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Microstructural evolution of the oxide film formed during high temperature oxidation of nickel evaluated by means of impedance spectroscopy
Scripta mater. 44 (2001) 601– 606 www.elsevier.com/locate/scriptamat
MICROSTRUCTURAL EVOLUTION OF THE OXIDE FILM FORMED DURING HIGH TEMPERATURE OXIDATION OF NICKEL EVALUATED BY MEANS OF IMPEDANCE SPECTROSCOPY S.-H. Song and P. Xiao* Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex UB8 3PH, UK (Received July 12, 2000) (Accepted in revised form September 19, 2000) Keywords: High-temperature oxidation; Nickel oxide; Oxide films; Impedance spectroscopy 1. Introduction Oxidation of metallic materials is an inevitable phenomenon at high temperatures. For this reason, high temperature materials, such as Fe or Ni-base heat-resistant alloys and steels, have been developed and widely employed in engineering applications. A primary requirement for application of a metallic material at high temperatures is its resistance to high temperature oxidation. This may be achieved by forming protective oxide films on its surface (1– 4). The protective ability of an oxide film is dependent on its ability to reduce the rate of oxidation reaction by acting as a diffusion barrier between the metallic material and the oxidising environment. Therefore, oxide films have a key function in high temperature applications of metallic materials. Most of the oxide films formed on metals and alloys are semiconductors. Their electrical conductivity is controlled by both electronic and ionic conductions. Usually, the electronic conduction is dominant. It is anticipated that a change in conductivity may be caused by a change in microstructural features like porosity and microcracks because of a change in the concentration of holes or electrons (4). As a consequence, we may examine its microstructural evolution during oxidation by examining its electrical properties. As is well known (1,5,6), NiO is a p-type semiconductor and its electrical conduction involves both ion and electron transport. The transference number of Ni ions in electrical conduction is 3.9 ⫻ 10⫺3 and the remainder is due to the electronic conduction (1). Consequently, its conductivity is almost entirely controlled by electronic conduction. The aim of the present work is to evaluate microstructural evolution of the oxide film formed on nickel during high-temperature oxidation by examining its electrical properties. The electrical properties of the oxide film can be determined by impedance measurements in conjunction with the film thickness determination (7) and in turn linked to its microstructural features. 2. Experimental Procedures The material used was a nickel foil (99.98 wt.% purity) with a thickness of 1.0 mm, provided by Goodfellow Limited. The foil was cut into specimens 12 mm ⫻ 12 mm in size. The specimens were * Corresponding author ([email protected]) 1359-6462/01/$–see front matter. © 2001 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00648-5
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polished with SiC paper in the sequence of 320, 800, and 1200 grit. These specimens were slowly heated to 700°C in air using a chamber furnace, oxidised there for 20,100 and 200h, respectively, and then furnace-cooled to room temperature. The effect of water vapour on the oxidation was negligible as the air in laboratory was generally dry. For impedance measurements, after oxidation the oxide layer on one side of the specimen was mechanically polished off and the free metal served as an electrode. Since nickel oxides are quite porous (8), it is difficult to use conductive paint electrodes because of paint penetration. For this reason, a platinum foil 0.1mm ⫻ 8 mm ⫻ 8mm in size was attached to the other side of the specimen and acted as the other electrode. In order to enhance the contact between the oxide film and the platinum foil, a uniform force was applied on the foil by a piece of metal 50g in weight, sandwiched with a mechanically polished alumina pellet for insulation. In this work, five specimens were used for each oxidation condition and the mean value of data points obtained together with the standard deviation was taken as the measured result. Impedance measurements were conducted using a Solarton SI 1255 HF frequency response analyser combined with a Solarton 1296 Dielectric Interface, which is computer-controlled. Spectra analysis was performed by means of a Zview impedance analysis software (Scribner Associates Inc, Southern Pines, NC) to extract the electrical and dielectric properties of the oxide film. In the measurements, an AC (alternating current) amplitude of 0.1 V was employed and the AC frequency was in the range of 1 Hz to 5 ⫻ 106 Hz. The measurements were performed at 200°C and therefore the influence of moisture on the electrical properties of the oxide film was considered to be negligible. A J840 scanning electron microscope equipped with an energy dispersive X-ray (EDX) microanalyzer was employed to evaluate the thickness of oxide film. In the thickness measurement, five positions for each specimen were chosen and the arithmetic mean of the data points acquired was taken as the measured value. Microanalysis was carried out with an electron beam of 20 keV to investigate the possible presence of impurities. Crystal structures of the oxide film were determined by X-ray diffraction.
