- Email: [email protected]
Magnetic entropy change of magnetic fluids
Physica B 321 (2002) 82–86
Magnetic entropy change of magnetic fluids I. Abu-Aljarayesh, A.F. Al-Jamel, M.R. Said* Physics Department, Yarmouk University, Irbid 21163, Jordan
Abstract Magnetization measurements of Co-, Fe-, and Fe3O4-based magnetic fluids were carried out in the temperature range 85 KoTo300 K and in magnetic fields up to 8 kOe. The magnetic entropy change, DSðH; TÞ; was calculated for each sample using the relevant thermodynamic Maxwell relation. DSðH; TÞ curves show similar qualitative behavior in all the studied samples. Each DSðTÞ curve shows a maximum change near the melting point of the corresponding liquid carrier, and another maximum change at B250 K. The results were discussed within the context of superparamagnetic theory. Comparison with results obtained for other related systems were made. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnetization; Magnetic fluid; Magnetic entropy
1. Introduction Magnetic fluids (MFs) are colloidal suspension of single domain ferromagnetic particles ( in a suitable liquid carrier, such as (DB100 A kerosene, decalin, diester, Isopar-M). Colloidal stability against sedimentation and agglomeration is achieved by making the particles as small as possible and by coating the particles with long chain surfactant molecules [1–8]. There are two distinct mechanisms via which the magnetic moments, m; of the particles reach thermal equilibrium. The first one is known as Ne! el relaxation [6,9], in which the magnetic moments of the particles rotate against the existing anisotropy barrier, DE; in a time tN : For a single domain particle with a uniaxial anisotropy in the absence of a magnetic field, the relaxation time, *Corresponding author. Tel.: +962-2-271100/2307; fax: +962-2-2747983. E-mail address: [email protected] (M.R. Said).
tN ; is given by [6,9] t1 N ¼ f0 expðxÞ
if x51;
1=2 t1 expðxÞ if x > 1; N ¼ f0 x
ð1aÞ ð1bÞ
where x ¼ KVm =kB T; K is the average anisotropy constant, Vm is the magnetic volume of the particle, kB is Boltzmann constant, T is the absolute temperature and f0 is an attempt frequency of the order 1011 s1. The second one is Brown relaxation [10]: The particles rotate physically [11] such that their easy axes align with the field, while the magnetic moments are held fixed in the direction of the easy axes. The Brown relaxation is characterized by the rotational diffusion time tB for a spherical particle [10] t1 B ¼
kB T ; 3Vh Z
ð2Þ
where Vh is the hydrodynamic volume of the particle, Z is the viscosity of the magnetic fluid. It is clear from Eq. (2) that the determining factor of tB
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 8 2 7 - X
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
is the viscosity Z of the magnetic fluid and the size of the particles. The viscosity of MFs is a sensitive function of the volumic packing fraction (j) of solid particles and of temperature. For a very diluted magnetic fluid, the viscosity can be approximated by the formula [1,2]: ZðjÞ ¼ Z0 ð1 þ aj þ bj2 Þ;
ð3Þ
where Z0 is the viscosity of a carrier fluid, a and b are positive constants. The temperature dependence form of ZðTÞ can be expressed as 8 B > > TBT0 ; < Z T T0 ð4Þ ln ¼ 0 > Z0 > : B T > T ; m Tn where B and B0 are characteristic positive constants, and T0 is the temperature below the melting point, Tm of the corresponding carrier fluid and n is the constant usually taken to be more than one [1]. The dominant relaxation mechanism is the one characterized by the shortest relaxation time. In a frozen fluid (ToTm ), the viscosity is very large, and as a consequence, only Nee" l mechanism is available. For T > Tm ; both relaxation mechanisms are available. The magnetocaloric effects, i.e., the adiabatic change of temperature or the isothermal change of the entropy upon application or removal of magnetic field have generated considerable interest in certain gadolimum alloys and fine magnetic particle systems, because of scientific and potential industrial applications [12–20]. The change in magnetic entropy can be calculated from the following Maxwell’s thermodynamic relation, i.e. [20], qM qS ¼ : ð5Þ qT H qH T Upon integrating of Eq. (5), it yields DS ¼ SðH; TÞ Sð0; TÞ Z H qM ¼ dH: qT H 0
ð6Þ
Thus, if the magnetization MðH; TÞ of a certain material is known, then one can estimate the
83
corresponding magnetic entropy change, utilizing Eq. (6). However, practical use of relation (6) would require accurate determination of the first derivative of the magnetization with respect to temperature in any fields. In this paper detailed magnetization curves MðH; TÞ were measured for five magnetic fluid samples with Co, Fe and Fe3O4 magnetic particles, in the temperature range 85 KoTo300 K and in magnetic fields up to 8 kOe. The magnetic entropy change DSðTÞ for each sample was deduced from the magnetization measurements, using Eq. (6).
