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Modified angular dependence of coercivity in inhomogenous magnets (part I: Sm2Fe17Nx)
~)
Pergamon
Solid State Communications, Vol. 89, No. 11, pp. 929-932, 1994 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0038-1098/94 $6.00+.00 0038-1098(94)E0060-O MODIFIED ANGULAR DEPENDENCE OF COERCIVITY IN INHOMOGENEOUS MAGNETS ( PART I: Sm2Fel7Nx) Jifan Hu, Bao-gen Shen, Fang-wei Fuming Yang and Zhenxi Wang
Wang, Ruwen Zhao,
State Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Shenjun Yu and Shouzeng Zhou Department of Materials Science and Engineering, University of Science and Technology, Beijing 100083, China (Received 11 October 1993, acceptedfor publication 20 December 1993 by Z Gan)
ABSTRACT In the present work, the modified angular dependences of coercivities in inhomogeneous magnets are analyzed with respect of the ratio KI'/K2' of reduced anisotropy constants in defect region of grains. Results indicate that below the value of 0.9 of ratio K~'/K2', the Hc(O)/Hc(0) increases with deviation angle between external field and c-axis of grain without a minimum. Above the value of 0.9 of KI'/K2', the angular dependence of Hc(O)/H~(0) has a minimum. The angular dependences of coercivities for NdFeB and SmFeN magnets have no minimum, which reflect the existence of inhomogeneous areas in grains where the anisotropy constants are greatly reduced. Meanwhile our results clearly indicate that the nucleation model agrees to the experimental results much better than the pinning model for SmFeN epoxy resin bonded magnet.
strongly depends on the ratio, K I ' / K 2 ' , of anisotropy constants in the defect area of grain. Below the value of 0.9 for ratio KI'/K2' , He(O)/He(0) increases with increasing of the angle between the external field and c axis without minimum. The angular dependence of coercivity Hc(O)/Hc(0) has a minimum at the ratio of KI'/K 2' above 0.9. By comparison of the pinning and nucleation model of the angular dependence of coercivity with experimental measured results, we find that the coercivity of SmEFewNx epoxy resin- bonded magnets is controlled by the nucleation field occurring in the defect area of Sm2Fe17Nx grain.
Recently it has been found that Sm2FeITNx nitride has a large anisotropy field, a reasonable saturation magnetization and a relative high Curie temperature, which makes it possible as a good candidate of permanent magnet [1]. The hardening mechanisms of magnets prepared by the hydrogen decrepitation process [2], the epoxy resin bonding method [3], metal bonding method [4-7], mechanical alloying process [8-9] and explosion sintering technique [10] have been studied by several authors. To give a complete understanding of the coercivity mechanisms in those magnets, we report our recent experimental results on the angular dependence of coercivity in Sm2FelTNx magnet. The effects of the defect region of grain on the angular dependence of the coercivity of inhomogeneous magnets are also analyzed. Results indicate that the angular dependence of coercivity of inhomogeneous magnet
Primary Sm2Fe17 alloys were prepared by arc- melting under argon atmosphere and subsequent vacuum annealing at 1020 C for three days. X-ray analysis indicates that the alloy is a single phase. The sample then was crushed and nitroge929
MODIFIED ANGULARDEPENDENCE OF COERCIVITY
930
Vol. 89, No. 11
1.00 --
/
0.95
E 0.90
K~
K2
0.85
I
0.80
I
30
J
60
90
0
Fig. I Angular dependence of coercivity for SmFeN epoxy resin bonded magnet.
nated at 500 C for 4 hours. The nitride powders were then mixed with epoxy-resin and aligned in 2 T for 4 hours. The field and angular dependences of coercivities were measured with a pulse high magnetic field. Our results indicate that the coercivity of Sm2Fel7N x increases with increasing t h e angle between the external field and aligned direction of magnet (see Fig.1 ), which is similar to the case in NdFeB sintered magnet [11-16]. Here our measured coercivities are determined as the external fields at which the susceptibility has a peak[11].
