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The effect of duration of diffusion on Ag diffusion coefficients in YBa2Cu3O7
ARTICLE IN PRESS
Journal of Quantitative Spectroscopy & Radiative Transfer 95 (2005) 263–269 www.elsevier.com/locate/jqsrt
Notes
The effect of duration of diffusion on Ag diffusion coefficients in YBa2Cu3O7 O. Dogan Department of Physics, Education Faculty, Selcuk University, Konya, Turkey Received 8 March 2004; accepted 8 September 2004
Abstract The Ag diffusion in superconducting YBa2Cu3O7 (YBaCuO) ceramic has been studied over the duration of the diffusion range 5–24 h in the temperature range 700–850 1C by the energy-dispersive X-ray fluorescence (EDXRF) technique. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The temperature dependences of silver diffusion coefficients in grains (D1) and over the grain boundaries in the range 700–850 1C (D2) are described by the relations D1 ¼ 1.4 102 exp[(1.1870.10)/kT] and D2 ¼ 3.1 104 exp[(0.8770.10)/kT]. r 2004 Elsevier Ltd. All rights reserved. Keywords: Ag diffusion; Superconducting properties; YBaCuO; Diffusion coefficient; Duration of diffusion; XRF technique
1. Introduction The partial substitution in the parent YBa2Cu3O7 structure has been investigated intensively in an attempt to clarify or improve the superconducting behaviour of this type of superconductors. It is now widely believed that superconductivity predominantly occurs in the Cu–O planes YBa2Cu3O7. Substitutions of ions for Y and Ba in YBaCuO have very little effect on superconductivity. Therefore, partial caution substitution is an important approach to elucidate the high-Tc superconductivity mechanism and possibilities of improving superconducting E-mail address: [email protected] (O. Dogan). 0022-4073/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.09.023
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properties of YBa2Cu3O7. A feature of YBa2Cu3O7 superconductors is an orthorhombic–tetragonal phase transition at 600–750 1C during crystal growth, heating, or cooling of the sample. The unit cell changes from tetragonal to orthorhombic during cooling from T4750 1C to room temperature. Preparation and doping processes of the oxide samples of the high-temperature superconductors proceed at high temperatures (850–950 1C) together with heating and cooling from the formation (or annealing) temperature to room temperature. In the latter case, the precipitation of impurity solid solution and formation of new phases can take place in the materials. The precipitation of solid solution and formation of inclusions of second phases are determined by the duration of maintaining the solid solution in supersaturated state. The kinetics of the removal of the solute from a supersaturated matrix by the growth of randomly distributed precipitate particles was considered by Shewmon [1]. The mathematical description of precipitation of supersaturated matrix atoms is given as follows: N 0 N ¼ Atn :
(1)
Here N0 is the initial concentration of matrix atoms, N is the matrix concentration in equilibrium with precipitates, t is the duration of precipitation, A is a parameter depending on the diffusion coefficient of atoms, and n is a parameter depending on the geometrical shape of the precipitate particles. It is seen from (1) that precipitation of a supersaturated solid solution defined by the difference of concentrations (N0N) is proportional to the duration of precipitation. The noble metals Ag and Au, in the same column as Cu in the Periodic Table, are of special interest. Silver changes the formation temperature of superconductor, increases density, improves microstructure and mechanical properties, changes critical temperature and critical current density, influences crystallization at grain boundaries, etc. [2–5]. Both the noble metals are low-resistivity ohmic contact materials to YBa2Cu3O7 [6]. It should be noticed that almost all studies of the YBa2Cu3O7–Ag and Au compounds were carried out on the samples doped and diffused by gold and silver before sintering [7–9]. Silver and gold are often used as the ohmic contact material to the cuprites superconductors. Silver is also widely applied for preparing sheathed tapes. Therefore, data on the diffusion parameters for silver and gold are of great interest for practical applications of the high-temperature superconductors. The diffusion method of impurity doping of ready YBa2Cu3O7 opens new possibilities for the controlled doping of samples at relatively low concentrations. Therefore, the diffusion studies of Ag may be useful for the determination of location sites of silver in lattice and for the understanding of the migration mechanism, changes of microstructure and superconducting properties of YBa2Cu3O7 under the low-level doping. Ag, Au and Cu diffusion in YBaCuO ceramics was studied in the range 500–800 1C by radio-tracer technique [10–12]. In addition, Ag diffusion was studied at lower temperatures, 100–500 1C. The concentration profiles of Ag, Au and Cu measured by a serialsectioning technique exhibited the same character. All three elements (particularly silver) deeply penetrate into the sample. Silver tracer diffusion in YBa2Cu3O7 also occurs at room temperature. Ag penetrates to a depth of 1 mm (with diffusion coefficient about 1012 cm2/s) during 220 days at room temperature [12]. The literature contains some papers concerning the diffusion of Ag and Au in YBa2Cu3O7 and BiPbSrCaCuO superconductors [13–15]. In this study, we report the results of the influence of silver diffusion in YBa2Cu3O7 at the duration of diffusion range 5–24 h and in the temperature range 700–850 1C. The data of the diffusion coefficients of silver in the YBa2Cu3O7 superconductors are also presented.
