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The effect of evolving grain shape and alignment on the coercivity in thermomechanically deformed Nd13.9(Fe0.92Co0.08)80.3B5.3Ga0.5 permanent magnets
Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
The e!ect of evolving grain shape and alignment on the coercivity in thermomechanically deformed Nd (Fe Co ) B Ga permanent magnets D.C. Crew , L.H. Lewis *, V. Panchanathan
Energy Sciences and Technology Department, Brookhaven National Laboratory, Building 480, Upton NY 11973-5000, USA Magnequench International, Inc., Anderson, IN, USA Received 10 July 2000; received in revised form 15 November 2000
Abstract A series of samples of nominally identical composition have been melt-quenched and thermomechanically deformed to varying degrees, resulting in a variation in crystallographic alignment. The e!ect of the alignment on the coercivity has been studied using measurements of the temperature dependence of coercivity. The analysis was performed using a well-known phenomenological model which relates the coercivity to the anisotropy "eld, through a parameter a, and the saturation magnetization, through an e!ective demagnetization coe$cient N . It was discovered that the trends in a and N as a function of crystallographic grain alignment are the opposite to what is expected and measured previously in analogous sintered samples of varying crystallographic alignment. An explanation for this behavior is proposed in which the evolving grain shape and grain boundary topography caused by deformation becomes the controlling factor in the coercivity rather than the crystallographic alignment of the grains. 2001 Elsevier Science B.V. All rights reserved. Keywords: Coercivity; Crystallographic alignment; Permanent magnet; Demagnetization
1. Introduction Studies to de"ne the microstructural factors affecting coercivity in advanced magnetic materials are necessary to their continued performance optimization. Control of the microstructure is the key to the development of desired values of coercivity, whether the objective is to attain a high value in permanent magnets or very low values in soft
* Corresponding author. Tel.: #1-631-344-2861; fax: #1631-344-4071. E-mail address: [email protected] (L.H. Lewis).
magnets. Knowledge of the microstructural in#uence on the properties of a magnet allows those properties to be tailored to the application. The coercivity, while an easily measured property, depends in a complicated manner on the constituent microstructure of the magnet. A number of approaches have been developed in an attempt to quantify the relationship between microstructure and coercivity. The simplest approach is phenomenological, originally based on the ideas of Brown [1] and Aharoni [2] and employed successfully by Hirosawa and Tsubokawa [3] and others [4}7]. In this approach, the coercivity is described as a function of the anisotropy "eld reduced by dipolar
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 2 7 2 - 5
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interactions within the material H (¹)"aH (¹)!N M (¹),
(1)
where H (¹) is the coercivity, H (¹) is the anisot ropy "eld and M (¹) is the saturation magneti zation of the material, all of which are temperature dependent. The parameter a describes the e!ect of the microstructure on the coercivity. a can range from 0 to 1, where a value of a"0 implies the maximum coercivity possible. The parameter N is an e!ective demagnetization factor which accounts for dipolar interactions and the e!ects of the demagnetization "eld at the corners of grains. These interactions assist in reversal and further reduce the coercivity. This approach was successfully used in the study of sintered NdFeB magnets in which the increase in coercivity after post-sintering heat treatment was followed [3]. In that study transmission electron microscopy measurements revealed that the increase in coercivity was accompanied by a smoothing of grain boundaries after the heat treatment. This smoothing appeared to cause a decrease in the value of N , indicating that the smoothing of grain boundaries caused a removal of areas of reverse nucleation which led to the increase in coercivity observed with annealing. The simple phenomenological formalism has been extended by KronmuK ller and co-workers [8}10] using an approach based on micromagnetic calculations in which the nucleation and pinning of domain walls occurs in regions of reduced anisotropy as compared with the bulk. The e!ects of texturing, di!erent reversal mechanisms and exchange interactions are included in the model by modifying the value of a. The phenomenological theory has also been extended in a di!erent direction into a &global' model of coercivity by Givord et al. [11]. In this latter model, the mechanism of magnetization reversal responsible for the behavior of coercivity is not postulated. The coercivity is instead deduced from consideration of the energy required to nucleate and propagate areas of reverse magnetization. The micromagnetic and global models of coercivity have been reviewed by Givord and Rossignol [12] and recently results of the two models have been compared in the same material by Kou et al. [13].
