Nanocrystalline Nickel Ferrite, NiFe2O4: Mechanosynthesis

J. Mantilla , L.León Félix , M.A. Rodriguez , F.H. Aragon , P.C. Morais , J.A.H. Coaquira ..... Synthesis and characterization of a CaFe 2 O 4 catal...
0 downloads 0 Views 441KB Size
Download PDF
5026

J. Phys. Chem. C 2007, 111, 5026-5033

Nanocrystalline Nickel Ferrite, NiFe2O4: Mechanosynthesis, Nonequilibrium Cation Distribution, Canted Spin Arrangement, and Magnetic Behavior Vladimir Sˇ epela´ k,*,†,‡ Ingo Bergmann,† Armin Feldhoff,§ Paul Heitjans,§ Frank Krumeich,| Dirk Menzel,⊥ Fred J. Litterst,⊥ Stewart J. Campbell,# and Klaus D. Becker† Institute of Physical and Theoretical Chemistry, Braunschweig UniVersity of Technology, Hans-Sommer-Strasse 10, D-38106 Braunschweig, Germany, Institute of Physical Chemistry and Electrochemistry, Leibniz UniVersity of HannoVer, Callinstrasse 3-3A, D-30167 HannoVer, Germany, Laboratory of Inorganic Chemistry, Swiss Federal Institute of Technology Zu¨rich, Ho¨nggerberg HCI-G105, CH-8093 Zurich, Switzerland, and Institute of Condensed Matter Physics, Braunschweig UniVersity of Technology, Mendelssohnstrasse 3, D-38106 Braunschweig, Germany ReceiVed: NoVember 16, 2006; In Final Form: December 29, 2006

Nickel ferrite (NiFe2O4) nanoparticles with an average crystallite size of about 8.6 nm were prepared by mechanochemical synthesis (mechanosynthesis). In-field Mo¨ssbauer spectroscopy and high-resolution TEM studies revealed a nonuniform structure of mechanosynthesized NiFe2O4 nanoparticles consisting of an ordered core surrounded by a disordered grain boundary (surface) region. The inner core of a NiFe2O4 nanoparticle is considered to possess a fully inverse spinel structure with a Ne´el-type collinear spin alignment, whereas the surface shell is found to be structurally and magnetically disordered due to the nearly random distribution of cations and the canted spin arrangement. As a consequence of frustrated superexchange interactions in the surface shell, the mechanosynthesized NiFe2O4 exhibits a reduced nonsaturating magnetization, an enhanced coercivity, and a shifted hysteresis loop. The study also demonstrates that one can tailor the magnetic properties of mechanosynthesized NiFe2O4 particles by suitably controlling their size. The thickness of the surface shell of about 1 nm estimated from size-dependent magnetization measurements is found to be in good agreement with that obtained from high-resolution TEM and Mo¨ssbauer experiments. On heating above 673 K, the mechanosynthesized NiFe2O4 relaxes to a structural and magnetic state that is similar to the bulk one.

Introduction Interest in nanosized spinel ferrites of the type MFe2O4 (M is a divalent metal cation) has greatly increased in the past few years due to their importance in understanding the fundamentals in nanomagnetism1a and their wide range of applications such as high-density data storage, ferrofluid technology, sensor technology, spintronics, magnetocaloric refrigeration, heterogeneous catalysis, magnetically guided drug delivery, and magnetic resonance imaging.1 To emphasize the site occupancy at the atomic level, the structural formula of 2-3 spinel ferrites 2+ 2+ 3+ Fe3+ may be written as (M1-λ λ )[Mλ Fe2-λ ]O4, where parentheses and square brackets denote cation sites of tetrahedral (A) and octahedral [B] coordination, respectively. λ represents the so-called degree of inversion defined as the fraction of the (A) sites occupied by Fe3+ cations. Nickel ferrite, NiFe2O4, as a soft magnetic n-type semiconducting material, is an important member of the spinel family with a fully inverse structure (λ ) 1) in the bulk state.2 Its preparation by the classical solid-state reaction requires a number * To whom correspondence should be addressed. Tel.: +49-5313917387. Fax: +49-531-3917305. E-mail: [email protected]. † Institute of Physical and Theoretical Chemistry, Braunschweig University of Technology. ‡ On leave from the Slovak Academy of Sciences, Kos ˇice, Slovakia. § Leibniz University of Hannover. | Swiss Federal Institute of Technology Zu ¨ rich. ⊥ Institute of Condensed Matter Physics, Braunschweig University of Technology. # The University of New South Wales, Australian Defence Force Academy, Canberra, Australia.

of stages, including homogenization of the powder precursors, compaction of the reactants, and finally prolonged heat treatment at considerably elevated temperatures.3 One goal of modern ferrite research and development has been to identify simpler processing schemes that do not rely upon high-temperature treatments for inducing solid-state reactions. Several techniques have already been used to produce NiFe2O4 nanoparticles, including hydrothermal reactions,4 coprecipitation,5 combustion synthesis,6 thermal decomposition,7 the sol-gel method,8 microwave processing,9 electrospinning,10 the reverse micelle technique,11 the plasma deposition method,12 the radio frequency thermal plasma torch technique,13 the pulsed wire discharge,14 sonochemical synthesis,15 and high-energy milling.2,16 The latter method can deliver nanocrystalline ferrites (and oxides in general) either by particle size reduction of bulk material to the nanometer scale without changes in its chemical composition2,16,17 or by inducing a heterogeneous solid-state chemical reaction between the ferrite precursors, i.e., by the mechanically induced formation reaction (mechanosynthesis).18 In this article, we will report on the single-step synthesis of nanocrystalline NiFe2O4 via high-energy milling of binary oxide precursors (RFe2O3 and NiO) at room-temperature. Although the mechanosynthesis of NiFe2O4 has already been reported in a few papers,19 to the best of our knowledge there is no report in the literature on the defect state or the disordered structure of NiFe2O4 prepared by the nonconventional mechanochemical route. Note that, in the above-mentioned papers, only the formation of mechanosynthesized NiFe2O4 has been established by X-ray diffraction and/or Mo¨ssbauer spectroscopy. In this article, we

10.1021/jp067620s CCC: $37.00 © 2007 American Chemical Society Published on Web 03/09/2007

