- Email: [email protected]
Diffusion of Fe, Co, Nd, and Dy in R2(Fe1−xCox)14B where R=Nd or Dy
LETTER TO THE EDITOR
Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
Letter to the Editor
Diffusion of Fe, Co, Nd, and Dy in R2(Fe1xCox)14B where R=Nd or Dy B.A. Cook*, J.L. Harringa, F.C. Laabs, K.W. Dennis, A.M. Russell, R.W. McCallum Ames Laboratory of the USDOE, Iowa State University, 253 Spedding Hall, Ames, IA 50011, USA Received 13 December 2000; received in revised form 16 May 2001
Abstract Transition metal and rare earth diffusion coefficients at 1323 K in Dy2yNdy(Fe1xCox )14B were determined by field emission energy dispersive spectroscopy compositional analysis of diffusion couple specimens. Various arrangements of component materials and temperatures were examined in order to understand the mechanisms affecting diffusion of the components and to predict the stability of functionally graded microstructures consisting of a dysprosium-rich (Dy2yNdy (Fe1xCox )14B) outer layer and a neodymium-rich (Nd2(Fe1xCox)14B) interior. Estimates of the mutual interdiffusion coefficients of Dy, Nd, Fe, and Co in this system were obtained from the preparation of arc melted and annealed polycrystalline specimens, assuming that the diffusion coefficients were independent of concentration (Grube solution). Fifteen diffusion couples were prepared and heat treated at 1323 K for various times in order to provide data for calculation of the diffusion coefficients. The results indicate that the diffusion coefficients of Fe and Co (DFe ¼ 3:28 1010 cm2/s and DCo ¼ 7:63 1010 cm2/s) were significantly higher at 1323 K in this system than those for Dy and Nd (DNd ¼ 2:3 1012 cm2/s and DDy ¼ 2:9 1012 cm2/s). r 2001 Elsevier Science B.V. All rights reserved. PACS: 75.50Ww; 66.30.Jt; 81.70.Jb Keywords: Diffusion coefficients; Rare earth–iron–cobalt–boron permanent magnets; SEM–EDS; Functionally graded microstructure
1. Introduction Use of high performance permanent magnets in elevated temperature applications requires that the material concurrently possess both a high Curie temperature, to resist temperature-dependent demagnetization, and a high coercivity to resist demagnetization in the presence of an externally *Corresponding author. Tel.: +515-294-9673; fax: +515294-9579. E-mail address: [email protected] (B.A. Cook).
imposed reverse magnetic field. Conventional SmCo5 magnets have a coercivity of 730 kA/m, a Curie temperature (Tc ) of 1000 K, and a maximum energy product of 175 kJ/m3 [1] which make them attractive for use in elevated temperature applications. However, replacement of SmCo5 with a material having a higher coercivity and maximum energy product would likely to result in a significant increase in operating efficiency. Permanent magnets based on the intermetallic compound Nd2Fe14B exhibit a higher energy product, 320 kJ/ m3, and a much larger coercivity, 1120 kA/m, than
0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 3 7 8 - X
LETTER TO THE EDITOR
B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
SmCo5 [1]. Unfortunately, the current generation of Nd2Fe14B magnets have a relatively low Curie temperature, 585 K, which is close to the heat rejection temperature of many high temperature engine configurations. Consequently, use of existing Nd2Fe14B under these conditions can lead to thermal demagnetization of the magnets, which becomes a significant concern at temperatures greater than 80% of Tc : Development of an advanced, high Tc permanent magnet would have significant implications in electric motor and generator technologies. A reasonable goal is the development of a material having a coercivity and energy product comparable to existing Nd–Fe–B but with a Curie temperature at least 100 K higher. Numerous investigators have attempted to raise the Curie temperature of Nd2Fe14B by altering its composition, and these efforts have shown that partially replacing Fe with Co in Nd2Fe14B increases the Curie temperature to near 1000 K [2]. However, the coercivity of these Nd2(Fe1xCox)14B magnets is relatively low [3]. The objective of this study was to overcome the poor coercivity of Nd2(Fe1xCox)14B magnets by diffusing Dy into the outer surface of each Nd2(Fe1xCox)14B particle used in sintering the bulk magnet. A thin Dy outer layer would serve to frustrate reverse