Yamamoto, H. Yanagida ŽEds.., Science and Technology of Zirconia: III, Am. Ceram. Soc., Columbus, 1988. w2x B.V.R. Chowdari ŽEd.., Proceedings of the 10th International Conference on Solid State Ionics, Special Volume of Solid State Ionics, North-Holland, Amsterdam, 1996. w3x P.J. Moles ŽEd.., Zirconium in Catalysis, Special Issue of Catal. Today, Elsevier, Amsterdam, 1994. w4x F. Shimojo, T. Okabe, F. Tachibana, M. Kobayashi, H. Okazaki, J. Phys. Soc. Jpn. 61 Ž1992. 2848. w5x F. Shimojo, H. Okazaki, J. Phys. Soc. Jpn. 61 Ž1992. 4106. w6x H. Okazaki, H. Suzuki, K. Ihata, J. Phys. Soc. Jpn. 63 Ž1994. 3556. w7x K. Suzuki, M. Kubo, Y. Oumi, R. Miura, H. Takaba, A. Fahmi, A. Miyamoto, Appl. Phys. Lett., under contribution. w8x K. Kawamura, Molecular Dynamics Simulation, SpringerVerlag, Berlin, 1992, p. 88. w9x R. Miura, H. Yamano, R. Yamauchi, M. Katagiri, M. Kubo, R. Vetrivel, A. Miyamoto, Catal. Today 23 Ž1995. 409. w10x T. Suemoto, M. Ishigame, Solid State Ionics 21 Ž1986. 225. w11x D.W. Strickler, W.G. Carlson, J. Am. Ceram. Soc. 47 Ž1964. 122.
Molecular dynamics simulations on oxygen ion diffusion in strained YSZrCeO 2 superlattice Ken Suzuki, Akira Endou, Ryuji Miura, Yasunori Oumi, Hiromitsu Takaba, Momoji Kubo, Abhijit Chatterjee, Adil Fahmi, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba Aramaki, Aoba-ku, Sendai 980-77, Japan Received 16 September 1997; accepted 22 December 1997
Abstract Our earlier molecular dynamics results show that the construction of a strained yttria-stabilized zirconia ŽYSZ.rCeO 2 superlattice considerably enhances oxygen ion diffusion. In the present study, effect of several parameters Že.g., Y2 O 3 concentrations, stacking periodicity, and temperature. on oxygen ion diffusion in strained YSZrCeO2 superlattice were optimized to rationalize the understanding of the process mechanism. We found that self-diffusion coefficient of O ions reaches a maximum at around 9.1 mol% Y2 O 3 concentration, and the increment of CeO 2rYSZ ratio enhances oxygen ion diffusion. Moreover, activation energy for oxygen ion diffusion in the YSZrCeO2 superlattice Ž9 kcalrmol. was found to be lower than that observed in the bulk YSZ Ž15 kcalrmol.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: YSZ; CeO 2 ; Strained superlattice; Oxygen ion diffusion; Molecular dynamics
1. Introduction A cubic yttria-stabilized zirconia ŽYSZ. described as ŽY2 O 3 .c ŽZrO 2 .1yc has gained much attention because of its various industrial applications such as fuel cells, sensors, catalysts, ceramics etc. w1–3x. It is observed that the functionality of this material is based on high diffusion of oxygen ions. The increment of oxygen ion diffusion leads to the enhancement of the material performance. Many studies have been focused on the synthesis of novel YSZ-based materials which have high oxygen ion diffusion. Effects of yttria concentration and temperature on )
Corresponding author. Fax: q81-22-217-7235; e-mail: [email protected].
oxygen ion diffusion in YSZ were experimentally well studied, and the diffusion coefficient, a well established phenomenon of oxygen ions, reaches a maximum at yttria concentration of 0.08–0.10. Theoretical studies on oxygen ion diffusion in YSZ w4–6x using molecular dynamics ŽMD. method were also reported. We in our earlier communication w7x had reported a novel technique to enhance oxygen ion diffusion in YSZ and confirmed its validity by MD simulations. Fig. 1 shows our model to explain the enhancement of oxygen ion diffusion in YSZ. We proposed that the construction of a strained YSZ lattice sandwiched by CeO 2 ŽYSZrCeO2 superlattice. leads to an increase of oxygen ion diffusion in YSZ. Since CeO 2 has similar structure as YSZ ŽCaF2-like cubic
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 2 - 3
546
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
Fig. 1. Model of enhancement in oxygen ion diffusion in YSZ. Sandwiching YSZ between CeO 2 with larger lattice parameters lead to an increment of YSZ lattice parameters Žstrain.. Consequently, oxygen ion diffusion increases.
˚ which structure. with a lattice parameter of 5.411 A, is 5.17% larger than that of the YSZ Ž10 mol% ˚ the a- and b-axis parameters are Y2 O 3 . 5.145 A; expanded which result in the cation–cation distances elongation in the YSZ part of the YSZrCeO 2 superlattice. These structural changes result in the decrease of the barrier height followed by acceleration of the oxygen ion diffusion. However, the detailed processes of the above mentioned enhancement have not been discussed in the previous letter. Hence, in the present study in order to optimize several conditions of the strained YSZrCeO2 superlattice, we investigated the effects of Y2 O 3 concentration, stacking periodicity, and temperature on oxygen ion diffusion in the YSZrCeO 2 superlattice by MD simulations.
