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Superparamagnetic behavior of Ni-Cu-Pd Spinodal alloy
61
Journal of Magnetism and Magnetic Materials 31-34 (1983) 61-62
S U P E R P A R A M A G N E T I C B E H A V I O R OF N i - C u - P d S P I N O D A L A L L O Y Y. M U R A T A * a n d Y. I W A M A ** • Department of Production Systems Engineering Toyohashi University of Technology, Hibarigaoka, Tenpaku-cho, Toyohashi 440, Japan • * Department of Crystalline Materials Science, Faculty of Engineering, Nagoya University, Furo.cho, Chikusa-ku, Nagoya 464, Japan
By the analysis of measured magnetization curves at various temperatures, it is found that spinodally decomposed NisoCu29Pd21 alloy has a sinusoidal form of fluctuations in Curie temperature. At a temperature closely under the maximum Curie temperature, the ferromagnetic regions in this alloy behave as superparamagnetic particles.
1. Introduction N i - C u - P d temay alloy has a miscibility gap region in the solid state [ 1]. A supersaturated solid solution can be spinodally decomposed at an appropriate temperature, resulting in a sinusoidal form of composition fluctuations. The wavelength of the fluctuations is in the order of nm [2]. Since the Curie temperature of the N i - C u - P d alloy is nearly proportional to the Ni content, the decomposed alloy has also a sinusoidal form of fluctuations in Curie temperatures similar to those in the composition, as schematically shown in fig. 1. Thus, when it is held at a temperature closely under the maximum Curie temperature, the alloy is composed of finely dispersed ferromagnetic regions embedded in a paramagnetic matrix, showing superparamagnetic behavior. In the present study the magnetic behavior of the spinodally decomposed alloy were investigated at various temperatures.
2. Experimental procedures The alloy specimen with a composition of NisoCu29Pd21 was chiefly used in the present study. After the specimen was subjected to a solution treatment, it was quenched into water, followed by annealing at 773 K for 40 min, to perform the spinodal decomposition. The magnetization curves were measured at
various temperatures using a vibrating sample magnetometer. Besides the above specimen, four specimens with different compositions of Ni j5 Cu 53Pd 32, Ni 30Cu43Pd 27, Ni40Cu36Pd24 and Ni93Pd 7 alloys were prepared to determine a composition dependence of the paramagnetic susceptibility at elevated temperatures above the Curie temperature. The susceptibility was measured by a magnetic balance.
3. Experimental results with discussion The M - H curve of the spinodally decomposed NisoCu29Pd21 alloy specimen was measured at various temperatures above the Curie temperature of the homogeneous NisoCu29Pd21 alloy, i.e., 270 K. The magnetization is represented by M = v i M I + v2~H,
(1)
where M 1 is the magnetization of the ferrromagnetic regions, ~ the mean susceptibility of the paramagnetic matrix, v~ and v 2 the volume fractions of both regions. Since, from the previous study [2], the composition fluctuations in the alloy as well as the composition
x10-'/ 8
~6
high f
c o
2 o
j
Ni-Cu-Pd
:
Curieconstont Curie temperature ~
. /
4
~ 270K n
0
L.)
low Fig. 1. One dimensional schematic diagram of Curie temperature fluctuation in spinodally decomposed Ni~oCu29Pd2~ alloy. T is the measured temperature and the hatched region is the ferromagnetic one.
A
/ o
,
,/•
/
S00 (:D
400
•
"c 2 -s U
800
~. Q~
00 jo
// /
°o
2'o 3'o go s'o s'o 7b go 90 0 at% Ni
Fig. 2. Hi content dependences of Curie constant (open circles) and Curie temperature (closed circles). The data of the closed circles were obtained from ref. [2].
