J. Phys. Chem. B 2001, 105, 7125-7132
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Chemical Heterogeneities in Nanometric Titanomagnetites Prepared by Soft Chemistry and Studied Ex Situ: Evidence for Fe-Segregation and Oxidation Kinetics N. Guigue-Millot,*,† Y. Champion,‡ M. J. Hy1 tch,‡ F. Bernard,† S. Be´ gin-Colin,§ and P. Perriat| Laboratoire de Recherches sur la Re´ actiVite´ des Solides, U.M.R. 5613 C.N.R.S./ UniVersite´ de Bourgogne, BP 400, 21011 Dijon Cedex, France, Centre d’Etudes de Chimie Me´ tallurgique, C.N.R.S., 15 rue G. Urbain, 94407 Vitry Cedex, France, Laboratoire de Science et Ge´ nie des Mate´ riaux Me´ talliques, U.M.R. 7584, 54042 Nancy Cedex, France, and Groupe d’Etudes de Me´ tallurgie Physique et de Physique des Mate´ riaux, I.N.S.A. de Lyon, 69621 Villeurbanne Cedex, France ReceiVed: February 19, 2001; In Final Form: May 2, 2001
Nanocrystalline Fe-based spinels with composition Fe3-xTixO4 are synthesized using soft chemistry. Two steps are involved: precipitation in an aqueous solution followed by thermal annealing under a reducing mixture of N2/H2/H2O gases. Fe-segregation is found inside stoichiometric particles when the powders are studied ex situ; they exhibit a strong surface iron enrichment. This heterogeneity is related to kinetic effects linked to the difference of mobility between Fe2+ and Ti4+ cations during the partial oxidation of cations occurring ex situ. Stresses in the grains induced by oxidation govern the oxidation kinetics and lead to an abrupt compositional variation inside each particle. These heterogeneities in stoichiometric powders have been investigated by a combination of averaging and local techniques: XRD and Mo¨ssbauer spectrometry for an average analysis of powders, XPS for an analysis of the surface of the grains, and HRTEM for a local analysis of single grains.
1. Introduction One of the most common groups of magnetic minerals is the titanomagnetite series and its oxidized phases. These compounds denoted (Fe3-xTix)1-δO4 have been widely investigated in the seventies as micrometric polycrystals;1,2 x is the titanium content in the spinel structure, and δ represents the deviation from oxygen stoichiometry. However, it was recently discovered that the earth’s crust contains also nanometer-scale clusters of titanomagnetites.3,4 Since data concerning nanometric compounds are rarely found in the literature, it may be interesting to study such materials to provide new information to scientists who investigate the paleomagnetic record. Moreover, titanomagnetite compounds are suitable for studying the properties of nanometric compounds as a function of deviation from oxygen stoichiometry. Indeed, magnetite is not thermodynamically stable for δ > 0.095 and maghemite is not stable for grain size L > 30 nm.6 In both cases, a transformation to a rhombohedric phase occurs for higher δ and L. Titanium ion insert in the magnetite structure in substitution of Fe3+ cations stabilizes the spinel structure and limits grain growth. In the spinel structure, two types of sites can be occupied by the cations: tetrahedral (A) or octahedral (B).7 When the ferrite contains some M cations, the cation distribution is not as simple as it is in magnetite where all Fe2+ are on B sites. In the case of titanium ferrite, the distribution of cations has been extensively studied using several methods. Every study found that * Corresponding author. Fax: (33) 3 80 39 61 67. E-mail: nmillot@ u-bourgogne.fr. † Laboratoire de Recherches sur la Re ´ activite´ des Solides, U.M.R. 5613 C.N.R.S./ Universite´ de Bourgogne. ‡ Centre d’Etudes de Chimie Me ´ tallurgique, C.N.R.S. § Laboratoire de Science et Ge ´ nie des Mate´riaux Me´talliques, U.M.R. 7584. | Groupe d’Etudes de Me ´ tallurgie Physique et de Physique des Mate´riaux, I.N.S.A. de Lyon.
the Ti4+ cations reside on octahedral sites but the location of the Fe2+ cations is still controversial, even when studied by the same technique.8-13 In the fifties, two extreme models were suggested. On the basis of magnetic measurements, Akimoto proposed that all the additional Fe2+ cations are on A sites:8
[Fe2+xFe3+1-x]A[Fe2+Fe3+1-xTi4+x]BO4 while, according to Ne´el9 and Chevalier,10 the distribution of the cations, which depends on x, exhibits the crystal-chemical preference of Fe2+ for the B sublattice and Fe3+ for the A sublattice.