2. Experimental Three samples of Fe, Co and Fe3O4 magnetic fluid samples were originally used for this study. The iron-based sample was then prepared by diluting it twice with proper amounts of decalin (decahydronaphthalene) to obtain another two samples. Table 1 summarizes the room temperature saturation magnetization, the liquid carrier and the volume packing fraction j ¼ ðMs =Msb Þ; where Ms is the saturation magnetization of the sample and Msb is the saturation magnetization of the corresponding bulk material, mean magnetic diameter, Dm the initial viscosity Z0 of the liquid carrier and the initial susceptibility wi of the studied samples. The magnetization measurements were carried out as follows: First, the sample was cooled down to liquid nitrogen temperature in zero applied field. Then, a set of isothermal magnetization
Table 1 Values of the magnetic and physical properties for all samples, Packing fraction (f), Liquid carrier (LC), (Isobar-M, IM, and ( Viscosity Decalin D), Mean magnetic diameter (MD) in A, (VIS), Density (r) in g cm3 and initial susceptibility (wi ) in emu g1 Oe1 Sample
j 102
LC
MD
Co Fe3O4 Fe Fe Fe
8.9 7.5 4.1 1.0 0.85
IM IM D D D
49 76
VIS 3.5 20
r
w 103
0.96
11
0.90
25
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
curves were obtained at selected temperatures for each sample in steps of 5 K. All the magnetization measurements were carried out in an automated Oxford Vibrating Sample Magnetometer, equipped with a low-temperature cryostat, using liquid nitrogen as a coolant.
10 1kOe 8 M(emu/gm)
84
6
3. Results and discussion
4
Isothermal magnetization curves were measured for each sample in fields up to 8 kOe in the temperature range 85–300 K in steps of 5 K. This provided us with 43 isothermal magnetization curves for each sample. For each isothermal curve the magnetization was recorded in steps of 0.1– 8 kOe. Fig. 1 shows selected magnetization data for the Co-based magnetic fluid. Similar magnetization curves were obtained for the Fe-, Fe3O4and the diluted Fe-based samples (j ¼ 0:01 and 0.0085). Points were taken from the isothermal curves of each sample to form the isofield MðTÞ curves for that sample. The isofield curves were obtained for fields from 0 to 8 kOe in steps of 0.1 kOe for each sample. Selected curves of MðTÞ are shown in Fig. 2 for Co-based magnetic fluid. All isofield curves, MðTÞ; were differentiated to yield the ðqM=qTÞH values and upon integration
2
15
M(emu/gm)
T=100K 10 T=140K T=200K T=240K 5 T=280K T=300K 0 0
2
4
6
8
H(kOe) Fig. 1. The isothermal magnetization versus applied magnetic field curves at selected temperatures for the Co-based MF sample with packing fraction j ¼ 0:089:
0.5kOe
0.2kOe
100
150
200
250
300
T(K) Fig. 2. The isofield magnetization versus temperature curves at selected fields for the Co-based MF sample with packing fraction j ¼ 0:089:
of ðqM=qTÞH versus H curves, using Eq. (6). The DSðTÞ curve was generated and plotted in Figs. 3 and 4, for the 5 samples. The basic features of the DSðTÞ curves are qualitatively similar in all examined samples. These curves can be readily explained by dividing the curves into three regions, i.e., for ToTmax ; Tmax oToTmin and T > Tmin : Here, Tmax ½Tmin is the temperature at which the DSðTÞ curve exhibits a maximum (a minimum) value, respectively. In the region ToTmax ; the magnetic fluid is frozen, i.e., the magnetic moments of the particles relax via the Ne! el mechanism only. As the temperature is increased, the alignment of the magnetic moments of the particles with the field decreases due to thermal agitation, i.e., the degree of ordering decreases, and hence DSðTÞ increases. This process of increasing the degree of disorder