0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
Y. Murata, Y. lwama / Superparamagnetism in N i - Cu- Pd spinodal alloy
62
dependence of Curie temperature, 0(c), have been already determined, the values of v I and v 2 are available. Accordingly, if the value of ~(c) can be determined, we can easily estimate the M - H curve of the isolated ferromagnetic regions, to investigate their superparamagnetic behavior. If the susceptibility of the alloy is assumed to obey the Curie law, it can be given by
X( c)
=
C( c ) / [ r - 0 ( c ) ] ,
(2)
where C(c) is the Curie constant, O(c) the Curie temperature, they depend on the chemical composition. Using several specimens described in section 2, we have determined the composition dependence of the Curie constant, C(c). The results thus obtained are shown together with #(c) in fig. 2, where the abscissa is taken as the Ni content instead of the ternary compositions. It can be noted the C(c) as well as 9(c) shows a linear dependence upon the Ni content. Now, we can use the available data of C(c), 8(c) and the composition fluctuations in the alloy, to calculate the weighted average of ~(T) at a given temperature, T. Thus, by using eq. (l), we have obtained the magnetization curve of the ferromagnetic regions, as shown by closed circles in fig. 3. If the ferromagnetic regions behave as superparamagnetic particles, the magnetization is represented by
[31 M ( T ) = M s ( T ) L ~ ( M s ( T ) [ H + wM(T)]/NkT), (3) where Ms(T ) is the saturation magnetization of the specimen, N the number of particles in unit volume, k the Boltzmann constant and w the molecular field constant [4], and L~¢ means the well-known Langevin function. It is to be noted, in addition, that with adequate consideration for magnetic interaction, probably through
xlO_2 lO
• 773K for 40 min
experiment
-- Langevin curve
~
8
~ 6
293K
~I3K
o 318 K • 323K zz 328 K [] 333K • 338K ® 343K
~.~
E 0.2
773K for 40 min
~ '~0.1
Aoe~
° ~
Langevin curve
f O "
~"
e~
=
i i 500 1000 Ms ( H ÷ w M ) / T M 0
i 1500 [(A/m)/K]
__
Fig. 4. MoM/M, vs. Ms(H + wM)/TMo plots demonstrating superparamagnetic behavior of ferromagnetic particles in spinodaUy decomposed NisoCu29Pd2~ alloy. conduction electrons, between particles separated with paramagnetic matrix, the molecular field wM is added to an applied field H. Thus, eq. (3) includes three parameters of M s, w and N, though N can be determined from the available data associated with the composition fluctuations. Thus, by suitably selecting the two parameters of M s and w, we have tried to allow the experimental data to fit eq. (3), so as to achieve the best fit in the higher field ranges. The Langevin curves thus obtained are drawn by solid lines in fig. 3. The theoretical curves are generally in well agreement with the experimental data, except of those measured at lower temperatures such as 303 and 297 K. The cause of the discrepancy in the latter data may be explained in the following. When T is lowered close to the Curie temperature, the ferromagnetic regions grow larger and connections are built up between particles, which may allow superparamagnetism to fade away. The break down is noticed particularly in the low field side of the curves. Concludingly, according to the approach by Abeledo et al. [3], many of experimental data can be put together to fall on a single Langevin curve, shown in fig. 4. Here, a reduced magnetization of MMo/M s is plotted against the parameter Ms(H+ w M ) / T M o, where M 0 is the magnetization at 0 K of the original Ni50Cu29Pd2j alloy. This result clearly confirm that the spinodally decomposed alloy has the expected composition fluctuations, showing superparamagnetism in a higher temperature range.
References 0
2
4
6
8
10
12
14
H (A/m) x105 Fig. 3. The m a g n e t ~ t t i o n curves of the ferromagnetic region
in Ni50Cu29Pd21 alloy annealed at 773 K for 40 rain. Closed circles are the experimental data and solid lines the calculated Langevin curves.
[1] E. Raub, O. Leoblich Jr, W. Plate and H. Krill, Z. Metallkde. 62 (1971) 826. [2] Y. Murata and Y. Iwama, Trans. JIM 22 0981) 433. [3] C.R. Abeledo and P.W. Selwood, J. Appl. Phys. 32 (1961) 229S. [4] F. Acker and R. Huguenin, J. Magn. Magn. Mat. 12 (1979) 58.