3. Results and Discussion In order to understand clearly the results, it is necessary to describe concisely the impedance spectroscopy technique. In impedance measurements, a sinusoidal potential perturbation is applied to the test electrodes, which are contacted with the electrolyte material to be examined. Impedance diagrams are acquired by measuring the magnitude and phase shift of the resulting current. There are two types of impedance diagrams, namely Nyquist plots and Bode plots. In a Nyquist plot, the impedance is represented by a real part Z⬘ and an imaginary part Z⬘⬘ with the formula Z(w) ⫽ Z⬘ ⫹ jZ⬘⬘, where j ⫽ ⻫-1. Therefore, the Nyquist plot is also termed the complex plane impedance plot. In a Bode plot, the modulus of the impedance and the phase angle are both plotted as a function of frequency. For a simple resistor-capacitor (R-C) circuit, the Nyquist plot is characterised by a semicircle. Usually, the Nyquist plot is used to determine the major parameters, such as resistance and capacitance corresponding to an electrochemical system. In a Nyquist plot which contains only one semicircle, the resistance value, R, is determined directly from the intercept with the real Z axis. The frequency at maximum in Z⬘⬘, i.e., the relaxation frequency, fR, is acquired from analysis of the spectrum (7). At a certain temperature, fR is a material constant, which is sensitive to the electrical conductivity. If the system is complicated, there may be a few semicircles present. In this scenario, the spectra have to be fitted with an equivalent circuit, which corresponds to a physical model of the system. The equivalent circuit represents the main electrical features of the model when fitting measured spectra (7,9).
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Figure 1. Typical Nyquist plots for the oxide films formed on nickel after oxidation at 700°C for different times, measured at 200°C.
With the resistance of the oxide film determined, its electrical conductivity, (the inverse of resistivity), can be obtained by (10,11)
⫽ d/RA
(1)
where R is the film resistance, A is the electrode area, and d is the film thickness. Typical Nyquist plots for the specimens oxidised for different times are represented in Figure 1. There is only one semicircle on each Nyquist plot, indicating a single oxide layer produced from oxidation. The resistance (shown by the diameter of semicircles) increases with increasing oxidation time. X-ray diffraction (see Figure 2) demonstrates that the oxide film is a pure NiO. No impurity was detected using EDX. The EDX sensitivity was approximately 100 wt-ppm, so the impurity content may have been less than the sensitivity. The relaxation frequency is plotted in Figure 3 as a function of oxidation time, indicating that the relaxation frequency for the 100 h-oxidised specimens is higher than that for the 20 or 200h-oxidised specimens. Since the relaxation frequency is independent of the geometric factor d/A, the difference in relaxation frequency means that there is a difference in conductivity. The change in the conductivity of the NiO films should be due to a change in its microstructural features, such as microcracks and porosity. The values of R (determined by IS) and d (determined by SEM) along with the R-d plot are shown in Figure 4 for the specimens oxidised for different times. The resistance R increases with increasing oxidation time. The film thickness d increases with respect to oxidation time (20hr to 100hr), but there
Figure 2. Typical X-ray diffraction pattern for the oxide film formed on nickel after oxidation at 700°C for 100 h.
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Figure 3. Relaxation frequencies for the oxide films formed on nickel after oxidation.
is no apparent increase from 100h to 200h oxidation. There is a non-linear relationship between resistance and film thickness, suggesting that there are different electrical conductivities in the NiO films produced from different oxidation conditions. The electrical conductivity, (determined from Equation (1)), is represented in Figure 5 as a function of oxidation time. Clearly, is different for different oxidation times and decreases from 100h to 20h and to 200h oxidation. This indicates that there are variations in microstructure between different oxidation times. The measured conductivity is in the range of ⬃8 ⫻ 10⫺7 ⍀⫺1 m⫺1 to ⬃3 ⫻ 10⫺6 ⍀⫺1 m⫺1. These values are lower than the value of about 10⫺5 ⍀⫺1 m⫺1 at 200°C, which was determined in a previous study (12). This is because the impedance measurements were conducted with a platinum foil as an electrode attached to the oxide film so that the effective electrode area was much smaller than the real surface area of the NiO film due to surface roughness (8,13). Nevertheless, we still can employ these measured properties to characterise the microstructural change in the oxide films during oxidation. In addition, since ƒR is independent of the specimen geometry, its measured value should be its true value. Cross sections of the specimens are shown in scanning electron micrographs (see Figure 6). Clearly, the film thickness is relatively uniform. However, microstructure is very different between different
Figure 4. The values of (a) R and (b) d with respect to oxidation time together with (c) the R-d plot for the oxide films formed on nickel oxidised in air at 700°C, measured at 200°C.