In the present work, the simpler phenomenological model of Hirosawa and Tsubokawa [3] has been used to study the e!ect of grain shape and grain alignment on coercivity, with the objective of elucidating the di!erent contributions to the coercivity through the variation of the parameters a and N . 2. Experimental A series of samples of nominally identical composition, Nd (Fe Co ) B Ga , were melt-quenched, hot-pressed then thermomechanically deformed (die-upset) to varying degrees to give an almost continuous variation of grain shape and crystallographic alignment. The degree of deformation was characterized by the percentage reduction in height of the samples. Materials studied had been deformed to 0%, 30%, 42%, 55%, 60% and 70% reductions. Additional details of the sample preparation are available in Ref. [14]. The samples for the magnetic study were needle shaped and cut from the center of each die-upset button, which was approximately 6 mm in height by 25 mm in diameter. The sample shape guaranteed a negligible demagnetization factor. The texture of these samples has been characterized as a function of position by synchrotron transmission X}ray diffraction measurements [14], the magnetization reversal mechanism has been studied by IRM and DCD measurements combined with reversible magnetization analysis [15] and the evolving domain structure with increasing applied "eld has been studied with magnetic force microscopy [16]. The experimental procedure employed in this work to determine the values of a and N consis ted of measuring a series of hysteresis loops for each deformed sample at increasing temperatures, from 100 K to room temperature, using a SQUID magnetometer with a maximum applied "eld of 50 kOe. For measurements below room temperature the sample was cooled from room temperature in a "eld of 50 kOe to ensure magnetic saturation prior to measurement. Below a temperature of 100 K the coercivity of the sample exceeded the maximum "eld available. It is usual in studies such as these to de"ne the coercivity as the "eld at which
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
263
the irreversible susceptibility reaches a maximum [12]. In the samples studied in this work the magnitude of the reversible susceptibility is small [15], thus the irreversible susceptibility is nearly the same as the total susceptibility. It was possible therefore to de"ne the coercivity as the "eld at which the hysteresis curve exhibits the maximum slope. Using Eq. (1) and plotting H /M vs. H /M as a function of temperature, the parameters a and N were determined by "tting the data to a straight line. The values of H used in Eq. (1) were taken from the paper of Grossinger et al. [17] and M (¹) was calculated by extrapolating the experi mentally measured high-"eld data ('25 kOe) using an expression of the form
a b . M(H)"M (¹) 1! ! H H
(2) Fig. 1. H /4pM vs. H /4pM for the 0%, 30% and 70% die upset samples. The lines shown are the lines of best "t used to determine a and N from Eq. (1).
3. Results and discussion The results for the plots of H /M vs. H /M for all samples were linear and gave well-characterized values of a and N , as evidenced by the data for the 0%, 30% and 70% deformed samples shown in Fig. 1. The resulting values of a and N are shown for all samples in Fig. 2. The samples are labeled by the degree of die-upset with the corresponding remanence ratio (M /M ) given in parentheses. The trend of decreasing coercivity of the investigated samples is indicated in the "gure by the arrow. As the alignment increases with degree of deformation, as measured by X-ray di!raction rocking curves [14], the coercivity was observed to decrease. Also shown in Fig. 2 for comparative purposes is data from the work of Hirosawa and Tsubokawa [3] for sintered PrFeB magnets with varying degrees of particle alignment, labeled by the remanence ratio (M /M ). The results of Fig. 2 show a distinct linkage between a and N as the degree of alignment is changed in both the melt-quenched and deformed samples as well as in the sintered samples shown for comparison. It should be noted, however, that the data from the melt-quenched and deformed samples display a trend with coercivity that is opposite
to those displayed by the sintered data. The sintered data show the expected behavior from measurements of coercivity as a function of orientation [12], i.e. as the degree of alignment is increased the coercivity decreases and a and N also de crease. The melt-quenched data show a decrease in coercivity as alignment is increased, but this is accompanied by an increase in a and N . To understand why the sintered material displays the expected behavior, the e!ect of increasing alignment on a and N must be carefully studied. The available experimental evidence and theoretical justi"cation for a decrease of a and N with increasing alignment has been summarized by Givord and Rossignol [12]. A brief summary of the explanation of the experimental evidence in the literature will be given here. If the coercivity is low relative to the anisotropy "eld, as in most permanent magnets, "eld-induced rotation of the moments out of the easy axis can be neglected. In this situation, only the component of applied "eld acting along the easy axis is responsible for switching the magnetization of the grain. The coercive "eld is then expected to vary as 1/cos h where h is the angle of the easy axis of the grain with respect to the "eld direction.
