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Kinetic paths for B2 order in nanocrystalline FeCo–Mo: a MÖssbauer spectroscopic study
Acta mater. 49 (2001) 1789–1792 www.elsevier.com/locate/actamat
KINETIC PATHS FOR B2 ORDER IN NANOCRYSTALLINE ¨ SSBAUER SPECTROSCOPIC STUDY FeCo–Mo: A MO S. SARKAR and C. BANSAL† School of Physics, University of Hyderabad, Hyderabad 500046, India ( Received 7 August 2000; received in revised form 2 January 2001; accepted 9 February 2001 )
Abstract—The kinetic evolution of B2 order in nanocrystalline FeCo–Mo alloys was studied at different temperatures using Mo¨ssbauer spectroscopy. The kinetic paths in the space spanned by the two short-range order parameters aCo/Fe and aMo/Fe were found to be independent of temperature within experimental errors. This behavior is to be compared with that observed in coarse-grained FeCo–Mo alloys, where the paths were not the same at different temperatures. This can be attributed to the presence of more grain boundary regions in the nanophase alloys, which provide short-circuited diffusion paths for atom movements. 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Mechanical alloying; Mo¨ssbauer effect; Kinetics; Ordering; Nanocrystalline alloys
1. INTRODUCTION
The kinetic evolution to the chemically ordered equilibrium state of an ordering alloy from its initial disordered state has been the subject of many interesting studies, but it is not yet fully understood [1, 2]. It has been argued that for a ternary alloy, in which the state of order is characterized by two order parameters, the alloy may develop various combinations of the order parameters in the approach to the final equilibrium state [3]. The initial and final states may be connected by different chains of intermediate states, i.e. for a given value of one order parameter, the other order parameter need not have a unique value. It was shown using the master equation formulation that these chains of kinetic evolution towards the final equilibrium order or “kinetic paths” were temperature dependent when the atomic species of the alloy had different activation energy barrier heights for diffusive jumps or different interatomic interactions. A Mo¨ssbauer spectroscopic study on the kinetics of chemical ordering in several piston-anvil quenched FeCo–X alloys (X = W, Nb, Mo, Cr, Ti, V, and Al) showed that the kinetics of B2 ordering was slowed down for the 4d and 5d solutes but the 3p and 3d series elements did not affect the ordering kinetics [4]. This was understood to arise due to the lesser mobility of the W, Nb and Mo solutes. A more
† To whom all correspondence should be addressed. Tel.: +91-40-301-0336; Fax: +91-40-301-0227. E-mail address: [email protected] (C. Bansal)
detailed investigation of the FeCo–Mo system was subsequently carried out to observe differences in kinetic paths of the Warren–Cowley short-range order parameters aMo/Fe and aCo/Fe at different temperatures [5]. The kinetic paths at 350 and 400°C were indeed observed to be different, albeit not as much as predicted from model calculations. The temperature dependence of kinetic paths was attributed to the high activation energy barrier for diffusive jumps of Mo atoms. In this work we studied the kinetic behavior of the FeCo–Mo alloy prepared in the nanocrystalline state by the process of mechanical alloying to see the effect of the nanocrystalline nature of the alloy on the ordering process. We found that the kinetic paths were essentially the same at different temperatures. This suggests that the larger grain boundary regions in these nanocrystalline alloys act as short-circuited diffusion paths and give rise to an increased rate of diffusion for all the atomic species constituting the alloy [6, 7]. The kinetic paths are therefore not expected to be observably different.