Mechanosynthesized Nickel Ferrite

J. Phys. Chem. C, Vol. 111, No. 13, 2007 5027

present a detailed study of the structural and magnetic disorder in nanosized mechanosynthesized NiFe2O4. For the first time, quantitative microstructural information is obtained on the nonequilibrium cation distribution and on the noncollinear spin arrangement in NiFe2O4 synthesized in a one-step mechanochemical process. The mechanochemical synthesis provides an opportunity to fabricate novel nanostructured solids with anomalous properties different from those of bulk samples prepared by the standard ceramic processing.17-20 For instance, an enhanced chemical reactivity, an enhanced magnetization, and an enhanced magnetic ordering temperature have been observed in nanosized mechanosynthesized spinel ferrites.21,22 However, precise knowledge of the relationships between particle shape and size, interior and surface structure, and the resulting properties of nanocrystalline ferrites is still lacking. In this paper, the magnetic behavior of mechanosynthesized NiFe2O4 is characterized, focusing on the study of the size-dependent magnetization. Mechanosynthesized spinel ferrites are often inherently unstable because of their small constituent sizes, disordered structural state, and high chemical activity.22 To gain insight into the thermal stability and relaxation of the structural disorder, the present experimental work also focuses on the study of the response of mechanosynthesized NiFe2O4 to changes in temperature. Experimental Section For the mechanochemical synthesis of NiFe2O4, stoichiometric mixtures of R-Fe2O3 and NiO reactants (Merck, Darmstadt, Germany) were used as starting materials. The R-Fe2O3/NiO mixtures (10 g) were milled for various times (up to 8 h) in a Pulverisette 6 planetary ball mill (Fritsch, Idar-Oberstein, Germany) at room temperature. A grinding chamber (250 cm3 in volume) and balls (10 mm in diameter) made of tungsten carbide were used. The ball-to-powder weight ratio was 20:1. Milling experiments were performed in air at 600 rpm. Additionally, bulk NiFe2O4, which served as a reference sample in this study, was prepared by the conventional solid-state (ceramic) route. The X-ray diffraction (XRD) patterns were collected using a URD 6 powder diffractometer (Seifert-FPM, Freiberg, Germany) with Fe KR radiation. The microstructural characteristics (crystallite size and strains) were obtained from the Rietveld analysis of the XRD data using the PowderCell program.23 The JCPDS PDF database24 was utilized for phase identification. Mo¨ssbauer spectra were taken in transmission geometry using a 57Co/Rh γ-ray source. High-field Mo¨ssbauer spectra were recorded at T ) 3 K in the presence of an external magnetic field of 5.5 T applied perpendicular to the γ-ray direction. The velocity scale was calibrated relative to 57Fe in Rh. Recoil spectral analysis software25 was used for the quantitative evaluation of the Mo¨ssbauer spectra. The degree of inversion, λ, was calculated from the Mo¨ssbauer subspectral intensities (I(A)/I[B] ) (f(A)/f[B])(λ/(2 - λ))), assuming that the ratio of the recoilless fractions is f[B]/f(A) ) 1 at 3 K and f[B]/f(A) ) 0.94 at room temperature.26 The average canting angle, Ψ, was calculated from the ratio of the intensities of lines 2 and 1, I2/ I1, according to formula Ψ ) 90° - arcsin{[3(I2/I1)/2]/[1+3(I2/I1)/4]}1/2.27 Magnetic measurements were made using a SQUID magnetometer. The morphology of powders and the sizes of individual crystallites were studied using a combined field-emission (scanning) transmission electron microscope (S)TEM (JOEL JEM-2100F) with an ultrahigh-resolution pole piece that pro-

Figure 1. Room-temperature Mo¨ssbauer spectra of the R-Fe2O3/NiO mixture milled for various times [(a) 0, (b) 0.25, (c) 0.5, (d) 1, (e) 2, (f) 4, and (g) 8 h] and of (h) bulk NiFe2O4.

vides a point resolution better than 0.19 nm at 200 kV. Prior to TEM investigations, powders were crushed in a mortar, dispersed in ethanol, and fixed on a copper-supported carbon film. Results and Discussion The mechanically induced evolution of the R-Fe2O3/NiO mixture submitted to high-energy milling was followed by 57Fe Mo ¨ ssbauer spectroscopic measurements. Figure 1a-g shows Mo¨ssbauer spectra of the R-Fe2O3/NiO mixture milled for various times. For comparison, the Mo¨ssbauer spectrum of a NiFe2O4 standard sample (bulk material prepared by the conventional ceramic route) is also presented in Figure 1h. The spectrum of the starting R-Fe2O3/NiO mixture (Figure 1a) shows a sextet with a magnetic hyperfine field of 52.26(4) T corresponding to R-Fe2O3. With increasing milling time, the sextet becomes asymmetric toward the inside of each line, slowly collapses, and is gradually replaced by a central doublet and a new broadened sextet (Figure 1a-g). The spectral components in the spectrum of the sample milled for 8 h (Figure 1g) can be understood to arise from 57Fe in small particles with relaxation times τ < τL (dominating superparamagnetic doublet) and τ > τL (minor sextet structure), where τL is the Larmor precession time of the nuclear magnetic moment (τL ≈ 1 × 10-8 - 1 × 10-9 s).28 The broad shape of these spectral components, in contrast to relatively narrow magnetically split lines for the bulk NiFe2O4 (compare lines g and h in Figure 1), provides clear evidence of a wide distribution of magnetic fields acting on the Fe3+ nuclei in the newly formed material.

5028 J. Phys. Chem. C, Vol. 111, No. 13, 2007

Figure 2. XRD patterns of the R-Fe2O3/NiO mixture milled for various times [(a) 0, (b) 0.25, (c) 0.5, (d) 1, (e) 2, (f) 4, and (g) 8 h] and of (h) bulk NiFe2O4. Diffraction peaks of the reaction precursors and the bulk NiFe2O4 are denoted by Miller indices.