Fig.3 The defect region in the grain surface, where the anisotropy of nearest surface region labeled as K 1' and K 2' is great reduced. K x and K2 represent the anisotropy constant inside grain without defect.
Fig.2 shows the field dependence of the coercivity for the aligned magnet [3]. The external demagnetizing field is applied upon the sample in the directions antiparallel and parallel to the aligned direction alternatively after magnetizing the sample parallel and antiparallel to the aligned direction, which are labeled with an arrow. It can be seen that the coercivity after magnetizing the sample antiparallel to the aligned direction is larger than that after magnetizing the sample parallel to the aligned direction below the magnetizing field of 3 T, even though the magnetizing field antiparallel to the aligned direction is smaller than that parallel to the aligned direction. Such phenomenon is not difficult to understand since the different external field magnetizing
1.2 1.0
4.5--
0.8
KI'/K 2' = 0. 7
4.03.5-
0.6
3.0
0.4
0!~6
2.5 ta
0.2
2.0 1.5
0
2
4 ~o Happ (T)
6
8
Fig.2 Magnetizing field dependence of the coercivity for aligned SmFeN epoxy resin bonded magnet. The arrow indicates the case where the magnetizing field is applied upon the sample antiparallel to the aligned direction.
1.0= O.5 0
[ 15
b 30
t 45
I 60
I 75
I
90
Fig.4 The calculated angular dependence of Hc(O)/Hc(0) for the different ratios of K 1'/K2' below 0.9.
931
MODIFIED ANGULARDEPENDENCE OF COERCIVITY
Vol. 89, No. 11
antiparall~l to the aligned direction of magnet will produce the quasi-misalignment behaviors. Another phenomenon that the coercivity of isotropic magnet is larger than that of aligned magnet also support our above experimental results. In Contrast to the angular dependence of coercivity for Sm2Fe17Nx, in Fes3Pr17B3o system with isolated Pr2FeI4B grain the minimum of coercivity at 45 has been observed [16] which agrees to the theoretical predicted behavior [11,12,15,16]. It implied, on the other hand, that the grain of Sm2Fe17N x are strongly coupled each other. Another factor which may be responsible to the increase of coercivity with the increasing of the deviation angle between external field and the aligned direction of magnet is the KI'/K2', the ratio of reduced anisotropy constants in the defect area of grain, considering almost all of experimental realized magnets are of inhomogeneity. Of those inhomogeneous behavior, the anisotropy in the defect area such as defect region at the grain surface are reduced greatly. Maybe the decrease degrees of K1 and K 2 in the defect area of the grain are different. In other words, the ratio of KI'/K 2' in the defect area may be different from the K1/K 2 inside of the grain without defect. The reduced anisotropy area are shown in Fig.3, where the anisotropy constants at surface are much reduced labeled as KI', K 2' comparing with the anisotropy inside the perfect grain K 1 and K 2. Based on the above assumption, we may think here that the angular dependence of the coercivity in inhomogeneous magnet maybe
depends on the reduced anisotropy K 1' and K 2' in the defect area of grain, which may be similar to the case of the coercivity. To illustrate the effect of the grain defect, we calculate the modified angular dependence of the coercivity of magnet with respect of the ratio K1 '/K2' in defect area instead of the value of ideal K1/K 2 of perfect grain in the well known equation [11,12,15,16].