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Fig. 2. N /4p vs. a for the melt-quenched NdFeB samples studied in this work and for a set of sintered PrFeB samples studied by Hirosawa and Tsubokawa [3]. The numbers on the data of Hirosawa and Tsubokawa [3] indicate the degree of alignment (M /M ) of the samples. The degree of alignment is also indicated in brackets for the melt-quenched samples. The trend of decreasing coercivity is shown by the arrows. The lines passing through the data are a guide to the eye. N /4p is plotted here rather than N to allow direct comparison with other researchers using SI units, rather than the CGS units used here.
If it is assumed that the coercivity of a selected grain follows a 1/cos h law as the easy axis is rotated by an angle h with respect to the "eld, then as the degree of alignment of the grains relative to the applied "eld axis increases, the coercivity decreases because the mean coercivity of the grains decreases. This argument leads to a decrease in the value of a. At the same time, as grains become more homogenous in their alignment, it is expected that dipolar interactions will decrease because misaligned grains are one source of divergent magnetization which leads to increased dipolar interactions. Thus as alignment of the grains increases the expected behavior is that a and N will
decrease. This matches the data observed in the sintered samples. To explain the observed trend in a in the meltquenched material as the degree of deformation, and hence crystallographic alignment, is increased, it is necessary to combine the dependence of coercivity H on the angle h with the degree of inter grain exchange interaction active in the material. For materials in which intergrain exchange interactions are small, such as commercial sintered NdFeB magnets, each grain reverses individually and the coercivity is determined by the mean coercivity of the individual grains (as discussed above). For materials with larger intergrain exchange interactions, such as melt-quenched NdFeB magnets, the coercivity of the ensemble will be determined by the minimum grain coercivity which acts as a weak link and gives rise to an avalanche-type magnetization reversal. Thus in melt-quenched materials a would be expected to remain approximately constant as the degree of crystallographic alignment is increased because the coercivity is determined by those grains with small orientations to the applied "eld direction. The samples investigated in this work show a trend of coercivity which is similar to that observed in the sintered samples, namely that coercivity decreases as alignment of the grains increases. However a and N display exactly the opposite trend to that expected because both parameters increase as the degree of alignment increases. This increase signals the presence of factors other than degree of grain alignment that a!ect the global coercivity in these melt-quenched samples. During the deformation process, as the constituent grain alignment increases the grain boundary topography and grain shape also change. The evolving grain character of the deformed samples is in contrast to that found in sintered samples. In sintered samples the grains are nominally identical in aligned and non-aligned material before sintering, and it is likely that grain boundary changes are similar in aligned and non-aligned material during the sintering process. It is postulated that thermomechanical deformation creates a changing grain boundary topography and grain shape in meltquenched and deformed samples that a!ects both a and N .