To determine the phase evolution of the R-Fe2O3/NiO mixture during high-energy milling in greater detail, the mechanochemical reaction was also followed by XRD. Figure 2 compares the XRD patterns of the R-Fe2O3/NiO mixtures milled for various times and the bulk NiFe2O4 standard. The XRD pattern of the starting powder (Figure 2a) is characterized by sharp diffraction peaks corresponding to crystalline R-Fe2O3 (JCPDS PDF 33-0664) and NiO (JCPDS PDF 47-1049).24 With increasing milling time, the diffraction peaks corresponding to the simple oxides gradually disappear (see Figure 2a-g). In the XRD pattern of the sample milled for 8 h (a product of the mechanochemical reaction), all diffraction peaks detected above the background are due to the NiFe2O4 phase (JCPDS PDF 100325).24 This confirms that the mechanochemical synthesis of NiFe2O4 is feasible and complete. The Rietveld analysis of the XRD data revealed both an average crystallite size of 8.6(3) nm and the presence of mean strains of 3.4(2) × 10-3 in the produced ferrite. Compared to other synthesis routes to NiFe2O4,4-16 the mechanochemical process used here represents a one-step, high-yielding, low-temperature and low-cost procedure for the synthesis of nanocrystalline NiFe2O4. Representative TEM micrographs of nanocrystalline mechanosynthesized material at low and high magnifications are shown in Figure 3, panels a and b, respectively. It has been revealed that the mechanosynthesized ferrite consists of crystallites mostly in the 6-13 nm size range, consistent with the average crystallite size determined by XRD. As shown in Figure 3a, nanoscale crystallites tend to agglomerate. They are found to be roughly spherical with the so-called core-shell structure consisting of

Sˇ epela´k et al. an ordered inner core surrounded by a disordered grain boundary (surface shell) region. The thickness of the disordered surface shell estimated from high-resolution TEM was found to be about 1 nm (Figure 3b). The nonuniform core-shell structure of nanoparticles has recently been reported for mechanosynthesized MgFe2O422 and ball-milled nanocrystalline LiNbO3.29 To determine both the ionic configuration and spin arrangement in mechanosynthesized ferrite nanoparticles, we found it necessary to perform low-temperature Mo¨ssbauer measurements in conjunction with large external magnetic fields. The highfield Mo¨ssbauer spectra for both bulk and nanosized mechanosynthesized NiFe2O4 taken at 3 K are compared in Figure 4. The Mo¨ssbauer spectrum of the bulk NiFe2O4 (Figure 4a) was fitted by a superposition of two subspectra corresponding to Fe3+(A) and Fe3+[B] ions. The degree of inversion of the bulk NiFe2O4, calculated from the subspectral intensity ratio I(A)/I[B], was found to be λ ) 0.996(3). The intensity ratio I2/I1 ≈ 4/3 for both (A) and [B] subspectra indicates that the spins are almost completely aligned (Ψ(A) ) 0.2(1)°, Ψ[B] ) 0.3(2)°) along the external magnetic field of 5.5 T. Thus, the bulk ferrite exhibits a fully inverse spinel structure with a Ne´eltype collinear spin arrangement of (Fev)[NiFeV]O4. Based on the results of the high-resolution TEM studies revealing the core-shell structure of the mechanosynthesized NiFe2O4 nanoparticles (Figure 3b), their high-field Mo¨ssbauer spectrum was fitted by a superposition of four subspectra; two accounting for Fe3+ nuclei at (A) and [B] sites of the particle core (denoted by (A)c and [B]c in Figure 4 and Table 1) and two associated with Fe3+ ions at (A) and [B] sites in the surface shell of the nanoparticles (denoted by (A)s and [B]s, respectively). To separate the surfaces effects from the bulk effects in the spectrum of mechanosynthesized NiFe2O4, we assumed that the core of the nanoparticles possesses the same structure as the bulk material. This fitting strategy has already been applied in the fitting of the in-field Mo¨ssbauer spectra of mechanosynthesized MgFe2O4; for details, see Sˇ epela´k et al.22 The hyperfine parameters of (A) and [B] site ferric ions resulting from the least-squares fittings of the spectra are presented in Table 1. Figure 5 compares the [B] site hyperfine field distributions (HFDs) derived from the high-field Mo¨ssbauer spectra of the bulk and mechanosynthesized NiFe2O4. It should be emphasized that HFDs provide the most detailed information on the local magnetic fields acting on iron nuclei located on a particular lattice site. As can be seen, the [B] site iron nuclei in the bulk NiFe2O4 experience the local fields from a relatively narrow interval (from about 53 to 58 T). This is in contrast to the nanosized material, where a broad distribution is observed ranging from about 45 to 58 T. This broad HFD indicates a strongly disturbed macroscopic magnetic state of the mechanosynthesized NiFe2O4 (see below). The magnetic hyperfine fields listed in Table 1 represent average values over the distributions. From the relative intensities of the (A)c, [B]c, (A)s, and [B]s sextets, one can easily deduce quantitative information on both the cation distribution and the spin configuration within the NiFe2O4 nanoparticles. The intensity ratio (I(A)s+I[B]s)/ (I(A)c+I[B]c+I(A)s+I[B]s) ) 0.548(7) indicates that about 50% of iron cations are located in the surface shell of NiFe2O4 nanoparticles. Assuming a spherical shape of mechanosynthesized nanoparticles and taking their average size as determined by XRD (8.6 nm), we estimated the thickness of the surface shell to be t ≈ 1 nm. This value is in good agreement with that determined from high-resolution TEM and is comparable to the lattice constant of NiFe2O4 (0.8339 nm).

Mechanosynthesized Nickel Ferrite

J. Phys. Chem. C, Vol. 111, No. 13, 2007 5029

Figure 3. (a) Low and (b) high magnification TEM images showing the core-shell structure of mechanosynthesized NiFe2O4 nanoparticles.

Figure 4. Mo¨ssbauer spectra of (a) bulk NiFe2O4 prepared by the ceramic method and (b) nanosized mechanosynthesized NiFe2O4. Spectra were taken at 3 K in the presence of an external magnetic field of 5.5 T applied perpendicular to the γ-ray direction. (A)c, [B]c and (A)s, [B]s denote cation sites of tetrahedral and octahedral coordination in the inner core and the surface shell of NiFe2O4 nanoparticles, respectively.