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2. Experimental technique YBa2Cu3O7x compound was prepared by the usual solid-state reaction method from highpurity starting powders Y2O3, BaCO3 and CuO. The powders were thoroughly mixed in desired proportions and then heated in flowing oxygen for 24 h at 900 1C. The calcining and pulverizing procedures were repeated several times to assure a thorough mixing of the components. This treated mixture was pressed into pellets, and then subjected to final sintering in flowing oxygen for 24 h at 945 1C. The density of sintered YBa2Cu3O7 pellets changed from 5.80 to 5.98 g/cm3. Silver diffusion in YBa2Cu3O7 pellets was carried out from the vacuum evaporated layer of silver (thickness of about 2 mm) on the face of the YBa2Cu3O7 samples. The diffusion annealing of samples with the deposited layer of silver was executed in flowing oxygen at a temperature of 850 1C. In some runs, silver diffusion was carried out from the layers deposited on both surfaces of the sample. On comparison, the undoped samples (without Ag layer) were also annealed under the same thermal conditions. The diffusion annealing was performed in a horizontal tube furnace, 120 cm of length, purchased from ‘‘Lenton Thermal Design’’ equipped by a programmable controller (Euroterm 818P). The length of constant temperature zone of the furnace was about 6–8 cm in the temperature range 700–900 1C. The sample in the form of a tablet was placed in the middle of the constant temperature zone and the thermocouple touched the tablet. The cooling rate (fast cooling) of approximately 1000 1C/min was estimated for the removal of the sample from the hot zone or to the heavy copper block to reach the room temperature. The X-ray diffraction (XRD) data were taken using a Rikaku D/Max-IIIC diffractrometer with Cu Ka radiation the range 2y ¼ 3–701 at the room temperature. The lattice parameters (a,b and c) of the samples were obtained from (0 0 6), (0 2 0), (2 0 0), (0 0 3), (1 0 0) and (0 1 0) peaks. The scan speed was 0.21/min in the 2y range 22–241 and 46–481, where most of the data were collected. The high annular resolution provided an accurate lattice parameter measurement (70.0005 A˚). The energy-dispersive X-ray fluorescence (EDXRF) technique was used for the determination of the concentration of Ag atoms in the diffusion region of YBa2Cu3O7 samples [16]. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The intensity measurement of Ag peaks was detected with a Si(Li) solid-state detector. Determination of the Ag concentration distribution was performed by the sequential removal of thin layers (about 10–20 mm) from the sample and measuring the EDXRF intensity. In our runs, the sensitivity of the EDXRF technique for the determination of Ag concentration was estimated as NX3 1018 cm3. The diffusion coefficient of Ag in YBa2Cu3O7 was determined by differentiation of the measured distribution curve of the residual EDXRF intensity with respect to the thickness of the sample [17].
3. Results and discussion XRD measurements (Fig. 1) of the initial YBa2Cu3O7 samples showed the typical orthorhombic symmetry, which agrees well with previously published data for YBa2Cu3O7x [18]. No additional phases such as YBa2Cu3O5 or BaCuO2 were found. Fig. 2 illustrates the concentration profile of Ag over the thickness of the sample exposed to silver diffusion at 850 1C for 14 h. The solid curves 1 and 2 represent the calculated concentration
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Fig. 1. X-ray diffraction patterns for YBa2Cu3O7.
