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Microstructural investigation of some biocompatible ferrofluids
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775 www.elsevier.com/locate/jmmm
Microstructural investigation of some biocompatible ferrofluids M. Ra˘cuciua,, D.E. Creanga˘b, V. Ba˘descuc, N. Sulitanub a
Faculty of Sciences, ‘‘Lucian Blaga’’ University, 10 Blvd. Victoriei, Sibiu 550012, Romania b Faculty of Physics, ‘‘Al. I. Cuza’’ University, 11A Blvd. Copou, 700506 Iasi, Romania c National Institute of Research and Development for Technical Physics, 47 Blvd. D. Mangeron, Iasi, Romania Available online 16 March 2007
Abstract Two batches of aqueous ferrofluids based on iron oxide particles as solid nanomagnetic phase have been prepared by applying the chemical precipitation method. Tetramethylammonium hydroxide (N(CH3)4OH) and citric acid (C6H8O7) were used to functionalize magnetic cores. Physical tests have been performed in order to reveal the microstructural and magnetic features, both needed for biomedical utilization. The particle size was investigated using transmission electron microscopy (TEM), magnetization measurements and X-ray diffraction (for composition and phase information). The dimensional distribution of the ferrophase physical diameter was comparatively discussed using the box-plot statistical method revealing the fulfilling of the main requirements for ferrofluid stability. r 2007 Elsevier B.V. All rights reserved. PACS: 47.65.Cb; 61.46.Df; 81.07.b; 68.37.Lp; 96.15.Pf; 75.60.Ej Keywords: Magnetite; Aqueous ferrofluid; XRD pattern; TEM investigation; Magnetic property
1. Introduction Stable concentrated suspensions of magnetic nanoparticles in either organic or inorganic solvents are called magnetic fluids or ferrofluids [1]. Magnetic fluids represent a welldefined category of magnetically controllable nanomaterials with fluid properties. NASA was the first to develop and characterize ferrofluids in 1960s by Stephen Papell [2]. Since then, ferrofluids have been used in many applications in both technical and life sciences. In recent years, researchers have prepared new ferrofluids and ferrofluid products with biomedical purposes [3–5]. Ferrofluids are suspensions of superparamagnetic particles—small single domain particles—that respond to a magnetic field but completely demagnetize when the field is removed. Colloidal stability is assured by coating the particle with a shell of nonmagnetic molecular surfactants which prevent close approach of the nanomagnetic cores thereby reducing the possibility of aggregation via Van der Waals or magnetic attractions. The magnetic colloidal particles usually have a small diameter, in the range of 10 nm that reduce the effect of Corresponding author. Tel.:+40 269217802; fax: +40 369814170.
E-mail address: [email protected] (M. Ra˘cuciu). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.03.095
the attractive interactions between the particles. Ferrofluid stability is the main characteristic that determines the possibility to exploit ferrofluids in different industrial and biomedical applications. In the present work, we describe the preparation and characterization of two batches of ferrofluid using tetramethylammonium hydroxide and citric acid to stabilize magnetic nanoparticles in colloidal suspension. In the future applications of the ferrofluids, we will focus more toward the biological uses where the ultra-fine ferrophase is particularly important for the penetration of the cell structures. 2. Experimental Two batches of aqueous ferrofluid prepared for biomedical use by applying basically the same preparation protocol have been analyzed. 2.1. Ferrofluid preparation The synthesis of magnetic nanoparticles has been carried out via a controlled chemical precipitation approach, at
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
room temperature, as described in Ref. [6]. Aqueous mixture of ferric and ferrous salts and NH3 as an alkali source were prepared as stock solutions. The stock solution of ferric and ferrous salts was prepared in presence of 2 M HCl solution since the acidic conditions prevent formation of iron hydroxides. We have combined 6.0 mL of 2 M stock FeCl2 solution and 24.0 mL of 1 M stock FeCl3 solution mixed under vigorous and continuous magnetic stirring with 300 mL of 0.7 M aqueous NH3 solution, added dropwise. A black precipitate of iron oxides, magnetite and maghemite, was formed immediately. The ferrophase was decanted in an inhomogeneous magnetic field and then filtration was carried out to separate the supernatant. The iron oxide powder was washed several times with deionized water—800 mL quantity in total. The ferrophase obtained (2.16 g) was vigorously mechanically mixed with 6 mL aqueous citric acid (C6H8O7) 25% solution and tetramethylammonium hydroxide (N(CH3)4OH) 25% solution. Both systems are designed to get the same interparticle interaction—electrostatic repulsion occurs due to the charges of citrate molecules and the tetramethylammonium cations adsorbed on the particles surface in water. Physical tests have been performed on these two ferrofluids.