continues until the temperature approaches the melting point of the fluid and the fluid gradually begins to melt. The rate of decrease of Z is given by Eq. (4). Due to the decrease of Z; the tB decreases, thus the two mechanisms (Ne! el and Brown) are available in this region, allowing for a portion of particles to align with the field. Thus, the degree of ordering increases, and as a consequence, the DSðTÞ decreases reaching a maximum at T ¼ Tmax ; which is near the freezing point of the corresponding liquid carrier. Upon further increase of T; the viscosity decreases rapidly, and not only do
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
- ∆S (emu/gm/K)
Table 2 The temperature position Tmax (Tmin ) of the maximum (minimum) DSðTÞ and their values in (erg g1 K1) for 8 kOe integrating magnetic field for the samples (a) Co(0.089), (b) Fe3O4(0.075), (c) Fe(0.041), (d) Fe(0.01) and (e) Fe(0.0085)
Fe3O4-MF, φ = 0.075 Co-MF, φ = 0.089
125
100 8 kOe
75
50
25 50
100
150
200
250
300
T(K) Fig. 3. The magnetic entropy change obtained for the integrating fields 8 kOe as a function of temperature for the Co- and Fe3O4-based MF samples with packing fraction f ¼ 0:089 and 0.0745, respectively.
90 F e- MF 80 φ=0.041
-∆S(emu/gm)
70 60 35
φ=0.01
30 25 φ=0.0085
20 15 100
150
200
85
250
300
T(K) Fig. 4. The magnetic entropy change obtained for the integrating fields 8 kOe as a function of temperature for the Fe-based MF samples with packing fraction f ¼ 0:01; 0.041 and 0.0085.
chain-like clusters begin to be formed with their easy axis direction toward the applied field, but the number of such chains as well as their lengths increase. Thus, the degree of ordering increases,
DSðTÞmax DSðTÞmin Tmax Tmin
a
b
c
d
e
29.1 131 145 250
58 90 145 240
61.7 122 145 255
19.3 35.5 150 255
15 30 160 255
whence DSðTÞ decreases. This process continues till a temperature Tmin ; where the violent Brownian motion of particles is large enough to break the chains and to make the magnetic moments orientation random, thus increasing DSðTÞ: Table 2 summarizes the recorded maximum and minimum values of DSðTÞ and their positions. At low fields (well away from saturation) or high temperatures, one can explain the results within the context of superparamagnetic theory, and argue that the DSðTÞ curve behaves like T 2 [13]. It is found that when we increase the applied magnetic field, the maximum value of DSðTÞ reduces by an amount not proportional to the integrating applied magnetic field. This can be explained by the fact that the contribution in DSðTÞ from low magnetic applied fields is more than that from high field values, since the isothermal magnetization reaches saturation at fields >4 kOe. The minimum values of DSðTÞ were found to decrease with increasing magnetic applied field, since the magnetic particles are easily aligned in a high-applied magnetic field. The magnetic entropy change was calculated from the magnetization measurements for the 11% Fe+silica gel nanocomposites [12]. The results show that the magnetic entropy change for the examined sample is similar to the magnetic entropy change of our samples at the position of maximum entropy change, and of the order B12 erg g1 K1.
4. Summary and conclusion The calorimetry measurements for MFs with different liquid carriers and concentrations are
86
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
needed to understand the magnetocaloric effect in these systems. It is relevant to mention that MF systems are unique among systems, because they exhibit two kinds of magnetic ordering: one is spatial (chain-like clusters, etc.), the other is magnetic dipoles ordering in which the magnetic moments align with the field.