1
rico) He(O)
6+
cosO ( i+ (tg0)2r$)$r~•
2KA (tg0}2~ ~ K~ 1+ (tB0}2~j
The calculated results of Hc(O)/H~(0) vs. KI'/K2' are shown in Fig.4-5. Our results indicate that below the value of 0.9 for ratio KI'/K2', H¢(O)/Hc(0) increases with the deviation angle between external field and c-axis without minimum (see Fig.4). The smaller KI'/K 2' is, the larger H¢(O)/H¢(0) becomes. It is also evident that above 0.9 of K 1'/K2', the angular dependence of coercivity H¢(O)/Hc(0) has a minimum (see Fig.5). Based on the above calculated results, it is not difficult to understand the fact that the angular dependence of coercivity in NdFeB and SmFeN magnets increases with increasing the deviation angle between external field and easy magnetization direction without a minimum, since there exist inhomogeneous areas where their anisotropy constants are greatly reduced in the magnets. • pin.
2.8 2.0
KI'/K2' = / 2.4
1.6
~
2.0 1.6
1.2
•
"
1.2
nuc. 0.9 1.0 exp.
0.8 0.5
l 15
I 30
I 45
L 60
I 75
I
0.81 0
r 15
I 30
q 45
I 60
I 75
} 90
90
Fig.5 The calculated angular dependence of Hc(O)/Hc(0) for the different ratios of KI'/K2' above 0.9.
Fig.6 The comparison of the experimental measured angular dependence of coercivity of SmFeN magnet and the calculated pinning and nucleation model (with KI'/K 2' =0.9 and 1.0).
932
MODIFIED ANGULARDEPENDENCEOF COERCIVITY
To investigate the hardening mechanism of epoxy resin bonded magnet, we fit the experimental result with the calculated pinning model and nucleation model (with parameter K I'/K 2' =0.9
Vol. 89, No. 1
and 1.0) of the angular dependences of coercivities shown in Fig.6. Results clearly indicate ihat the nucleation model agrees to the experimental results much better than the pinning model.
References 1. J.M.D. Coey and H. Sun, J.Magn. Magn. Mater., 87(1990)L251. 2. Jifan Hu, X.C. Kou, H. Kronmiiller and Shouzeng Zhou, Phys. Stat. Sol., (a) 134(1992)499. 3. Jifan Hu, Fuming Yang, Ruwen Zhao, Zhenxi Wang, Shenjun Yu, Shouzeng Zhou, Boping Hu and Yizhong Wang,. Submitted to J. Magn. Magn. Mater. 4. Jifan Hu, I. Kleinschroth, R.Reisser, H. Kronmiiller and Shouzeng Zhou, Phys. Stat. Sol., (a), 138 ~1993)257. 7~ 5. R. Skomski, K.-H. MUller, P.A.P. Wgndhausen and J.M.D. Coey, J.Appl. Phys., 73(1993)6047. 6. P.A.P. Wendhausen, K.-H. Miiller, A. Handstein, D. Eckert, W. Pitschke and Bo-ping Hu, FC-05, INTERMAG'93, Stockholm, 1993 7. A.E. Platts, I.R. Harris and J.M.D. Coey, J. Alloys Comp. 177(1991)L11.
8. J. Ding, R. Street and P. G. McCormick, J. Magn. Magn. Mater., 115(1992)211. 9. X. C. Kou, W.J. Qiang, H. Kronmiiller and L. Schultz, Submitted to J. Appl. Phys. 10. Jifan Hu, X.C. Kou, T. Dragon, H. Kronmiiller and Bo-ping Hu, Phys. Stat. Sol., (a) 139(1993)199. 11. H. Kronmiiller, K.-D. Durst and G. Martinek, J. Magn.Magn. Mater., 69(1987)149. 12. H. Kronrn'dller, in: Hard Magnetic Material, Eds: G.J. Long and F. Grandjean, Kluwer Acad. Publ., 1991, pp.461 13. D. Givord, P. Tenaud and T. Viadieu, IEEE Trans. Magn., 24(1988)1921. 14. D. Givord, P. Tenaud and T. Viadieu, J. Magn. Magn. Mater., 72(1988)247. 15. H. Kronmiiller, K.-D. Durst and M. Sagawa, J. Magn.Magn. Mater., 74(1988)291. 16. G. Martinek, H. Kronmliller and S. Hirosawa, J. Magn. Magn. Mater., 89(1990)369.