2. EXPERIMENTAL
FeCo–4 at.% Mo alloys were prepared by direct mechanical milling of the elemental powders in a SPEX 8000 Mixer Mill using hardened steel balls and a vial. A set of six balls (two of diameter 12⬙ and four of diameter 1/4⬙) was used for milling. The ball to powder weight ratio was chosen to be 5:1. Elemental Fe (99.99% purity, fine gray powder from Aldrich–
1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 0 8 1 - 7
1790
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
Sigma Chemicals), Co (m2N8, spherical -325 mesh, from Alfa Products) and Mo (m3N±, -200 mesh, from Alfa Products) powders were weighed according to the required stoichiometric ratio and transferred to the vial. Milling was carried out under high-purity Argon (IOLAR grade II from British Oxygen Company) atmosphere. The sample was initially milled for 24 h, but this was not sufficient to produce a completely disordered alloy. The alloy was in a partially ordered state as evident from the area of the satellite peak in the Mo¨ ssbauer spectra, being less than that expected for a random distribution. The milling time was therefore increased to 50 h to obtain a completely disordered alloy with the satellite peak area corresponding to that of a binomial distribution of a random alloy. The as-milled alloys were formed into a singlephase disordered bcc structure as confirmed by the X-ray diffraction (XRD) pattern. Using the Debye– Scherrer formula for line broadening of the (110) fundamental line of the disordered bcc phase as-milled alloys, the average grain size obtained from the XRD pattern was found to be about 10 nm. Both the 24- and 50-h milled samples were heat treated under argon atmosphere in borosilicate glass ampoules at a pressure of 0.05 Torr for various periods of time, ranging from a few minutes to several hours. Heat treatment was carried out at 250, 300, 350 and 400°C to follow the evolution of B2 ordering in these samples. Mo¨ ssbauer spectra with good statistics were recorded in transmission geometry using a 10 mCi 57 Co in Rh source. Hyperfine magnetic field (hmf) distributions were evaluated from the Mo¨ ssbauer spectra using the method of Le Cae¨ r and Dubois [8]. To derive the hmf distributions from the Mo¨ ssbauer spectra the standard procedure adopted [9] is to consider the isomer shift (I) as a linear function of the hmf (H) in the form: I(H) = aH + b
3. RESULTS AND DISCUSSION
Figure 1 shows the Mo¨ ssbauer spectra for the asmilled FeCo and FeCo–4 at.% Mo alloys. Also shown in the figure is the difference spectrum between the two alloy systems. The difference spectrum corresponds to a hyperfine field of 54 KOe lower than the average hyperfine field for FeCo. This is attributed to the presence of Mo atoms in the first near neighbour (1nn) environment of Fe. The presence of satellite lines in FeCo–Mo at lower field values is similar to that observed by adding a few atomic percent solutes to pure iron in several Fe–X (where X=few atomic percent Si, Al, Mn, Cr, Mo etc.) alloys [12]. The observed field shift of 54 KOe for the satellite line is in good agreement with earlier work [4]. It is important to mention that in the Mo¨ ssbauer spectra of the as-milled alloys we could not identify any separate contribution, which could be attributed to 57Fe atoms residing near or at grain boundaries. In the case of nanocrystalline Fe [13, 14] as well as in some concentrated binary Fe alloys [15] separate hmf contributions were observed for grain boundary atoms which were about 10–20 KOe less than the in-grain field. However, in our system this field component if present would merge with the main peak which has a width of about 50 KOe and would therefore be difficult to identify separately. Moreover, in all these systems the grain size obtained was of the order of 8 nm or less and it was observed by Fultz et al. [15] that the contributions from grain boundary Fe atoms were difficult to identify if the grain size was 10 nm or more. The assignment of the satellite peak to Mo atoms in the neighbourhood of Fe atoms was also supported by the observed area of the satellite peak
(1)
This type of correlation is justified because the isomer shift in the Mo¨ ssbauer spectrum is directly proportional to the total s electron density at the nuclear site, whereas the magnetic field is proportional to the difference between the spin up and spin down s electron density at the nuclear site. A change in hmf arises from a change in the spin up or spin down s electron density which also changes the total s electron density and hence the isomer shift proportionally. This general systematic between isomer shift and the hmf works very well in a wide variety of alloy systems [10, 11]. The constant coefficients a and b were optimized to get a minimum c2. The hmf distributions thus obtained were fitted to two Gaussian distributions, one corresponding to the main peak and the other corresponding to the satellite peak.
Fig. 1. Mo¨ ssbauer spectra for nanocrystalline disordered bcc FeCo and FeCo–4 at.% Mo alloys (open circles: experimental; solid line: fit). The difference spectrum shows that Mo addition to FeCo gives rise to a satellite line corresponding to a reduced hyperfine field value.