Fig. 2. Distribution of Ag concentration over thickness of YBa2Cu3O7. Diffusion-doped by silver at 850 1C for 14 h (solid curves 1 and 2 are erfc-curves).
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profiles of the impurity diffusion from a constant source into a semi-infinite solid [17]: x Nðx; tÞ ¼ N 0 1 erf pffiffiffiffiffiffi ; 2 Dt
(2)
where N0 ¼ N(0,t) is the constant concentration on the surface of the sample, N(x,t) is the impurity concentration at depth x, D is the diffusion coefficient, t is the duration of the diffusion, and erf x/2(Dt)1/2 is the error function. The surface concentration of silver was changed from 2 1019 to 9 1019 cm3. The experimental data in Fig. 2 are sufficiently approximated by two theoretical concentration distributions: curve 1 for the near-surface region (x ¼ 0–80 mm) and curve 2 for the inner region (x ¼ 80–240 mm) of sample. The diffusion coefficients in these regions are D1 ¼ 1.53 109 cm2/s and D2 ¼ 4.51 109 cm2/s, respectively. The other diffusion coefficients in the different durations of diffusion and temperatures are given in Table 1. Similar two-region concentration profiles of silver in YBa2Cu3O7 were also observed at other temperatures of the diffusion process. The temperature dependences of the Ag diffusion coefficients D1 and D2 at 700–850 1C (Fig. 3) are described by the following relations: D1 ¼ 1:4 102 exp½ð1:18 0:10Þ=kT ;
(3)
D2 ¼ 3:1 104 exp½ð0:87 0:10Þ=kT :
(4)
The present results are compared with results of Dzhafarov (D0 ¼ 1.0 102 cm2/s and activation energy 1.1 eV in the temperature range 500–800 1C) [12]. It is known that the concentration and depth of diffusion penetration of impurity in solids decrease with decreasing temperature (at a given diffusion time). In our runs, the error in determination of the impurity concentration in the sample, thereby of the diffusion coefficient of impurity, is increased with decreasing of diffusion temperature from 850 to 700 1C. Table 1 Diffusion coefficients at 5–24 h and in the temperature range 700–850 1C Duration of diffusion (h)
Temperature (1C) 850
5 8 11 14 17 20 24
6.85 109 9.08 109 5.01 109 7.96 109 3.05 109 5.67 109 1.53 109 4.51 109
800
1.78 109 2.02 109 8.59 1010 1.62 109 5.14 1010 8.45 1010 3.64 1011 5.89 1010
750
7.84 1010 1.17 109 5.02 1010 8.72 1010 3.12 1011 5.35 1010 2.57 1011 3.64 1010
700
3.89 1011 6.65 1010 3.04 1011 2.78 1010 2.02 1011 1.09 1010 1.02 1011 8.21 1011
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Fig. 3. Temperature dependences of the diffusion coefficients of silver in the (1) near-surface and (2) inner region of YBa2Cu3O7.
Fig. 4. Duration of the diffusion dependences of the diffusion coefficients of Ag.
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Fig. 4 illustrates the duration of the diffusion dependences of the silver diffusion coefficients (D1 and D2). It is to be noted that the impurity diffusion in a polycrystalline sample of YBa2Cu3O7 ceramic takes place simultaneously over the grain boundaries and into grains [13–15]. Therefore, the fast silver diffusion (D2) may be related with migration over grain boundaries, pores, and other defects. The slow diffusion of silver in YBa2Cu3O7 (D1) may be caused by migration into grains. In conclusion, Ag diffusion coefficients in YBa2Cu3O7 at 700–850 1C have decreased with increasing duration of diffusion. In the temperature range 700–850 1C, diffusion of Ag in the YBa2Cu3O7 sample takes place with two diffusion coefficients D1 and D2 (activation energies 1.18 and 0.87 eV) which are attributed to the relatively slow migration on the grain and fast silver migration over the grain boundaries, respectively. Our results are in good agreement with the other experimental results.