[Fe3+]A[Fe1+x2+Fe1-2x3+Ti4+x]BO4 for x e 0.5 [Fe2-2x3+Fe2x-12+]A[Fe2-x2+Ti4+x]BO4for x > 0.5 More sophisticated distributions have since been proposed. An intermediate model, following that of Akimoto in the range 0.2 e x e 0.8 but that of Ne´el and Chevalier otherwise, has been proposed by O’Reilly11. Moreover, the cation distribution has been shown to be temperature dependent from thermoelectric coefficient measurements by Trestman-Matts12 in accordance with that predicted by O’Neill and Navrotsky13. In any case, the controversy may originate from differences in several experimental conditions and control parameters such as temperature, grain size, deviation from stoichiometry, method of synthesis, etc. Previous studies have shown that to synthesize a large quantity of dispersed nanometric powders, a soft chemistry route can be chosen.14,15 To have a good cation/oxygen ratio, the powders are subsequently annealed under an appropriate H2/ H2O gas mixture (low temperatures are required to stabilize nanometer-sized grains; for higher temperatures, powders are
10.1021/jp010661y CCC: $20.00 © 2001 American Chemical Society Published on Web 06/30/2001
7126 J. Phys. Chem. B, Vol. 105, No. 29, 2001 annealed under CO/CO2 gas mixture).16 However, as Fe2+ cations are not thermodynamically stable in air, a significant amount of Fe2+ cations are oxidized when powders are studied in room conditions. Fe2+ oxidation takes place at the gas/solid interface, since nanoparticles have a large specific area presenting a high reactivity toward oxygen. Under normal oxygen pressure the oxidation process begins by dissociative oxygen adsorption on the particle surface. This phenomenon induces an electronic exchange between Fe2+ cations located at the surface and the oxygen atoms. These two quick steps generate Fe3+ cations and cation vacancies at the surface of the material, thus inducing composition gradients between the surface and the bulk. These gradients do not generate any crystallographic transformation but induce the diffusion of the different cations. Vacancies which are created at the surface during the incorporation of oxygen into the lattice diffuse into the particle. The vacancy diffusion occurs in conjunction with the counterdiffusion of the more mobile cations, here the iron cations. Indeed, measurements of cationic diffusion coefficients performed at high temperature on micrometric titanomagnetites show clearly that titanium cations are less mobile than iron cations.17,18 This is due to the high valence of Ti4+ cations: they are strongly bound to the oxygen anions and consequently their mobility is lower.19 Therefore, whereas near the surface there may be mainly Fe3+ cations, in the bulk of the particle the Fe2+ and Ti4+ cations are expected to predominate. A mechanism for segregation in nanometric (Fe3-xMox)1-δO4 ferrite has been previously proposed taking into account the stresses induced in the grains by the oxidation reaction.20 Classical models related to atomic diffusion via point defects are not able to explain completely the kinetics of oxidation which are experimentally observed in finely divided ferrites at low temperature. Such an oxidation phenomenon has been explained on the basis of very significant stresses generated in the particles by the chemical gradient induced during the oxidation mechanism.20 For high stresses, the grain has an external shell almost completely oxidized and an internal core which remains unoxidized. Indeed, fast oxidation in the external shell takes place followed by slow oxidation in the bulk. Due to compressive stresses, the diffusion strongly decreases and, in some cases, even stops. The aim of this