Journal of Magnetism and Magnetic Materials 31-34 (1983) 61-62
S U P E R P A R A M A G N E T I C B E H A V I O R OF N i - C u - P d S P I N O D A L A L L O Y Y. M U R A T A * a n d Y. I W A M A ** • Department of Production Systems Engineering Toyohashi University of Technology, Hibarigaoka, Tenpaku-cho, Toyohashi 440, Japan • * Department of Crystalline Materials Science, Faculty of Engineering, Nagoya University, Furo.cho, Chikusa-ku, Nagoya 464, Japan
By the analysis of measured magnetization curves at various temperatures, it is found that spinodally decomposed NisoCu29Pd21 alloy has a sinusoidal form of fluctuations in Curie temperature. At a temperature closely under the maximum Curie temperature, the ferromagnetic regions in this alloy behave as superparamagnetic particles.
1. Introduction N i - C u - P d temay alloy has a miscibility gap region in the solid state [ 1]. A supersaturated solid solution can be spinodally decomposed at an appropriate temperature, resulting in a sinusoidal form of composition fluctuations. The wavelength of the fluctuations is in the order of nm [2]. Since the Curie temperature of the N i - C u - P d alloy is nearly proportional to the Ni content, the decomposed alloy has also a sinusoidal form of fluctuations in Curie temperatures similar to those in the composition, as schematically shown in fig. 1. Thus, when it is held at a temperature closely under the maximum Curie temperature, the alloy is composed of finely dispersed ferromagnetic regions embedded in a paramagnetic matrix, showing superparamagnetic behavior. In the present study the magnetic behavior of the spinodally decomposed alloy were investigated at various temperatures.
2. Experimental procedures The alloy specimen with a composition of NisoCu29Pd21 was chiefly used in the present study. After the specimen was subjected to a solution treatment, it was quenched into water, followed by annealing at 773 K for 40 min, to perform the spinodal decomposition. The magnetization curves were measured at
various temperatures using a vibrating sample magnetometer. Besides the above specimen, four specimens with different compositions of Ni j5 Cu 53Pd 32, Ni 30Cu43Pd 27, Ni40Cu36Pd24 and Ni93Pd 7 alloys were prepared to determine a composition dependence of the paramagnetic susceptibility at elevated temperatures above the Curie temperature. The susceptibility was measured by a magnetic balance.
3. Experimental results with discussion The M - H curve of the spinodally decomposed NisoCu29Pd21 alloy specimen was measured at various temperatures above the Curie temperature of the homogeneous NisoCu29Pd21 alloy, i.e., 270 K. The magnetization is represented by M = v i M I + v2~H,
(1)
where M 1 is the magnetization of the ferrromagnetic regions, ~ the mean susceptibility of the paramagnetic matrix, v~ and v 2 the volume fractions of both regions. Since, from the previous study [2], the composition fluctuations in the alloy as well as the composition
x10-'/ 8
~6
high f
c o
2 o
j
Ni-Cu-Pd
:
Curieconstont Curie temperature ~
. /
4
~ 270K n
0
L.)
low Fig. 1. One dimensional schematic diagram of Curie temperature fluctuation in spinodally decomposed Ni~oCu29Pd2~ alloy. T is the measured temperature and the hatched region is the ferromagnetic one.
A
/ o
,
,/•
/
S00 (:D
400
•
"c 2 -s U
800
~. Q~
00 jo
// /
°o
2'o 3'o go s'o s'o 7b go 90 0 at% Ni
Fig. 2. Hi content dependences of Curie constant (open circles) and Curie temperature (closed circles). The data of the closed circles were obtained from ref. [2].