domain nucleation at the particle surface. Since reverse magnetic domains nucleate at particle surfaces, the Dy layer is expected to resist demagnetization of the entire particle in the presence of a reverse magnetic field, thereby increasing coercivity because of the higher magnetocrystalline anisotropy of the heavy rare earth [4]. Although the maximum theoretical energy product for Dy2Fe14B is significantly lower than that of Nd2Fe14B due to its lower saturation magnetization [4], the presence of Dy in a thin surface layer resulting from partial substitution in Nd2(Fe1xCox)14B would reduce the energy product of only a small fraction of total particle volume. The resulting functionally graded magnet may possess both a high coercivity and a high Curie temperature, while still maintaining an energy product nearly as large as that of pure Nd2Fe14B. A necessary requisite for this study is the determination of transition and rare earth metal diffusion coefficients in order to predict the stability of the
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functionally graded composition. In materials where composition gradients of these substitutional atoms exist, the mobility of the atoms is difficult to predict since no diffusion data have been reported. This study was performed in order to measure the diffusion coefficients for Fe and Co in Nd2(FexCo1x)14B, Nd in Dy2(FexCo1x)14B, and Dy in Nd2(FexCo1x)14B.
2. Experimental procedure Diffusion coefficients were measured by assembling pairs of cast and annealed single-phase compositions of either Nd2(FexCo1x)14B (for determination of transition metal diffusion) or R2(Fe0.714Co0.286)14B where R ¼ Nd or Dy (for determination of rare earth diffusion). The surfaces were ground with 320 and 600 grit SiC, polished using 1 m diamond paste, and rinsed with hexane. The specimens were placed with their polished surfaces facing each other in a BN-coated graphite holder which was positioned inside a controlled atmosphere furnace. The specimens were held together by a 560 g static load and the atmospheric pressure was reduced to 107 Torr. Fifteen diffusion couples were prepared and held at a temperature of 1323 K for various times in order to provide data for calculation of the transition metal and rare earth diffusion coefficients. Transition metal diffusion coefficient couples were held at this temperature for 30 min (1800 s) while the Nd and Dy diffusion couples were held for 300 min (18000 s) in order to accommodate the slower diffusion rates of the lanthanides. Analysis of the diffusion coefficients was accomplished by slicing each couple longitudinally, mounting in copper diallylphthalate resin along with DyFe2 and Nd2Fe8Co6B standards, and polishing with 0.25 m diamond paste. The compositional profiles were determined using an Amray field emission SEM equipped with an Oxford 1515 energy dispersive spectoscopy (EDS) system. Standardless, semi-quantitative SEM–EDS data generally lacks sufficient accuracy to enable determination of diffusion coefficients, since the
LETTER TO THE EDITOR
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typical tungsten filament forms a ‘‘bloom’’ of electron–specimen interaction volume below the surface that degrades spatial resolution. Moreover, oxide or hydroxide layers over the polished surface absorb and scatter different wavelengths of emitted X-rays by varying amounts. For these reasons, the field emission SEM used in this study was operated at low accelerating voltages (10 kV) to produce a smaller, cleaner beam footprint with the necessary spatial resolution. In addition, standards with fixed compositions were mounted beside each specimen to standardize the EDS spectra and minimize errors associated with oxide and hydroxide layers on the specimen surfaces. The diffusion coefficients were determined by employing a solution to Fick’s second law corresponding to a constant and finite concentration of the diffusive species within the bulk of each component. The diffusion coefficients were assumed to be independent of concentration. Initial rare earth diffusion tests were conducted on pairs of disks with identical transition metal concentrations and only slightly different rare earth concentrations, Nd1.5Dy0.5Fe8Co6B and Nd2Fe8Co6B. Samples with a composition of Nd2Fe10Co4B were observed