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Mössbauer study of the ferrite decomposition in unaged duplex stainless steels
Scripta Materialia, Vol. 39, No. 1, pp. 61– 66, 1998 Elsevier Science Ltd Copyright © 1998 Acta Metallurgica Inc. Printed in the USA. All rights reserved. 1359-6462/98 $19.00 1 .00
Pergamon PII S1359-6462(98)00133-X
¨ SSBAUER STUDY OF THE FERRITE DECOMPOSITION IN MO UNAGED DUPLEX STAINLESS STEELS C. Lemoine*, A. Fnidiki*, J. Teillet*, M. He´din** and F. Danoix** *Magne´tisme et Applications and **Sonde atomique et Microstructures, GMP-UMR CNRS 6634, Universite´ de Rouen, 76821 Mont-Saint-Aignan Ce´dex, France (Received December 19, 1997) (Accepted March 30, 1998)
Introduction Mechanical properties of duplex stainless steels degrade during holding in the temperature range 300 – 400°C. While no evolution is observed in the austenite, the microstructural evolution of the ferritic phase is the main cause of the embrittlement. This evolution occurs through the spinodal decomposition of the Fe-Cr solid solution, resulting in Cr concentration fluctuations leading to the formation of an interconnected network of homophase a9 Cr-enriched and a Fe-enriched domains (1, 2, 3). Some works report that even in unaged specimen the ferrite may be decomposed (4, 5). It was demonstrated that the initial decomposition amplitude is related to the quenching rate and is most probably due to the a-a9 spinodal decomposition. The more rapidly the sample is quenched after homogeneisation, the less it decomposes (5). Furthermore, regarding the material embrittlement, the initial decomposition state is also an important parameter as it influences the rate of development of the spinodal decomposition. Thanks to its spatial and mass resolutions, the atom probe has been shown to be a very suitable technique for studying the interconnected a-a9 network developed on a nanometer scale during spinodal decomposition (6). From the atom probe results, the extent of spinodal amplitude in the ferrite phase may be quantified by the statistical distance (called variation V) between experimental and binomial chromium concentration frequency distribution (7, 8). The statistical distance is the integral area difference between the two distributions. Because these two distributions are normalized, V varies in the range of 0 (undecomposed) to 2 (completely decomposed). Nevertheless, due to its low level, the initial concentration amplitude is very difficult to quantify and when V is smaller than about 0.1, the result has to be interpreted with care because of statistical fluctuations in the experimental set of data (5). On the other hand, Mo¨ssbauer spectroscopy was often used to analyze ferrite decomposition above 475°C because it can easily detect a9 domains since there are weakly or non magnetic, whereas a is magnetic (9, 10, 11). However, for duplex stainless steels containing both ferrite (a bcc) and austenite (g fcc), the paramagnetic g phase limits the detection of the a9 phase and thus prevents the study of the a-a9 decomposition. To overcome this problem a method to extract the austenite contribution from the experimental spectrum was developed. As a result, the contribution of a phase in experimental spectra can be deduced and the evolution of the a-a9 decomposition followed. This paper demonstrates that Mo¨ssbauer spectroscopy can be extended to the analysis of industrial duplex steels, and that this technique is more accurate than atom probe in characterizing weakly decomposed ferrites. 61
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TABLE 1 Bulk Composition of the Specimen Measured by Electron Microprobe, and Ferrite Composition Measured by Atom Probe. The Ferrite Content of the Specimen Obtained with a Sigmameter, is About 30% Component
Cr
Ni
Mo
C
Si
Mn
Fe
Specimen. (% atom.) Ferrite. (% atom.)