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
Two mechanisms have been identi"ed which result in alignment of grains during the die-upsetting process in Nd Fe B. Firstly, the rotation of grains into favorable orientations is aided by a liquid grain boundary phase [14]. If the liquid grain boundary phase, on solidi"cation, caused a decrease in grain boundary defects then an increase in the value of a would be observed because potential sites of reverse nucleation would be removed, promoting a more ideal reversal mechanism. The second mechanism for grain alignment during deformation is preferential growth in the (ab) plane of favorably oriented grains. During the deformation process this preferential grain growth in the (ab) plane changes the grain shape, an e!ect that could result in an increase in N if the grain became more angular with sharp corners. These two e!ects resulting from the alignment mechanisms during deformation, grain rotation and shape change, could result in the linked increase in a and N observed in the deformed, melt-quenched material. It is postulated that the coercivity still decreases, even though a increases, because the variation of coercivity is dominated by the increase in N . This behavior indicates that the changing grain shape has a marked e!ect on coercivity in this material, and is more important than grain boundary topographic or chemical changes. The values of a and N measured in this work for deformed melt-quenched materials can be compared with the values measured by Rieger et al. [18] for isotropic melt-quenched NdFeB containing Ga and Mo alloying additions, subject to various heat treatments. The values of a measured in the present work must be multiplied by a factor of 2 to compare with the values of a measured by ) Rieger et al. to account for the di!erence between Eq. (1) and that used by Rieger et al. Apart from the undeformed (0%) sample the values of a measured in the present work are somewhat lower than those measured by Rieger et al., consistent with the lower coercivities of the present samples. Similar trends were observed however by Rieger et al. in that both a and N were correlated, both generally increas ing with annealing treatment. From electron microscopy studies Rieger et al. concluded that in their samples the correlated increase of a and
265
N resulted from the annealing treatment which produced not only more perfect grain boundaries, increasing a, but also a polyhedral grain shape, increasing N . This conclusion is similar to the hypothesis presented in this paper that the thermomechanical deformation process results in more perfect grain boundaries but also sharper, more polyhedral, grains.
4. Conclusion In die-upset melt-quenched NdFeB magnets, the empirical parameters a and N increase as the degree of crystallographic alignment of the grains in the magnet increases. This trend is the opposite to that observed in sintered magnets. The trend of increasing values of a and N as the coercivity decreases, while opposite to that of sintered magnets, is similar to that observed in isotropic meltquenched magnets subject to various annealing treatments. The trend in a and N with degree of deformation is most likely caused by the changes in the morphology of the grains as a result of the deformation process. The trend in a and N ob served can be explained by the grain boundary becoming more perfect as deformation progresses, which increases a, while at the same time the grains become more polyhedral, with sharp corners, which increases N and ultimately is the control ling factor in leading to a decrease in coercivity with increased thermomechanical deformation.
Acknowledgements D.C.C. and L.H.L. would like to acknowledge helpful discussions with Dr. D. Givord. This research was performed under the auspices of the US Department of Energy, Division of Material Sciences, O$ce of Basic Energy Sciences under Contract No. DE-AC02-98CH10886.
References [1] W.F. Brown, Rev. Mod. Phys. 17 (1945) 15. [2] A. Aharoni, Rev. Mod. Phys. 34 (1962) 227.
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[3] S. Hirosawa, Y. Tsubokawa, J. Magn. Magn. Mater. 84 (1990) 309. [4] M. Sagawa, S. Hirosawa, H. Yamamoto, S. Fujimura, Y. Matsuura, Jpn. J. Appl. Phys. 26 (1987) 785. [5] M. Sagawa, S. Hirosawa, J. Phys. (Paris) 49 (1988) C8}617. [6] S. Hirosawa, Y. Tsubokawa, R. Shimizu, Tenth International Workshop on Rare-Earth Magnets and Their Applications, The Society of Non-Traditional Technology, Tokyo, 1989, p. 465. [7] W. Tang, S. Zhou, R. Wang, J. Magn. Magn. Mater. 75 (1988) 416. [8] H. KronmuK ller, Phys. Stat. Sol. B 144 (1987) 385. [9] H. KronmuK ller, K.D. Durst, G. Martinek, J. Magn. Magn. Mater. 69 (1987) 149. [10] H. KronmuK ller, K.D. Durst, S. Hock, G. Martinek, J. Phys (Paris) 49 (1988) C8}623.