to retain a singlephase microstructure following a high temperature anneal. However, compositions with higher Co/Fe ratios, such as Nd2Fe8Co6B, were found to segregate into three phases upon annealing. The reason for this decomposition remains uncertain and is the subject of a separate publication [5]. The presence of multiple phases complicates analysis due to the need for the electron beam path to fall within a single-phase region. Once the beam strikes a secondary phase, the anomalous composition violates boundary conditions assumed in the solution of Fick’s law. Moreover, it was found that the relatively small difference in rare earth concentration between these two samples did not provide sufficiently good statistics to enable reliable calculation of the diffusion coefficients. Another concern with the possible phase decomposition of the material is the formation of a large number of sub-micron interfaces between the matrix and precipitate phase, which could serve as diffusional ‘‘short circuit’’ paths giving rise to anomalous values for the diffusivity. These pre-
cipitates may nucleate as nanometer-sized zones, as observed in aged metastable Al–Cu alloys, the size of which would lie below the resolution limit of the SEM. For these reasons, additional diffusion couples were prepared with the nominal compositions Nd2Fe10Co4B and Dy2Fe10Co4B. A single-phase microstructure was observed in these systems which enabled determination of the rare earth diffusivity using the SEM–EDS method described above. It should be noted that studies of diffusion phenomena in condensed matter are best conducted on oriented, single crystal specimens, for which the absence of defects allows unambiguous interpretation of compositional data. For example, at moderate temperatures grain boundary diffusion occurs at a faster rate than bulk diffusion. The presence of defects (porosity, secondary phase precipitates, and oxide inclusions) complicates interpretation of elemental analysis using energy dispersive techniques. Consequently, compositional profiles obtained by EDS do not directly lead to partitioning of the data into grain boundary versus lattice diffusion. As a result, interpretation of the active diffusion mechanisms is somewhat limited. However, preparation of single crystalline samples was beyond the scope of this project, prediction of the relative diffusivities of the rare earth and transition metal atoms based on cast and annealed polycrystalline samples provides a useful approximation of the true diffusion coefficients.
3. Diffusion coefficient results The transition metal diffusion coefficients were determined by employing the Grube solution to Fick’s second law for a pair of semi-infinite solids, wherein the diffusion coefficients are independent of concentration. Within this framework, the solution to Fick’s second law takes the form CðxÞ ¼ Cl þ
C0 Cl ½1 erf ðbÞ; 2
ð1Þ
where CðxÞ is the composition at a point x along the composition gradient, Cl the value of the bulk
LETTER TO THE EDITOR
B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
composition of the ith species along the compositional gradient at a point far from the interface, C0 the bulk composition of the ith species against the compositional gradient, also at a point far from the interface, and the parameter b is given by x b ¼ pffiffiffiffiffiffi; 2 Dt where D is the (temperature dependent) diffusion coefficient and t the time. The error function, erfðbÞ; is given by Z b 2 2 p ffiffiffi erfðbÞ ¼ ey dy: p 0 Analysis of the concentration profiles of the Fe and Co at various positions and substitution of the appropriate values in the above equations gave the following results: DðFeÞ ¼ 3:28 1010 cm2/s and DðCoÞ ¼ 7:63 1010 cm2/s, both at a temperature of 1323 K. A typical EDS profile used for determination of the Fe and Co diffusion coefficients is shown in Fig. 1.
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Determination of rare earth diffusion coefficients was enabled by examining couples prepared with differing rare earth compositions, Nd2Fe10Co4B and Dy2Fe10Co4B, as shown in Fig. 2. The results of this calculation indicate that the rare earth diffusivity is much lower than that of the transition metals: DðNdÞ ¼ 2:3 1012 cm2/s and DðDyÞ ¼ 2:9 1012 cm2/s, also at a temperature of 1323 K.