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Shewmon PG. Diffusion in solids. New York: McGraw-Hill Publishers Co.; 1963. p. 19. Cloy JH, Jung DY, Grenier JC, Park JC, Wattianux A. Mater Lett 1990;10:121. Tachikawa A, Inoune T, Zama K, Hikichi Y. Supercond Sci Technol 1992;5:386. Yun Y, Harmer MP, Chou YT. J Mater Res 1994;9:1342. Kao YH, Yao YD, Yang LY, et al. J Appl Phys 1990;67:353. Mizushima K, Sagoi M, Miura T, Yoshida J. Appl Phys Lett 1988;52:1101. Cieplak MZ, Gang Xiao, Xiao C, Chien CL, et al. Phys Rev B 1990;42:6200. Renevier H, Hodeau JL, Fournier T, Bordet P, Mazezio M. Physica C 1990;172:183. Xiao G, Streitz FH, Cieplak MZ, Bakhsai A, Gavrin A, Chien CL. Phys Rev B 1988;38:776. Gafarov SF, Dzhafarov TD, Kulikov GS, Malkovich RSh, Skoryıatına EA, Usacheva VP, Tekh Zh. Fiz Pisma 1989;15:66. Dzhafarov TD, Asadov YuG, Gafarov SF, Kulikov GS, Malkovich RSh, Skoryıatına EA. Preprint of Institute of Physics, Baku, No. 360; 1990. Dzhafarov TD. Review article. Phys Stat Sol (a) 1996;158:335. Dzhafarov TD, Asadov YG, Bayramov AI, et al. Preprint of Institute of Physics, Baku¨ N360; 1990. p. 3–29. Dzhafarov TD, Altunbas- M, Varilci A, C - evik U, Kobya AI˙. Mater Lett 1996;26:305–11. Dzhafarov TD. Radiation-stimulated diffusion in semiconductors. Moskow: Energoatomizdat; 1992 51. Dog˘an O, Ertug˘rul M, C - evik U, Bacaksız E, Tıras-og˘lu E, Kobya AI˙. Diffusion coefficients of Ag in Yba2Cu3O7 using energy dispersive X-ray fluorescence (EDXRF) technique. X-ray spectrometry 2003;32:363–6. Abdullaev GB, Dzhafarov TD. Atomic diffusion in semiconductor structures. New York: Harwood; 1987. Kikuchi M, Syono Y, Tokiwa A, Oh-ishi K, Hiraga K, Kabayashi N, Sasaoka T, Muto Y. Jap J Appl Phys 1987;26:L1066.
Journal of Quantitative Spectroscopy & Radiative Transfer 95 (2005) 263–269 www.elsevier.com/locate/jqsrt
Notes
The effect of duration of diffusion on Ag diffusion coefficients in YBa2Cu3O7 O. Dogan Department of Physics, Education Faculty, Selcuk University, Konya, Turkey Received 8 March 2004; accepted 8 September 2004
Abstract The Ag diffusion in superconducting YBa2Cu3O7 (YBaCuO) ceramic has been studied over the duration of the diffusion range 5–24 h in the temperature range 700–850 1C by the energy-dispersive X-ray fluorescence (EDXRF) technique. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The temperature dependences of silver diffusion coefficients in grains (D1) and over the grain boundaries in the range 700–850 1C (D2) are described by the relations D1 ¼ 1.4 102 exp[(1.1870.10)/kT] and D2 ¼ 3.1 104 exp[(0.8770.10)/kT]. r 2004 Elsevier Ltd. All rights reserved. Keywords: Ag diffusion; Superconducting properties; YBaCuO; Diffusion coefficient; Duration of diffusion; XRF technique
1. Introduction The partial substitution in the parent YBa2Cu3O7 structure has been investigated intensively in an attempt to clarify or improve the superconducting behaviour of this type of superconductors. It is now widely believed that superconductivity predominantly occurs in the Cu–O planes YBa2Cu3O7. Substitutions of ions for Y and Ba in YBaCuO have very little effect on superconductivity. Therefore, partial caution substitution is an important approach to elucidate the high-Tc superconductivity mechanism and possibilities of improving superconducting E-mail address: [email protected] (O. Dogan). 0022-4073/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.09.023