Pergamon
Solid State Communications, Vol. 89, No. 11, pp. 929-932, 1994 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0038-1098/94 $6.00+.00 0038-1098(94)E0060-O MODIFIED ANGULAR DEPENDENCE OF COERCIVITY IN INHOMOGENEOUS MAGNETS ( PART I: Sm2Fel7Nx) Jifan Hu, Bao-gen Shen, Fang-wei Fuming Yang and Zhenxi Wang
Wang, Ruwen Zhao,
State Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Shenjun Yu and Shouzeng Zhou Department of Materials Science and Engineering, University of Science and Technology, Beijing 100083, China (Received 11 October 1993, acceptedfor publication 20 December 1993 by Z Gan)
ABSTRACT In the present work, the modified angular dependences of coercivities in inhomogeneous magnets are analyzed with respect of the ratio KI'/K2' of reduced anisotropy constants in defect region of grains. Results indicate that below the value of 0.9 of ratio K~'/K2', the Hc(O)/Hc(0) increases with deviation angle between external field and c-axis of grain without a minimum. Above the value of 0.9 of KI'/K2', the angular dependence of Hc(O)/H~(0) has a minimum. The angular dependences of coercivities for NdFeB and SmFeN magnets have no minimum, which reflect the existence of inhomogeneous areas in grains where the anisotropy constants are greatly reduced. Meanwhile our results clearly indicate that the nucleation model agrees to the experimental results much better than the pinning model for SmFeN epoxy resin bonded magnet.
strongly depends on the ratio, K I ' / K 2 ' , of anisotropy constants in the defect area of grain. Below the value of 0.9 for ratio KI'/K2' , He(O)/He(0) increases with increasing of the angle between the external field and c axis without minimum. The angular dependence of coercivity Hc(O)/Hc(0) has a minimum at the ratio of KI'/K 2' above 0.9. By comparison of the pinning and nucleation model of the angular dependence of coercivity with experimental measured results, we find that the coercivity of SmEFewNx epoxy resin- bonded magnets is controlled by the nucleation field occurring in the defect area of Sm2Fe17Nx grain.
Recently it has been found that Sm2FeITNx nitride has a large anisotropy field, a reasonable saturation magnetization and a relative high Curie temperature, which makes it possible as a good candidate of permanent magnet [1]. The hardening mechanisms of magnets prepared by the hydrogen decrepitation process [2], the epoxy resin bonding method [3], metal bonding method [4-7], mechanical alloying process [8-9] and explosion sintering technique [10] have been studied by several authors. To give a complete understanding of the coercivity mechanisms in those magnets, we report our recent experimental results on the angular dependence of coercivity in Sm2FelTNx magnet. The effects of the defect region of grain on the angular dependence of the coercivity of inhomogeneous magnets are also analyzed. Results indicate that the angular dependence of coercivity of inhomogeneous magnet
Primary Sm2Fe17 alloys were prepared by arc- melting under argon atmosphere and subsequent vacuum annealing at 1020 C for three days. X-ray analysis indicates that the alloy is a single phase. The sample then was crushed and nitroge929
MODIFIED ANGULARDEPENDENCE OF COERCIVITY
930
Vol. 89, No. 11
1.00 --
/
0.95
E 0.90
K~
K2
0.85
I
0.80
I
30
J
60
90
0
Fig. I Angular dependence of coercivity for SmFeN epoxy resin bonded magnet.
nated at 500 C for 4 hours. The nitride powders were then mixed with epoxy-resin and aligned in 2 T for 4 hours. The field and angular dependences of coercivities were measured with a pulse high magnetic field. Our results indicate that the coercivity of Sm2Fel7N x increases with increasing t h e angle between the external field and aligned direction of magnet (see Fig.1 ), which is similar to the case in NdFeB sintered magnet [11-16]. Here our measured coercivities are determined as the external fields at which the susceptibility has a peak[11].