4. Discussion The atomic radius of Nd is about 5% larger than that of Dy, and the covalent radius of Nd is about 3% larger than that of Dy. This would suggest, to a first approximation, that Nd might possess a lower diffusion coefficient than Dy in (Nd1xDyx)2(Fe0.714Co0.286)14B, which is consistent with the observations of this study. The observed difference in diffusivity between the two rare earth species is not large, DðNdÞ ¼ 2:3 1012 cm2/s and DðDyÞ ¼ 2:9 1012 cm2/s,
Fig. 1. Typical compositional profiles resulting from bonding of Nd2Fe8Co6B and Nd2Fe10Co4B at 1323 K for 1800 s.
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Fig. 2. Compositional profiles resulting from bonding of Nd2Fe10Co4B and Dy2Fe10Co4B at 1323 K for 18000 s. (structural details of the rare earth composition curves are shown in the insert).
yet the 20% difference exceeds the estimated experimental error of 10%. Given that the melting temperature of Nd metal is 1289 K while that of Dy is 1682 K, it would appear that rare earth atom size plays a more dominant role in determining lattice diffusion rates in the 2–14–1 system than relative bond strength. It is significant that the diffusion coefficients for Nd and Dy are relatively small in the 2–14–1 lattice. This suggests that the compositional gradient required to enable a functionally graded microstructure may be stable against the deleterious diffusional effects associated with an elevated temperature environment. For example, it would be possible in principle to form single domain powder particles of Nd2Fe10Co4B that are coated with an epitaxial layer of Dy2Fe10Co4B. Such a graded microstructure is expected to provide the high-energy product of Nd2Fe10Co4B and a Curie temperature of approximately 800 K, while the high coercivity of the Dy2Fe10Co4B outer layer would suppress nucleation of a reverse domain, a
process that occurs at particle surfaces. Such a graded microstructure could substantially raise the effective operating temperature of 2–14–1 permanent magnets. The diffusion coefficients for Nd and Dy in the 2–14–1 lattice as determined in this study suggest that a graded microstructure, once formed, would resist homogenization by diffusion during prolonged operation at elevated temperatures.
5. Conclusion The Grube solution to Fick’s second law was employed to estimate the diffusion coefficients of Fe and Co in Nd2(FexCo1x)14B and of Nd in Dy2(FexCo1x)14B and Dy in Nd2(FexCo1x)14B at 1323 K. Diffusion couples were assembled, annealed, sectioned, and analyzed with an EDS detector in a field emission electron microscope. Results for Fe and Co diffusion in Nd2(FexCo1x)14B gave values for the respective diffusion
LETTER TO THE EDITOR
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coefficients as DðFeÞ ¼ 3:28 1010 cm2/s and DðCoÞ ¼ 7:63 1010 cm2/s. The rare earth diffusivity in this system was found to be significantly lower than that of the transition metals, with DðNdÞ ¼2:3 1012 cm2/s in Dy2(FexCo1x)14B and DðDyÞ ¼ 2:9 1012 cm2/s in Nd2(FexCo1x)14B.
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contract W-7405-ENG-82. Funding was provided by the US Department of Energy Oakland Operations Office under contract DE-AC0398SF21560.
References Acknowledgements The authors wish to thank Larry Jones, Les Reed, and the staff of the Materials Preparation Center of Ames Laboratory for their assistance in preparing the samples used in these experiments. This work was performed at Ames Laboratory, operated by the US Department of Energy by Iowa State University under
[1] Group Arnold technical specifications, Group Arnold, Marengo, IL, USA, www.grouparnold.com. . [2] R. Grossinger, R. Krewenka, X.K. Sun, R. Eibler, H.R. Kirchmayr, K.H.J. Buschow, J. Less-Common Met. 124 (1986) 165. [3] C.D. Fuerst, J.F. Herbst, Appl. Phys. Lett. 54 (1989) 1068. [4] J.F. Herbst, Rev. Mod. Phys. 63 (4) (1991) 838. [5] K.W. Dennis, F.A. Laabs, B.A Cook, J.L. Harringa, A.M. Russell, R.W. McCallum, Observations of multi-phase microstructures in R2(Fe1xCox)14B where R=Nd or Dy, J. Magn. Magn. Mater., in press.
Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
Letter to the Editor
Diffusion of Fe, Co, Nd, and Dy in R2(Fe1xCox)14B where R=Nd or Dy B.A. Cook*, J.L. Harringa, F.C. Laabs, K.W. Dennis, A.M. Russell, R.W. McCallum Ames Laboratory of the USDOE, Iowa State University, 253 Spedding Hall, Ames, IA 50011, USA Received 13 December 2000; received in revised form 16 May 2001
Abstract Transition metal and rare earth diffusion coefficients at 1323 K in Dy2yNdy(Fe1xCox )14B were determined by field emission energy dispersive spectroscopy compositional analysis of diffusion couple specimens. Various arrangements of component materials and temperatures were examined in order to understand the mechanisms affecting diffusion of the components and to predict the stability of functionally graded microstructures consisting of a dysprosium-rich (Dy2yNdy (Fe1xCox )14B) outer layer and a neodymium-rich (Nd2(Fe1xCox)14B) interior. Estimates of the mutual interdiffusion coefficients of Dy, Nd, Fe, and Co in this system were obtained from the preparation of arc melted and annealed polycrystalline specimens, assuming that the diffusion coefficients were independent of concentration (Grube solution). Fifteen diffusion couples were prepared and heat treated at 1323 K for various times in order to provide data for calculation of the diffusion coefficients. The results indicate that the diffusion coefficients of Fe and Co (DFe ¼ 3:28 1010 cm2/s and DCo ¼ 7:63 1010 cm2/s) were significantly higher at 1323 K in this system than those for Dy and Nd (DNd ¼ 2:3 1012 cm2/s and DDy ¼ 2:9 1012 cm2/s). r 2001 Elsevier Science B.V. All rights reserved. PACS: 75.50Ww; 66.30.Jt; 81.70.Jb Keywords: Diffusion coefficients; Rare earth–iron–cobalt–boron permanent magnets; SEM–EDS; Functionally graded microstructure
1. Introduction Use of high performance permanent magnets in elevated temperature applications requires that the material concurrently possess both a high Curie temperature, to resist temperature-dependent demagnetization, and a high coercivity to resist demagnetization in the presence of an externally *Corresponding author. Tel.: +515-294-9673; fax: +515294-9579. E-mail address: [email protected] (B.A. Cook).
imposed reverse magnetic field. Conventional SmCo5 magnets have a coercivity of 730 kA/m, a Curie temperature (Tc ) of 1000 K, and a maximum energy product of 175 kJ/m3 [1] which make them attractive for use in elevated temperature applications. However, replacement of SmCo5 with a material having a higher coercivity and maximum energy product would likely to result in a significant increase in operating efficiency. Permanent magnets based on the intermetallic compound Nd2Fe14B exhibit a higher energy product, 320 kJ/ m3, and a much larger coercivity, 1120 kA/m, than
0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 3 7 8 - X
LETTER TO THE EDITOR
B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
SmCo5 [1]. Unfortunately, the current generation of Nd2Fe14B magnets have a relatively low Curie temperature, 585 K, which is close to the heat rejection temperature of many high temperature engine configurations. Consequently, use of existing Nd2Fe14B under these conditions can lead to thermal demagnetization of the magnets, which becomes a significant concern at temperatures greater than 80% of Tc : Development of an advanced, high Tc permanent magnet would have significant implications in electric motor and generator technologies. A reasonable goal is the development of a material having a coercivity and energy product comparable to existing Nd–Fe–B but with a Curie temperature at least 100 K higher. Numerous investigators have attempted to raise the Curie temperature of Nd2Fe14B by altering its composition, and these efforts have shown that partially replacing Fe with Co in Nd2Fe14B increases the Curie temperature to near 1000 K [2]. However, the coercivity of these Nd2(Fe1xCox)14B magnets is relatively low [3]. The objective of this study was to overcome the poor coercivity of Nd2(Fe1xCox)14B magnets by diffusing Dy into the outer surface of each Nd2(Fe1xCox)14B particle used in sintering the bulk magnet. A