Whereas the core is considered to possess the fully inverse spinel structure (λc ) 1), the shell region is found to be structurally disordered. The subspectral intensity ratio I(A)s/I[B]s ) 0.505(5) indicates that the major feature of the atomic configuration in the shell is a nonequilibrium cation distribution characterized by a reduced fraction of iron cations on (A) sites, λs ) 0.671(1). It should be noted that this value of the degree of inversion corresponds nearly to the random distribution of cations (λ ) 2/3) with maximum configurational entropy.30 The present observation of the nonuniform cation distribution within NiFe2O4 nanoparticles is consistent with previous findings18h,22 showing that mechanosynthesized ferrites consist of two spinel phases with different cation distributions. Another striking feature of the present Mo¨ssbauer data is the observed difference between the intensity ratios of spectral lines 2 and 1 for the inner core (I(A)c2/I(A)c1, I[B]c2/I[B]c1) and the surface region (I(A)s2/I(A)s1, I[B]s2/I[B]s1), which is a direct indication of a nonuniform spin arrangement within a nanoparticle. Whereas

the magnetic moments located at (A) and [B] sites of the particle core are assumed to exhibit a perfect alignment with the external field (I(A)c2/I(A)c1 ) I[B]c2I[B]c1 ) 4/3), the spins in the shell region are found to be canted. The average canting angles, calculated from the intensity ratios I(A)s2/I(A)s1 and I[B]s2/I[B]s1, were found to be Ψ(A)s ) 28.0(7)° and Ψ[B]s ) 40.2(6)°, respectively. Thus, the spins located on the two sublattices in the surface regions of mechanosynthesized NiFe2O4 nanoparticles are found to behave differently under an external field of 5.5 T. This results is also consistent with previous work, where different spin canting in the (A) and [B] sublattices of spinel nanostructures was observed.22,31 The nonuniform nanostructure of mechanosynthesized NiFe2O4 is presented in Figure 6. It is found that the average sublattice magnetic fields experienced by Fe3+ ions located in the near-surface layers (〈B〉(A)s ≈ 48.4 T, 〈B〉[B]s ≈ 51.9 T) are reduced in comparison with those acting on iron nuclei in the inner core (〈B〉(A)c ≈ 51.6 T, 〈B〉[B]c ≈ 55.8 T) of NiFe2O4 nanoparticles (see Table 1). This could be explained by the effect of frustrated superexchange interactions due to the above-described structural and magnetic disorder of the surface atoms. Reduced sublattice magnetic fields have already been reported for other nanosized mechanochemically prepared ferrites.2,22,32 SQUID measurements have revealed that the magnetic behavior of mechanosynthesized NiFe2O4 is different from that of the NiFe2O4 powder prepared using the conventional ceramic method. As can be seen (Figure 7a), the magnetization of the mechanosynthesized sample does not saturate even at the maximum field attainable (Hext ) 5 T). This is in contrast to the magnetic behavior of the bulk NiFe2O4, whose saturation magnetization reaches the value of Msat0 ) 54.5 emu/g. By extrapolating the high-field region (Hext > 3.5 T) of the M(Hext) curve to infinite field, we estimated the Msat value of mechanosynthesized NiFe2O4 to be approximately 24.4 emu/g, which is about 55% lower than the saturation magnetization for bulk NiFe2O4. In this context, it should be noted that even if the ionic configuration in the surface shell of NiFe2O4 nanoparticles, characterized by the nearly random distribution of cations (λ ≈ 0.67), results in an enhanced saturation magnetization,33 the reduced magnetization measured for the mechanosynthesized material is attributed to the effect of spin canting that dominates over the effect of site exchange of cations in the surface shell. This is opposite to the case of nanoscale mechanosynthesized MgFe2O4,22 where a competition between the effects of spin canting and site exchange of surface cations results in an enhancement of the saturation magnetization of about 50% (relative to Msat for bulk MgFe2O4).

Sˇ epela´k et al.

5030 J. Phys. Chem. C, Vol. 111, No. 13, 2007

TABLE 1: Parameters Obtained by Fitting the High-Field Mo1 ssbauer Spectra Taken at 3 K for Bulk NiFe2O4 and Nanosized Mechanosynthesized NiFe2O4a sample

subspectrum component

bulk NiFe2O4

(A) [B]

nanosized NiFe2O4

(A)c [B]c (A)s [B]s component 1 component 2 component 3

IS (mm/s)

p

B (T)

σ (T)

0.25(3) 1.00 51.62(2) 0.93(5) 0.36(3) 1.00 55.83(1) 0.98(9) I(A)/I[B] ) 0.992(1), I(A)2/I(A)1 ) 1.333(3), I[B]2/I[B]1 ) 1.333(2), λ ) 0.996(3), Ψ(A) ) 0.2(1)°, Ψ[B] ) 0.3(2)° 0.25b 0.36b 0.25(4) 0.36(5)

1.00 1.00 1.00

51.62b 55.83b 48.44(2)

1.10(4) 1.18(2) 1.41(3)

0.412 53.52(2) 1.22(4) 0.356 51.49(8) 2.3(7) 0.232 49.50(3) 3.7(8) I(A)c/I[B]c ) 1b, I(A)c2/I(A)c1 ) I[B]c2/I[B]c1 ) 4/3b, λc ) 1, Ψ(A)c ) Ψ[B]c ) 0°, I(A)s/I[B]s ) 0.505(5), I(A)s2/I(A)s1 ) 0.850(2), I[B]s2/I[B]s1 ) 0.549(1), λs ) 0.671(1), Ψ(A)s ) 28.0(7)°, Ψ[B]s ) 40.2(6)°, 〈B〉[B]s ) 51.91(5) T

I 0.498(1) 0.502(2)

0.226(5) 0.226(4) 0.184(2) 0.364(5) 0.150(2) 0.130(1) 0.084(4)

a (A) ) tetrahedrally coordinated site; [B] ) octahedrally coordinated site; IS ) average isomer shift; p ) weight of the spectral component; σ ) Gaussian width of the component; I ) relative intensity of the component; B ) magnetic hyperfine field; 〈B〉 ) average value of the magnetic hyperfine field distribution; λ ) degree of inversion; Ψ ) average canting angle; 1 ) first spectral line; 2 ) second spectral line; c ) inner core of a nanoparticle; s ) surface shell of a nanoparticle. b Fixed parameter.

Figure 5. [B] site HFDs derived from the high-field Mo¨ssbauer spectra of the (a) bulk and (b) nanosized mechanosynthesized NiFe2O4. The [B] site HFD of the mechanosynthesized material is a superposition of the core ([B]c) and shell ([B]s) contributions.

Figure 7. (a) Magnetization hysteresis loops for bulk and nanoscale mechanosynthesized NiFe2O4 measured at 3 K after field cooling with Hext ) 5 T. (b) Zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves for mechanosynthesized NiFe2O4 taken at Hext ) 0.1 T. Figure 6. Nonuniform structure of mechanosynthesized NiFe2O4 nanoparticles characterized quantitatively by approximate values of λ and Ψ. The crystal chemical formulas emphasize the spin alignment and the site occupancy at the atomic level within the particle core and shell.