0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
Y. Murata, Y. lwama / Superparamagnetism in N i - Cu- Pd spinodal alloy
62
dependence of Curie temperature, 0(c), have been already determined, the values of v I and v 2 are available. Accordingly, if the value of ~(c) can be determined, we can easily estimate the M - H curve of the isolated ferromagnetic regions, to investigate their superparamagnetic behavior. If the susceptibility of the alloy is assumed to obey the Curie law, it can be given by
X( c)
=
C( c ) / [ r - 0 ( c ) ] ,
(2)
where C(c) is the Curie constant, O(c) the Curie temperature, they depend on the chemical composition. Using several specimens described in section 2, we have determined the composition dependence of the Curie constant, C(c). The results thus obtained are shown together with #(c) in fig. 2, where the abscissa is taken as the Ni content instead of the ternary compositions. It can be noted the C(c) as well as 9(c) shows a linear dependence upon the Ni content. Now, we can use the available data of C(c), 8(c) and the composition fluctuations in the alloy, to calculate the weighted average of ~(T) at a given temperature, T. Thus, by using eq. (l), we have obtained the magnetization curve of the ferromagnetic regions, as shown by closed circles in fig. 3. If the ferromagnetic regions behave as superparamagnetic particles, the magnetization is represented by
[31 M ( T ) = M s ( T ) L ~ ( M s ( T ) [ H + wM(T)]/NkT), (3) where Ms(T ) is the saturation magnetization of the specimen, N the number of particles in unit volume, k the Boltzmann constant and w the molecular field constant [4], and L~¢ means the well-known Langevin function. It is to be noted, in addition, that with adequate consideration for magnetic interaction, probably through
xlO_2 lO
• 773K for 40 min
experiment
-- Langevin curve
~
8
~ 6
293K
~I3K
o 318 K • 323K zz 328 K [] 333K • 338K ® 343K
~.~
E 0.2
773K for 40 min
~ '~0.1
Aoe~
° ~
Langevin curve
f O "
~"
e~
=
i i 500 1000 Ms ( H ÷ w M ) / T M 0
i 1500 [(A/m)/K]
__
Fig. 4. MoM/M, vs. Ms(H + wM)/TMo plots demonstrating superparamagnetic behavior of ferromagnetic particles in spinodaUy decomposed NisoCu29Pd2~ alloy. conduction electrons, between particles separated with paramagnetic matrix, the molecular field wM is added to an applied field H. Thus, eq. (3) includes three parameters of M s, w and N, though N can be determined from the available data associated with the composition fluctuations. Thus, by suitably selecting the two parameters of M s and w, we have tried to allow the experimental data to fit eq. (3), so as to achieve the best fit in the higher field ranges. The Langevin curves thus obtained are drawn by solid lines in fig. 3. The theoretical curves are generally in well agreement with the experimental data, except of those measured at lower temperatures such as 303 and 297 K. The cause of the discrepancy in the latter data may be explained in the following. When T is lowered close to the Curie temperature, the ferromagnetic regions grow larger and connections are built up between particles, which may allow superparamagnetism to fade away. The break down is noticed particularly in the low field side of the curves. Concludingly, according to the approach by Abeledo et al. [3], many of experimental data can be put together to fall on a single Langevin curve, shown in fig. 4. Here, a reduced magnetization of MMo/M s is plotted against the parameter Ms(H+ w M ) / T M o, where M 0 is the magnetization at 0 K of the original Ni50Cu29Pd2j alloy. This result clearly confirm that the spinodally decomposed alloy has the expected composition fluctuations, showing superparamagnetism in a higher temperature range.
References 0
2
4
6
8
10
12
14
H (A/m) x105 Fig. 3. The m a g n e t ~ t t i o n curves of the ferromagnetic region
in Ni50Cu29Pd21 alloy annealed at 773 K for 40 rain. Closed circles are the experimental data and solid lines the calculated Langevin curves.
[1] E. Raub, O. Leoblich Jr, W. Plate and H. Krill, Z. Metallkde. 62 (1971) 826. [2] Y. Murata and Y. Iwama, Trans. JIM 22 0981) 433. [3] C.R. Abeledo and P.W. Selwood, J. Appl. Phys. 32 (1961) 229S. [4] F. Acker and R. Huguenin, J. Magn. Magn. Mat. 12 (1979) 58.