Acknowledgements We are thankful to Prof. N.Y. Ayoub from our Department for providing us with the original samples.
References [1] R. Rosensweig, Ferrohydrodynamics, Cambridge University Press, New York, 1985. [2] E. Blums, A. Cebers, M.M. Maiorov, Magnetic Fluids, Walter de Gruyter, Berlin, New York, 1997. [3] S.W. Charles, J. Popplewell, in: E.P. Wholfarth (Ed.), Ferromagnetic Materials, Vol. 2, North-Holland, Amsterdam, 1980. [4] P.C. Scholten, J. Magn. Magn. Mater. 39 (1983) 99. [5] V.E. Fertman, Magnetic Fluid, Hemisphere, New York, 1990. [6] M.I. Shliomis, Sov. Phys. Usp. 17 (1974) 153.
[7] R. Kaiser, G. Miskolczy, J. Appl. Phys. 41 (1970) 3. [8] J.C. Bacri, R. Perzynski, D. Salin, V. Cabuil, R. Massart, J. Magn. Magn. Mater. 62 (1986) 36. [9] L. N!eel, Ann. Geophys. 5 (1949) 99. [10] W.F. Brown, J. Appl. Phys. 34 (1963) 1314; W.F. Brown, Phys. Rev. 130 (1963) 1677. [11] N.A. Yusuf, D.A. Manasrah, M.A. Abdallah, H. AbuSafia, I. Abu-Aljaraesh, J. Magn. Magn. Mater. 138 (1994) 173. [12] R.D. Shull, R.D. McMicheal, L.J. Swartzendruber, L.H. Bennett, in: J.L. Dormann, D. Fiorani (Eds.), Magnetic Properties of Fine Particles, North-Holland Delta Series, Amsterdam, 1992, p. 161. [13] R.D. McMichael, R.D. Shull, L.J. Swartzendruber, L.H. Bennett, R.E. Watson, J. Magn. Magn. Mater. 111 (1992) 29. [14] L.H. Bennett, R.D. McMichael, L.J. Swartzendruber, R.D. Shull, R.E. Watson, J. Magn. Magn. Mater. 104–107 (1992) 1094. [15] H. Huang, Z.B. Cuo, D.H. Wang, Y.W. Du, J. Magn. Magn. Mater. 173 (1997) 302. [16] G. Kloos, J. Magn. Magn. Mater. 172 (1997) 247. [17] A.M. Tishin, J. Magn. Magn. Mater. 184 (1998) 62–66. [18] S. Chaudhary, V. Sunil Kumar, S.B. Roy, P. Chaddah, S.R. Krishnakumar, V.G. Sathe, A. Kumar, D.D. Sarma, J. Magn. Magn. Mater. 202 (1999) 47–52. [19] R.D. McMichael, J.J. Ritter, R.D. Shull, J. Appl. Phys. 73 (1993) 6946. [20] A.M. Tishin, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 12, North-Holland, New York, 1999, p. 395.
Magnetic entropy change of magnetic fluids I. Abu-Aljarayesh, A.F. Al-Jamel, M.R. Said* Physics Department, Yarmouk University, Irbid 21163, Jordan
Abstract Magnetization measurements of Co-, Fe-, and Fe3O4-based magnetic fluids were carried out in the temperature range 85 KoTo300 K and in magnetic fields up to 8 kOe. The magnetic entropy change, DSðH; TÞ; was calculated for each sample using the relevant thermodynamic Maxwell relation. DSðH; TÞ curves show similar qualitative behavior in all the studied samples. Each DSðTÞ curve shows a maximum change near the melting point of the corresponding liquid carrier, and another maximum change at B250 K. The results were discussed within the context of superparamagnetic theory. Comparison with results obtained for other related systems were made. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnetization; Magnetic fluid; Magnetic entropy
1. Introduction Magnetic fluids (MFs) are colloidal suspension of single domain ferromagnetic particles ( in a suitable liquid carrier, such as (DB100 A kerosene, decalin, diester, Isopar-M). Colloidal stability against sedimentation and agglomeration is achieved by making the particles as small as possible and by coating the particles with long chain surfactant molecules [1–8]. There are two distinct mechanisms via which the magnetic moments, m; of the particles reach thermal equilibrium. The first one is known as Ne! el relaxation [6,9], in which the magnetic moments of the particles rotate against the existing anisotropy barrier, DE; in a time tN : For a single domain particle with a uniaxial anisotropy in the absence of a magnetic field, the relaxation time, *Corresponding author. Tel.: +962-2-271100/2307; fax: +962-2-2747983. E-mail address: [email protected] (M.R. Said).