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
1791
which corresponded to a random distribution of Mo first neighbours to Fe, as calculated using a binomial distribution. If the satellite peak consisted of grain boundary components also, the area of the peak was expected to be more than what was experimentally observed. The satellite peak could not be attributed to Mo segregation to grain boundaries because this would also have given rise to Mo rich regions and different first and second neighbour probabilities than what was observed. After ordering heat treatments, the width of the main peak as well as the intensity of the satellite peak decreases, as shown in Fig. 2. The area of the main peak on the other hand increases. The hyperfine magnetic field distributions evaluated from the Mo¨ ssbauer spectra are shown in Fig. 3. From these observations and also from earlier studies of disorder→B2 order transformation in pure FeCo it is known that the width of the hyperfine distribution decreases with an increase in the chemical order due to a change in the 1nn environment from a random distribution to that of an ordered arrangement of all Co neighbours. The width of the main peak is therefore an appropriate measure of the ⬍Co/Fe> correlation. Similarly, as the order develops, more and more configurations correspond to an Fe atom with Co neighbours and the area of the main peak increases; therefore, this area can also be considered as a measure of the ⬍Co/Fe> correlation. The area of the satellite peak corresponds to the ⬍Mo/Fe> correlation. A decrease in the Mo satellite area (Fig. 3) as ordering takes place shows that Mo atoms move away from the 1nn shell of the Fe to a Co near neighbour environment. This is in agreement with the metallic bonding theory of Miedema et al.
[16], according to which Co–Mo bonding is preferred to Fe–Mo bonding. Figures 4 and 5 show the kinetic paths for the nanocrystalline FeCo–4 at.% Mo alloy at different temperatures in the space spanned by the order parameters ⬍Mo/Fe> and ⬍Co/Fe>. These plots include points for both the 24- and 50-h milled alloys. It is interesting to note that these paths are essentially the same within experimental errors at all the temperatures and for both the initial states of the alloys.
Fig. 2. Mo¨ ssbauer spectra showing the effect of ordering heat treatments in FeCo and FeCo–Mo (open circles: experimental; solid line: fit). There is a decrease in line broadening for both systems and also a decrease in satellite line intensity for FeCo– Mo.
Fig. 4. Kinetic paths for B2 ordering in nanocrystalline FeCo– Mo at different temperatures. The ⬍Co/Fe> and ⬍Mo/Fe> correlations are measured by the width of the main peak and the intensity of the satellite peak, respectively.
Fig. 3. Hyperfine magnetic field distributions evaluated from the Mo¨ ssbauer spectra. The evolution of B2 order is reflected from the decrease in the widths and increase in the intensities of the main peak as well as from the decrease in the intensity of the satellite peak.
1792
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
circuited paths may not be substantially different and thus give rise to identical kinetic paths for ordering. 4. CONCLUSIONS
In conclusion our study of the kinetic evolution of B2 order in nanocrystalline FeCo–Mo alloys shows that the ordering proceeds along the same path at many different temperatures. It may therefore not be possible to develop new ordered microstructures in the nanocrystalline system by simple thermal processing at different temperatures as was found possible for macrocrystalline FeCo–Mo alloys [5]. A possible explanation for the difference lies in the larger grain boundary volume in the nano-system compared to that of microcrystalline alloys, which provide high diffusivity paths for all constituent atomic species in the alloy. Fig. 5. An alternative representation of the kinetic paths for B2 ordering in terms of the intensity of the satellite peak and the intensity of the main peak.
Acknowledgements—This work was supported by the Council of Scientific and Industrial Research (India) under grant no. 3 (795)/96/EMR-II.