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properties of YBa2Cu3O7. A feature of YBa2Cu3O7 superconductors is an orthorhombic–tetragonal phase transition at 600–750 1C during crystal growth, heating, or cooling of the sample. The unit cell changes from tetragonal to orthorhombic during cooling from T4750 1C to room temperature. Preparation and doping processes of the oxide samples of the high-temperature superconductors proceed at high temperatures (850–950 1C) together with heating and cooling from the formation (or annealing) temperature to room temperature. In the latter case, the precipitation of impurity solid solution and formation of new phases can take place in the materials. The precipitation of solid solution and formation of inclusions of second phases are determined by the duration of maintaining the solid solution in supersaturated state. The kinetics of the removal of the solute from a supersaturated matrix by the growth of randomly distributed precipitate particles was considered by Shewmon [1]. The mathematical description of precipitation of supersaturated matrix atoms is given as follows: N 0 N ¼ Atn :
(1)
Here N0 is the initial concentration of matrix atoms, N is the matrix concentration in equilibrium with precipitates, t is the duration of precipitation, A is a parameter depending on the diffusion coefficient of atoms, and n is a parameter depending on the geometrical shape of the precipitate particles. It is seen from (1) that precipitation of a supersaturated solid solution defined by the difference of concentrations (N0N) is proportional to the duration of precipitation. The noble metals Ag and Au, in the same column as Cu in the Periodic Table, are of special interest. Silver changes the formation temperature of superconductor, increases density, improves microstructure and mechanical properties, changes critical temperature and critical current density, influences crystallization at grain boundaries, etc. [2–5]. Both the noble metals are low-resistivity ohmic contact materials to YBa2Cu3O7 [6]. It should be noticed that almost all studies of the YBa2Cu3O7–Ag and Au compounds were carried out on the samples doped and diffused by gold and silver before sintering [7–9]. Silver and gold are often used as the ohmic contact material to the cuprites superconductors. Silver is also widely applied for preparing sheathed tapes. Therefore, data on the diffusion parameters for silver and gold are of great interest for practical applications of the high-temperature superconductors. The diffusion method of impurity doping of ready YBa2Cu3O7 opens new possibilities for the controlled doping of samples at relatively low concentrations. Therefore, the diffusion studies of Ag may be useful for the determination of location sites of silver in lattice and for the understanding of the migration mechanism, changes of microstructure and superconducting properties of YBa2Cu3O7 under the low-level doping. Ag, Au and Cu diffusion in YBaCuO ceramics was studied in the range 500–800 1C by radio-tracer technique [10–12]. In addition, Ag diffusion was studied at lower temperatures, 100–500 1C. The concentration profiles of Ag, Au and Cu measured by a serialsectioning technique exhibited the same character. All three elements (particularly silver) deeply penetrate into the sample. Silver tracer diffusion in YBa2Cu3O7 also occurs at room temperature. Ag penetrates to a depth of 1 mm (with diffusion coefficient about 1012 cm2/s) during 220 days at room temperature [12]. The literature contains some papers concerning the diffusion of Ag and Au in YBa2Cu3O7 and BiPbSrCaCuO superconductors [13–15]. In this study, we report the results of the influence of silver diffusion in YBa2Cu3O7 at the duration of diffusion range 5–24 h and in the temperature range 700–850 1C. The data of the diffusion coefficients of silver in the YBa2Cu3O7 superconductors are also presented.