thin Dy outer layer would serve to frustrate reverse domain nucleation at the particle surface. Since reverse magnetic domains nucleate at particle surfaces, the Dy layer is expected to resist demagnetization of the entire particle in the presence of a reverse magnetic field, thereby increasing coercivity because of the higher magnetocrystalline anisotropy of the heavy rare earth [4]. Although the maximum theoretical energy product for Dy2Fe14B is significantly lower than that of Nd2Fe14B due to its lower saturation magnetization [4], the presence of Dy in a thin surface layer resulting from partial substitution in Nd2(Fe1xCox)14B would reduce the energy product of only a small fraction of total particle volume. The resulting functionally graded magnet may possess both a high coercivity and a high Curie temperature, while still maintaining an energy product nearly as large as that of pure Nd2Fe14B. A necessary requisite for this study is the determination of transition and rare earth metal diffusion coefficients in order to predict the stability of the
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functionally graded composition. In materials where composition gradients of these substitutional atoms exist, the mobility of the atoms is difficult to predict since no diffusion data have been reported. This study was performed in order to measure the diffusion coefficients for Fe and Co in Nd2(FexCo1x)14B, Nd in Dy2(FexCo1x)14B, and Dy in Nd2(FexCo1x)14B.
2. Experimental procedure Diffusion coefficients were measured by assembling pairs of cast and annealed single-phase compositions of either Nd2(FexCo1x)14B (for determination of transition metal diffusion) or R2(Fe0.714Co0.286)14B where R ¼ Nd or Dy (for determination of rare earth diffusion). The surfaces were ground with 320 and 600 grit SiC, polished using 1 m diamond paste, and rinsed with hexane. The specimens were placed with their polished surfaces facing each other in a BN-coated graphite holder which was positioned inside a controlled atmosphere furnace. The specimens were held together by a 560 g static load and the atmospheric pressure was reduced to 107 Torr. Fifteen diffusion couples were prepared and held at a temperature of 1323 K for various times in order to provide data for calculation of the transition metal and rare earth diffusion coefficients. Transition metal diffusion coefficient couples were held at this temperature for 30 min (1800 s) while the Nd and Dy diffusion couples were held for 300 min (18000 s) in order to accommodate the slower diffusion rates of the lanthanides. Analysis of the diffusion coefficients was accomplished by slicing each couple longitudinally, mounting in copper diallylphthalate resin along with DyFe2 and Nd2Fe8Co6B standards, and polishing with 0.25 m diamond paste. The compositional profiles were determined using an Amray field emission SEM equipped with an Oxford 1515 energy dispersive spectoscopy (EDS) system. Standardless, semi-quantitative SEM–EDS data generally lacks sufficient accuracy to enable determination of diffusion coefficients, since the
LETTER TO THE EDITOR
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B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
typical tungsten filament forms a ‘‘bloom’’ of electron–specimen interaction volume below the surface that degrades spatial resolution. Moreover, oxide or hydroxide layers over the polished surface absorb and scatter different wavelengths of emitted X-rays by varying amounts. For these reasons, the field emission SEM used in this study was operated at low accelerating voltages (10 kV) to produce a smaller, cleaner beam footprint with the necessary spatial resolution. In addition, standards with fixed compositions were mounted beside each specimen to standardize the EDS spectra and minimize errors associated with oxide and hydroxide layers on the specimen surfaces. The diffusion coefficients were determined by employing a solution to Fick’s second law corresponding to a constant and finite concentration of the diffusive species within the bulk of each component. The diffusion coefficients were assumed to be independent