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Figure 5. The values for the oxide films formed on nickel oxidised in air at 700°C for different times, measured at 200°C.
conditions. The porosity in the oxide film is the highest in the specimen oxidised for 100 hrs. It appears that blistering and microcracking have both occurred in the film produced from 100h oxidation. The free spaces within the film are therefore considerably increased. As described in Ref. (4), the hole concentration in NiO is proportional to (oxygen partial pressure)1/4, and the transport of holes is dominant in its electrical conduction. Normally, the oxygen partial pressure decreases moving from the outer surface of the film to the film-substrate interface. Since the free spaces in the film decrease from the 100hr oxidation specimen to the 20hr oxidation specimen and the 200hr oxidation specimen, the oxygen partial pressure in the film should be also reduced, leading to an increase in the hole concentration. This may be the reason why the conductivity is at its highest for the 100h-oxidised specimen.
Figure 6. Typical scanning electron micrographs showing the cross sections of (a) 20h, (b) 100h and (c) 200h oxidised specimens.
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As depicted in Refs. (1,3), the stresses in an oxide film on metals or alloys are roughly proportional to the film thickness and the volume ratio (the ratio of the volume per metal ion in the oxide to the volume per metal atom in the substrate, 1.65 for NiO on Ni). The film thickness normally increases with increasing oxidation time. The stresses in the NiO film should therefore increase with increasing oxidation time. When these internal stresses reach a critical level to overcome the oxide grain boundary cohesion and/or the oxide-to-substrate adhesion, microcracking and/or blistering will take place to release the stresses. After this, oxygen can easily penetrate into the film through these microstructural defects and meet Ni ions there, leading to the oxidation reaction occuring inside the film (3). The newly grown oxide may fill up the spaces created by microstructural defects to reduce the free spaces within the film. It may be envisaged that if the oxidation of a specimen continued the internal stresses would be gradually increased and would result in the repetition of the above process. Summary The oxide film formed during high-temperature oxidation of nickel was evaluated by virtue of impedance spectroscopy combined with scanning electron microscopy and X-ray diffraction. The film was found to be composed of NiO with no impurity. The porosity and the microcrack density within the film initially increased with increasing oxidation time up to 100hrs, leading to an increase in relaxation frequency which corresponds to an increase in electrical conductivity. Further oxidation resulted in reducing conductivity because internal oxidation occurred at pores and microcracks and filled up the spaces created by these microstructural defects, which lead to a decrease in relaxation frequency and an increase in electrical conductivity. Acknowledgments This work was supported by EPSRC under grant no. GR/M86743 References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
O. Kubaschewski and B. E. Hopkins, Oxidation of Metals and Alloys, 2nd edn., Butterworths, London (1967). G. Y. Lai, High-Temperature Corrosion of Engineering Alloys, ASM International, Materials Park, OH (1990). M. Schutze, Protective Oxide Scales and Their Breakdown, John Wiley and Sons, Chichester (1997). N. Birks and G. H. Meier, Introduction to High Temperature Oxidation of Metals, Edward Arnold, London (1983). A. Atkinson, R. I. Taylor, and A. E. Hughes, Phil. Mag. A45, 823 (1982). H. Li, F. Czerwinski, A. Zhilyaev, and J. A. Szpunar, Corros. Sci. 39, 1211 (1997). J. R. MacDonald, editor, Impedance Spectroscopy, Wiley, Chichester (1987). F. Czerwinski and J. A. Szpunar, Mater. Sci. Forum. 497, 204 (1996). J. G. Fletcher, A. R. West, and J. T. S. Irvine, J. Electrochem. Soc. 142, 2650 (1995). A. J. Moulson and J. M. Herbert, Electroceramics, Chapman and Hall, London (1990). E. M. Purcell, Electricity and Magnetism, 2nd edn., McGraw-Hill, London (1985). G. V. Samsonov, The Oxide Handbook, IFI/Plenum, New York (1973). Czerwinski and J. A. Szpunar, Corros. Sci. 39, 147 (1997).