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2. Experimental technique YBa2Cu3O7x compound was prepared by the usual solid-state reaction method from highpurity starting powders Y2O3, BaCO3 and CuO. The powders were thoroughly mixed in desired proportions and then heated in flowing oxygen for 24 h at 900 1C. The calcining and pulverizing procedures were repeated several times to assure a thorough mixing of the components. This treated mixture was pressed into pellets, and then subjected to final sintering in flowing oxygen for 24 h at 945 1C. The density of sintered YBa2Cu3O7 pellets changed from 5.80 to 5.98 g/cm3. Silver diffusion in YBa2Cu3O7 pellets was carried out from the vacuum evaporated layer of silver (thickness of about 2 mm) on the face of the YBa2Cu3O7 samples. The diffusion annealing of samples with the deposited layer of silver was executed in flowing oxygen at a temperature of 850 1C. In some runs, silver diffusion was carried out from the layers deposited on both surfaces of the sample. On comparison, the undoped samples (without Ag layer) were also annealed under the same thermal conditions. The diffusion annealing was performed in a horizontal tube furnace, 120 cm of length, purchased from ‘‘Lenton Thermal Design’’ equipped by a programmable controller (Euroterm 818P). The length of constant temperature zone of the furnace was about 6–8 cm in the temperature range 700–900 1C. The sample in the form of a tablet was placed in the middle of the constant temperature zone and the thermocouple touched the tablet. The cooling rate (fast cooling) of approximately 1000 1C/min was estimated for the removal of the sample from the hot zone or to the heavy copper block to reach the room temperature. The X-ray diffraction (XRD) data were taken using a Rikaku D/Max-IIIC diffractrometer with Cu Ka radiation the range 2y ¼ 3–701 at the room temperature. The lattice parameters (a,b and c) of the samples were obtained from (0 0 6), (0 2 0), (2 0 0), (0 0 3), (1 0 0) and (0 1 0) peaks. The scan speed was 0.21/min in the 2y range 22–241 and 46–481, where most of the data were collected. The high annular resolution provided an accurate lattice parameter measurement (70.0005 A˚). The energy-dispersive X-ray fluorescence (EDXRF) technique was used for the determination of the concentration of Ag atoms in the diffusion region of YBa2Cu3O7 samples [16]. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The intensity measurement of Ag peaks was detected with a Si(Li) solid-state detector. Determination of the Ag concentration distribution was performed by the sequential removal of thin layers (about 10–20 mm) from the sample and measuring the EDXRF intensity. In our runs, the sensitivity of the EDXRF technique for the determination of Ag concentration was estimated as NX3 1018 cm3. The diffusion coefficient of Ag in YBa2Cu3O7 was determined by differentiation of the measured distribution curve of the residual EDXRF intensity with respect to the thickness of the sample [17].
3. Results and discussion XRD measurements (Fig. 1) of the initial YBa2Cu3O7 samples showed the typical orthorhombic symmetry, which agrees well with previously published data for YBa2Cu3O7x [18]. No additional phases such as YBa2Cu3O5 or BaCuO2 were found. Fig. 2 illustrates the concentration profile of Ag over the thickness of the sample exposed to silver diffusion at 850 1C for 14 h. The solid curves 1 and 2 represent the calculated concentration
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Fig. 1. X-ray diffraction patterns for YBa2Cu3O7.
Fig. 2. Distribution of Ag concentration over thickness of YBa2Cu3O7. Diffusion-doped by silver at 850 1C for 14 h (solid curves 1 and 2 are erfc-curves).
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profiles of the impurity diffusion from a constant source into a semi-infinite solid [17]: x Nðx; tÞ ¼ N 0 1 erf pffiffiffiffiffiffi ; 2 Dt
(2)
where N0 ¼ N(0,t) is the constant concentration on the surface of the sample, N(x,t) is the impurity concentration at depth x, D is the diffusion coefficient, t is the duration of the diffusion, and erf x/2(Dt)1/2 is the error function. The surface concentration of silver was changed from 2 1019 to 9 1019 cm3. The experimental data in Fig. 2 are sufficiently approximated by two theoretical concentration distributions: curve 1 for the near-surface region (x ¼ 0–80 mm) and curve 2 for the inner region (x ¼ 80–240 mm) of sample. The diffusion coefficients in these regions are D1 ¼ 1.53 109 cm2/s and D2 ¼ 4.51 109 cm2/s, respectively. The other diffusion coefficients in the different durations of diffusion and temperatures are given in Table 1. Similar two-region concentration profiles of silver in YBa2Cu3O7 were also observed at other temperatures of the diffusion process. The temperature dependences of the Ag diffusion coefficients D1 and D2 at 700–850 1C (Fig. 3) are described by the following relations: D1 ¼ 1:4 102 exp½ð1:18 0:10Þ=kT ;
(3)
D2 ¼ 3:1 104 exp½ð0:87 0:10Þ=kT :
(4)
The present results are compared with results of Dzhafarov (D0 ¼ 1.0 102 cm2/s and activation energy 1.1 eV in the temperature range 500–800 1C) [12]. It is known that the concentration and depth of diffusion penetration of impurity in solids decrease with decreasing temperature (at a given diffusion time). In our runs, the error in determination of the impurity concentration in the sample, thereby of the diffusion coefficient of impurity, is increased with decreasing of diffusion temperature from 850 to 700 1C. Table 1 Diffusion coefficients at 5–24 h and in the temperature range 700–850 1C Duration of diffusion (h)
Temperature (1C) 850
5 8 11 14 17 20 24
6.85 109 9.08 109 5.01 109 7.96 109 3.05 109 5.67 109 1.53 109 4.51 109
800
1.78 109 2.02 109 8.59 1010 1.62 109 5.14 1010 8.45 1010 3.64 1011 5.89 1010
750
7.84 1010 1.17 109 5.02 1010 8.72 1010 3.12 1011 5.35 1010 2.57 1011 3.64 1010
700
3.89 1011 6.65 1010 3.04 1011 2.78 1010 2.02 1011 1.09 1010 1.02 1011 8.21 1011
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Fig. 3. Temperature dependences of the diffusion coefficients of silver in the (1) near-surface and (2) inner region of YBa2Cu3O7.