22.0 25.0
8.9 6.6
1.4 2.6
0.14 0
2.0 2.7
0.9 0.5
64.5 62.3
Experimental The samples were supplied by Electricite´ de France. The specimen composition and the corresponding ferrite composition are reported in the Table 1. The parallelepiped-shaped samples (1531130.4 mm) were machined from a cast which was solution treated for three hours at 1080°C and then quenched. The cast is about 120 mm thick, so the quenching rate (Q) of a sample depends on the depth at which it was taken from. Q is estimated to be 2°C/s in the core and 10°C/s close to the skin. To expand the studied domain of quenching rates, a thin specimen was re-solution treated at 1080°C/s and then water quenched. Q is then estimated to be 20°C/s. After mechanical polishing, samples were analyzed by Conversion Electron Mo¨ssbauer Spectrometry (CEMS), which analyzes the first 200 nm in depth from the sample surface. The experiments were performed at 300K using a home-made counter at room temperature and a 57Co source in a rhodium matrix. The samples were set perpendicular to the incident g beam direction. The isomer shift (IS) at 57Fe nuclei was given relative to a-Fe at room temperature. All the details concerning atom probe analysis of the same specimens are given in a previous paper (5). Austenite Extraction Method and Its Validation The Figure 1 represents experimental Mo¨ssbauer spectra of specimens cooled with different quenching rates Q. The spectra consist of a central paramagnetic peak due to the austenite and a magnetic contribution due to the ferrite. The Mo¨ssbauer spectra were globally fitted with a least-square technique (12). The mean hyperfine field (,Bhf.) fluctuates around 22T, and the isomer shift seems to be constant at 10.01 mm/s for the ferrite and 20.097 mm/s for the austenite, in good agreement with Solomon results (11). But as a consequence of the overlap of the a and g signals around the weak fields, there is a large uncertainty in the estimate of the hyperfine parameters. In particular, it is impossible to compare the decomposition amount of the ferrite of the various specimens, as it directly derives from the hyperfine parameters. To overcome this drawback, the ferrite spectrum must be isolated. An iterative method consisting in substrating the austenite contribution from the experimental spectrum is proposed. To validate this procedure, i.e. to prove that the austenite solely is extracted without any contribution from the ferrite, a very decomposed specimen (aged 2500h at 350°C) has been analysed by CEMS. The experimental spectrum and the two elemental contributions (namely g and a) are shown Figure 2-a-b-c. The constant background noise level of the austenite spectrum indicates that no contribution from the ferrite signal is included in it, and therefore that the austenite contribution is correctly extracted. The ferrite spectrum consists of six broadened peaks, and is similar to ferrite spectrum as previously observed in pure ferritic steels (11). The broadening is attributed to the difference in the environment of the iron atoms. The spectrum is actually a superimposition of several sextets each with different
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63
Figure 1. Experimental spectra of specimens which experienced different quenching rate Q.
Mo¨ssbauer hyperfine interaction parameters depending on the number of iron neighbours of the resonantly absorbing 57Fe atom. Indeed, the corresponding hyperfine field distribution (p(Bhf)) shown Figure 2d, is composed of two contributions, one centered on 10T and the other on 25T, again in good agreement with literature data for decomposed ferrite (13). The high field contribution reflects the presence of the a Fe-rich domains, whereas the low field contribution reflects the existence of the a9 Cr-rich domains. Indeed, in the a domains, each iron atom is preferentially surrounded by Fe atoms. In the a9 domains, the iron concentration is reduced, and iron neighbours are progressively replaced by Cr neighbours. As Cr atoms reduce the hyperfine field (14), the a9 contribution to p(Bhf) is shifted towards the low fields, while a contribution is shifted towards high fields, with respect to a random solid solution. All the above results show that the proposed method is efficient to isolate ferrite spectra and can be applied to the study of a-a9 decomposition in duplex stainless steels. CEMS and Atom Probe Results on Ferrite of Unaged Samples The evolution of the decomposition extent with respect to the quenching rate was studied with the proposed method. The ferrite experimental spectra derived from the experimental data shown Figure 1 are represented Figure 3. The six peaks constituting the ferrite spectrum tend to broaden as Q decreases indicating an evolution in the 57Fe environment takes place during the quench. The hyperfine field distributions derived from the previous spectra (Figure 4) look like gaussian curves, centered on 22T, slightly broadened and asymmetric. The broadening is attributed to the overlapping of the two contributions corresponding to the a and a9 domains. The corresponding mean hyperfine field (,Bhf.) is 21.99T, 21.72T and 21.27T for Q is 2°C/s, 5°C/s and 20°C/s respectively. These results indicate a
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Figure 2. a) Experimental spectrum of a specimen aged 2500h at 350°C; b) The extracted austenite spectrum; c) The ferrite spectrum; d) The corresponding hyperfine distribution.
