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Growth mechanism of YBCO film by TFA-MOD process
Physica C 392–396 (2003) 882–886 www.elsevier.com/locate/physc
Growth mechanism of YBCO film by TFA-MOD process Ryo Teranishi a,*,1, Tetsuji Honjo a, Yuichi Nakamura a,b, Hiroshi Fuji a, Yoshitaka Tokunaga a, Junko Matsuda a, Teruo Izumi a, Yuh Shiohara a a
Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan b Toyohashi University of Technology, 1-1 Hibarigaoka, Tenpaku, Toyohashi, Aichi 441-8580, Japan Received 13 November 2002; accepted 7 February 2003
Abstract The growth rate expression in the TFA-MOD process for fabrication of coated conductors was revised according to the measurement of the growth rate using a long tape. The P (H2 O) distribution along the gas flow-direction was calculated by the advection diffusion model. The above two outputs were combined to predict the minimum annealing time for complete reaction in the sample tape with a finite width. The prediction from the model was in good agreement with the experimental results. 2003 Elsevier B.V. All rights reserved. PACS: 81.15.)z; 74.76.)w; 81.10.Jt Keywords: TFA-MOD process; Growth rate; YBCO
1. Introduction The metal organic deposition (MOD) using a precursor solution containing metal trifluoroacetates (TFA) is an attractive process to provide the YBa2 Cu3 O7y (YBCO) coated conductors because of the high critical current density (Jc ) [1–5]. Additionally, since the TFA-MOD process is a nonvacuum system, it is strongly expected to be a low cost process in a future. In order to obtain high critical currents (Ic ), the thicker films keeping high
*
Corresponding author. Tel.: +81-3-3536-5711; fax: +81-33536-5714. E-mail address: [email protected] (R. Teranishi). 1 Research fellow of the Japan Society of the Promotion of Science.
Jc value are required. In the same time, a long tape fabricating process has to be developed for proceeding it to applications. In this development, the required annealing time is an important factor to design a long tape fabrication equipment. The investigation of the growth mechanism for the YBCO films in this process is essential not only for improvement of Ic value but for development of a long tape processing. It has been reported that the Y2 Cu2 O5 , BaF2 and CuO are converted into YBCO by releasing HF with supplying H2 O at the reaction interface in this process [2,6]. Consequently, the water vapor pressure, P (H2 O), during crystallization is a key factor to control the supersaturation which determines the YBCO growth rate by the conversion reaction kinetics. We have proposed the onedimensional analysis of YBCO growth during post
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01197-3
R. Teranishi et al. / Physica C 392–396 (2003) 882–886
annealing process considering both diffusion in the gas boundary layer and the growth kinetics at the precursor/YBCO interface in this process [7]. From this growth model, the fundamental idea of the YBCO growth mechanism has been obtained. However, we have recently found that the growth rate strongly depended on the sample size. This suggests the effect of the two-dimensional diffusion is not negligible. In this study, the parameters in the growth model were experimentally revised and the model was combined with the P (H2 O) distribution predicted by the analysis of the advection diffusion, in order to apply the model to the long tape processing.
2. Experimental The TFA precursor solution for fabrication of the YBCO films was prepared by dissolving the TFA salts of Y, Ba and Cu with 1:2:3 cation ratio into a sufficient amount of methyl alcohol. The TFA solution was controlled to have the total metal ion concentration of 1.5 mol/l and was coated onto the single crystalline substrate of LaAlO3 (1 0 0) by the spin-coating method. The length of the substrate was changed from 10 to 40 mm with the same width of 10 mm. The heat treatment of the coating films was performed in the two stages with the heating profile reported by the M.I.T. group [1]. In this study, a humid gas for the reaction to form the YBCO phase was flowed in the transverse direction to the long one of the substrate. The flow rate of the inlet gas to the furnace was about 8.5 · 103 m/s. In order to evaluate the growth rate, in situ electrical conductance of the precursor film during the crystallization was measured by the DC four-probe method [8]. It is a similar measurement technique of a film conductance fabricated by an ex situ process that has been reported by Suenaga et al. [9–11]. The Ag electrodes for this measurement were deposited onto the precursor film in advance by evaporation. The several measurement points were prepared along the gas flow-direction on the substrate at the center of the length.