tN ; is given by [6,9] t1 N ¼ f0 expðxÞ
if x51;
1=2 t1 expðxÞ if x > 1; N ¼ f0 x
ð1aÞ ð1bÞ
where x ¼ KVm =kB T; K is the average anisotropy constant, Vm is the magnetic volume of the particle, kB is Boltzmann constant, T is the absolute temperature and f0 is an attempt frequency of the order 1011 s1. The second one is Brown relaxation [10]: The particles rotate physically [11] such that their easy axes align with the field, while the magnetic moments are held fixed in the direction of the easy axes. The Brown relaxation is characterized by the rotational diffusion time tB for a spherical particle [10] t1 B ¼
kB T ; 3Vh Z
ð2Þ
where Vh is the hydrodynamic volume of the particle, Z is the viscosity of the magnetic fluid. It is clear from Eq. (2) that the determining factor of tB
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 8 2 7 - X
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
is the viscosity Z of the magnetic fluid and the size of the particles. The viscosity of MFs is a sensitive function of the volumic packing fraction (j) of solid particles and of temperature. For a very diluted magnetic fluid, the viscosity can be approximated by the formula [1,2]: ZðjÞ ¼ Z0 ð1 þ aj þ bj2 Þ;
ð3Þ
where Z0 is the viscosity of a carrier fluid, a and b are positive constants. The temperature dependence form of ZðTÞ can be expressed as 8 B > > TBT0 ; < Z T T0 ð4Þ ln ¼ 0 > Z0 > : B T > T ; m Tn where B and B0 are characteristic positive constants, and T0 is the temperature below the melting point, Tm of the corresponding carrier fluid and n is the constant usually taken to be more than one [1]. The dominant relaxation mechanism is the one characterized by the shortest relaxation time. In a frozen fluid (ToTm ), the viscosity is very large, and as a consequence, only Nee" l mechanism is available. For T > Tm ; both relaxation mechanisms are available. The magnetocaloric effects, i.e., the adiabatic change of temperature or the isothermal change of the entropy upon application or removal of magnetic field have generated considerable interest in certain gadolimum alloys and fine magnetic particle systems, because of scientific and potential industrial applications [12–20]. The change in magnetic entropy can be calculated from the following Maxwell’s thermodynamic relation, i.e. [20], qM qS ¼ : ð5Þ qT H qH T Upon integrating of Eq. (5), it yields DS ¼ SðH; TÞ Sð0; TÞ Z H qM ¼ dH: qT H 0
ð6Þ
Thus, if the magnetization MðH; TÞ of a certain material is known, then one can estimate the
83
corresponding magnetic entropy change, utilizing Eq. (6). However, practical use of relation (6) would require accurate determination of the first derivative of the magnetization with respect to temperature in any fields. In this paper detailed magnetization curves MðH; TÞ were measured for five magnetic fluid samples with Co, Fe and Fe3O4 magnetic particles, in the temperature range 85 KoTo300 K and in magnetic fields up to 8 kOe. The magnetic entropy change DSðTÞ for each sample was deduced from the magnetization measurements, using Eq. (6).