Fig.3 The defect region in the grain surface, where the anisotropy of nearest surface region labeled as K 1' and K 2' is great reduced. K x and K2 represent the anisotropy constant inside grain without defect.
Fig.2 shows the field dependence of the coercivity for the aligned magnet [3]. The external demagnetizing field is applied upon the sample in the directions antiparallel and parallel to the aligned direction alternatively after magnetizing the sample parallel and antiparallel to the aligned direction, which are labeled with an arrow. It can be seen that the coercivity after magnetizing the sample antiparallel to the aligned direction is larger than that after magnetizing the sample parallel to the aligned direction below the magnetizing field of 3 T, even though the magnetizing field antiparallel to the aligned direction is smaller than that parallel to the aligned direction. Such phenomenon is not difficult to understand since the different external field magnetizing
1.2 1.0
4.5--
0.8
KI'/K 2' = 0. 7
4.03.5-
0.6
3.0
0.4
0!~6
2.5 ta
0.2
2.0 1.5
0
2
4 ~o Happ (T)
6
8
Fig.2 Magnetizing field dependence of the coercivity for aligned SmFeN epoxy resin bonded magnet. The arrow indicates the case where the magnetizing field is applied upon the sample antiparallel to the aligned direction.
1.0= O.5 0
[ 15
b 30
t 45
I 60
I 75
I
90
Fig.4 The calculated angular dependence of Hc(O)/Hc(0) for the different ratios of K 1'/K2' below 0.9.
931
MODIFIED ANGULARDEPENDENCE OF COERCIVITY
Vol. 89, No. 11
antiparall~l to the aligned direction of magnet will produce the quasi-misalignment behaviors. Another phenomenon that the coercivity of isotropic magnet is larger than that of aligned magnet also support our above experimental results. In Contrast to the angular dependence of coercivity for Sm2Fe17Nx, in Fes3Pr17B3o system with isolated Pr2FeI4B grain the minimum of coercivity at 45 has been observed [16] which agrees to the theoretical predicted behavior [11,12,15,16]. It implied, on the other hand, that the grain of Sm2Fe17N x are strongly coupled each other. Another factor which may be responsible to the increase of coercivity with the increasing of the deviation angle between external field and the aligned direction of magnet is the KI'/K2', the ratio of reduced anisotropy constants in the defect area of grain, considering almost all of experimental realized magnets are of inhomogeneity. Of those inhomogeneous behavior, the anisotropy in the defect area such as defect region at the grain surface are reduced greatly. Maybe the decrease degrees of K1 and K 2 in the defect area of the grain are different. In other words, the ratio of KI'/K 2' in the defect area may be different from the K1/K 2 inside of the grain without defect. The reduced anisotropy area are shown in Fig.3, where the anisotropy constants at surface are much reduced labeled as KI', K 2' comparing with the anisotropy inside the perfect grain K 1 and K 2. Based on the above assumption, we may think here that the angular dependence of the coercivity in inhomogeneous magnet maybe
depends on the reduced anisotropy K 1' and K 2' in the defect area of grain, which may be similar to the case of the coercivity. To illustrate the effect of the grain defect, we calculate the modified angular dependence of the coercivity of magnet with respect of the ratio K1 '/K2' in defect area instead of the value of ideal K1/K 2 of perfect grain in the well known equation [11,12,15,16].
1
rico) He(O)
6+
cosO ( i+ (tg0)2r$)$r~•
2KA (tg0}2~ ~ K~ 1+ (tB0}2~j
The calculated results of Hc(O)/H~(0) vs. KI'/K2' are shown in Fig.4-5. Our results indicate that below the value of 0.9 for ratio KI'/K2', H¢(O)/Hc(0) increases with the deviation angle between external field and c-axis without minimum (see Fig.4). The smaller KI'/K 2' is, the larger H¢(O)/H¢(0) becomes. It is also evident that above 0.9 of K 1'/K2', the angular dependence of coercivity H¢(O)/Hc(0) has a minimum (see Fig.5). Based on the above calculated results, it is not difficult to understand the fact that the angular dependence of coercivity in NdFeB and SmFeN magnets increases with increasing the deviation angle between external field and easy magnetization direction without a minimum, since there exist inhomogeneous areas where their anisotropy constants are greatly reduced in the magnets. • pin.