paper is to illustrate this extreme phenomenon. As measurements of cationic diffusion coefficients cannot be carried out for nanometric powders as the high temperature required leads to grain growth, other techniques are used here: X-ray diffraction (XRD), Mo¨ssbauer spectrometry, X-ray photoelectron spectroscopy (XPS), and high-resolution transmission electron microscopy (HRTEM). XRD and Mo¨ssbauer spectrometry experiments, well-known for giving averaged information concerning the bulk, lead also, in the case of nanometric compounds, to surface information. Indeed, in nanometric powders, the surface contribution is no longer negligible and contributes in XRD and Mo¨ssbauer spectrometry profiles. XPS investigations can give us some relevant information about the surface content. To obtain local information about the structure of nanoparticles, HRTEM was carried out. The images were analyzed using a combination of real space and Fourier space information21 which leads to the investigation of local variations in the structure of the grains. Combining all these results allows a rather complete investigation of the segregation phenomenon. 2. Experimental Procedure 2.1. Powder Synthesis. The general procedure of soft chemistry is as follows:
Guigue-Millot et al. (1) Suitable amounts of ferrous, ferric, and titanium chloride are dissolved in a HCl solution. Cations concentrations (≈0.3 mol L-1) and pH ( 1000 °C). In our case, the experimental values are in good agreement with the theoretical predictions9,10 and with those calculated by the Poix method25-27]. For the latter, the cation-oxygen distances used were the following: Fe2+B-O2- and Fe3+B-O2- 2.132 Å27 and 2.020 Å,26 respectively, and Ti4+B-O2- 1.944 Å.25 Having nanometric ferrites particles allows, on one hand, to decrease the temperature of the thermal treatment (about 500 °C instead of 1000 °C), and permit, on the other hand, to locate the totality of the Fe2+ cations in octahedral sites as predicted by theory.9-10 These observations show that it is both possible to obtain the spinel structure and to control grain growth whatever the Ti content. Now it is essential to provide evidence for the segregation phenomenon observed in nanometric powders after their reducing thermal treatment when they are studied under air atmosphere.
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TABLE 1: Particle Size and Lattice Parameter Deduced from X-ray Diffraction Analyses of Ti Ferrites Powders with the Two Extremes Deviation from Oxygen Stoichiometry δ ) δmax and δ ) 0a Ti content x
calcination temperature (°C)
particle size (δ ) δmax) (nm)
lattice parameter (δ ) δmax) (Å)
reduction temperature (°C)
particle size (δ ) 0) (nm)
lattice parameter (δ ) 0) (Å)
0 0.25 0.5 0.75 1
330 380 380 380 380
18 ( 2 10 ( 2 15 ( 2 18 ( 2 21 ( 2
8.340 ( 0.001 8.345 ( 0.001 8.340 ( 0.001 8.341 ( 0.001 8.343 ( 0.001
460 460 460 650 700
100 ( 5 15 ( 2/120 ( 10 18 ( 2 85 ( 5 105 ( 5
8.396 ( 0.001 8.408 ( 0.001 8.424 ( 0.001 8.493 ( 0.001 8.527 ( 0.001
a The particle size is deduced from the Halder & Wagner method. Given are the temperatures of the thermal treatments under air (calcination) and under N2/H2/H2O gases (reduction). The granulometric distribution of the titanium ferrite Fe2.75Ti0.25O4 is bimodal due to a freeze-drying not optimized in its case. Error in lattice parameter is over-estimated for the biggest particles in order to be comparable with those of the smallest.
Figure 1. Scanning electron micrograph of the Fe2.5Ti0.5O4 titanium ferrite (a) after the oxidizing thermal treatment under air at 380 °C (δ ) δmax), (b) after the reducing thermal treatment under N2/H2/H2O gas mixtures at 460 °C (δ ) 0).