2. Experimental Three samples of Fe, Co and Fe3O4 magnetic fluid samples were originally used for this study. The iron-based sample was then prepared by diluting it twice with proper amounts of decalin (decahydronaphthalene) to obtain another two samples. Table 1 summarizes the room temperature saturation magnetization, the liquid carrier and the volume packing fraction j ¼ ðMs =Msb Þ; where Ms is the saturation magnetization of the sample and Msb is the saturation magnetization of the corresponding bulk material, mean magnetic diameter, Dm the initial viscosity Z0 of the liquid carrier and the initial susceptibility wi of the studied samples. The magnetization measurements were carried out as follows: First, the sample was cooled down to liquid nitrogen temperature in zero applied field. Then, a set of isothermal magnetization
Table 1 Values of the magnetic and physical properties for all samples, Packing fraction (f), Liquid carrier (LC), (Isobar-M, IM, and ( Viscosity Decalin D), Mean magnetic diameter (MD) in A, (VIS), Density (r) in g cm3 and initial susceptibility (wi ) in emu g1 Oe1 Sample
j 102
LC
MD
Co Fe3O4 Fe Fe Fe
8.9 7.5 4.1 1.0 0.85
IM IM D D D
49 76
VIS 3.5 20
r
w 103
0.96
11
0.90
25
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
curves were obtained at selected temperatures for each sample in steps of 5 K. All the magnetization measurements were carried out in an automated Oxford Vibrating Sample Magnetometer, equipped with a low-temperature cryostat, using liquid nitrogen as a coolant.
10 1kOe 8 M(emu/gm)
84
6
3. Results and discussion
4
Isothermal magnetization curves were measured for each sample in fields up to 8 kOe in the temperature range 85–300 K in steps of 5 K. This provided us with 43 isothermal magnetization curves for each sample. For each isothermal curve the magnetization was recorded in steps of 0.1– 8 kOe. Fig. 1 shows selected magnetization data for the Co-based magnetic fluid. Similar magnetization curves were obtained for the Fe-, Fe3O4and the diluted Fe-based samples (j ¼ 0:01 and 0.0085). Points were taken from the isothermal curves of each sample to form the isofield MðTÞ curves for that sample. The isofield curves were obtained for fields from 0 to 8 kOe in steps of 0.1 kOe for each sample. Selected curves of MðTÞ are shown in Fig. 2 for Co-based magnetic fluid. All isofield curves, MðTÞ; were differentiated to yield the ðqM=qTÞH values and upon integration
2
15
M(emu/gm)
T=100K 10 T=140K T=200K T=240K 5 T=280K T=300K 0 0
2
4
6
8
H(kOe) Fig. 1. The isothermal magnetization versus applied magnetic field curves at selected temperatures for the Co-based MF sample with packing fraction j ¼ 0:089:
0.5kOe
0.2kOe
100
150
200
250
300
T(K) Fig. 2. The isofield magnetization versus temperature curves at selected fields for the Co-based MF sample with packing fraction j ¼ 0:089:
of ðqM=qTÞH versus H curves, using Eq. (6). The DSðTÞ curve was generated and plotted in Figs. 3 and 4, for the 5 samples. The basic features of the DSðTÞ curves are qualitatively similar in all examined samples. These curves can be readily explained by dividing the curves into three regions, i.e., for ToTmax ; Tmax oToTmin and T > Tmin : Here, Tmax ½Tmin is the temperature at which the DSðTÞ curve exhibits a maximum (a minimum) value, respectively. In the region ToTmax ; the magnetic fluid is frozen, i.e., the magnetic moments of the particles relax via the Ne! el mechanism only. As the temperature is increased, the alignment of the magnetic moments of the particles with the field decreases due to thermal agitation, i.e., the degree of ordering decreases, and hence DSðTÞ increases. This process of increasing the degree of disorder continues until the temperature approaches the melting point of the fluid and the fluid gradually begins to melt. The rate of decrease of Z is given by Eq. (4). Due to the decrease of Z; the tB decreases, thus the two mechanisms (Ne! el and Brown) are available in this region, allowing for a portion of particles to align with the field. Thus, the degree of ordering increases, and as a consequence, the DSðTÞ decreases reaching a maximum at T ¼ Tmax ; which is near the freezing point of the corresponding liquid carrier. Upon further increase of T; the viscosity decreases rapidly, and not only do
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
- ∆S (emu/gm/K)
Table 2 The temperature position Tmax (Tmin ) of the maximum (minimum) DSðTÞ and their values in (erg g1 K1) for 8 kOe integrating magnetic field for the samples (a) Co(0.089), (b) Fe3O4(0.075), (c) Fe(0.041), (d) Fe(0.01) and (e) Fe(0.0085)
Fe3O4-MF, φ = 0.075 Co-MF, φ = 0.089
125
100 8 kOe
75
50
25 50
100
150
200
250
300
T(K) Fig. 3. The magnetic entropy change obtained for the integrating fields 8 kOe as a function of temperature for the Co- and Fe3O4-based MF samples with packing fraction f ¼ 0:089 and 0.0745, respectively.