[11] D. Givord, P. Tenaud, T. Viadieu, IEEE Trans. Magn. 24 (1988) 1921. [12] D. Givord, M.F. Rossignol, Coercivity; in: J.M.D. Coey (Ed.), Rare-earth iron permanent magnets, Clarendon Press, Oxford, 1966, ch. 5. [13] X.C. Kou, H. KronmuK ller, D. Givord, M.F. Rossignol, Phys. Rev. B 50 (1994) 3849. [14] L.H. Lewis, T.R. Thurston, V. Panchanathan, U. Wildgruber, D.O. Welch, J. Appl. Phys. 82 (1997) 3430. [15] D.C. Crew, L.H. Lewis, D.O. Welch, V. Panchanathan, J. Appl. Phys. 87 (2000) 6571. [16] D.C. Crew, L.H. Lewis, V. Panchanathan, unpublished. [17] R. Grossinger, X.K. Sun, R. Eibler, K.H.J. Buschow, H.R. Kirchmayr, J. Magn. Magn. Mater. 58 (1986) 55. [18] G. Rieger, M. Seeger, L. Sun, H. KronmuK ller, J. Magn. Magn. Mater. 151 (1995) 193.
The e!ect of evolving grain shape and alignment on the coercivity in thermomechanically deformed Nd (Fe Co ) B Ga permanent magnets D.C. Crew , L.H. Lewis *, V. Panchanathan
Energy Sciences and Technology Department, Brookhaven National Laboratory, Building 480, Upton NY 11973-5000, USA Magnequench International, Inc., Anderson, IN, USA Received 10 July 2000; received in revised form 15 November 2000
Abstract A series of samples of nominally identical composition have been melt-quenched and thermomechanically deformed to varying degrees, resulting in a variation in crystallographic alignment. The e!ect of the alignment on the coercivity has been studied using measurements of the temperature dependence of coercivity. The analysis was performed using a well-known phenomenological model which relates the coercivity to the anisotropy "eld, through a parameter a, and the saturation magnetization, through an e!ective demagnetization coe$cient N . It was discovered that the trends in a and N as a function of crystallographic grain alignment are the opposite to what is expected and measured previously in analogous sintered samples of varying crystallographic alignment. An explanation for this behavior is proposed in which the evolving grain shape and grain boundary topography caused by deformation becomes the controlling factor in the coercivity rather than the crystallographic alignment of the grains. 2001 Elsevier Science B.V. All rights reserved. Keywords: Coercivity; Crystallographic alignment; Permanent magnet; Demagnetization
1. Introduction Studies to de"ne the microstructural factors affecting coercivity in advanced magnetic materials are necessary to their continued performance optimization. Control of the microstructure is the key to the development of desired values of coercivity, whether the objective is to attain a high value in permanent magnets or very low values in soft
* Corresponding author. Tel.: #1-631-344-2861; fax: #1631-344-4071. E-mail address: [email protected] (L.H. Lewis).