e773
3. Results and discussions The obtained ferrofluids were dark brown, exhibited positive magnetic behavior in the presence of a permanent magnet, and kept their colloidal characteristics for up to 3 months. Low level of ferrofluids sedimentation in time was observed. One might presume that magnetite and maghemite are components of the obtained ferrophase since the oxidation reactions could not be totally avoided during chemical synthesis and solid powder washings. In Fig. 1a, TEM image of the ferrophase particles coated with tetramethylammonium hydroxide (TMA-FF sample) is shown. Mainly spherical particles are evidenced with some rare aggregates; the same situation being characteristic also for the ferrophase coated with citric acid (CA-FF sample). The analysis of all TEM pictures measurements resulted in diameter distribution histograms (Fig. 2) having maximum frequency at about 11.4 nm in CA-FF sample and 7.9 nm in TMA-FF sample. Some large aggregates and particle chains, especially for CA-FF sample, have been also observed. In Fig. 3, the box-plot diagram is presented for comparative discussion of dimensional distributions of water-based ferrofluids. The distribution curves are represented by two boxes accordingly to Ref. [7], the box edges being given by the
2.2. Structural investigation Transmission electron microscopy (TEM) investigations were carried out. TEM was the main investigation method for assessing the ferrophase particle size. A TESLA device with a resolution of 1.0 nm was utilized (sample deposition of collodion sheet after 104 dilution). In order to characterize the crystalline structure of the magnetic nanoparticles, X-ray diffraction (XRD) measurements were performed on powder samples obtained after evaporation of the liquid carrier, using a DRON 2.0 X-ray diffractometer and Cu Ka radiation at 1.5418 A˚. 2.3. Magnetic properties
2.4. Statistical analysis The box-plot representation of the distribution curves [7] was applied in order to compare ferrophase diameter histograms.
CA-FF
TMA-FF
100
Particles number
200 Particles number
Magnetic susceptibility and magnetization measurements were carried out by Gouy method. Magnetic field intensity was measured by means of a Walker Scientific MG 50D Gaussmeter with a Hall probe. For sample weight was used an electronic balance ACULAB-200 with 104 g accuracy. The measurements were performed at constant temperature (22.070.1 1C), using in all cases the same air-tight nonmagnetic cylindrical sample holder with 3 mm diameter and 25 cm length, placed perpendicular to the magnetic field.
Fig. 1. TEM image for TMA-FF sample.
50
0
0
5
10
15 20 d(nm)
25
30
100
0
0
5
10 15 d(nm)
20
25
Fig. 2. Histograms for the analyzed ferrofluids. CA-FF: coated with citric acid. TMA-FF: coated with tetramethylammonium hydroxide.
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
e774 30
25
25
20
TMA-FF
M(kA/m)
d(nm)
20 15
CA-FF
15
10
10 5
5
0
0
0
CA.FF ferrofluid samples
Fig. 3. Box-plot diagram for ferrofluid batches. ‘‘&’’ represent average dimension of magnetic nanoparticles and ‘‘K’’exceptionally small or large values of magnetic particles diameter.
values of 25% and 75% of cumulated frequency of data appearance (usually noted as Q1 and Q3). The median value is given by the cumulated frequency of 50%, for symmetrical distributions this value being practically the same with the average value—represented by the open point within the box—as in the case of our two distributions. One might see that the smaller size of colloidal particles and a symmetrical box was obtained to TMA-FF ferrofluid batch. The asymmetry tendency toward the high diameter values is suggested by the black points, i.e. data satisfying the formula: d4Q3 þ 3ðQ3 Q1 Þ,
200
300
400
500
H(kA/m)
Fig. 4. Magnetization curves of ferrofluids. TMA-FF: coated with tetramethylammonium hydroxide. CA-FF: coated with citric acid.