Eq. Ž1., the first and second terms refer to Coulomb and exchange repulsion interactions, respectively.
2. Method
3. Results and discussion
MD simulations were carried out using MXDORTO program developed by Kawamura w8x. The Verlet algorithm was used for the calculation of the atomic motions, while the Ewald method was applied for the calculation of the electrostatic interactions under three-dimensional periodic boundary conditions. Temperature and pressure were controlled by scaling atom velocities and unit cell parameters, respectively. The calculations were performed for 50,000 steps with a time step of 2.0 = 10y1 5 s. The two-body interatomic potential, as shown in Eq. Ž1., was used for all calculations. In
3.1. Effect of Y2 O3 concentration in the YSZ part of the strained YSZ r CeO2 superlattice on the oxygen ion diffusion
U Ž ri j . s Zi Z j e 2rr i j q f 0 Ž bi q bj . = exp Ž a i q a j y ri j . r Ž bi q bj .
Ž 1.
where Zi is the atomic charge, e the elementary electric charge, ri j the interatomic distance, and f 0 a constant. The parameters a and b in Eq. Ž1. represent the size and stiffness, respectively. The potential parameters were determined, as reported in Ref. w7x. They reproduce the lattice constants and expansion coefficients of YSZ Ž10 mol% Y2 O 3 ., Y2 O 3 , and CeO 2 crystals. Dynamic features of the oxygen ion diffusion process were investigated by three-dimensional visualization programs MOMOVIE and RYUGA w9x developed in our group.
Y2 O 3 concentration in the YSZ part of the strained YSZrCeO 2 superlattice is one of the dominant parameters which affect the oxygen ion diffusion. MD simulations were carried out for four different concentrations of Y2 O 3 in the YSZ part of the YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells. superlattice: 4.3, 9.1, 14.3, and 20.0 mol% Y2 O 3 at 18008C. The mean square displacements ŽMSD. of the oxygen ion dif-
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
Fig. 2. MSD of oxygen ions in the YSZ part of four strained YSZrCeO2 superlattices with 4.3, 9.1, 14.3, and 20.0 mol% Y2 O 3 concentrations as a function of time at 18008C.
fusion as a function of time for all dopant concentrations were shown in Fig. 2. The self-diffusion coefficient Ž D . of O ions obtained from the slope of the MSD values shows a maximum at the concentration of 9.1 mol% Y2 O 3 . This tendency is similar to that observed in the bulk YSZ as obtained both by experiments w10x and previous MD simulations w4,5,7x. 3.2. Effect of stacking periodicity on the oxygen ion diffusion The stacking periodicity of the strained YSZrCeO 2 superlattice may greatly influence the oxygen ion diffusion. Hence, we constructed three YSZrCeO 2 superlattice models with different stacking combinations of YSZ, such as YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO 2 Ž1 unit cell., and the effect of stacking periodicity on the oxygen ion diffusion was investigated. The above models were constructed only for the YSZrCeO 2 superlattice with 9.1 mol% Y2 O 3 which has a maximum oxygen ion diffusion among all dopant concentrations as observed in Section 3.1. The cell parameTable 1 Induced strain Ž D ar a 0 . at the YSZ part in the three strained YSZrCeO2 superlattice models Ž9.1 mol% Y2 O 3 in YSZ.: YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO2 Ž1 unit cell. Models
Induced strain Ž D ar a 0 .
YSZŽ1 unit cell.rCeO 2 Ž3 unit cells. YSZŽ2 unit cells.rCeO 2 Ž2 unit cells. YSZŽ3 unit cells.rCeO 2 Ž1 unit cells.
4.5% 3.2% 1.7%
547
Fig. 3. MSD of oxygen ions in the YSZ part of the three strained YSZrCeO2 superlattice models Ž9.1 mol% Y2 O 3 in YSZ. as a function of time at 18008C: YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells., YSZ Ž2 unit cells.rCeO 2 Ž2 unit cells., and YSZ Ž3 unit cells.rCeO 2 Ž1 unit cell.. MSD of oxygen ions in the bulk YSZ Ž9.1 mol% Y2 O 3 . is also shown.