MICROSTRUCTURAL EVOLUTION OF THE OXIDE FILM FORMED DURING HIGH TEMPERATURE OXIDATION OF NICKEL EVALUATED BY MEANS OF IMPEDANCE SPECTROSCOPY S.-H. Song and P. Xiao* Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex UB8 3PH, UK (Received July 12, 2000) (Accepted in revised form September 19, 2000) Keywords: High-temperature oxidation; Nickel oxide; Oxide films; Impedance spectroscopy 1. Introduction Oxidation of metallic materials is an inevitable phenomenon at high temperatures. For this reason, high temperature materials, such as Fe or Ni-base heat-resistant alloys and steels, have been developed and widely employed in engineering applications. A primary requirement for application of a metallic material at high temperatures is its resistance to high temperature oxidation. This may be achieved by forming protective oxide films on its surface (1– 4). The protective ability of an oxide film is dependent on its ability to reduce the rate of oxidation reaction by acting as a diffusion barrier between the metallic material and the oxidising environment. Therefore, oxide films have a key function in high temperature applications of metallic materials. Most of the oxide films formed on metals and alloys are semiconductors. Their electrical conductivity is controlled by both electronic and ionic conductions. Usually, the electronic conduction is dominant. It is anticipated that a change in conductivity may be caused by a change in microstructural features like porosity and microcracks because of a change in the concentration of holes or electrons (4). As a consequence, we may examine its microstructural evolution during oxidation by examining its electrical properties. As is well known (1,5,6), NiO is a p-type semiconductor and its electrical conduction involves both ion and electron transport. The transference number of Ni ions in electrical conduction is 3.9 ⫻ 10⫺3 and the remainder is due to the electronic conduction (1). Consequently, its conductivity is almost entirely controlled by electronic conduction. The aim of the present work is to evaluate microstructural evolution of the oxide film formed on nickel during high-temperature oxidation by examining its electrical properties. The electrical properties of the oxide film can be determined by impedance measurements in conjunction with the film thickness determination (7) and in turn linked to its microstructural features. 2. Experimental Procedures The material used was a nickel foil (99.98 wt.% purity) with a thickness of 1.0 mm, provided by Goodfellow Limited. The foil was cut into specimens 12 mm ⫻ 12 mm in size. The specimens were * Corresponding author ([email protected]) 1359-6462/01/$–see front matter. © 2001 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00648-5
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polished with SiC paper in the sequence of 320, 800, and 1200 grit. These specimens were slowly heated to 700°C in air using a chamber furnace, oxidised there for 20,100 and 200h, respectively, and then furnace-cooled to room temperature. The effect of water vapour on the oxidation was negligible as the air in laboratory was generally dry. For impedance measurements, after oxidation the oxide layer on one side of the specimen was mechanically polished off and the free metal served as an electrode. Since nickel oxides are quite porous (8), it is difficult to use conductive paint electrodes because of paint penetration. For this reason, a platinum foil 0.1mm ⫻ 8 mm ⫻ 8mm in size was attached to the other side of the specimen and acted as the other electrode. In order to enhance the contact between the oxide film and the platinum foil, a uniform force was applied on the foil by a piece of metal 50g in weight, sandwiched with a mechanically polished alumina pellet for insulation. In this work, five specimens were used for each oxidation condition and the mean value of data points obtained together with the standard deviation was taken as the measured result. Impedance measurements were conducted using a Solarton SI 1255 HF frequency response analyser combined with a Solarton 1296 Dielectric Interface, which is computer-controlled. Spectra analysis was performed by means of a Zview impedance analysis software (Scribner Associates Inc, Southern Pines, NC) to extract the electrical and dielectric properties of the oxide film. In the measurements, an AC (alternating current) amplitude of 0.1 V was employed and the AC frequency was in the range of 1 Hz to 5 ⫻ 106 Hz. The measurements were performed at 200°C and therefore the influence of moisture on the electrical properties of the oxide film was considered to be negligible. A J840 scanning electron microscope equipped with an energy dispersive X-ray (EDX) microanalyzer was employed to evaluate the thickness of oxide film. In the thickness measurement, five positions for each specimen were chosen and the arithmetic mean of the data points acquired was taken as the measured value. Microanalysis was carried out with an electron beam of 20 keV to investigate the possible presence of impurities. Crystal structures of the oxide film were determined by X-ray diffraction.