progressive ferrite microstructural evolution with respect to the quenching rate. This evolution can not be explained by the formation of the s phase. Indeed, the s phase being paramagnetic, no contribution is expected in the isolated ferrite Mo¨ssbauer spectra. On the other hand, the distribution shapes prove that the transformation mechanism is of a spinodal type and not nucleation and growth. If it was nucleation and growth there would be a significant contribution at low fields corresponding to the precipitates which would have their final composition since the beginning of the transformation. Furthermore, the hyperfine field distributions shift progressively towards high fields as Q decreases. Pollak reported the same phenomenon but during thermal ageing (15), which he attributed to the segregation amplitude evolution during spinodal decomposition. In some respects, the evolution observed during the quench can be considered as the first stages of this thermal ageing. Indeed, the slower a specimen is quenched, the longer its temperature remains in the domain where a spinodal decomposition can take place, leading to more pronounced ferrite transformation. This transformation is not a classical spinodal decomposition as the temperature is not constant during the quench. Nevertheless, it is of a spinodal type since no energy barrier has to be jumped over to initiate the decomposition. As a conclusion, not only the hyperfine field distribution study proves that a transfor-
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¨ SSBAUER STUDY OF THE FERRITE MO
65
Figure 3. Experimental spectra of the ferritic phase obtained after the austenite extraction.
mation takes place in the ferritic phase during the quench, but also confirms that it is a spinodal mechanism. Atom probe analyses were carried out to quantify differently the decomposition of the same specimen. The parameter V was determined and drawn versus the mean hyperfine field of the field distributions. It appears that ,Bhf. increases linearly with V (Fig. 5). The linear law confirms the two techniques do actually see the same phenomenon, i.e the local environment evolution of the atoms in the ferritic phase. According to the error bars related to the two techniques, it clearly appears that CEMS is more sensitive to small evolutions in the ferrite phase, even though the accuracy of the V parameter seems better than it had been previously estimated (5).
Figure 4. Hyperfine field distributions of the ferrite.
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Figure 5. The mean hyperfine field versus V and the corresponding estimated quenching rate.
Conclusion As a conclusion, an austenite extraction method has been proposed to isolate the ferrite contribution in duplex stainless steels Mo¨ssbauer spectra. The mean hyperfine field ,Bhf. derived from fitted ferrite spectra is shown to be very sensitive to a change of the local environment of 57Fe atom, and then able to quantify the extent of the spinodal decomposition amplitude even for the very weak decompositions. Therefore, CEMS has a better accuracy than the atom probe to follow the very weak composition fluctuations that take place during the first stages of spinodal decomposition. Moreover, CEMS use would be preferable to atom probe one as it is less constraining. On a metallurgical point of view, the results also confirm that a transformation may occur during the quench of duplex stainless steels via a spinodal mechanism. Acknowledgment These researches are financially supported by Electricite´ de France, De´partement Etude des Mate´riaux, under contract EDF/CNRS No. 509511. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. K. Miller, J. Bentley, S. S. Brenner, and J.A. Spitznagel, J. Phys. (Paris). 45, C9 –385 (1984). T. J. Godfrey and G. D. W. Smith, J. Phys. 47, C7–217 (1986). J. Bourgoin and M. Guttmann, Mat. Sci. Technol. 6, 301 (1990). J. C. Lasalle and L. H. Schwartz, Acta Metall. 34, 6, 989 (1986). M. Hedin, J. P. Massoud, and F. Danoix, J. Phys. IV6, C5–235 (1996). M. K. Miller and G. D. W. Smith, Atom Probe Microanalysis: Principles and Applications to Materials Science, Materials Research Society, Pittsburgh, PA (1989). D. Blavette, G. Grancher, and A. Bostel, J. Phys 49, C6 – 433 (1988). F. Danoix, P. Auger, A. Bostel, and D. Blavette, Surf. Sci. 246, 260 (1991). D. Chandra and L. H. Schartz, Met. Trans. 2, 511 (1971). T. De Nys and P. M. Gierler, Met. Trans. 2, 1423 (1971). H. D. Solomon, Lionel M. Levinson, Acta Metall. 26, 429 (1978). J. Teillet and F. Varret, unpublished MOSFIT program. H. Kuwano, Y. Ishikawa, T. Yoshimura, and Y. Hamaguchi, Hyp. Int. 92, 987 (1994). S. M. Dubiel and J. Zukrowski, J. Magn. Magn. Mat. 23, 214 (1981). H. Pollak, U. Karfunkel, J. A. Lodya, and N. Mala, Hyp. Int. 94, 2355 (1994).