magnets. Knowledge of the microstructural in#uence on the properties of a magnet allows those properties to be tailored to the application. The coercivity, while an easily measured property, depends in a complicated manner on the constituent microstructure of the magnet. A number of approaches have been developed in an attempt to quantify the relationship between microstructure and coercivity. The simplest approach is phenomenological, originally based on the ideas of Brown [1] and Aharoni [2] and employed successfully by Hirosawa and Tsubokawa [3] and others [4}7]. In this approach, the coercivity is described as a function of the anisotropy "eld reduced by dipolar
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 2 7 2 - 5
262
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
interactions within the material H (¹)"aH (¹)!N M (¹),
(1)
where H (¹) is the coercivity, H (¹) is the anisot ropy "eld and M (¹) is the saturation magneti zation of the material, all of which are temperature dependent. The parameter a describes the e!ect of the microstructure on the coercivity. a can range from 0 to 1, where a value of a"0 implies the maximum coercivity possible. The parameter N is an e!ective demagnetization factor which accounts for dipolar interactions and the e!ects of the demagnetization "eld at the corners of grains. These interactions assist in reversal and further reduce the coercivity. This approach was successfully used in the study of sintered NdFeB magnets in which the increase in coercivity after post-sintering heat treatment was followed [3]. In that study transmission electron microscopy measurements revealed that the increase in coercivity was accompanied by a smoothing of grain boundaries after the heat treatment. This smoothing appeared to cause a decrease in the value of N , indicating that the smoothing of grain boundaries caused a removal of areas of reverse nucleation which led to the increase in coercivity observed with annealing. The simple phenomenological formalism has been extended by KronmuK ller and co-workers [8}10] using an approach based on micromagnetic calculations in which the nucleation and pinning of domain walls occurs in regions of reduced anisotropy as compared with the bulk. The e!ects of texturing, di!erent reversal mechanisms and exchange interactions are included in the model by modifying the value of a. The phenomenological theory has also been extended in a di!erent direction into a &global' model of coercivity by Givord et al. [11]. In this latter model, the mechanism of magnetization reversal responsible for the behavior of coercivity is not postulated. The coercivity is instead deduced from consideration of the energy required to nucleate and propagate areas of reverse magnetization. The micromagnetic and global models of coercivity have been reviewed by Givord and Rossignol [12] and recently results of the two models have been compared in the same material by Kou et al. [13].
In the present work, the simpler phenomenological model of Hirosawa and Tsubokawa [3] has been used to study the e!ect of grain shape and grain alignment on coercivity, with the objective of elucidating the di!erent contributions to the coercivity through the variation of the parameters a and N . 2. Experimental A series of samples of nominally identical composition, Nd (Fe Co ) B Ga , were melt-quenched, hot-pressed then thermomechanically deformed (die-upset) to varying degrees to give an almost continuous variation of grain shape and crystallographic alignment. The degree of deformation was characterized by the percentage reduction in height of the samples. Materials studied had been deformed to 0%, 30%, 42%, 55%, 60% and 70% reductions. Additional details of the sample preparation are available in Ref. [14]. The samples for the magnetic study were needle shaped and cut from the center of each die-upset button, which was approximately 6 mm in height by 25 mm in diameter. The sample shape guaranteed a negligible demagnetization factor. The texture of these samples has been characterized as a function of position by synchrotron transmission X}ray diffraction measurements [14], the magnetization reversal mechanism has been studied by IRM and DCD measurements combined with reversible magnetization analysis [15] and the evolving domain structure with increasing applied "eld has been studied with magnetic force microscopy [16]. The experimental procedure employed in this work to determine the values of a and N consis ted of measuring a series of hysteresis loops for each deformed sample at increasing temperatures, from 100 K to room temperature, using a SQUID magnetometer with a maximum applied "eld of 50 kOe. For measurements below room temperature the sample was cooled from room temperature in a "eld of 50 kOe to ensure magnetic saturation prior to measurement. Below a temperature of 100 K the coercivity of the sample exceeded the maximum "eld available. It is usual in studies such as these to de"ne the coercivity as the "eld at which
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
263
the irreversible susceptibility reaches a maximum [12]. In the samples studied in this work the magnitude of the reversible susceptibility is small [15], thus the irreversible susceptibility is nearly the same as the total susceptibility. It was possible therefore to de"ne the coercivity as the "eld at which the hysteresis curve exhibits the maximum slope. Using Eq. (1) and plotting H /M vs. H /M as a function of temperature, the parameters a and N were determined by "tting the data to a straight line. The values of H used in Eq. (1) were taken from the paper of Grossinger et al. [17] and M (¹) was calculated by extrapolating the experi mentally measured high-"eld data ('25 kOe) using an expression of the form
a b . M(H)"M (¹) 1! ! H H
(2) Fig. 1. H /4pM vs. H /4pM for the 0%, 30% and 70% die upset samples. The lines shown are the lines of best "t used to determine a and N from Eq. (1).