This observation should be compared to the behavior of piston-anvil quenched polycrystalline FeCo–Mo alloys [5], in which these kinetic paths were seen to be distinctly different at 350 and 400°C. The absolute rate of change of these correlations at these temperatures in nanocrystalline alloys was also seen to be substantially faster compared to those observed in the previous study [5]. This observation prompted us to study the evolution of order at a lower temperature of 250°C to see whether a higher activation barrier for Mo diffusion would give rise to a difference in the kinetic path at a lower temperature. The rate of change of correlations was observed to be slower, as expected at lower temperatures, but the kinetic path followed was the same as that at 350 and 400°C. We are therefore convinced that the kinetic path behavior of the nanocrystalline system is intrinsically related to the nanocrystalline nature of the ball-milled alloys. The main difference between the macrocrystalline and nanocrystalline systems is the presence of a large volume fraction of grain boundary regions. These boundary regions provide short-circuited paths for diffusion of atoms [6, 7]. The activation energy of diffusion for the different atoms along these short-
1. H. Chen and V. K. Vasudevan (eds), Kinetics of Ordering Transformations in Metals. TMS, Warrendale, 1992. 2. B. Fultz, R. W. Cahn and D. Gupta (eds), Diffusion in Ordered Alloys. TMS, Warrendale, 1993. 3. Fultz, B., Acta metall., 1989, 37, 823. 4. Fultz, B., Hyperfine Int., 1988, 41, 607. 5. Fultz, B., Hamdeh, H. H. and Pearson, D. H., Acta metall., 1989, 37, 2841. 6. Murch, G. E., in Phase Transformations in Materials, ed. R. W. Cahn, P. Haasen and E. J. Kramer, VCH, Weinheim, 1991, p. 90. 7. Porter, D. A. and Easterling, K. E., Phase Transformations in Metals and Alloys, 2nd edn. Chapman and Hall, 1992, (p. 98). 8. Le Cae¨ r, G. and Dubois, J. M., J. Phys. E, 1979, 12, 1083. 9. Fultz, B., Gao, Z. Q., Hamdeh, H. H. and Oliver, S. R., Phys. Rev. B, 1994, 49, 6312. 10. Sarkar, S., Bansal, C. and Chatterjee, A., Phys. Rev. B, 2000, 62, 3218. 11. Bansal, C., Gao, Z. Q., Hong, L. B. and Fultz, B., J. Appl. Phys., 1994, 76, 5961. 12. Sterns, A. B., Phys. Rev. B, 1966, 147, 439. 13. Herr, U., Jing, J., Birringer, R., Gonser, U. and Gleiter, H., Appl. Phys. Lett., 1987, 50, 472. 14. Sinha, P. and Collins, G. S., Hyperfine Int., 1994, 92, 949. 15. Fultz, B., Kuwano, H. and Ouyang, H., J. Appl. Phys., 1995, 77, 3458. 16. Miedema, A. R., deChatel, P. F. and deBoer, F. R., Physica B, 1980, 100, 1.
REFERENCES
KINETIC PATHS FOR B2 ORDER IN NANOCRYSTALLINE ¨ SSBAUER SPECTROSCOPIC STUDY FeCo–Mo: A MO S. SARKAR and C. BANSAL† School of Physics, University of Hyderabad, Hyderabad 500046, India ( Received 7 August 2000; received in revised form 2 January 2001; accepted 9 February 2001 )
Abstract—The kinetic evolution of B2 order in nanocrystalline FeCo–Mo alloys was studied at different temperatures using Mo¨ssbauer spectroscopy. The kinetic paths in the space spanned by the two short-range order parameters aCo/Fe and aMo/Fe were found to be independent of temperature within experimental errors. This behavior is to be compared with that observed in coarse-grained FeCo–Mo alloys, where the paths were not the same at different temperatures. This can be attributed to the presence of more grain boundary regions in the nanophase alloys, which provide short-circuited diffusion paths for atom movements. 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Mechanical alloying; Mo¨ssbauer effect; Kinetics; Ordering; Nanocrystalline alloys
1. INTRODUCTION
The kinetic evolution to the chemically ordered equilibrium state of an ordering alloy from its initial disordered state has been the subject of many interesting studies, but it is not yet fully understood [1, 2]. It has been argued that for a ternary alloy, in which the state of order is characterized by two order parameters, the alloy may develop various combinations of the order parameters in the approach to the final equilibrium state [3]. The initial and final states may be connected by different chains of intermediate states, i.e. for a given value of one order parameter, the other order parameter need not have a unique value. It was shown using the master equation formulation that these chains of kinetic evolution towards the final equilibrium order or “kinetic paths” were temperature dependent when the atomic species of the alloy had different activation energy barrier heights for diffusive jumps or different interatomic interactions. A Mo¨ssbauer spectroscopic study on the kinetics of chemical ordering in several piston-anvil quenched FeCo–X alloys (X = W, Nb, Mo, Cr, Ti, V, and Al) showed that the kinetics of B2 ordering was slowed down for the 4d and 5d solutes but the 3p and 3d series elements did not affect the ordering kinetics [4]. This was understood to arise due to the lesser mobility of the W, Nb and Mo solutes. A more
† To whom all correspondence should be addressed. Tel.: +91-40-301-0336; Fax: +91-40-301-0227. E-mail address: [email protected] (C. Bansal)
detailed investigation of the FeCo–Mo system was subsequently carried out to observe differences in kinetic paths of the Warren–Cowley short-range order parameters aMo/Fe and aCo/Fe at different temperatures [5]. The kinetic paths at 350 and 400°C were indeed observed to be different, albeit not as much as predicted from model calculations. The temperature dependence of kinetic paths was attributed to the high activation energy barrier for diffusive jumps of Mo atoms. In this work we studied the kinetic behavior of the FeCo–Mo alloy prepared in the nanocrystalline state by the process of mechanical alloying to see the effect of the nanocrystalline nature of the alloy on the ordering process. We found that the kinetic paths were essentially the same at different temperatures. This suggests that the larger grain boundary regions in these nanocrystalline alloys act as short-circuited diffusion paths and give rise to an increased rate of diffusion for all the atomic species constituting the alloy [6, 7]. The kinetic paths are therefore not expected to be observably different.