883
3. Results and discussion Fig. 1 shows the schematic drawings for the measurement of the time dependence of the converted YBCO layer thickness. In this study, the measurements were taken place at the 2 points, which were the windward and leeward regions along y-direction on the substrate at the center of the length, for the samples with different lengths, L, annealing under the condition of 4.2 vol% in P (H2 O) and 750 C of the annealing temperature. The time for the complete reaction was defined as the minimum annealing time, t . Fig. 2 shows the film length dependence of t at the substrate position of the leeward region at the center of the length. It showed that the t increased with increasing the film length. However, in the case of the film with longer than 20 mm, the t became a
Fig. 1. Schematic drawings for the measurement of the time dependence of the converted YBCO layer thickness. The measurements were taken place at the 2 points, which were the windward and leeward regions along y-direction on the substrate at the center of the length, for the samples with different lengths, L, annealing under the condition of 4.2 vol% in P (H2 O) and 750 C of the annealing temperature.
Fig. 2. Film length, L, dependence of the minimum annealing time, t , at the substrate position of the leeward region at the center of the length.
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R. Teranishi et al. / Physica C 392–396 (2003) 882–886
kind of saturation. This means that the influence of the two-dimensional diffusion that results from x-direction in the Fig. 1 can be neglected in these samples under the growth conditions in this study. Then, we tried to modify the growth rate expression that was previously reported [7]. According to the report [7], the growth rate can be expressed by the following equation; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VYBCO Dg Ke XH2 O R¼ 4Vgas dg
ð1Þ
where, VYBCO is the molar volume of the YBCO crystal and Vgas is that of gas, respectively, which gives the coefficient VYBCO =2Vgas is about 5.7 · 104 . The Dg is the mass diffusivity in the gas boundary layer and dg is the boundary layer thickness, respectively. Although the exact values of diffusivity of H2 O in a gas system are not well measured, the mass diffusivities in the Ar–O2 and N2 –O2 systems can be calculated as 1.92 and 2.03 cm2 /s, respectively, at 775 C as typical values [7]. We use 2 cm2 / s of the Dg in this analysis for simplicity. Also, the dg is estimated to be 1.25 cm in this system. Here, Ke value is the equilibrium constant for the reaction to produce the YBCO phase, which is again an unknown factor. Then, we obtained this value from the experimental result. The growth rate at the position of the windward edge was evaluated to determine the Ke value, because this position should always feel the given P (H2 O) without the influence of the reaction in the other regions. Finally, the Ke value was estimated to be 7.5 · 109 from the results of the growth rate measurement obtained as to be 1.02 · 1010 m/s, the above parameters and Eq. (1). In order to investigate the t dependence along the direction of the width, the P (H2 O) distribution along the width-direction was estimated using the advection diffusion. Fig. 3 shows the physical image of the local cross-section during the YBCO growth. We presume that the diffusion boundary layer exists onto the precursor layer. The mass transfer on both y- and z-direction in Fig. 3 and the P (H2 O) distribution in the diffusion boundary layer were discussed. The mass transfer equations for H2 O on both directions can be expressed as follows:
Fig. 3. Physical image of the local cross-section during the YBCO growth. The diffusion boundary layer assumed to be onto the precursor layer. JH2 O;y and JH2 O;z are the mass diffusion fluxes and Vy and Vz are the velocity of the H2 O gas on each direction, respectively, XH2 O is the H2 O concentration, and XH2 O;0 is the H2 O concentration which can be given as an experimental parameter.