Another feature observed is that the nanoscale NiFe2O4 exhibits an enhanced magnetic hardness, i.e., the coercive field of the nanomaterial (HC ≈ 0.35 T) is about 35 times larger than that of the bulk NiFe2O4 (HC ≈ 0.01 T). It is also found that the field-cooled hysteresis loop of the mechanosynthesized

sample is not symmetrical about the origin but is shifted to the left (the shift ∆HC is about 0.03 T). Such an asymmetric hysteresis loop has been reported for exchange-coupled systems34 and is explained in terms of exchange coupling between the collinear spins in the core and the canted spins in the shell.35 Figure 7b shows the zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves of mechanosynthesized NiFe2O4 measured in the temperature range from 2 to 250 K. Above 2 K, the increase with temperature of the ZFC curve can be ascribed to the presence of superparamagnetic crystallites, which give rise to a single maximum at about TB ) 60 K. This points

Mechanosynthesized Nickel Ferrite

J. Phys. Chem. C, Vol. 111, No. 13, 2007 5031

Figure 8. (left) Room-temperature Mo¨ssbauer spectra of mechanosynthesized NiFe2O4 after annealing at various temperatures [(a) 573, (b) 673, (c) 773, (d) 873, (e) 973, (f) 1073, (g) 1173, and (h) 1273 K] for 30 min (right) TEM bright-field images of mechanosynthesized NiFe2O4 after annealing at 973, 1073, and 1273 K (from top to bottom) reveal different crystallite sizes.

to a single-stage process of the crystallite blocking.36 The point at which the ZFC and FC curves start to separate (Ts ≈ 70 K) is associated with the blocking temperature of bigger crystallites. The relatively small difference between TB and Ts (∼10 K) indicates that the mechanosynthesized NiFe2O4 possesses a relatively narrow distribution of particle sizes. The nanostructured NiFe2O4 prepared by high-energy milling is metastable with respect to structural changes at elevated temperatures. Figure 8 shows the room-temperature Mo¨ssbauer spectra of the mechanosynthesized material taken after annealing at various temperatures for 30 min. It was observed that in the temperature range 293-673 K, the shape of the spectra remains unchanged (compare Figures 1g and 8a,b). This demonstrates that the range of the thermal stability of the mechanosynthesized product extends up to 673 K. However, at T > 673 K, the superparamagnetic doublet gradually vanishes because of particle growth of the spinel phase. Simultaneously, the sextet structure, typical of the long-range ferrimagnetic state, develops because of the thermally induced changes in the spin configuration. The spectrum of the mechanosynthesized NiFe2O4 after annealing at 1273 K (Figure 8h) consists of two sextets with the average magnetic hyperfine fields 〈B〉(A) ) 49.21(3) T and 〈B〉[B] ) 52.90(2) T, values that are well comparable with those of the bulk material.2,12 The quantitative evaluation of this spectrum revealed that the annealed sample exhibits the fully inverse spinel structure with a collinear spin alignment. This indicates that the nonequilibrium cation distribution and the canted spin arrangement resulting from the mechanochemical synthesis route are metastable; that is, during the annealing process, they relax toward their equilibrium configuration. Both XRD and TEM confirmed that the average size of NiFe2O4 particles increases with rising annealing temperatures. The variation of the particle diameter D with annealing

TABLE 2: Average Crystallite Diameter (D), Saturation Magnetization (Msat), and Coercivity (HC) for Mechanosynthesized and Subsequently Annealed NiFe2O4 sample

D (nm)a

Msat (emu/g)b

HC (T)

mechanosynthesized NiFe2O4 NiFe2O4 annealed at 973 K NiFe2O4 annealed at 1073 K NiFe2O4 annealed at 1273 K

8.6(3) 16.7(4) 38.9(8) 82.8(9)

24.35 34.55 49.22 53.62

0.351 0.107 0.024 0.013

a Values of the average crystallite size determined by XRD. b Values of the saturation magnetization at T ) 3 K obtained by linear extrapolation of the high-field region (Hext > 3.5 T) of the M(Hext) curves to infinite field.

temperature is given in Table 2. The D values determined by TEM are in reasonable agreement with those obtained by XRD (see Figure 8 and Table 2). As can be seen in Figure 9a, the saturation magnetization of the mechanosynthesized NiFe2O4 increases with increasing annealing temperature (i.e., with increasing crystallite size). After annealing at 1273 K, it reaches the value of Msat ) 53.6 emu/g, which is close to the bulk one. Increasing annealing temperatures also result in a continuous decrease of coercivity from HC ) 0.351 T (before annealing) to HC ) 0.013 T for the sample after annealing at 1273 K (see Figure 9a and Table 2). The observed magnetic softening is accompanied by the disappearance of the asymmetry of the field-cooled hysteresis loop. Thus, on heating, the mechanosynthesized NiFe2O4 has relaxed to a magnetic state that is similar to the bulk one. The thermally induced increase of the saturation magnetization (Figure 9a) suggests that the surface-to-volume fraction in the mechanosynthesized material decreases with increasing annealing temperature. Assuming a spherical shape of mechanosynthesized and subsequently annealed NiFe2O4 particles, in the following, we will estimate the shell thickness (t) using the

5032 J. Phys. Chem. C, Vol. 111, No. 13, 2007

Figure 9. (a) Hysteresis loops measured at 3 K for mechanosynthesized and subsequently annealed NiFe2O4 samples. The annealing temperatures and corresponding crystallite sizes are shown in the figure. (b) M1/3 sat vs 1/D plot, where Msat is the saturation magnetization and D is the crystallite diameter.

experimentally determined D and Msat values of the samples annealed at various temperatures (see Table 2). Assuming that t is independent of D and that the shell is magnetically “dead”37 (M ) 0), the variation of Msat with D will then be described by