90 F e- MF 80 φ=0.041
-∆S(emu/gm)
70 60 35
φ=0.01
30 25 φ=0.0085
20 15 100
150
200
85
250
300
T(K) Fig. 4. The magnetic entropy change obtained for the integrating fields 8 kOe as a function of temperature for the Fe-based MF samples with packing fraction f ¼ 0:01; 0.041 and 0.0085.
chain-like clusters begin to be formed with their easy axis direction toward the applied field, but the number of such chains as well as their lengths increase. Thus, the degree of ordering increases,
DSðTÞmax DSðTÞmin Tmax Tmin
a
b
c
d
e
29.1 131 145 250
58 90 145 240
61.7 122 145 255
19.3 35.5 150 255
15 30 160 255
whence DSðTÞ decreases. This process continues till a temperature Tmin ; where the violent Brownian motion of particles is large enough to break the chains and to make the magnetic moments orientation random, thus increasing DSðTÞ: Table 2 summarizes the recorded maximum and minimum values of DSðTÞ and their positions. At low fields (well away from saturation) or high temperatures, one can explain the results within the context of superparamagnetic theory, and argue that the DSðTÞ curve behaves like T 2 [13]. It is found that when we increase the applied magnetic field, the maximum value of DSðTÞ reduces by an amount not proportional to the integrating applied magnetic field. This can be explained by the fact that the contribution in DSðTÞ from low magnetic applied fields is more than that from high field values, since the isothermal magnetization reaches saturation at fields >4 kOe. The minimum values of DSðTÞ were found to decrease with increasing magnetic applied field, since the magnetic particles are easily aligned in a high-applied magnetic field. The magnetic entropy change was calculated from the magnetization measurements for the 11% Fe+silica gel nanocomposites [12]. The results show that the magnetic entropy change for the examined sample is similar to the magnetic entropy change of our samples at the position of maximum entropy change, and of the order B12 erg g1 K1.
4. Summary and conclusion The calorimetry measurements for MFs with different liquid carriers and concentrations are
86
I. Abu-Aljarayesh et al. / Physica B 321 (2002) 82–86
needed to understand the magnetocaloric effect in these systems. It is relevant to mention that MF systems are unique among systems, because they exhibit two kinds of magnetic ordering: one is spatial (chain-like clusters, etc.), the other is magnetic dipoles ordering in which the magnetic moments align with the field.
Acknowledgements We are thankful to Prof. N.Y. Ayoub from our Department for providing us with the original samples.
References [1] R. Rosensweig, Ferrohydrodynamics, Cambridge University Press, New York, 1985. [2] E. Blums, A. Cebers, M.M. Maiorov, Magnetic Fluids, Walter de Gruyter, Berlin, New York, 1997. [3] S.W. Charles, J. Popplewell, in: E.P. Wholfarth (Ed.), Ferromagnetic Materials, Vol. 2, North-Holland, Amsterdam, 1980. [4] P.C. Scholten, J. Magn. Magn. Mater. 39 (1983) 99. [5] V.E. Fertman, Magnetic Fluid, Hemisphere, New York, 1990. [6] M.I. Shliomis, Sov. Phys. Usp. 17 (1974) 153.
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