JH2 O;y ¼ D
oXH2 O þ XH2 O Vy oy
ð2Þ
oXH2 O þ XH2 O Vz ð3Þ oz where JH2 O;y and JH2 O;z are the mass diffusion fluxes and Vy and Vz are the velocity of the H2 O gas on each direction, respectively, XH2 O is the H2 O concentration, and D is the mass diffusivity in the gas boundary layer. Additionally, considering the steady state gas flow condition, the mass diffusion flux of H2 O needs to satisfy the following equation: JH2 O;z ¼ D
oJH2 O;y oJH2 O;z þ ¼0 oy oz
ð4Þ
The boundary conditions shown in Fig. 3 in this study are summarized as follows: ðB:C:1Þ Z ¼ 0; XH2 O ¼ XH2 O;0 ðB:C:2Þ Z ¼ 1; XH2 O ¼ 0 where XH2 O;0 is the H2 O concentration which can be given as an experimental parameter. D was again used to be 2 cm2 /s in this analysis. Finally,
R. Teranishi et al. / Physica C 392–396 (2003) 882–886
Fig. 4. The P (H2 O) distribution in the diffusion boundary layer along the film width-direction. It was calculated by solving the equations from (2)–(4) under the boundary conditions of B.C.1 and B.C.2 and the reaction parameters.
we obtained the P (H2 O) distribution, shown in Fig. 4, by solving the equations from (2)–(4) under the boundary conditions of B.C.1 and B.C.2 and the reaction parameters. Consequently, it can be calculated the existence of the P (H2 O) distribution along the width-direction. Then, the estimated t values depended on the film width were discussed combining the onedimensional analysis for the mass transfer expressed as Eq. (1) with the P (H2 O) distribution at the surface of the diffusion boundary layer. The moving boundary interface and quasi-steady state model was applied for this estimation. The schematic model of the model concept in this study was shown in Fig. 5. We presume that each lattice point is divided as a width of Dy ¼ 1 mm on the yaxis at the surface of the boundary layer, and the each lattice point is expressed as yn . The P (H2 O) at yn would be estimated by the P (H2 O) distribution curve obtained by the above calculation. The P (H2 O)n value was obtained by averaging the values at the edges of the nth cell. This value was assumed to be constant until the annealing of the node would be finished. Also, we presume that the fresh gas with the P (H2 O)g , which is given experimentally, always comes from the windward side. When the first cell finishes the reaction, the given P (H2 O)g is shifted from y1 to y2 . This manner will be successively proceeded by finishing the reaction in the entire film. Finally, we could predict the required annealing time for the complete reaction
885
Fig. 5. Schematic model of the moving boundary interface and quasi-steady state. Each lattice point assumed to be divided as a width of Dy ¼ 1 mm on the y-axis at the surface of the boundary layer, and the each lattice point is expressed as yn .
Table 1 The required annealing time estimated by the model of moving boundary interface and quasi-steady state for different samples with different P (H2 O) P (H2 O) (vol%) 4.2 9.1
W (mm)
t Cal. (min)
t Ex. (min)
10 10
79.8 53.4
71.3 47.2
The experimental results were shown for comparison.
for different samples with different partial pressure, P (H2 O), as shown in Table 1, with the experimental results for comparison. Comparing these values, it could be found that the predictions were in good agreement with the experimental results within the errors of only 10%.
4. Conclusion The film length, L, dependence of the YBCO growth rate was investigated by in situ monitoring of the conductance of the precursor film during YBCO crystallization using the DC four-probe method. As a result, the time for the complete reaction, t , increased with increase of L and be saturated for the sample longer than L ¼ 20 mm. This suggests that the influence of the twodimensional diffusion can be neglected for the film
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R. Teranishi et al. / Physica C 392–396 (2003) 882–886
longer than 20 mm under the growth conditions at least in this study. Then, in order to modify the YBCO growth rate model expressed as Eq. (1), the equilibrium constant, Ke , was re-estimated by the growth rate measurement using the film with 30 mm in length. From the result, we obtained the Ke value of 7.6 · 109 . In order to investigate the t dependence along the direction of the width, the P (H2 O) distribution along the film width was calculated by using the advection model. The estimation of t distribution in the width-direction was discussed combining the onedimensional analysis for the mass transfer with the P (H2 O) distribution at the surface of the diffusion boundary layer. Comparing these values, it could be found that the predictions are in good agreement with the experimental results within the error of only 10%.
Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] P.C. Mclntyre, M.J. Cima, J.A. Smith, R.B. Hallock, M.P. Siegal, J.M. Phillips, J. Appl. Phys. 71 (1992) 1868. [2] J.A. Smith, M.J. Cima, N. Sonnenberg, IEEE Trans. Appl. Supercond. 9 (1999) 1531. [3] M. Paranthaman, T.G. Chirayil, S. Sathyamurthy, D.B. Deach, A. Goyal, F.A. List, D.F. Lee, X. Cui, S.W. Lu, B. Kang, E.D. Specht, P.M. Martin, D.M. Kroeger, R. Feenstra, C. Cantoni, D.K. Christen, IEEE Trans. Appl. Supercond. 11 (2001) 3146. [4] J.T. Dawley, P.G. Clem, M.P. Siegal, D.L. Overmyer, M.A. Rodriguez, IEEE Trans. Appl. Supercond. 11 (2001) 2873. [5] M.W. Rupich, Q. Li, S. Annavarapu, C. Thieme, W. Zhang, V. Prunier, M. Paranthaman, A. Goyal, D.F. Lee, E.D. Specht, F.A. List, IEEE Trans. Appl. Supercond. 11 (2001) 2927. [6] J. Shibata, T. Honjo, H. Fuji, T. Araki, I. Hirabayashi, T. Hirayama, T. Izumi, Y. Shiohara, T. Yamamoto, Y. Ikuhara, J. Mater. Res. 17 (2002) 1266. [7] T. Honjo, Y. Nakamura, R. Teranishi, H. Fuji, J. Shibata, T. Izumi, Y. Shiohara, IEEE Trans. Appl. Supercond., submitted. [8] R. Teranishi, H. Fuji, T. Honjo, Y. Nakamura, T. Izumi, Y. Shiohara, J. Shibata, T. Yamamoto, Y. Ikuhara, M. Yoshimura, Physica C 378–381 (2002) 1033. [9] V.F. Solovyov, H.J. Weismann, L. Wu, M. Suenaga, IEEE Trans. Appl. Supercond. 9 (1999) 1467. [10] V.F. Solovyov, H.J. Weismann, L. Wu, Y. Zhu, M. Suenaga, Appl. Phys. Lett. 76 (2000) 1911. [11] V.F. Solovyov, H.J. Weismann, M. Suenaga, Physica C 357 (2001) 14.
Growth mechanism of YBCO film by TFA-MOD process Ryo Teranishi a,*,1, Tetsuji Honjo a, Yuichi Nakamura a,b, Hiroshi Fuji a, Yoshitaka Tokunaga a, Junko Matsuda a, Teruo Izumi a, Yuh Shiohara a a
Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan b Toyohashi University of Technology, 1-1 Hibarigaoka, Tenpaku, Toyohashi, Aichi 441-8580, Japan Received 13 November 2002; accepted 7 February 2003
Abstract The growth rate expression in the TFA-MOD process for fabrication of coated conductors was revised according to the measurement of the growth rate using a long tape. The P (H2 O) distribution along the gas flow-direction was calculated by the advection diffusion model. The above two outputs were combined to predict the minimum annealing time for complete reaction in the sample tape with a finite width. The prediction from the model was in good agreement with the experimental results. 2003 Elsevier B.V. All rights reserved. PACS: 81.15.)z; 74.76.)w; 81.10.Jt Keywords: TFA-MOD process; Growth rate; YBCO
1. Introduction The metal organic deposition (MOD) using a precursor solution containing metal trifluoroacetates (TFA) is an attractive process to provide the YBa2 Cu3 O7y (YBCO) coated conductors because of the high critical current density (Jc ) [1–5]. Additionally, since the TFA-MOD process is a nonvacuum system, it is strongly expected to be a low cost process in a future. In order to obtain high critical currents (Ic ), the thicker films keeping high
*
Corresponding author. Tel.: +81-3-3536-5711; fax: +81-33536-5714. E-mail address: [email protected] (R. Teranishi). 1 Research fellow of the Japan Society of the Promotion of Science.