Msat ) Msat0(D - 2t)3/D3, or Msat1/3 ) Msat01/3(1 - 2t/D) where Msat0 is the saturation magnetization of bulk NiFe2O4. As can be seen in Figure 9b, the present experimental data M1/3 sat and 1/D indeed show a good linear relationship. Note that the intercept at 1/D ) 0 and the slope of the straight line 1/3 correspond to M1/3 sat0 and 2tMsat0, respectively. From a linear fit to the data points, the saturation magnetization of the bulk material and the thickness of the shell were estimated to be Msat0 ≈ 57.2 emu/g and t ≈ 1.1 nm, respectively. Msat0 thus obtained is close to the value of the saturation magnetization measured for bulk NiFe2O4, 54.5 emu/g. The value of the shell thickness obtained is in reasonable agreement with that estimated from TEM and Mo¨ssbauer experiments (1.0 nm). The shell thickness in mechanosynthesized NiFe2O4 is also comparable to that obtained from magnetic measurements on mechanosynthesized MnFe2O4 nanoparticles (0.91 nm)18c and ball-milled NiFe2O4 (0.88 nm),38a as well as from Mo¨ssbauer experiments on nanosized CoFe2O4 (1.0-1.6 nm)38b and mechanosynthesized MgFe2O4 (0.9 nm).22 We note that, in general, 1 nm is also a typical thickness of grain boundary regions in nonmagnetic nanocrystalline materials.29,39 Conclusions The present study demonstrates that nanosized NiFe2O4 with an average crystallite size of about 8.6 nm can be synthesized from binary oxide precursors in a relatively short reaction time

Sˇ epela´k et al. (8 h) in a one-step mechanochemical route. This nonconventional approach offers several advantages over traditional processing routes, including low-temperature solid-state reactions, fewer processing steps, and suitability for the low cost, large-scale production of nanopowders. In this respect, the present work contributes to the search for novel sustainable production routes of functionally tailored nanomaterials. Based on the results of both high-resolution TEM and infield Mo¨ssbauer investigations, it is concluded that the mechanosynthesized NiFe2O4 nanoparticles possess a nonuniform structure consisting of an ordered core surrounded by a disordered grain boundary (surface) region. Due to the ability of 57Fe Mo¨ssbauer spectroscopy to reveal the noncollinearity of the spin arrangement and to discriminate between probe nuclei on inequivalent crystallographic sites provided by the spinel structure, valuable insight into a local disorder in mechanosynthesized NiFe2O4 was obtained. It, thus, was revealed for the first time that the surface shell of NiFe2O4 nanoparticles is structurally and magnetically disordered due to the nearly random distribution of cations (λs ≈ 0.67) and the canted spin arrangement (Ψ(A)s ≈ 28°, Ψ[B]s ≈ 40°). This is in contrast to the ordered core of the nanoparticles, which exhibits an inverse spinel structure (λc ) 1) with a collinear spin alignment (Ψ(A)c ) Ψ[B]c ) 0°). From an analysis of Mo¨ssbauer spectra, it is concluded that the fraction of cations located in the surface shell of NiFe2O4 nanoparticles is about 50%. The thickness of the surface shell obtained from Mo¨ssbauer experiments (t ) 1.0 nm) is found to be in agreement with that estimated from both high-resolution TEM and size-dependent magnetization measurements (1.1 nm). Quantitative information on the distribution of local magnetic fields and on the canted spin arrangement within the NiFe2O4 nanoparticles provided by Mo¨ssbauer spectroscopy is complemented by investigations of their magnetic behavior on the macroscopic scale. SQUID measurements show that magnetic properties are strongly influenced by the mechanochemical processing: the saturation magnetization of mechanosynthesized NiFe2O4 takes a value of Msat ) 24.4 emu/g, which is about 55% lower than Msat0 ) 54.5 emu/g for bulk NiFe2O4. It is also found that the nanoscale NiFe2O4 exhibits an enhanced magnetic hardness (Hc ) 0.351 T). The magnetic behavior of the mechanosynthesized material is attributed to the effect of spin canting that dominates over the effect of the changed cation distribution in the surface shell of nanoparticles. The study also demonstrates that one can tailor the magnetic properties of mechanosynthesized NiFe2O4 particles by suitably controlling their size. Increasing particle size induced by annealing at elevated temperatures brings about an increase in the saturation magnetization of mechanosynthesized NiFe2O4 to a value of Msat ) 53.6 emu/g which is close to the bulk one. The particle growth of NiFe2O4 particles is accompanied by decrease of coercivity. The range of the thermal stability of the mechanosynthesized product is found to extend up to about 673 K. Upon annealing at T > 673 K, the nonequilibrium cation distribution and the canted spin arrangement resulting from the mechanochemical synthesis route, relax toward their equilibrium configuration (λ ≈ 1, Ψ(A) ) Ψ[B] ≈ 0°). Thus, on heating, the mechanosynthesized NiFe2O4 relaxes to a structural and magnetic state that is similar to the bulk one. Acknowledgment. The present work was supported by the Deutsche Forschungsgemeinschaft. Partial support by the Grant Agency of the Ministry of Education of the Slovak Republic and of the Slovak Academy of Sciences (Grant 2/5146/25) and