2. EXPERIMENTAL
FeCo–4 at.% Mo alloys were prepared by direct mechanical milling of the elemental powders in a SPEX 8000 Mixer Mill using hardened steel balls and a vial. A set of six balls (two of diameter 12⬙ and four of diameter 1/4⬙) was used for milling. The ball to powder weight ratio was chosen to be 5:1. Elemental Fe (99.99% purity, fine gray powder from Aldrich–
1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 0 8 1 - 7
1790
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
Sigma Chemicals), Co (m2N8, spherical -325 mesh, from Alfa Products) and Mo (m3N±, -200 mesh, from Alfa Products) powders were weighed according to the required stoichiometric ratio and transferred to the vial. Milling was carried out under high-purity Argon (IOLAR grade II from British Oxygen Company) atmosphere. The sample was initially milled for 24 h, but this was not sufficient to produce a completely disordered alloy. The alloy was in a partially ordered state as evident from the area of the satellite peak in the Mo¨ ssbauer spectra, being less than that expected for a random distribution. The milling time was therefore increased to 50 h to obtain a completely disordered alloy with the satellite peak area corresponding to that of a binomial distribution of a random alloy. The as-milled alloys were formed into a singlephase disordered bcc structure as confirmed by the X-ray diffraction (XRD) pattern. Using the Debye– Scherrer formula for line broadening of the (110) fundamental line of the disordered bcc phase as-milled alloys, the average grain size obtained from the XRD pattern was found to be about 10 nm. Both the 24- and 50-h milled samples were heat treated under argon atmosphere in borosilicate glass ampoules at a pressure of 0.05 Torr for various periods of time, ranging from a few minutes to several hours. Heat treatment was carried out at 250, 300, 350 and 400°C to follow the evolution of B2 ordering in these samples. Mo¨ ssbauer spectra with good statistics were recorded in transmission geometry using a 10 mCi 57 Co in Rh source. Hyperfine magnetic field (hmf) distributions were evaluated from the Mo¨ ssbauer spectra using the method of Le Cae¨ r and Dubois [8]. To derive the hmf distributions from the Mo¨ ssbauer spectra the standard procedure adopted [9] is to consider the isomer shift (I) as a linear function of the hmf (H) in the form: I(H) = aH + b
3. RESULTS AND DISCUSSION
Figure 1 shows the Mo¨ ssbauer spectra for the asmilled FeCo and FeCo–4 at.% Mo alloys. Also shown in the figure is the difference spectrum between the two alloy systems. The difference spectrum corresponds to a hyperfine field of 54 KOe lower than the average hyperfine field for FeCo. This is attributed to the presence of Mo atoms in the first near neighbour (1nn) environment of Fe. The presence of satellite lines in FeCo–Mo at lower field values is similar to that observed by adding a few atomic percent solutes to pure iron in several Fe–X (where X=few atomic percent Si, Al, Mn, Cr, Mo etc.) alloys [12]. The observed field shift of 54 KOe for the satellite line is in good agreement with earlier work [4]. It is important to mention that in the Mo¨ ssbauer spectra of the as-milled alloys we could not identify any separate contribution, which could be attributed to 57Fe atoms residing near or at grain boundaries. In the case of nanocrystalline Fe [13, 14] as well as in some concentrated binary Fe alloys [15] separate hmf contributions were observed for grain boundary atoms which were about 10–20 KOe less than the in-grain field. However, in our system this field component if present would merge with the main peak which has a width of about 50 KOe and would therefore be difficult to identify separately. Moreover, in all these systems the grain size obtained was of the order of 8 nm or less and it was observed by Fultz et al. [15] that the contributions from grain boundary Fe atoms were difficult to identify if the grain size was 10 nm or more. The assignment of the satellite peak to Mo atoms in the neighbourhood of Fe atoms was also supported by the observed area of the satellite peak