3. Results and Discussion In order to understand clearly the results, it is necessary to describe concisely the impedance spectroscopy technique. In impedance measurements, a sinusoidal potential perturbation is applied to the test electrodes, which are contacted with the electrolyte material to be examined. Impedance diagrams are acquired by measuring the magnitude and phase shift of the resulting current. There are two types of impedance diagrams, namely Nyquist plots and Bode plots. In a Nyquist plot, the impedance is represented by a real part Z⬘ and an imaginary part Z⬘⬘ with the formula Z(w) ⫽ Z⬘ ⫹ jZ⬘⬘, where j ⫽ ⻫-1. Therefore, the Nyquist plot is also termed the complex plane impedance plot. In a Bode plot, the modulus of the impedance and the phase angle are both plotted as a function of frequency. For a simple resistor-capacitor (R-C) circuit, the Nyquist plot is characterised by a semicircle. Usually, the Nyquist plot is used to determine the major parameters, such as resistance and capacitance corresponding to an electrochemical system. In a Nyquist plot which contains only one semicircle, the resistance value, R, is determined directly from the intercept with the real Z axis. The frequency at maximum in Z⬘⬘, i.e., the relaxation frequency, fR, is acquired from analysis of the spectrum (7). At a certain temperature, fR is a material constant, which is sensitive to the electrical conductivity. If the system is complicated, there may be a few semicircles present. In this scenario, the spectra have to be fitted with an equivalent circuit, which corresponds to a physical model of the system. The equivalent circuit represents the main electrical features of the model when fitting measured spectra (7,9).
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Figure 1. Typical Nyquist plots for the oxide films formed on nickel after oxidation at 700°C for different times, measured at 200°C.
With the resistance of the oxide film determined, its electrical conductivity, (the inverse of resistivity), can be obtained by (10,11)
⫽ d/RA
(1)
where R is the film resistance, A is the electrode area, and d is the film thickness. Typical Nyquist plots for the specimens oxidised for different times are represented in Figure 1. There is only one semicircle on each Nyquist plot, indicating a single oxide layer produced from oxidation. The resistance (shown by the diameter of semicircles) increases with increasing oxidation time. X-ray diffraction (see Figure 2) demonstrates that the oxide film is a pure NiO. No impurity was detected using EDX. The EDX sensitivity was approximately 100 wt-ppm, so the impurity content may have been less than the sensitivity. The relaxation frequency is plotted in Figure 3 as a function of oxidation time, indicating that the relaxation frequency for the 100 h-oxidised specimens is higher than that for the 20 or 200h-oxidised specimens. Since the relaxation frequency is independent of the geometric factor d/A, the difference in relaxation frequency means that there is a difference in conductivity. The change in the conductivity of the NiO films should be due to a change in its microstructural features, such as microcracks and porosity. The values of R (determined by IS) and d (determined by SEM) along with the R-d plot are shown in Figure 4 for the specimens oxidised for different times. The resistance R increases with increasing oxidation time. The film thickness d increases with respect to oxidation time (20hr to 100hr), but there
Figure 2. Typical X-ray diffraction pattern for the oxide film formed on nickel after oxidation at 700°C for 100 h.
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Figure 3. Relaxation frequencies for the oxide films formed on nickel after oxidation.
is no apparent increase from 100h to 200h oxidation. There is a non-linear relationship between resistance and film thickness, suggesting that there are different electrical conductivities in the NiO films produced from different oxidation conditions. The electrical conductivity, (determined from Equation (1)), is represented in Figure 5 as a function of oxidation time. Clearly, is different for different oxidation times and decreases from 100h to 20h and to 200h oxidation. This indicates that there are variations in microstructure between different oxidation times. The measured conductivity is in the range of ⬃8 ⫻ 10⫺7 ⍀⫺1 m⫺1 to ⬃3 ⫻ 10⫺6 ⍀⫺1 m⫺1. These values are lower than the value of about 10⫺5 ⍀⫺1 m⫺1 at 200°C, which was determined in a previous study (12). This is because the impedance measurements were conducted with a platinum foil as an electrode attached to the oxide film so that the effective electrode area was much smaller than the real surface area of the NiO film due to surface roughness (8,13). Nevertheless, we still can employ these measured properties to characterise the microstructural change in the oxide films during oxidation. In addition, since ƒR is independent of the specimen geometry, its measured value should be its true value. Cross sections of the specimens are shown in scanning electron micrographs (see Figure 6). Clearly, the film thickness is relatively uniform. However, microstructure is very different between different
Figure 4. The values of (a) R and (b) d with respect to oxidation time together with (c) the R-d plot for the oxide films formed on nickel oxidised in air at 700°C, measured at 200°C.