0.3 TMA-FF
CA-FF
200000 300000 H(A/m)
400000
0.25 0.2 χ(u.SI)
TMA.FF
100
0.15 0.1 0.05 0 0
100000
500000
(1)
where d is the diameter. For both ferrofluids analyzed, exceptionally large size particles ranged between 20 and 25 nm. The XRD investigation was carried out on uncoated ferrophase. Average crystallite size was estimated using the Debye–Scherrer equation (Dhkl ¼ 0:9l=B cos y), in which B is the effective full-width at half-maximum of the XRD diffraction line [8] confirming the previous results regarding the average size of magnetic particles. The value provided by the above formula was 7.6 nm. Magnetization curves obtained by Gouy method for TMA-FF and CA-FF ferrofluid samples are presented in Fig. 4. Magnetization curves can be used for the study of both particle interactions and agglomerate formation, processes that strongly influence the rheological behavior of ferrofluids. The saturation magnetization was obtained from magnetization versus 1=H curves, by extrapolating to 1=H ¼ 0. For the ferrofluid coated with citric acid (CA-FF), the saturation magnetization value is 23 kA/m while for the ferrofluid coated with tetramethylammonium hydroxide (TMA-FF) the corresponding value is 10 kA/m, being one order of magnitude lower than the magnetite saturation magnetization reported in literature. These are concordant with the previous presumption that magnetite and maghemite are both present within the ferrophase composition and also with the data regarding the ferrophase volume fractions that were equal to 2.50% for TMA-FF sample and 5.75%
Fig. 5. Susceptibility curves of ferrofluids. TMA-FF: coated with tetramethylammonium hydroxide. CA-FF: coated with citric acid.
for CA-FF sample. The initial susceptibility wi was determined from the susceptibility curve registered by extrapolating the initial linear curve to H ¼ 0. Initial magnetic susceptibility value for the analyzed ferrofluids was 0.17 for CA-FF sample and 0.3 for TMA-FF sample. In Fig. 5 the susceptibility curves for TMA-FF and CA-FF ferrofluid samples are presented. The differences between the magnetic parameter values in the case of the two ferrofluids could be related mainly to the efficiency of the solid core stabilization that appears to be different in the case of the two chemical species used to cover the ferrophase (uncoated ferrophase being eliminated by centrifugal purification). Also, larger diameter particles of the citrate-coated ferrophase could result following supernatant centrifugal separation—so, possibly more large particles remained in this ferrofluid sample compared to the TMA-FF one. 4. Conclusions In this study, two batches of water-based ferrofluids were prepared. The stabilization of magnetic nanoparticles for biological uses was accomplished by coating the magnetite with citric acid and tetramethylammonium hydroxide shell. The availability for biological purposes is assured by the fine ferrophase diameter while the high magnetic properties
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
are also suggested. Their future destination for living tissue applications will be accompanied by adequate measurements of the biological effects. References [1] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1981. [2] S.S. Papell, US Patent 3, 215, 1965, 572. [3] C. Grob, K. Bu¨scher, E. Romanus, C.A. Helm, W. Weitschies, Eur. Cells Mater. 3 (2) (2002) 163.
e775
[4] L.M. Lacava, Z.G. Lacava, M.F. Da Silva, O. Silva, S.B. Chaves, R.B. Azevedo, F. Pelegrini, C. Gansau, N. Buske, D. Sabolovic, P.C. Morais, Biophys. J. 80 (2001) 2483. [5] Z.G.M. Lacava, R.B. De Azevedo, L.M. Lacava, E.V. Martins, V.A.P. Garcia, C.A. Re´bola, A.P.C. Lemos, M.H. Sousa, F.A. Tourinho, P.C. Morais, M.F. Da Silva, J. Magn. Magn. Mater. 194 (1–3) (1999) 90. [6] J. Breitzer, G. Lisensky, J. Chem. Educ. 76 (1999) 943. [7] L.H. Koopmans, Introduction to Contemporary Statistical Methods, Duxbury Boston, 1987. [8] B.D. Cullity, Elements of X-ray Diffraction, A.W.P.C., Massachusetts, 1967.
Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775 www.elsevier.com/locate/jmmm
Microstructural investigation of some biocompatible ferrofluids M. Ra˘cuciua,, D.E. Creanga˘b, V. Ba˘descuc, N. Sulitanub a
Faculty of Sciences, ‘‘Lucian Blaga’’ University, 10 Blvd. Victoriei, Sibiu 550012, Romania b Faculty of Physics, ‘‘Al. I. Cuza’’ University, 11A Blvd. Copou, 700506 Iasi, Romania c National Institute of Research and Development for Technical Physics, 47 Blvd. D. Mangeron, Iasi, Romania Available online 16 March 2007
Abstract Two batches of aqueous ferrofluids based on iron oxide particles as solid nanomagnetic phase have been prepared by applying the chemical precipitation method. Tetramethylammonium hydroxide (N(CH3)4OH) and citric acid (C6H8O7) were used to functionalize magnetic cores. Physical tests have been performed in order to reveal the microstructural and magnetic features, both needed for biomedical utilization. The particle size was investigated using transmission electron microscopy (TEM), magnetization measurements and X-ray diffraction (for composition and phase information). The dimensional distribution of the ferrophase physical diameter was comparatively discussed using the box-plot statistical method revealing the fulfilling of the main requirements for ferrofluid stability. r 2007 Elsevier B.V. All rights reserved. PACS: 47.65.Cb; 61.46.Df; 81.07.b; 68.37.Lp; 96.15.Pf; 75.60.Ej Keywords: Magnetite; Aqueous ferrofluid; XRD pattern; TEM investigation; Magnetic property
1. Introduction Stable concentrated suspensions of magnetic nanoparticles in either organic or inorganic solvents are called magnetic fluids or ferrofluids [1]. Magnetic fluids represent a welldefined category of magnetically controllable nanomaterials with fluid properties. NASA was the first to develop and characterize ferrofluids in 1960s by Stephen Papell [2]. Since then, ferrofluids have been used in many applications in both technical and life sciences. In recent years, researchers have prepared new ferrofluids and ferrofluid products with biomedical purposes [3–5]. Ferrofluids are suspensions of superparamagnetic particles—small single domain particles—that respond to a magnetic field but completely demagnetize when the field is removed. Colloidal stability is assured by coating the particle with a shell of nonmagnetic molecular surfactants which prevent close approach of the nanomagnetic cores thereby reducing the possibility of aggregation via Van der Waals or magnetic attractions. The magnetic colloidal particles usually have a small diameter, in the range of 10 nm that reduce the effect of Corresponding author. Tel.:+40 269217802; fax: +40 369814170.
E-mail address: [email protected] (M. Ra˘cuciu). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.03.095
the attractive interactions between the particles. Ferrofluid stability is the main characteristic that determines the possibility to exploit ferrofluids in different industrial and biomedical applications. In the present work, we describe the preparation and characterization of two batches of ferrofluid using tetramethylammonium hydroxide and citric acid to stabilize magnetic nanoparticles in colloidal suspension. In the future applications of the ferrofluids, we will focus more toward the biological uses where the ultra-fine ferrophase is particularly important for the penetration of the cell structures. 2. Experimental Two batches of aqueous ferrofluid prepared for biomedical use by applying basically the same preparation protocol have been analyzed. 2.1. Ferrofluid preparation The synthesis of magnetic nanoparticles has been carried out via a controlled chemical precipitation approach, at
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
room temperature, as described in Ref. [6]. Aqueous mixture of ferric and ferrous salts and NH3 as an alkali source were prepared as stock solutions. The stock solution of ferric and ferrous salts was prepared in presence of 2 M HCl solution since the acidic conditions prevent formation of iron hydroxides. We have combined 6.0 mL of 2 M stock FeCl2 solution and 24.0 mL of 1 M stock FeCl3 solution mixed under vigorous and continuous magnetic stirring with 300 mL of 0.7 M aqueous NH3 solution, added dropwise. A black precipitate of iron oxides, magnetite and maghemite, was formed immediately. The ferrophase was decanted in an inhomogeneous magnetic field and then filtration was carried out to separate the supernatant. The iron oxide powder was washed several times with deionized water—800 mL quantity in total. The ferrophase obtained (2.16 g) was vigorously mechanically mixed with 6 mL aqueous citric acid (C6H8O7) 25% solution and tetramethylammonium hydroxide (N(CH3)4OH) 25% solution. Both systems are designed to get the same interparticle interaction—electrostatic repulsion occurs due to the charges of citrate molecules and the tetramethylammonium cations adsorbed on the particles surface in water. Physical tests have been performed on these two ferrofluids.