(1)
This type of correlation is justified because the isomer shift in the Mo¨ ssbauer spectrum is directly proportional to the total s electron density at the nuclear site, whereas the magnetic field is proportional to the difference between the spin up and spin down s electron density at the nuclear site. A change in hmf arises from a change in the spin up or spin down s electron density which also changes the total s electron density and hence the isomer shift proportionally. This general systematic between isomer shift and the hmf works very well in a wide variety of alloy systems [10, 11]. The constant coefficients a and b were optimized to get a minimum c2. The hmf distributions thus obtained were fitted to two Gaussian distributions, one corresponding to the main peak and the other corresponding to the satellite peak.
Fig. 1. Mo¨ ssbauer spectra for nanocrystalline disordered bcc FeCo and FeCo–4 at.% Mo alloys (open circles: experimental; solid line: fit). The difference spectrum shows that Mo addition to FeCo gives rise to a satellite line corresponding to a reduced hyperfine field value.
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
1791
which corresponded to a random distribution of Mo first neighbours to Fe, as calculated using a binomial distribution. If the satellite peak consisted of grain boundary components also, the area of the peak was expected to be more than what was experimentally observed. The satellite peak could not be attributed to Mo segregation to grain boundaries because this would also have given rise to Mo rich regions and different first and second neighbour probabilities than what was observed. After ordering heat treatments, the width of the main peak as well as the intensity of the satellite peak decreases, as shown in Fig. 2. The area of the main peak on the other hand increases. The hyperfine magnetic field distributions evaluated from the Mo¨ ssbauer spectra are shown in Fig. 3. From these observations and also from earlier studies of disorder→B2 order transformation in pure FeCo it is known that the width of the hyperfine distribution decreases with an increase in the chemical order due to a change in the 1nn environment from a random distribution to that of an ordered arrangement of all Co neighbours. The width of the main peak is therefore an appropriate measure of the ⬍Co/Fe> correlation. Similarly, as the order develops, more and more configurations correspond to an Fe atom with Co neighbours and the area of the main peak increases; therefore, this area can also be considered as a measure of the ⬍Co/Fe> correlation. The area of the satellite peak corresponds to the ⬍Mo/Fe> correlation. A decrease in the Mo satellite area (Fig. 3) as ordering takes place shows that Mo atoms move away from the 1nn shell of the Fe to a Co near neighbour environment. This is in agreement with the metallic bonding theory of Miedema et al.
[16], according to which Co–Mo bonding is preferred to Fe–Mo bonding. Figures 4 and 5 show the kinetic paths for the nanocrystalline FeCo–4 at.% Mo alloy at different temperatures in the space spanned by the order parameters ⬍Mo/Fe> and ⬍Co/Fe>. These plots include points for both the 24- and 50-h milled alloys. It is interesting to note that these paths are essentially the same within experimental errors at all the temperatures and for both the initial states of the alloys.
Fig. 2. Mo¨ ssbauer spectra showing the effect of ordering heat treatments in FeCo and FeCo–Mo (open circles: experimental; solid line: fit). There is a decrease in line broadening for both systems and also a decrease in satellite line intensity for FeCo– Mo.
Fig. 4. Kinetic paths for B2 ordering in nanocrystalline FeCo– Mo at different temperatures. The ⬍Co/Fe> and ⬍Mo/Fe> correlations are measured by the width of the main peak and the intensity of the satellite peak, respectively.