Mechanosynthesized Nickel Ferrite by the Alexander von Humboldt Foundation is gratefully acknowledged. We are grateful to J. Caro for the opportunity to use the TEM facility. References and Notes (1) (a) Zhou, C.; Schulthess, T. C.; Landau, D. P. J. Appl. Phys. 2006, 99, 08H906. (b) Wang, Z. L.; Liu, Y.; Zhang, Z. Handbook of Nanophase and Nanostructured Materials. Vol. 3; Kluwer Academic/Plenum Publishers: New York, 2002. (c) Sugimoto, M. J. Am. Ceram. Soc. 1999, 82, 269. (d) Willard, M. A.; Kurihara, L. K.; Carpenter, E. E.; Calvin, S.; Harris, V. G. Int. Mater. ReV. 2004, 49, 125. (e) Lu¨ders, U.; Barthe´le´my, A.; Bibes, M.; Bouzehouane, K.; Fusil, S.; Jacquet, E.; Contour, J.-P.; Bobo, J.-F.; Fontcuberta, J.; Fert, A. AdV. Mater. 2006, 18, 1733. (2) Sˇ epela´k, V.; Baabe, D.; Mienert, D.; Schultze, D.; Krumeich, F.; Litterst, F. J.; Becker, K. D. J. Magn. Magn. Mater. 2003, 257, 377. (3) Novelo, F.; Valenzuela, R. Mater. Res. Bull. 1995, 30, 335. (4) (a) Wang, J. Mater. Sci. Eng. B 2006, 127, 81. (b) Zhou, J.; Ma, J.; Sun, C.; Xie, L.; Zhao, Z.; Tian, H.; Wang, Y.; Tao, J.; Zhu, X. J. Am. Ceram. Soc. 2005, 88, 3535. (c) Cheng, Y.; Zheng, Y.; Wang, Y.; Bao, F.; Qin, Y. J. Solid State Chem. 2005, 178, 2394. (d) Satyanarayana, L.; Reddy, K. M.; Manorama, S. V. Mater. Chem. Phys. 2003, 82, 21. (5) (a) Rashad, M. M.; Fouad, O. A. Mater. Chem. Phys. 2005, 94, 365. (b) Albuquerque, A. S.; Ardisson, J. D.; Macedo, W. A. A.; Lo´pez, J. L.; Paniago, R.; Persiano, A. I. C. J. Magn. Magn. Mater. 2001, 226-230, 1379. (c) Ramankutty, C. G.; Sugunan, S. Appl. Catal. A-Gen. 2001, 218, 39. (6) (a) Rezlescu, N.; Iftimie, N.; Rezlescu, E.; Doroftei, C.; Popa, P. D. Sens. Actuators, B 2006, 114, 427. (b) Costa, A. C. F. M.; Lula, R. T.; Kiminami, R. H. G. A.; Gama, L. F. V.; De Jesus, A. A.; Andrade, H. M. C. J. Mater. Sci. 2006, 41, 4871. (c) Vivekanandhan, S.; Venkateswarlu, M.; Satyanarayana, N. Mater. Lett. 2004, 58, 2717. (7) Heegn, H.; Trinkler, M.; Langbein, H. Cryst. Res. Technol. 2000, 35, 255. (8) (a) Liu, J. H.; Wang, L.; Li, F. S. J. Mater. Sci. 2005, 40, 2573. (b) Chakraverty, S.; Mandal, K.; Mitra, S.; Chattopadhyay, S.; Kumar, S. Jpn. J. Appl. Phys. 2004, 43, 7782. (c) Silva, M. N. B.; Duque, J. G. D. S.; Gouveia, D. X.; de Paiva, J. A. C.; Macedo, M. A. Jpn. J. Appl. Phys. 2004, 43, 5249. (9) Komarneni, S.; D’Arrigo, M. C.; Leionelli, C.; Pellacani, G. C.; Katsuki, H. J. Am. Ceram. Soc. 1998, 81, 3041. (10) Li, D.; Herricks, T.; Xia, Y. Appl. Phys. Lett. 2003, 83, 4586. (11) (a) Kale, A.; Gubbala, S.; Misra, R. D. K. J. Magn. Magn. Mater. 2004, 277, 350. (b) Fang, J.; Shama, N.; Tung, L. D.; Shin, E. Y.; O’Connor, C. J.; Stokes, K. L.; Caruntu, G.; Wiley, J. B.; Spinu, L.; Tang, J. J. Appl. Phys. 2003, 93, 7483. (12) De Marco, M.; Wang, X. W.; Snyder, R. L.; Simmins, J.; Bayya, S.; White, M.; Naughton, M. J. J. Appl. Phys. 1993, 73, 6287. (13) Son, S.; Taheri, M.; Carpenter, E.; Harris, V. G.; McHenry, M. E. J. Appl. Phys. 2002, 91, 7589. (14) Lee, P. Y.; Ishizaka, K.; Suematsu, H.; Jiang, W.; Yatsui, K. J. Nanopart. Res. 2006, 8, 29. (15) (a) Shafi, K. V. P. M.; Koltypin, Y.; Gedanken, A.; Prozorov, R.; Balogh, J.; Lendvai, J.; Felner, I. J. Phys. Chem. B 1997, 101, 6409. (b) Baranchikov, A. Ye.; Ivanov, V. K.; Tretyakov, Y. D. Ultrason. Sonochem. 2007, 14, 131. (16) (a) Pavlyukhin, Y. T.; Medikov, Y. Y.; Boldyrev, V. V. J. Solid State Chem. 1984, 53, 155. (b) Sˇ epela´k, V.; Baabe, D.; Becker, K. D. J. Mater. Synth. Process. 2000, 8, 333. (c) Chinnasamy, C. N.; Narayanasamy, A.; Ponpandian, N.; Chattopadhyay, K.; Shinoda, K.; Jeyadevan, B.; Tohji, K.; Nakatsuka, K.; Furubayashi, T.; Nakatani, I. Phys. ReV. B 2001, 63, 184108. (d) Helgason, O.; Jiang, J. Z. Hyperfine Interact. 2002, 139-140, 325. (17) (a) Sˇ epela´k, V.; Bergmann, I.; Kipp, S.; Becker, K. D. Z. Anorg. Allg. Chem. 2005, 631, 993. (b) Sˇ epela´k, V. Ann. Chim.-Sci. Mater. 2002, 27, 61. (c) Sˇ epela´k, V.; Becker, K. D. J. Mater. Synth. Process. 2000, 8, 155. (18) (a) Sˇepela´k, V.; Steinike, U.; Uecker, D. C.; Wissmann, S.; Becker, K. D. J. Solid State Chem. 1998, 135, 52. (b) Goya, G. F.; Rechenberg, H. R.; Chen, M.; Yelon, W. B. J. Appl. Phys. 2000, 87, 8005. (c) Muroi, M.; Street, R.; McCormick, P. G.; Amighian, J. Phys. ReV. B 2001, 63, 184414. (d) Kim, W.; Saito, F. Powder Technol. 2001, 114, 12. (e) Harris, V. G.; Fatemi, D. J.; Cross, J. O.; Carpenter, E. E.; Browning, V. M.; Kirkland, J.