Pergamon PII S1359-6462(98)00133-X
¨ SSBAUER STUDY OF THE FERRITE DECOMPOSITION IN MO UNAGED DUPLEX STAINLESS STEELS C. Lemoine*, A. Fnidiki*, J. Teillet*, M. He´din** and F. Danoix** *Magne´tisme et Applications and **Sonde atomique et Microstructures, GMP-UMR CNRS 6634, Universite´ de Rouen, 76821 Mont-Saint-Aignan Ce´dex, France (Received December 19, 1997) (Accepted March 30, 1998)
Introduction Mechanical properties of duplex stainless steels degrade during holding in the temperature range 300 – 400°C. While no evolution is observed in the austenite, the microstructural evolution of the ferritic phase is the main cause of the embrittlement. This evolution occurs through the spinodal decomposition of the Fe-Cr solid solution, resulting in Cr concentration fluctuations leading to the formation of an interconnected network of homophase a9 Cr-enriched and a Fe-enriched domains (1, 2, 3). Some works report that even in unaged specimen the ferrite may be decomposed (4, 5). It was demonstrated that the initial decomposition amplitude is related to the quenching rate and is most probably due to the a-a9 spinodal decomposition. The more rapidly the sample is quenched after homogeneisation, the less it decomposes (5). Furthermore, regarding the material embrittlement, the initial decomposition state is also an important parameter as it influences the rate of development of the spinodal decomposition. Thanks to its spatial and mass resolutions, the atom probe has been shown to be a very suitable technique for studying the interconnected a-a9 network developed on a nanometer scale during spinodal decomposition (6). From the atom probe results, the extent of spinodal amplitude in the ferrite phase may be quantified by the statistical distance (called variation V) between experimental and binomial chromium concentration frequency distribution (7, 8). The statistical distance is the integral area difference between the two distributions. Because these two distributions are normalized, V varies in the range of 0 (undecomposed) to 2 (completely decomposed). Nevertheless, due to its low level, the initial concentration amplitude is very difficult to quantify and when V is smaller than about 0.1, the result has to be interpreted with care because of statistical fluctuations in the experimental set of data (5). On the other hand, Mo¨ssbauer spectroscopy was often used to analyze ferrite decomposition above 475°C because it can easily detect a9 domains since there are weakly or non magnetic, whereas a is magnetic (9, 10, 11). However, for duplex stainless steels containing both ferrite (a bcc) and austenite (g fcc), the paramagnetic g phase limits the detection of the a9 phase and thus prevents the study of the a-a9 decomposition. To overcome this problem a method to extract the austenite contribution from the experimental spectrum was developed. As a result, the contribution of a phase in experimental spectra can be deduced and the evolution of the a-a9 decomposition followed. This paper demonstrates that Mo¨ssbauer spectroscopy can be extended to the analysis of industrial duplex steels, and that this technique is more accurate than atom probe in characterizing weakly decomposed ferrites. 61
¨ SSBAUER STUDY OF THE FERRITE MO
62
Vol. 39, No. 1
TABLE 1 Bulk Composition of the Specimen Measured by Electron Microprobe, and Ferrite Composition Measured by Atom Probe. The Ferrite Content of the Specimen Obtained with a Sigmameter, is About 30% Component
Cr
Ni
Mo
C
Si
Mn
Fe
Specimen. (% atom.) Ferrite. (% atom.)