of concentration. Initial rare earth diffusion tests were conducted on pairs of disks with identical transition metal concentrations and only slightly different rare earth concentrations, Nd1.5Dy0.5Fe8Co6B and Nd2Fe8Co6B. Samples with a composition of Nd2Fe10Co4B were observed to retain a singlephase microstructure following a high temperature anneal. However, compositions with higher Co/Fe ratios, such as Nd2Fe8Co6B, were found to segregate into three phases upon annealing. The reason for this decomposition remains uncertain and is the subject of a separate publication [5]. The presence of multiple phases complicates analysis due to the need for the electron beam path to fall within a single-phase region. Once the beam strikes a secondary phase, the anomalous composition violates boundary conditions assumed in the solution of Fick’s law. Moreover, it was found that the relatively small difference in rare earth concentration between these two samples did not provide sufficiently good statistics to enable reliable calculation of the diffusion coefficients. Another concern with the possible phase decomposition of the material is the formation of a large number of sub-micron interfaces between the matrix and precipitate phase, which could serve as diffusional ‘‘short circuit’’ paths giving rise to anomalous values for the diffusivity. These pre-
cipitates may nucleate as nanometer-sized zones, as observed in aged metastable Al–Cu alloys, the size of which would lie below the resolution limit of the SEM. For these reasons, additional diffusion couples were prepared with the nominal compositions Nd2Fe10Co4B and Dy2Fe10Co4B. A single-phase microstructure was observed in these systems which enabled determination of the rare earth diffusivity using the SEM–EDS method described above. It should be noted that studies of diffusion phenomena in condensed matter are best conducted on oriented, single crystal specimens, for which the absence of defects allows unambiguous interpretation of compositional data. For example, at moderate temperatures grain boundary diffusion occurs at a faster rate than bulk diffusion. The presence of defects (porosity, secondary phase precipitates, and oxide inclusions) complicates interpretation of elemental analysis using energy dispersive techniques. Consequently, compositional profiles obtained by EDS do not directly lead to partitioning of the data into grain boundary versus lattice diffusion. As a result, interpretation of the active diffusion mechanisms is somewhat limited. However, preparation of single crystalline samples was beyond the scope of this project, prediction of the relative diffusivities of the rare earth and transition metal atoms based on cast and annealed polycrystalline samples provides a useful approximation of the true diffusion coefficients.
3. Diffusion coefficient results The transition metal diffusion coefficients were determined by employing the Grube solution to Fick’s second law for a pair of semi-infinite solids, wherein the diffusion coefficients are independent of concentration. Within this framework, the solution to Fick’s second law takes the form CðxÞ ¼ Cl þ
C0 Cl ½1 erf ðbÞ; 2
ð1Þ
where CðxÞ is the composition at a point x along the composition gradient, Cl the value of the bulk
LETTER TO THE EDITOR
B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
composition of the ith species along the compositional gradient at a point far from the interface, C0 the bulk composition of the ith species against the compositional gradient, also at a point far from the interface, and the parameter b is given by x b ¼ pffiffiffiffiffiffi; 2 Dt where D is the (temperature dependent) diffusion coefficient and t the time. The error function, erfðbÞ; is given by Z b 2 2 p ffiffiffi erfðbÞ ¼ ey dy: p 0 Analysis of the concentration profiles of the Fe and Co at various positions and substitution of the appropriate values in the above equations gave the following results: DðFeÞ ¼ 3:28 1010 cm2/s and DðCoÞ ¼ 7:63 1010 cm2/s, both at a temperature of 1323 K. A typical EDS profile used for determination of the Fe and Co diffusion coefficients is shown in Fig. 1.