ters were optimized, and the induced strain D ara0 ˚ . was calculated ŽTable 1.. It is obŽ a 0 s 5.243 A served that the stacking combination, YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. model has the highest strain. It indicates that the stacking periodicity has influences the strain value which further shows that higher strain in the superlattice is induced with increase in the CeO 2rYSZ ratio. MSDŽ t . values of the O ions in the YSZ part of the above three superlattice models are presented as a function time in Fig. 3. The diffusion coefficient of the oxygen ions in all three YSZrCeO 2 superlattice was more than 1.3 times larger than that observed in the bulk YSZ. Especially, YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. model has the maximum oxygen ion diffusion among all the three models Ž2.0 times larger than that in the bulk YSZ., which is due to the maximum induced strain. We conclude from the current data set that the stacking periodicity is one of the important factors which influences the oxygen ion diffusion in the YSZrCeO 2 superlattice and the increase of the CeO 2rYSZ ratio enhances oxygen ion diffusion. 3.3. Effect of temperature on the oxygen ion diffusion Experimentally, temperature also plays a key role in controlling oxygen ion diffusion in YSZ. Hence, we simulated the oxygen ion diffusion in the YSZ part of the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice Ž9.1 mol% Y2 O 3 in YSZ., which has a maximum oxygen ion diffusion among three models employed in Section 3.2 in the temperature range of
K. Suzuki et al.r Applied Surface Science 130–132 (1998) 545–548
548
Table 2 Temperature-dependency of the self-diffusion coefficients of the oxygen ion diffusion in the bulk YSZ and YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. Ž9.1 mol% Y2 O 3 in YSZ. superlattice Temperature ŽC8.
800 1000 1200 1500 1800
Self-diffusion coefficient Ž=10y6 cm2 rs. Bulk YSZ
YSZ Ž1 unit cell.r CeO 2 Ž3 unit cells.
0.11 0.18 0.36 0.80 1.76
0.47 0.67 1.65 1.97 3.75
8008C–18008C. The oxygen ion diffusion in the bulk YSZ was also simulated, as a reference to compare. Table 2 shows the temperature-dependency of the self-diffusion coefficients of oxygen ions in the bulk YSZ and in the above YSZrCeO2 superlattice. It was found that the temperature greatly influences the oxygen ion diffusion and high temperature enhances the oxygen ion diffusion in the YSZrCeO 2 superlattice. Following Arrhenius law for temperature-dependency of the diffusion coefficient, we derive the value of activation energy for oxygen ion diffusion in the YSZ part of the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice. Fig. 4 shows the Arrhenius plot which gives an activation energy of 15 kcalrmol for the bulk YSZ and 9 kcalrmol for YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice, respectively. The activation energy for the bulk YSZ as obtained by MD simulations, matches with the experimental value of 18 kcalrmol w11x. The activation energy for oxygen ion diffusion in the above YSZrCeO 2 super-
Fig. 4. Arrhenius plots for oxygen ion diffusion in the bulk YSZ and the YSZ Ž1 unit cell.rCeO 2 Ž3 unit cells. superlattice Ž9.1 mol% Y2 O 3 in YSZ..
lattice was less than that in the bulk YSZ. According to results w4,5x, the barrier for oxygen ion diffusion is located at the center of two cations ŽZr–Zr, Zr–Y and Y–Y.. Hence, the above results indicate that the oxygen ions can easily cross the center of two cations and migrate towards a neighboring tetrahedron in the YSZrCeO 2 superlattice, which is due to the elongation of the cation–cation distance and also due to the reduction of the activation barrier. Finally, we established that the construction of a strained YSZrCeO 2 superlattice decreases the activation energy barrier for the oxygen ion diffusion in the YSZ. 4. Conclusion In the present study, we successfully simulated the oxygen ion diffusion in several YSZrCeO 2 superlattices with different Y2 O 3 concentration and stacking periodicity using MD simulation. We optimized several conditions of the YSZrCeO 2 superlattice structure and identified YSZrCeO 2 superionic conductor model with higher oxygen ion diffusion Ž2.0 times. than that in the bulk YSZ. Moreover, we found that the activation energy barrier for oxygen ion diffusion in the above YSZrCeO 2 superlattice is much lower than that observed for the bulk YSZ. References w1x S. Somiya, N. Yamamoto, H. Yanagida ŽEds.., Science and Technology of Zirconia: III, Am. Ceram. Soc., Columbus, 1988. w2x B.V.R. Chowdari ŽEd.., Proceedings of the 10th International Conference on Solid State Ionics, Special Volume of Solid State Ionics, North-Holland, Amsterdam, 1996. w3x P.J. Moles ŽEd.., Zirconium in Catalysis, Special Issue of Catal. Today, Elsevier, Amsterdam, 1994. w4x F. Shimojo, T. Okabe, F. Tachibana, M. Kobayashi, H. Okazaki, J. Phys. Soc. Jpn. 61 Ž1992. 2848. w5x F. Shimojo, H. Okazaki, J. Phys. Soc. Jpn. 61 Ž1992. 4106. w6x H. Okazaki, H. Suzuki, K. Ihata, J. Phys. Soc. Jpn. 63 Ž1994. 3556. w7x K. Suzuki, M. Kubo, Y. Oumi, R. Miura, H. Takaba, A. Fahmi, A. Miyamoto, Appl. Phys. Lett., under contribution. w8x K. Kawamura, Molecular Dynamics Simulation, SpringerVerlag, Berlin, 1992, p. 88. w9x R. Miura, H. Yamano, R. Yamauchi, M. Katagiri, M. Kubo, R. Vetrivel, A. Miyamoto, Catal. Today 23 Ž1995. 409. w10x T. Suemoto, M. Ishigame, Solid State Ionics 21 Ž1986. 225. w11x D.W. Strickler, W.G. Carlson, J. Am. Ceram. Soc. 47 Ž1964. 122.