Fig. 4. Duration of the diffusion dependences of the diffusion coefficients of Ag.
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Fig. 4 illustrates the duration of the diffusion dependences of the silver diffusion coefficients (D1 and D2). It is to be noted that the impurity diffusion in a polycrystalline sample of YBa2Cu3O7 ceramic takes place simultaneously over the grain boundaries and into grains [13–15]. Therefore, the fast silver diffusion (D2) may be related with migration over grain boundaries, pores, and other defects. The slow diffusion of silver in YBa2Cu3O7 (D1) may be caused by migration into grains. In conclusion, Ag diffusion coefficients in YBa2Cu3O7 at 700–850 1C have decreased with increasing duration of diffusion. In the temperature range 700–850 1C, diffusion of Ag in the YBa2Cu3O7 sample takes place with two diffusion coefficients D1 and D2 (activation energies 1.18 and 0.87 eV) which are attributed to the relatively slow migration on the grain and fast silver migration over the grain boundaries, respectively. Our results are in good agreement with the other experimental results.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Shewmon PG. Diffusion in solids. New York: McGraw-Hill Publishers Co.; 1963. p. 19. Cloy JH, Jung DY, Grenier JC, Park JC, Wattianux A. Mater Lett 1990;10:121. Tachikawa A, Inoune T, Zama K, Hikichi Y. Supercond Sci Technol 1992;5:386. Yun Y, Harmer MP, Chou YT. J Mater Res 1994;9:1342. Kao YH, Yao YD, Yang LY, et al. J Appl Phys 1990;67:353. Mizushima K, Sagoi M, Miura T, Yoshida J. Appl Phys Lett 1988;52:1101. Cieplak MZ, Gang Xiao, Xiao C, Chien CL, et al. Phys Rev B 1990;42:6200. Renevier H, Hodeau JL, Fournier T, Bordet P, Mazezio M. Physica C 1990;172:183. Xiao G, Streitz FH, Cieplak MZ, Bakhsai A, Gavrin A, Chien CL. Phys Rev B 1988;38:776. Gafarov SF, Dzhafarov TD, Kulikov GS, Malkovich RSh, Skoryıatına EA, Usacheva VP, Tekh Zh. Fiz Pisma 1989;15:66. Dzhafarov TD, Asadov YuG, Gafarov SF, Kulikov GS, Malkovich RSh, Skoryıatına EA. Preprint of Institute of Physics, Baku, No. 360; 1990. Dzhafarov TD. Review article. Phys Stat Sol (a) 1996;158:335. Dzhafarov TD, Asadov YG, Bayramov AI, et al. Preprint of Institute of Physics, Baku¨ N360; 1990. p. 3–29. Dzhafarov TD, Altunbas- M, Varilci A, C - evik U, Kobya AI˙. Mater Lett 1996;26:305–11. Dzhafarov TD. Radiation-stimulated diffusion in semiconductors. Moskow: Energoatomizdat; 1992 51. Dog˘an O, Ertug˘rul M, C - evik U, Bacaksız E, Tıras-og˘lu E, Kobya AI˙. Diffusion coefficients of Ag in Yba2Cu3O7 using energy dispersive X-ray fluorescence (EDXRF) technique. X-ray spectrometry 2003;32:363–6. Abdullaev GB, Dzhafarov TD. Atomic diffusion in semiconductor structures. New York: Harwood; 1987. Kikuchi M, Syono Y, Tokiwa A, Oh-ishi K, Hiraga K, Kabayashi N, Sasaoka T, Muto Y. Jap J Appl Phys 1987;26:L1066.