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Figure 5. The values for the oxide films formed on nickel oxidised in air at 700°C for different times, measured at 200°C.
conditions. The porosity in the oxide film is the highest in the specimen oxidised for 100 hrs. It appears that blistering and microcracking have both occurred in the film produced from 100h oxidation. The free spaces within the film are therefore considerably increased. As described in Ref. (4), the hole concentration in NiO is proportional to (oxygen partial pressure)1/4, and the transport of holes is dominant in its electrical conduction. Normally, the oxygen partial pressure decreases moving from the outer surface of the film to the film-substrate interface. Since the free spaces in the film decrease from the 100hr oxidation specimen to the 20hr oxidation specimen and the 200hr oxidation specimen, the oxygen partial pressure in the film should be also reduced, leading to an increase in the hole concentration. This may be the reason why the conductivity is at its highest for the 100h-oxidised specimen.
Figure 6. Typical scanning electron micrographs showing the cross sections of (a) 20h, (b) 100h and (c) 200h oxidised specimens.
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As depicted in Refs. (1,3), the stresses in an oxide film on metals or alloys are roughly proportional to the film thickness and the volume ratio (the ratio of the volume per metal ion in the oxide to the volume per metal atom in the substrate, 1.65 for NiO on Ni). The film thickness normally increases with increasing oxidation time. The stresses in the NiO film should therefore increase with increasing oxidation time. When these internal stresses reach a critical level to overcome the oxide grain boundary cohesion and/or the oxide-to-substrate adhesion, microcracking and/or blistering will take place to release the stresses. After this, oxygen can easily penetrate into the film through these microstructural defects and meet Ni ions there, leading to the oxidation reaction occuring inside the film (3). The newly grown oxide may fill up the spaces created by microstructural defects to reduce the free spaces within the film. It may be envisaged that if the oxidation of a specimen continued the internal stresses would be gradually increased and would result in the repetition of the above process. Summary The oxide film formed during high-temperature oxidation of nickel was evaluated by virtue of impedance spectroscopy combined with scanning electron microscopy and X-ray diffraction. The film was found to be composed of NiO with no impurity. The porosity and the microcrack density within the film initially increased with increasing oxidation time up to 100hrs, leading to an increase in relaxation frequency which corresponds to an increase in electrical conductivity. Further oxidation resulted in reducing conductivity because internal oxidation occurred at pores and microcracks and filled up the spaces created by these microstructural defects, which lead to a decrease in relaxation frequency and an increase in electrical conductivity. Acknowledgments This work was supported by EPSRC under grant no. GR/M86743 References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
O. Kubaschewski and B. E. Hopkins, Oxidation of Metals and Alloys, 2nd edn., Butterworths, London (1967). G. Y. Lai, High-Temperature Corrosion of Engineering Alloys, ASM International, Materials Park, OH (1990). M. Schutze, Protective Oxide Scales and Their Breakdown, John Wiley and Sons, Chichester (1997). N. Birks and G. H. Meier, Introduction to High Temperature Oxidation of Metals, Edward Arnold, London (1983). A. Atkinson, R. I. Taylor, and A. E. Hughes, Phil. Mag. A45, 823 (1982). H. Li, F. Czerwinski, A. Zhilyaev, and J. A. Szpunar, Corros. Sci. 39, 1211 (1997). J. R. MacDonald, editor, Impedance Spectroscopy, Wiley, Chichester (1987). F. Czerwinski and J. A. Szpunar, Mater. Sci. Forum. 497, 204 (1996). J. G. Fletcher, A. R. West, and J. T. S. Irvine, J. Electrochem. Soc. 142, 2650 (1995). A. J. Moulson and J. M. Herbert, Electroceramics, Chapman and Hall, London (1990). E. M. Purcell, Electricity and Magnetism, 2nd edn., McGraw-Hill, London (1985). G. V. Samsonov, The Oxide Handbook, IFI/Plenum, New York (1973). Czerwinski and J. A. Szpunar, Corros. Sci. 39, 147 (1997).