e773
3. Results and discussions The obtained ferrofluids were dark brown, exhibited positive magnetic behavior in the presence of a permanent magnet, and kept their colloidal characteristics for up to 3 months. Low level of ferrofluids sedimentation in time was observed. One might presume that magnetite and maghemite are components of the obtained ferrophase since the oxidation reactions could not be totally avoided during chemical synthesis and solid powder washings. In Fig. 1a, TEM image of the ferrophase particles coated with tetramethylammonium hydroxide (TMA-FF sample) is shown. Mainly spherical particles are evidenced with some rare aggregates; the same situation being characteristic also for the ferrophase coated with citric acid (CA-FF sample). The analysis of all TEM pictures measurements resulted in diameter distribution histograms (Fig. 2) having maximum frequency at about 11.4 nm in CA-FF sample and 7.9 nm in TMA-FF sample. Some large aggregates and particle chains, especially for CA-FF sample, have been also observed. In Fig. 3, the box-plot diagram is presented for comparative discussion of dimensional distributions of water-based ferrofluids. The distribution curves are represented by two boxes accordingly to Ref. [7], the box edges being given by the
2.2. Structural investigation Transmission electron microscopy (TEM) investigations were carried out. TEM was the main investigation method for assessing the ferrophase particle size. A TESLA device with a resolution of 1.0 nm was utilized (sample deposition of collodion sheet after 104 dilution). In order to characterize the crystalline structure of the magnetic nanoparticles, X-ray diffraction (XRD) measurements were performed on powder samples obtained after evaporation of the liquid carrier, using a DRON 2.0 X-ray diffractometer and Cu Ka radiation at 1.5418 A˚. 2.3. Magnetic properties
2.4. Statistical analysis The box-plot representation of the distribution curves [7] was applied in order to compare ferrophase diameter histograms.
CA-FF
TMA-FF
100
Particles number
200 Particles number
Magnetic susceptibility and magnetization measurements were carried out by Gouy method. Magnetic field intensity was measured by means of a Walker Scientific MG 50D Gaussmeter with a Hall probe. For sample weight was used an electronic balance ACULAB-200 with 104 g accuracy. The measurements were performed at constant temperature (22.070.1 1C), using in all cases the same air-tight nonmagnetic cylindrical sample holder with 3 mm diameter and 25 cm length, placed perpendicular to the magnetic field.
Fig. 1. TEM image for TMA-FF sample.
50
0
0
5
10
15 20 d(nm)
25
30
100
0
0
5
10 15 d(nm)
20
25
Fig. 2. Histograms for the analyzed ferrofluids. CA-FF: coated with citric acid. TMA-FF: coated with tetramethylammonium hydroxide.
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
e774 30
25
25
20
TMA-FF
M(kA/m)
d(nm)
20 15
CA-FF
15
10
10 5
5
0
0
0
CA.FF ferrofluid samples
Fig. 3. Box-plot diagram for ferrofluid batches. ‘‘&’’ represent average dimension of magnetic nanoparticles and ‘‘K’’exceptionally small or large values of magnetic particles diameter.
values of 25% and 75% of cumulated frequency of data appearance (usually noted as Q1 and Q3). The median value is given by the cumulated frequency of 50%, for symmetrical distributions this value being practically the same with the average value—represented by the open point within the box—as in the case of our two distributions. One might see that the smaller size of colloidal particles and a symmetrical box was obtained to TMA-FF ferrofluid batch. The asymmetry tendency toward the high diameter values is suggested by the black points, i.e. data satisfying the formula: d4Q3 þ 3ðQ3 Q1 Þ,
200
300
400
500
H(kA/m)
Fig. 4. Magnetization curves of ferrofluids. TMA-FF: coated with tetramethylammonium hydroxide. CA-FF: coated with citric acid.