22.0 25.0
8.9 6.6
1.4 2.6
0.14 0
2.0 2.7
0.9 0.5
64.5 62.3
Experimental The samples were supplied by Electricite´ de France. The specimen composition and the corresponding ferrite composition are reported in the Table 1. The parallelepiped-shaped samples (1531130.4 mm) were machined from a cast which was solution treated for three hours at 1080°C and then quenched. The cast is about 120 mm thick, so the quenching rate (Q) of a sample depends on the depth at which it was taken from. Q is estimated to be 2°C/s in the core and 10°C/s close to the skin. To expand the studied domain of quenching rates, a thin specimen was re-solution treated at 1080°C/s and then water quenched. Q is then estimated to be 20°C/s. After mechanical polishing, samples were analyzed by Conversion Electron Mo¨ssbauer Spectrometry (CEMS), which analyzes the first 200 nm in depth from the sample surface. The experiments were performed at 300K using a home-made counter at room temperature and a 57Co source in a rhodium matrix. The samples were set perpendicular to the incident g beam direction. The isomer shift (IS) at 57Fe nuclei was given relative to a-Fe at room temperature. All the details concerning atom probe analysis of the same specimens are given in a previous paper (5). Austenite Extraction Method and Its Validation The Figure 1 represents experimental Mo¨ssbauer spectra of specimens cooled with different quenching rates Q. The spectra consist of a central paramagnetic peak due to the austenite and a magnetic contribution due to the ferrite. The Mo¨ssbauer spectra were globally fitted with a least-square technique (12). The mean hyperfine field (,Bhf.) fluctuates around 22T, and the isomer shift seems to be constant at 10.01 mm/s for the ferrite and 20.097 mm/s for the austenite, in good agreement with Solomon results (11). But as a consequence of the overlap of the a and g signals around the weak fields, there is a large uncertainty in the estimate of the hyperfine parameters. In particular, it is impossible to compare the decomposition amount of the ferrite of the various specimens, as it directly derives from the hyperfine parameters. To overcome this drawback, the ferrite spectrum must be isolated. An iterative method consisting in substrating the austenite contribution from the experimental spectrum is proposed. To validate this procedure, i.e. to prove that the austenite solely is extracted without any contribution from the ferrite, a very decomposed specimen (aged 2500h at 350°C) has been analysed by CEMS. The experimental spectrum and the two elemental contributions (namely g and a) are shown Figure 2-a-b-c. The constant background noise level of the austenite spectrum indicates that no contribution from the ferrite signal is included in it, and therefore that the austenite contribution is correctly extracted. The ferrite spectrum consists of six broadened peaks, and is similar to ferrite spectrum as previously observed in pure ferritic steels (11). The broadening is attributed to the difference in the environment of the iron atoms. The spectrum is actually a superimposition of several sextets each with different
Vol. 39, No. 1
¨ SSBAUER STUDY OF THE FERRITE MO
63
Figure 1. Experimental spectra of specimens which experienced different quenching rate Q.
Mo¨ssbauer hyperfine interaction parameters depending on the number of iron neighbours of the resonantly absorbing 57Fe atom. Indeed, the corresponding hyperfine field distribution (p(Bhf)) shown Figure 2d, is composed of two contributions, one centered on 10T and the other on 25T, again in good agreement with literature data for decomposed ferrite (13). The high field contribution reflects the presence of the a Fe-rich domains, whereas the low field contribution reflects the existence of the a9 Cr-rich domains. Indeed, in the a domains, each iron atom is preferentially surrounded by Fe atoms. In the a9 domains, the iron concentration is reduced, and iron neighbours are progressively replaced by Cr neighbours. As Cr atoms reduce the hyperfine field (14), the a9 contribution to p(Bhf) is shifted towards the low fields, while a contribution is shifted towards high fields, with respect to a random solid solution. All the above results show that the proposed method is efficient to isolate ferrite spectra and can be applied to the study of a-a9 decomposition in duplex stainless steels. CEMS and Atom Probe Results on Ferrite of Unaged Samples The evolution of the decomposition extent with respect to the quenching rate was studied with the proposed method. The ferrite experimental spectra derived from the experimental data shown Figure 1 are represented Figure 3. The six peaks constituting the ferrite spectrum tend to broaden as Q decreases indicating an evolution in the 57Fe environment takes place during the quench. The hyperfine field distributions derived from the previous spectra (Figure 4) look like gaussian curves, centered on 22T, slightly broadened and asymmetric. The broadening is attributed to the overlapping of the two contributions corresponding to the a and a9 domains. The corresponding mean hyperfine field (,Bhf.) is 21.99T, 21.72T and 21.27T for Q is 2°C/s, 5°C/s and 20°C/s respectively. These results indicate a
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Figure 2. a) Experimental spectrum of a specimen aged 2500h at 350°C; b) The extracted austenite spectrum; c) The ferrite spectrum; d) The corresponding hyperfine distribution.