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Determination of rare earth diffusion coefficients was enabled by examining couples prepared with differing rare earth compositions, Nd2Fe10Co4B and Dy2Fe10Co4B, as shown in Fig. 2. The results of this calculation indicate that the rare earth diffusivity is much lower than that of the transition metals: DðNdÞ ¼ 2:3 1012 cm2/s and DðDyÞ ¼ 2:9 1012 cm2/s, also at a temperature of 1323 K.
4. Discussion The atomic radius of Nd is about 5% larger than that of Dy, and the covalent radius of Nd is about 3% larger than that of Dy. This would suggest, to a first approximation, that Nd might possess a lower diffusion coefficient than Dy in (Nd1xDyx)2(Fe0.714Co0.286)14B, which is consistent with the observations of this study. The observed difference in diffusivity between the two rare earth species is not large, DðNdÞ ¼ 2:3 1012 cm2/s and DðDyÞ ¼ 2:9 1012 cm2/s,
Fig. 1. Typical compositional profiles resulting from bonding of Nd2Fe8Co6B and Nd2Fe10Co4B at 1323 K for 1800 s.
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Fig. 2. Compositional profiles resulting from bonding of Nd2Fe10Co4B and Dy2Fe10Co4B at 1323 K for 18000 s. (structural details of the rare earth composition curves are shown in the insert).
yet the 20% difference exceeds the estimated experimental error of 10%. Given that the melting temperature of Nd metal is 1289 K while that of Dy is 1682 K, it would appear that rare earth atom size plays a more dominant role in determining lattice diffusion rates in the 2–14–1 system than relative bond strength. It is significant that the diffusion coefficients for Nd and Dy are relatively small in the 2–14–1 lattice. This suggests that the compositional gradient required to enable a functionally graded microstructure may be stable against the deleterious diffusional effects associated with an elevated temperature environment. For example, it would be possible in principle to form single domain powder particles of Nd2Fe10Co4B that are coated with an epitaxial layer of Dy2Fe10Co4B. Such a graded microstructure is expected to provide the high-energy product of Nd2Fe10Co4B and a Curie temperature of approximately 800 K, while the high coercivity of the Dy2Fe10Co4B outer layer would suppress nucleation of a reverse domain, a
process that occurs at particle surfaces. Such a graded microstructure could substantially raise the effective operating temperature of 2–14–1 permanent magnets. The diffusion coefficients for Nd and Dy in the 2–14–1 lattice as determined in this study suggest that a graded microstructure, once formed, would resist homogenization by diffusion during prolonged operation at elevated temperatures.
5. Conclusion The Grube solution to Fick’s second law was employed to estimate the diffusion coefficients of Fe and Co in Nd2(FexCo1x)14B and of Nd in Dy2(FexCo1x)14B and Dy in Nd2(FexCo1x)14B at 1323 K. Diffusion couples were assembled, annealed, sectioned, and analyzed with an EDS detector in a field emission electron microscope. Results for Fe and Co diffusion in Nd2(FexCo1x)14B gave values for the respective diffusion
LETTER TO THE EDITOR
B.A. Cook et al. / Journal of Magnetism and Magnetic Materials 233 (2001) L136–L141
coefficients as DðFeÞ ¼ 3:28 1010 cm2/s and DðCoÞ ¼ 7:63 1010 cm2/s. The rare earth diffusivity in this system was found to be significantly lower than that of the transition metals, with DðNdÞ ¼2:3 1012 cm2/s in Dy2(FexCo1x)14B and DðDyÞ ¼ 2:9 1012 cm2/s in Nd2(FexCo1x)14B.
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contract W-7405-ENG-82. Funding was provided by the US Department of Energy Oakland Operations Office under contract DE-AC0398SF21560.
References Acknowledgements The authors wish to thank Larry Jones, Les Reed, and the staff of the Materials Preparation Center of Ames Laboratory for their assistance in preparing the samples used in these experiments. This work was performed at Ames Laboratory, operated by the US Department of Energy by Iowa State University under
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