Jc value are required. In the same time, a long tape fabricating process has to be developed for proceeding it to applications. In this development, the required annealing time is an important factor to design a long tape fabrication equipment. The investigation of the growth mechanism for the YBCO films in this process is essential not only for improvement of Ic value but for development of a long tape processing. It has been reported that the Y2 Cu2 O5 , BaF2 and CuO are converted into YBCO by releasing HF with supplying H2 O at the reaction interface in this process [2,6]. Consequently, the water vapor pressure, P (H2 O), during crystallization is a key factor to control the supersaturation which determines the YBCO growth rate by the conversion reaction kinetics. We have proposed the onedimensional analysis of YBCO growth during post
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01197-3
R. Teranishi et al. / Physica C 392–396 (2003) 882–886
annealing process considering both diffusion in the gas boundary layer and the growth kinetics at the precursor/YBCO interface in this process [7]. From this growth model, the fundamental idea of the YBCO growth mechanism has been obtained. However, we have recently found that the growth rate strongly depended on the sample size. This suggests the effect of the two-dimensional diffusion is not negligible. In this study, the parameters in the growth model were experimentally revised and the model was combined with the P (H2 O) distribution predicted by the analysis of the advection diffusion, in order to apply the model to the long tape processing.
2. Experimental The TFA precursor solution for fabrication of the YBCO films was prepared by dissolving the TFA salts of Y, Ba and Cu with 1:2:3 cation ratio into a sufficient amount of methyl alcohol. The TFA solution was controlled to have the total metal ion concentration of 1.5 mol/l and was coated onto the single crystalline substrate of LaAlO3 (1 0 0) by the spin-coating method. The length of the substrate was changed from 10 to 40 mm with the same width of 10 mm. The heat treatment of the coating films was performed in the two stages with the heating profile reported by the M.I.T. group [1]. In this study, a humid gas for the reaction to form the YBCO phase was flowed in the transverse direction to the long one of the substrate. The flow rate of the inlet gas to the furnace was about 8.5 · 103 m/s. In order to evaluate the growth rate, in situ electrical conductance of the precursor film during the crystallization was measured by the DC four-probe method [8]. It is a similar measurement technique of a film conductance fabricated by an ex situ process that has been reported by Suenaga et al. [9–11]. The Ag electrodes for this measurement were deposited onto the precursor film in advance by evaporation. The several measurement points were prepared along the gas flow-direction on the substrate at the center of the length.
883
3. Results and discussion Fig. 1 shows the schematic drawings for the measurement of the time dependence of the converted YBCO layer thickness. In this study, the measurements were taken place at the 2 points, which were the windward and leeward regions along y-direction on the substrate at the center of the length, for the samples with different lengths, L, annealing under the condition of 4.2 vol% in P (H2 O) and 750 C of the annealing temperature. The time for the complete reaction was defined as the minimum annealing time, t . Fig. 2 shows the film length dependence of t at the substrate position of the leeward region at the center of the length. It showed that the t increased with increasing the film length. However, in the case of the film with longer than 20 mm, the t became a
Fig. 1. Schematic drawings for the measurement of the time dependence of the converted YBCO layer thickness. The measurements were taken place at the 2 points, which were the windward and leeward regions along y-direction on the substrate at the center of the length, for the samples with different lengths, L, annealing under the condition of 4.2 vol% in P (H2 O) and 750 C of the annealing temperature.
Fig. 2. Film length, L, dependence of the minimum annealing time, t , at the substrate position of the leeward region at the center of the length.