3. Results and discussion The results for the plots of H /M vs. H /M for all samples were linear and gave well-characterized values of a and N , as evidenced by the data for the 0%, 30% and 70% deformed samples shown in Fig. 1. The resulting values of a and N are shown for all samples in Fig. 2. The samples are labeled by the degree of die-upset with the corresponding remanence ratio (M /M ) given in parentheses. The trend of decreasing coercivity of the investigated samples is indicated in the "gure by the arrow. As the alignment increases with degree of deformation, as measured by X-ray di!raction rocking curves [14], the coercivity was observed to decrease. Also shown in Fig. 2 for comparative purposes is data from the work of Hirosawa and Tsubokawa [3] for sintered PrFeB magnets with varying degrees of particle alignment, labeled by the remanence ratio (M /M ). The results of Fig. 2 show a distinct linkage between a and N as the degree of alignment is changed in both the melt-quenched and deformed samples as well as in the sintered samples shown for comparison. It should be noted, however, that the data from the melt-quenched and deformed samples display a trend with coercivity that is opposite
to those displayed by the sintered data. The sintered data show the expected behavior from measurements of coercivity as a function of orientation [12], i.e. as the degree of alignment is increased the coercivity decreases and a and N also de crease. The melt-quenched data show a decrease in coercivity as alignment is increased, but this is accompanied by an increase in a and N . To understand why the sintered material displays the expected behavior, the e!ect of increasing alignment on a and N must be carefully studied. The available experimental evidence and theoretical justi"cation for a decrease of a and N with increasing alignment has been summarized by Givord and Rossignol [12]. A brief summary of the explanation of the experimental evidence in the literature will be given here. If the coercivity is low relative to the anisotropy "eld, as in most permanent magnets, "eld-induced rotation of the moments out of the easy axis can be neglected. In this situation, only the component of applied "eld acting along the easy axis is responsible for switching the magnetization of the grain. The coercive "eld is then expected to vary as 1/cos h where h is the angle of the easy axis of the grain with respect to the "eld direction.
264
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
Fig. 2. N /4p vs. a for the melt-quenched NdFeB samples studied in this work and for a set of sintered PrFeB samples studied by Hirosawa and Tsubokawa [3]. The numbers on the data of Hirosawa and Tsubokawa [3] indicate the degree of alignment (M /M ) of the samples. The degree of alignment is also indicated in brackets for the melt-quenched samples. The trend of decreasing coercivity is shown by the arrows. The lines passing through the data are a guide to the eye. N /4p is plotted here rather than N to allow direct comparison with other researchers using SI units, rather than the CGS units used here.
If it is assumed that the coercivity of a selected grain follows a 1/cos h law as the easy axis is rotated by an angle h with respect to the "eld, then as the degree of alignment of the grains relative to the applied "eld axis increases, the coercivity decreases because the mean coercivity of the grains decreases. This argument leads to a decrease in the value of a. At the same time, as grains become more homogenous in their alignment, it is expected that dipolar interactions will decrease because misaligned grains are one source of divergent magnetization which leads to increased dipolar interactions. Thus as alignment of the grains increases the expected behavior is that a and N will
decrease. This matches the data observed in the sintered samples. To explain the observed trend in a in the meltquenched material as the degree of deformation, and hence crystallographic alignment, is increased, it is necessary to combine the dependence of coercivity H on the angle h with the degree of inter grain exchange interaction active in the material. For materials in which intergrain exchange interactions are small, such as commercial sintered NdFeB magnets, each grain reverses individually and the coercivity is determined by the mean coercivity of the individual grains (as discussed above). For materials with larger intergrain exchange interactions, such as melt-quenched NdFeB magnets, the coercivity of the ensemble will be determined by the minimum grain coercivity which acts as a weak link and gives rise to an avalanche-type magnetization reversal. Thus in melt-quenched materials a would be expected to remain approximately constant as the degree of crystallographic alignment is increased because the coercivity is determined by those grains with small orientations to the applied "eld direction. The samples investigated in this work show a trend of coercivity which is similar to that observed in the sintered samples, namely that coercivity decreases as alignment of the grains increases. However a and N display exactly the opposite trend to that expected because both parameters increase as the degree of alignment increases. This increase signals the presence of factors other than degree of grain alignment that a!ect the global coercivity in these melt-quenched samples. During the deformation process, as the constituent grain alignment increases the grain boundary topography and grain shape also change. The evolving grain character of the deformed samples is in contrast to that found in sintered samples. In sintered samples the grains are nominally identical in aligned and non-aligned material before sintering, and it is likely that grain boundary changes are similar in aligned and non-aligned material during the sintering process. It is postulated that thermomechanical deformation creates a changing grain boundary topography and grain shape in meltquenched and deformed samples that a!ects both a and N .