2.8 2.0
KI'/K2' = / 2.4
1.6
~
2.0 1.6
1.2
•
"
1.2
nuc. 0.9 1.0 exp.
0.8 0.5
l 15
I 30
I 45
L 60
I 75
I
0.81 0
r 15
I 30
q 45
I 60
I 75
} 90
90
Fig.5 The calculated angular dependence of Hc(O)/Hc(0) for the different ratios of KI'/K2' above 0.9.
Fig.6 The comparison of the experimental measured angular dependence of coercivity of SmFeN magnet and the calculated pinning and nucleation model (with KI'/K 2' =0.9 and 1.0).
932
MODIFIED ANGULARDEPENDENCEOF COERCIVITY
To investigate the hardening mechanism of epoxy resin bonded magnet, we fit the experimental result with the calculated pinning model and nucleation model (with parameter K I'/K 2' =0.9
Vol. 89, No. 1
and 1.0) of the angular dependences of coercivities shown in Fig.6. Results clearly indicate ihat the nucleation model agrees to the experimental results much better than the pinning model.
References 1. J.M.D. Coey and H. Sun, J.Magn. Magn. Mater., 87(1990)L251. 2. Jifan Hu, X.C. Kou, H. Kronmiiller and Shouzeng Zhou, Phys. Stat. Sol., (a) 134(1992)499. 3. Jifan Hu, Fuming Yang, Ruwen Zhao, Zhenxi Wang, Shenjun Yu, Shouzeng Zhou, Boping Hu and Yizhong Wang,. Submitted to J. Magn. Magn. Mater. 4. Jifan Hu, I. Kleinschroth, R.Reisser, H. Kronmiiller and Shouzeng Zhou, Phys. Stat. Sol., (a), 138 ~1993)257. 7~ 5. R. Skomski, K.-H. MUller, P.A.P. Wgndhausen and J.M.D. Coey, J.Appl. Phys., 73(1993)6047. 6. P.A.P. Wendhausen, K.-H. Miiller, A. Handstein, D. Eckert, W. Pitschke and Bo-ping Hu, FC-05, INTERMAG'93, Stockholm, 1993 7. A.E. Platts, I.R. Harris and J.M.D. Coey, J. Alloys Comp. 177(1991)L11.
8. J. Ding, R. Street and P. G. McCormick, J. Magn. Magn. Mater., 115(1992)211. 9. X. C. Kou, W.J. Qiang, H. Kronmiiller and L. Schultz, Submitted to J. Appl. Phys. 10. Jifan Hu, X.C. Kou, T. Dragon, H. Kronmiiller and Bo-ping Hu, Phys. Stat. Sol., (a) 139(1993)199. 11. H. Kronmiiller, K.-D. Durst and G. Martinek, J. Magn.Magn. Mater., 69(1987)149. 12. H. Kronrn'dller, in: Hard Magnetic Material, Eds: G.J. Long and F. Grandjean, Kluwer Acad. Publ., 1991, pp.461 13. D. Givord, P. Tenaud and T. Viadieu, IEEE Trans. Magn., 24(1988)1921. 14. D. Givord, P. Tenaud and T. Viadieu, J. Magn. Magn. Mater., 72(1988)247. 15. H. Kronmiiller, K.-D. Durst and M. Sagawa, J. Magn.Magn. Mater., 74(1988)291. 16. G. Martinek, H. Kronmliller and S. Hirosawa, J. Magn. Magn. Mater., 89(1990)369.