Fig. 3. Hyperfine magnetic field distributions evaluated from the Mo¨ ssbauer spectra. The evolution of B2 order is reflected from the decrease in the widths and increase in the intensities of the main peak as well as from the decrease in the intensity of the satellite peak.
1792
SARKAR and BANSAL: B2 ORDER IN NANOCRYSTALLINE FeCo–Mo
circuited paths may not be substantially different and thus give rise to identical kinetic paths for ordering. 4. CONCLUSIONS
In conclusion our study of the kinetic evolution of B2 order in nanocrystalline FeCo–Mo alloys shows that the ordering proceeds along the same path at many different temperatures. It may therefore not be possible to develop new ordered microstructures in the nanocrystalline system by simple thermal processing at different temperatures as was found possible for macrocrystalline FeCo–Mo alloys [5]. A possible explanation for the difference lies in the larger grain boundary volume in the nano-system compared to that of microcrystalline alloys, which provide high diffusivity paths for all constituent atomic species in the alloy. Fig. 5. An alternative representation of the kinetic paths for B2 ordering in terms of the intensity of the satellite peak and the intensity of the main peak.
Acknowledgements—This work was supported by the Council of Scientific and Industrial Research (India) under grant no. 3 (795)/96/EMR-II.
This observation should be compared to the behavior of piston-anvil quenched polycrystalline FeCo–Mo alloys [5], in which these kinetic paths were seen to be distinctly different at 350 and 400°C. The absolute rate of change of these correlations at these temperatures in nanocrystalline alloys was also seen to be substantially faster compared to those observed in the previous study [5]. This observation prompted us to study the evolution of order at a lower temperature of 250°C to see whether a higher activation barrier for Mo diffusion would give rise to a difference in the kinetic path at a lower temperature. The rate of change of correlations was observed to be slower, as expected at lower temperatures, but the kinetic path followed was the same as that at 350 and 400°C. We are therefore convinced that the kinetic path behavior of the nanocrystalline system is intrinsically related to the nanocrystalline nature of the ball-milled alloys. The main difference between the macrocrystalline and nanocrystalline systems is the presence of a large volume fraction of grain boundary regions. These boundary regions provide short-circuited paths for diffusion of atoms [6, 7]. The activation energy of diffusion for the different atoms along these short-
1. H. Chen and V. K. Vasudevan (eds), Kinetics of Ordering Transformations in Metals. TMS, Warrendale, 1992. 2. B. Fultz, R. W. Cahn and D. Gupta (eds), Diffusion in Ordered Alloys. TMS, Warrendale, 1993. 3. Fultz, B., Acta metall., 1989, 37, 823. 4. Fultz, B., Hyperfine Int., 1988, 41, 607. 5. Fultz, B., Hamdeh, H. H. and Pearson, D. H., Acta metall., 1989, 37, 2841. 6. Murch, G. E., in Phase Transformations in Materials, ed. R. W. Cahn, P. Haasen and E. J. Kramer, VCH, Weinheim, 1991, p. 90. 7. Porter, D. A. and Easterling, K. E., Phase Transformations in Metals and Alloys, 2nd edn. Chapman and Hall, 1992, (p. 98). 8. Le Cae¨ r, G. and Dubois, J. M., J. Phys. E, 1979, 12, 1083. 9. Fultz, B., Gao, Z. Q., Hamdeh, H. H. and Oliver, S. R., Phys. Rev. B, 1994, 49, 6312. 10. Sarkar, S., Bansal, C. and Chatterjee, A., Phys. Rev. B, 2000, 62, 3218. 11. Bansal, C., Gao, Z. Q., Hong, L. B. and Fultz, B., J. Appl. Phys., 1994, 76, 5961. 12. Sterns, A. B., Phys. Rev. B, 1966, 147, 439. 13. Herr, U., Jing, J., Birringer, R., Gonser, U. and Gleiter, H., Appl. Phys. Lett., 1987, 50, 472. 14. Sinha, P. and Collins, G. S., Hyperfine Int., 1994, 92, 949. 15. Fultz, B., Kuwano, H. and Ouyang, H., J. Appl. Phys., 1995, 77, 3458. 16. Miedema, A. R., deChatel, P. F. and deBoer, F. R., Physica B, 1980, 100, 1.
REFERENCES