D.C. Crew et al. / Journal of Magnetism and Magnetic Materials 223 (2001) 261}266
Two mechanisms have been identi"ed which result in alignment of grains during the die-upsetting process in Nd Fe B. Firstly, the rotation of grains into favorable orientations is aided by a liquid grain boundary phase [14]. If the liquid grain boundary phase, on solidi"cation, caused a decrease in grain boundary defects then an increase in the value of a would be observed because potential sites of reverse nucleation would be removed, promoting a more ideal reversal mechanism. The second mechanism for grain alignment during deformation is preferential growth in the (ab) plane of favorably oriented grains. During the deformation process this preferential grain growth in the (ab) plane changes the grain shape, an e!ect that could result in an increase in N if the grain became more angular with sharp corners. These two e!ects resulting from the alignment mechanisms during deformation, grain rotation and shape change, could result in the linked increase in a and N observed in the deformed, melt-quenched material. It is postulated that the coercivity still decreases, even though a increases, because the variation of coercivity is dominated by the increase in N . This behavior indicates that the changing grain shape has a marked e!ect on coercivity in this material, and is more important than grain boundary topographic or chemical changes. The values of a and N measured in this work for deformed melt-quenched materials can be compared with the values measured by Rieger et al. [18] for isotropic melt-quenched NdFeB containing Ga and Mo alloying additions, subject to various heat treatments. The values of a measured in the present work must be multiplied by a factor of 2 to compare with the values of a measured by ) Rieger et al. to account for the di!erence between Eq. (1) and that used by Rieger et al. Apart from the undeformed (0%) sample the values of a measured in the present work are somewhat lower than those measured by Rieger et al., consistent with the lower coercivities of the present samples. Similar trends were observed however by Rieger et al. in that both a and N were correlated, both generally increas ing with annealing treatment. From electron microscopy studies Rieger et al. concluded that in their samples the correlated increase of a and
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N resulted from the annealing treatment which produced not only more perfect grain boundaries, increasing a, but also a polyhedral grain shape, increasing N . This conclusion is similar to the hypothesis presented in this paper that the thermomechanical deformation process results in more perfect grain boundaries but also sharper, more polyhedral, grains.
4. Conclusion In die-upset melt-quenched NdFeB magnets, the empirical parameters a and N increase as the degree of crystallographic alignment of the grains in the magnet increases. This trend is the opposite to that observed in sintered magnets. The trend of increasing values of a and N as the coercivity decreases, while opposite to that of sintered magnets, is similar to that observed in isotropic meltquenched magnets subject to various annealing treatments. The trend in a and N with degree of deformation is most likely caused by the changes in the morphology of the grains as a result of the deformation process. The trend in a and N ob served can be explained by the grain boundary becoming more perfect as deformation progresses, which increases a, while at the same time the grains become more polyhedral, with sharp corners, which increases N and ultimately is the control ling factor in leading to a decrease in coercivity with increased thermomechanical deformation.
Acknowledgements D.C.C. and L.H.L. would like to acknowledge helpful discussions with Dr. D. Givord. This research was performed under the auspices of the US Department of Energy, Division of Material Sciences, O$ce of Basic Energy Sciences under Contract No. DE-AC02-98CH10886.
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