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R. Teranishi et al. / Physica C 392–396 (2003) 882–886
kind of saturation. This means that the influence of the two-dimensional diffusion that results from x-direction in the Fig. 1 can be neglected in these samples under the growth conditions in this study. Then, we tried to modify the growth rate expression that was previously reported [7]. According to the report [7], the growth rate can be expressed by the following equation; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VYBCO Dg Ke XH2 O R¼ 4Vgas dg
ð1Þ
where, VYBCO is the molar volume of the YBCO crystal and Vgas is that of gas, respectively, which gives the coefficient VYBCO =2Vgas is about 5.7 · 104 . The Dg is the mass diffusivity in the gas boundary layer and dg is the boundary layer thickness, respectively. Although the exact values of diffusivity of H2 O in a gas system are not well measured, the mass diffusivities in the Ar–O2 and N2 –O2 systems can be calculated as 1.92 and 2.03 cm2 /s, respectively, at 775 C as typical values [7]. We use 2 cm2 / s of the Dg in this analysis for simplicity. Also, the dg is estimated to be 1.25 cm in this system. Here, Ke value is the equilibrium constant for the reaction to produce the YBCO phase, which is again an unknown factor. Then, we obtained this value from the experimental result. The growth rate at the position of the windward edge was evaluated to determine the Ke value, because this position should always feel the given P (H2 O) without the influence of the reaction in the other regions. Finally, the Ke value was estimated to be 7.5 · 109 from the results of the growth rate measurement obtained as to be 1.02 · 1010 m/s, the above parameters and Eq. (1). In order to investigate the t dependence along the direction of the width, the P (H2 O) distribution along the width-direction was estimated using the advection diffusion. Fig. 3 shows the physical image of the local cross-section during the YBCO growth. We presume that the diffusion boundary layer exists onto the precursor layer. The mass transfer on both y- and z-direction in Fig. 3 and the P (H2 O) distribution in the diffusion boundary layer were discussed. The mass transfer equations for H2 O on both directions can be expressed as follows:
Fig. 3. Physical image of the local cross-section during the YBCO growth. The diffusion boundary layer assumed to be onto the precursor layer. JH2 O;y and JH2 O;z are the mass diffusion fluxes and Vy and Vz are the velocity of the H2 O gas on each direction, respectively, XH2 O is the H2 O concentration, and XH2 O;0 is the H2 O concentration which can be given as an experimental parameter.
JH2 O;y ¼ D
oXH2 O þ XH2 O Vy oy
ð2Þ
oXH2 O þ XH2 O Vz ð3Þ oz where JH2 O;y and JH2 O;z are the mass diffusion fluxes and Vy and Vz are the velocity of the H2 O gas on each direction, respectively, XH2 O is the H2 O concentration, and D is the mass diffusivity in the gas boundary layer. Additionally, considering the steady state gas flow condition, the mass diffusion flux of H2 O needs to satisfy the following equation: JH2 O;z ¼ D
oJH2 O;y oJH2 O;z þ ¼0 oy oz
ð4Þ
The boundary conditions shown in Fig. 3 in this study are summarized as follows: ðB:C:1Þ Z ¼ 0; XH2 O ¼ XH2 O;0 ðB:C:2Þ Z ¼ 1; XH2 O ¼ 0 where XH2 O;0 is the H2 O concentration which can be given as an experimental parameter. D was again used to be 2 cm2 /s in this analysis. Finally,
R. Teranishi et al. / Physica C 392–396 (2003) 882–886
Fig. 4. The P (H2 O) distribution in the diffusion boundary layer along the film width-direction. It was calculated by solving the equations from (2)–(4) under the boundary conditions of B.C.1 and B.C.2 and the reaction parameters.
we obtained the P (H2 O) distribution, shown in Fig. 4, by solving the equations from (2)–(4) under the boundary conditions of B.C.1 and B.C.2 and the reaction parameters. Consequently, it can be calculated the existence of the P (H2 O) distribution along the width-direction. Then, the estimated t values depended on the film width were discussed combining the onedimensional analysis for the mass transfer expressed as Eq. (1) with the P (H2 O) distribution at the surface of the diffusion boundary layer. The moving boundary interface and quasi-steady state model was applied for this estimation. The schematic model of the model concept in this study was shown in Fig. 5. We presume that each lattice point is divided as a width of Dy ¼ 1 mm on the yaxis at the surface of the boundary layer, and the each lattice point is expressed as yn . The P (H2 O) at yn would be estimated by the P (H2 O) distribution curve obtained by the above calculation. The P (H2 O)n value was obtained by averaging the values at the edges of the nth cell. This value was assumed to be constant until the annealing of the node would be finished. Also, we presume that the fresh gas with the P (H2 O)g , which is given experimentally, always comes from the windward side. When the first cell finishes the reaction, the given P (H2 O)g is shifted from y1 to y2 . This manner will be successively proceeded by finishing the reaction in the entire film. Finally, we could predict the required annealing time for the complete reaction
885
Fig. 5. Schematic model of the moving boundary interface and quasi-steady state. Each lattice point assumed to be divided as a width of Dy ¼ 1 mm on the y-axis at the surface of the boundary layer, and the each lattice point is expressed as yn .