J. Phys. Chem. C, Vol. 111, No. 13, 2007 5033 P.; Mohan, A.; Long, G. J. J. Appl. Phys. 2003, 94, 496. (f) Guigue-Millot, N.; Begin-Colin, S.; Champion, Y.; Hytch, M. J.; Le Cae¨r, G.; Perriat, P. J. Solid State Chem. 2003, 170, 30. (g) Manova, E.; Kunev, B.; Paneva, D.; Mitov, I.; Petrov, L.; Estourne`s, C.; D’Orle´ans, C.; Rehspringer, J.-L.; Kurmoo, M. Chem. Mater. 2004, 16, 5689. (h) Pradhan, S. K.; Bid, S.; Gateshki, M.; Petkov, V. Mater. Chem. Phys. 2005, 93, 224. (i) Osmokrovic´, P.; Jovalekic´, C ˇ .; Manojlovic´, D.; Pavlovic´, M. B. J. Optoelectron. AdV. Mater. 2006, 8, 312. (j) Dasgupta, S.; Kim, K. B.; Ellrich, J.; Eckert, J.; Manna, I. J. Alloy. Compd. 2006, 424, 13. (19) (a) Jovalekic´, C ˇ .; Zdujic´, M.; Radakovic´, A.; Mitric´, M. Mater. Lett. 1995, 24, 365. (b) Shi, Y.; Ding, J.; Liu, X.; Wang, J. J. Magn. Magn. Mater. 1999, 205, 249. (c) Zhou, Z. H.; Xue, J. M.; Wang, J.; Chan, H. S. O.; Yu, T.; Shen, Z. X. J. Appl. Phys. 2002, 91, 6015. (d) Rabanal, M. E.; Varez, A.; Levenfeld, B.; Torralba, J. M. Mater. Sci. Forum 2003, 426432, 4349. (e) Sˇ epela´k, V.; Menzel, M.; Bergmann, I.; Wiebcke, M.; Krumeich, F.; Becker, K. D. J. Magn. Magn. Mater. 2004, 272-276, 1616. (f) Yang, H.; Zhang, X.; Ao, W.; Qiu, G. Mater. Res. Bull. 2004, 39, 833. (20) (a) Boldyrev, V. V. Russ. Chem. ReV. 2006, 75, 177. (b) Chicinas, I. J. Optoelectron. AdV. Mater. 2006, 8, 439. (21) (a) Sˇ epela´k, V.; Menzel, M.; Becker, K. D.; Krumeich, F. J. Phys. Chem. B 2002, 106, 6672. (b) Sˇ epela´k, V.; Steinike, U.; Uecker, D. C.; Trettin, R.; Wissmann, S.; Becker, K. D. Solid State Ionics 1997, 101103, 1343. (c) Bhowmik, R. N.; Ranganathan, R.; Nagarajan, R.; Ghosh, B.; Kumar, S. Phys. ReV. B 2005, 72, 094405. (d) Goya, G. F.; Rechenberg, H. R. J. Magn. Magn. Mater. 1999, 196-197, 191. (e) Bhowmik, R. N.; Ranganathan, R.; Sarkar, S.; Bansal, C.; Nagarajan, R. Phys. ReV. B 2003, 68, 134433. (22) Sˇ epela´k, V.; Feldhoff, A.; Heitjans, P.; Krumeich, F.; Menzel, D.; Litterst, F. J.; Bergmann, I.; Becker, K. D. Chem. Mater. 2006, 18, 3057. (23) Kraus, W.; Nolze, G. PowderCell for Windows, version 2.4; Federal Institute for Materials Research and Testing: Berlin, Germany, 2000. (24) Joint Committee on Powder Diffraction Standards (JCPDS) Powder Diffraction File (PDF); International Centre for Diffraction Data: Newton Square, PA, 2004. (25) Lagarec, K.; Rancourt, D. G. Recoil - Mo¨ssbauer Spectral Analysis Software for Windows, version 1.02; Department of Physics, University of Ottawa: Ottawa, ON, 1998. (26) Sawatzky, G. A.; Van Der Woude, F.; Morrish, A. H. Phys. ReV. 1969, 183, 383. (27) Vandenberghe, R. E.; De Grave, E. In Mo¨ssbauer Spectroscopy Applied to Inorganic Chemistry; Long, G. J., Grandjean, F., Eds.; Plenum Press: New York, 1989; Vol. 3, p 115. (28) Mørup, S. In Mo¨ssbauer Spectroscopy Applied to Inorganic Chemistry; Long, G. J., Ed.; Plenum Press: New York, 1987; Vol. 2, p 89. (29) Heitjans, P.; Masoud, M.; Feldhoff, A.; Wilkening, M. Faraday Discuss. 2007, 134, 67. (30) Sickafus, K. E.; Wills, J. M.; Grimes, N. W. J. Am. Ceram. Soc. 1999, 82, 3279. (31) (a) Ammar, S.; Jouini, N.; Fie´vet, F.; Beji, Z.; Smiri, L.; Moline´, P.; Danot, M.; Greneche, J.-M. J. Phys.: Condens. Matter 2006, 18, 9055. (b) Ponpandian, N.; Narayanasamy, A.; Chinnasamy, C. N.; Sivakumar, N.; Greneche, J.-M.; Chattopadhyay, K.; Shinoda, K.; Jeyadevan, B.; Tohji, K. Appl. Phys. Lett. 2005, 86, 192510. (c) Helgason, O ¨ .; Greneche, J.-M.; Berry, F. J.; Mosselmans, F. J. Phys.: Condens. Matter 2003, 15, 2907. (d) Goya, G. F.; Leite, E. R. J. Phys.: Condens. Matter 2003, 15, 641. (32) (a) Sˇ epela´k, V.; Baabe, D.; Litterst, F. J.; Becker, K. D. J. Appl. Phys. 2000, 88, 5884. (b) Sˇ epela´k, V.; Baabe, D.; Mienert, D.; Litterst, F. J.; Becker, K. D. Scr. Mater. 2003, 48, 961. (33) Lu¨ders, U.; Bibes, M.; Bobo, J.-F.; Cantoni, M.; Bertacco, R.; Fontcuberta, J. Phys. ReV. B 2005, 71, 134419. (34) Nogue´s, J.; Sort, J.; Langlais, V.; Skumryev, V.; Surin˜ach, S.; Mun˜oz, J. S.; Baro´, M. D. Phys. Rep. 2005, 422, 65. (35) (a) Kodama, R. H.; Berkowitz, A. E.; McNiff, E. J.; Foner, S. J. Appl. Phys. 1997, 81, 5552. (b) Kodama, R. H.; Berkowitz, A. E. Phys. ReV. B 1999, 59, 6321. (36) Yu, S. C.; Song, Y. Y.; Kiss, L. F.; Vincze, I. J. Magn. Magn. Mater. 1999, 203, 316. (37) George, M.; John, A. M.; Nair, S. S.; Joy, P. A.; Anantharaman, M. R. J. Magn. Magn. Mater. 2006, 302, 190. (38) (a) Zhang, Y. D.; Ge, S. H.; Zhang, H.; Hui, S.; Budnick, J. I.; Hines, W. A.; Yacaman, M. J.; Miki, M. J. Appl. Phys. 2004, 95, 7130. (b) Haneda, K.; Morrish, A. H. J. Appl. Phys. 1988, 63, 4258. (39) (a) Heitjans, P.; Indris, S. J. Phys.: Condens. Matter 2003, 15, R1257. (b) Heitjans, P.; Indris, S. J. Mater. Sci. 2004, 39, 5091.