0.3 TMA-FF
CA-FF
200000 300000 H(A/m)
400000
0.25 0.2 χ(u.SI)
TMA.FF
100
0.15 0.1 0.05 0 0
100000
500000
(1)
where d is the diameter. For both ferrofluids analyzed, exceptionally large size particles ranged between 20 and 25 nm. The XRD investigation was carried out on uncoated ferrophase. Average crystallite size was estimated using the Debye–Scherrer equation (Dhkl ¼ 0:9l=B cos y), in which B is the effective full-width at half-maximum of the XRD diffraction line [8] confirming the previous results regarding the average size of magnetic particles. The value provided by the above formula was 7.6 nm. Magnetization curves obtained by Gouy method for TMA-FF and CA-FF ferrofluid samples are presented in Fig. 4. Magnetization curves can be used for the study of both particle interactions and agglomerate formation, processes that strongly influence the rheological behavior of ferrofluids. The saturation magnetization was obtained from magnetization versus 1=H curves, by extrapolating to 1=H ¼ 0. For the ferrofluid coated with citric acid (CA-FF), the saturation magnetization value is 23 kA/m while for the ferrofluid coated with tetramethylammonium hydroxide (TMA-FF) the corresponding value is 10 kA/m, being one order of magnitude lower than the magnetite saturation magnetization reported in literature. These are concordant with the previous presumption that magnetite and maghemite are both present within the ferrophase composition and also with the data regarding the ferrophase volume fractions that were equal to 2.50% for TMA-FF sample and 5.75%
Fig. 5. Susceptibility curves of ferrofluids. TMA-FF: coated with tetramethylammonium hydroxide. CA-FF: coated with citric acid.
for CA-FF sample. The initial susceptibility wi was determined from the susceptibility curve registered by extrapolating the initial linear curve to H ¼ 0. Initial magnetic susceptibility value for the analyzed ferrofluids was 0.17 for CA-FF sample and 0.3 for TMA-FF sample. In Fig. 5 the susceptibility curves for TMA-FF and CA-FF ferrofluid samples are presented. The differences between the magnetic parameter values in the case of the two ferrofluids could be related mainly to the efficiency of the solid core stabilization that appears to be different in the case of the two chemical species used to cover the ferrophase (uncoated ferrophase being eliminated by centrifugal purification). Also, larger diameter particles of the citrate-coated ferrophase could result following supernatant centrifugal separation—so, possibly more large particles remained in this ferrofluid sample compared to the TMA-FF one. 4. Conclusions In this study, two batches of water-based ferrofluids were prepared. The stabilization of magnetic nanoparticles for biological uses was accomplished by coating the magnetite with citric acid and tetramethylammonium hydroxide shell. The availability for biological purposes is assured by the fine ferrophase diameter while the high magnetic properties
ARTICLE IN PRESS M. Ra˘cuciu et al. / Journal of Magnetism and Magnetic Materials 316 (2007) e772–e775
are also suggested. Their future destination for living tissue applications will be accompanied by adequate measurements of the biological effects. References [1] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1981. [2] S.S. Papell, US Patent 3, 215, 1965, 572. [3] C. Grob, K. Bu¨scher, E. Romanus, C.A. Helm, W. Weitschies, Eur. Cells Mater. 3 (2) (2002) 163.
e775
[4] L.M. Lacava, Z.G. Lacava, M.F. Da Silva, O. Silva, S.B. Chaves, R.B. Azevedo, F. Pelegrini, C. Gansau, N. Buske, D. Sabolovic, P.C. Morais, Biophys. J. 80 (2001) 2483. [5] Z.G.M. Lacava, R.B. De Azevedo, L.M. Lacava, E.V. Martins, V.A.P. Garcia, C.A. Re´bola, A.P.C. Lemos, M.H. Sousa, F.A. Tourinho, P.C. Morais, M.F. Da Silva, J. Magn. Magn. Mater. 194 (1–3) (1999) 90. [6] J. Breitzer, G. Lisensky, J. Chem. Educ. 76 (1999) 943. [7] L.H. Koopmans, Introduction to Contemporary Statistical Methods, Duxbury Boston, 1987. [8] B.D. Cullity, Elements of X-ray Diffraction, A.W.P.C., Massachusetts, 1967.