Table 1 The required annealing time estimated by the model of moving boundary interface and quasi-steady state for different samples with different P (H2 O) P (H2 O) (vol%) 4.2 9.1
W (mm)
t Cal. (min)
t Ex. (min)
10 10
79.8 53.4
71.3 47.2
The experimental results were shown for comparison.
for different samples with different partial pressure, P (H2 O), as shown in Table 1, with the experimental results for comparison. Comparing these values, it could be found that the predictions were in good agreement with the experimental results within the errors of only 10%.
4. Conclusion The film length, L, dependence of the YBCO growth rate was investigated by in situ monitoring of the conductance of the precursor film during YBCO crystallization using the DC four-probe method. As a result, the time for the complete reaction, t , increased with increase of L and be saturated for the sample longer than L ¼ 20 mm. This suggests that the influence of the twodimensional diffusion can be neglected for the film
886
R. Teranishi et al. / Physica C 392–396 (2003) 882–886
longer than 20 mm under the growth conditions at least in this study. Then, in order to modify the YBCO growth rate model expressed as Eq. (1), the equilibrium constant, Ke , was re-estimated by the growth rate measurement using the film with 30 mm in length. From the result, we obtained the Ke value of 7.6 · 109 . In order to investigate the t dependence along the direction of the width, the P (H2 O) distribution along the film width was calculated by using the advection model. The estimation of t distribution in the width-direction was discussed combining the onedimensional analysis for the mass transfer with the P (H2 O) distribution at the surface of the diffusion boundary layer. Comparing these values, it could be found that the predictions are in good agreement with the experimental results within the error of only 10%.
Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] P.C. Mclntyre, M.J. Cima, J.A. Smith, R.B. Hallock, M.P. Siegal, J.M. Phillips, J. Appl. Phys. 71 (1992) 1868. [2] J.A. Smith, M.J. Cima, N. Sonnenberg, IEEE Trans. Appl. Supercond. 9 (1999) 1531. [3] M. Paranthaman, T.G. Chirayil, S. Sathyamurthy, D.B. Deach, A. Goyal, F.A. List, D.F. Lee, X. Cui, S.W. Lu, B. Kang, E.D. Specht, P.M. Martin, D.M. Kroeger, R. Feenstra, C. Cantoni, D.K. Christen, IEEE Trans. Appl. Supercond. 11 (2001) 3146. [4] J.T. Dawley, P.G. Clem, M.P. Siegal, D.L. Overmyer, M.A. Rodriguez, IEEE Trans. Appl. Supercond. 11 (2001) 2873. [5] M.W. Rupich, Q. Li, S. Annavarapu, C. Thieme, W. Zhang, V. Prunier, M. Paranthaman, A. Goyal, D.F. Lee, E.D. Specht, F.A. List, IEEE Trans. Appl. Supercond. 11 (2001) 2927. [6] J. Shibata, T. Honjo, H. Fuji, T. Araki, I. Hirabayashi, T. Hirayama, T. Izumi, Y. Shiohara, T. Yamamoto, Y. Ikuhara, J. Mater. Res. 17 (2002) 1266. [7] T. Honjo, Y. Nakamura, R. Teranishi, H. Fuji, J. Shibata, T. Izumi, Y. Shiohara, IEEE Trans. Appl. Supercond., submitted. [8] R. Teranishi, H. Fuji, T. Honjo, Y. Nakamura, T. Izumi, Y. Shiohara, J. Shibata, T. Yamamoto, Y. Ikuhara, M. Yoshimura, Physica C 378–381 (2002) 1033. [9] V.F. Solovyov, H.J. Weismann, L. Wu, M. Suenaga, IEEE Trans. Appl. Supercond. 9 (1999) 1467. [10] V.F. Solovyov, H.J. Weismann, L. Wu, Y. Zhu, M. Suenaga, Appl. Phys. Lett. 76 (2000) 1911. [11] V.F. Solovyov, H.J. Weismann, M. Suenaga, Physica C 357 (2001) 14.