progressive ferrite microstructural evolution with respect to the quenching rate. This evolution can not be explained by the formation of the s phase. Indeed, the s phase being paramagnetic, no contribution is expected in the isolated ferrite Mo¨ssbauer spectra. On the other hand, the distribution shapes prove that the transformation mechanism is of a spinodal type and not nucleation and growth. If it was nucleation and growth there would be a significant contribution at low fields corresponding to the precipitates which would have their final composition since the beginning of the transformation. Furthermore, the hyperfine field distributions shift progressively towards high fields as Q decreases. Pollak reported the same phenomenon but during thermal ageing (15), which he attributed to the segregation amplitude evolution during spinodal decomposition. In some respects, the evolution observed during the quench can be considered as the first stages of this thermal ageing. Indeed, the slower a specimen is quenched, the longer its temperature remains in the domain where a spinodal decomposition can take place, leading to more pronounced ferrite transformation. This transformation is not a classical spinodal decomposition as the temperature is not constant during the quench. Nevertheless, it is of a spinodal type since no energy barrier has to be jumped over to initiate the decomposition. As a conclusion, not only the hyperfine field distribution study proves that a transfor-
Vol. 39, No. 1
¨ SSBAUER STUDY OF THE FERRITE MO
65
Figure 3. Experimental spectra of the ferritic phase obtained after the austenite extraction.
mation takes place in the ferritic phase during the quench, but also confirms that it is a spinodal mechanism. Atom probe analyses were carried out to quantify differently the decomposition of the same specimen. The parameter V was determined and drawn versus the mean hyperfine field of the field distributions. It appears that ,Bhf. increases linearly with V (Fig. 5). The linear law confirms the two techniques do actually see the same phenomenon, i.e the local environment evolution of the atoms in the ferritic phase. According to the error bars related to the two techniques, it clearly appears that CEMS is more sensitive to small evolutions in the ferrite phase, even though the accuracy of the V parameter seems better than it had been previously estimated (5).
Figure 4. Hyperfine field distributions of the ferrite.
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Figure 5. The mean hyperfine field versus V and the corresponding estimated quenching rate.
Conclusion As a conclusion, an austenite extraction method has been proposed to isolate the ferrite contribution in duplex stainless steels Mo¨ssbauer spectra. The mean hyperfine field ,Bhf. derived from fitted ferrite spectra is shown to be very sensitive to a change of the local environment of 57Fe atom, and then able to quantify the extent of the spinodal decomposition amplitude even for the very weak decompositions. Therefore, CEMS has a better accuracy than the atom probe to follow the very weak composition fluctuations that take place during the first stages of spinodal decomposition. Moreover, CEMS use would be preferable to atom probe one as it is less constraining. On a metallurgical point of view, the results also confirm that a transformation may occur during the quench of duplex stainless steels via a spinodal mechanism. Acknowledgment These researches are financially supported by Electricite´ de France, De´partement Etude des Mate´riaux, under contract EDF/CNRS No. 509511. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. K. Miller, J. Bentley, S. S. Brenner, and J.A. Spitznagel, J. Phys. (Paris). 45, C9 –385 (1984). T. J. Godfrey and G. D. W. Smith, J. Phys. 47, C7–217 (1986). J. Bourgoin and M. Guttmann, Mat. Sci. Technol. 6, 301 (1990). J. C. Lasalle and L. H. Schwartz, Acta Metall. 34, 6, 989 (1986). M. Hedin, J. P. Massoud, and F. Danoix, J. Phys. IV6, C5–235 (1996). M. K. Miller and G. D. W. Smith, Atom Probe Microanalysis: Principles and Applications to Materials Science, Materials Research Society, Pittsburgh, PA (1989). D. Blavette, G. Grancher, and A. Bostel, J. Phys 49, C6 – 433 (1988). F. Danoix, P. Auger, A. Bostel, and D. Blavette, Surf. Sci. 246, 260 (1991). D. Chandra and L. H. Schartz, Met. Trans. 2, 511 (1971). T. De Nys and P. M. Gierler, Met. Trans. 2, 1423 (1971). H. D. Solomon, Lionel M. Levinson, Acta Metall. 26, 429 (1978). J. Teillet and F. Varret, unpublished MOSFIT program. H. Kuwano, Y. Ishikawa, T. Yoshimura, and Y. Hamaguchi, Hyp. Int. 92, 987 (1994). S. M. Dubiel and J. Zukrowski, J. Magn. Magn. Mat. 23, 214 (1981). H. Pollak, U. Karfunkel, J. A. Lodya, and N. Mala, Hyp. Int. 94, 2355 (1994).