TABLE 2: δ, Deviation from Oxygen Stoichiometry of Titanium Ferrites (Fe3-xTix)1-δO4 Deduced from Thermogravimetric Analyses: in Situ Just after the Reduction Treatment under N2/H2/H2O Gases, in Situ after Quenching under N2 Atmosphere, Ex Situ after 4 Months under Air Atmosphere at 25°C. The Granulometric Distribution of the Titanium Ferrite Fe2.75Ti0.25O4 Is Bimodal Due to a Freeze-drying Not Optimized in Its Case particle sizeDRX (nm) δin situ at Treduction δin situ after quenching under N2 atmosphere δex situ after 4 months under air atmosphere at 25 °C
xTi ) 0
xTi ) 0.25
xTi ) 0.5
xTi ) 0.75
xTi ) 1
100 ( 5 0.005 ( 0.005
15 ( 2/120 ( 10 0.008 ( 0.005
18 ( 2 0.003 ( 0.005
105 ( 5 0.027 ( 0.005
0.015 ( 0.005
0.024 ( 0.005
0.040 ( 0.005
85 ( 5 0.020 ( 0.005 0.033 ( 0.005 0.042 ( 0.005
In Table 2, the deviation from oxygen stoichiometry, δ, of titanium ferrites (Fe3-xTix)1-δO4 is deduced from thermogravimetric analyses: in situ just after the reducing thermal treatment under N2/H2/H2O gases, in situ after quenching under N2 atmosphere and ex situ after 4 months under air atmosphere at ambient temperature. First, we can notice that δ is not equal to 0 for x ) 0.75 and x ) 1 studied in situ, contrary to the other compositions. Higher temperatures should have been used in order to obtain the stoichiometric state δ ) 0. Second, we can confirm that under nitrogen, whose partial oxygen pressure is 10-6 Pa, or under laboratory conditions, Fe2+ cations are not thermodynamically stable. Indeed, during the sample quenching under N2 atmosphere in the TGA apparatus, part of the Fe2+ cations are oxidized. This is revealed by δ which increases from 0.020 to 0.033 in the case of the (Fe2.25Ti0.75)1-δO4 ferrite. Table 2 also shows two phenomena. First of all, the oxidation is all the more important when the grain size is small. Indeed, it is the Fe2.5Ti0.5O4 composition whose grain size is equal to 18 nm which exhibits the highest oxidation. The smaller the grain size, the higher the surface area and the more important the incorporation of oxygen in the lattice. Second, the oxidation is
0.068 ( 0.005
more important when stresses generated by the Fe-Ti segregation inside the grains are high. Indeed, high Ti content leads to a very large lattice parameter difference between the stoichiometric bulk and the γ-Fe2O3 surface of the particles. Heterogeneities which are observed in reduced powders are now studied by comparing average chemical composition and surface Ti/Fe-ratios. The average composition was obtained from EDS and ICP-AES. Ti and Fe surface content was investigated by XPS: indeed, the XPS analysis depth is about 1-3 nm whereas the particle size is about 20 nm; XPS therefore provides average information about the particle surface composition. The results suggest (see Table 3) an Fe enrichment at the particle surface. These heterogeneities may be attributed to the Fe-Ti segregation, a phenomenon which can be related to kinetic effects linked to the partial oxidation of Fe cations occurring when nanoparticles are studied in room conditions. At ambient temperature, only Fe cations diffuse toward the new units cells formed on the surface, thus explaining why Ti is no longer detected by XPS. Therefore, whereas near the surface the cations are mainly Fe3+, in the bulk of the particle the Fe2+ and Ti cations predominate (Figure 2a). As explained in the Introduc-
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Figure 2. (a) Oxidation scheme: Vacancies which are created at the surface during the incorporation of oxygen in the lattice diffuse in the particle. The vacancy diffusion occurs in conjunction with the counterdiffusion of the more mobile cations, here the iron cations. (b) “frozen” state after partial oxidation in room-conditions: significant stresses are generated in the particles by the chemical gradient induced during the oxidation mechanism. Due to compressive stresses in the bulk of the particle, diffusion strongly decreases and even stops.
TABLE 3: Comparison of Bulk and Surface Ti/Fe Ratio in Titanium Ferrites (Fe3-xTix)1-δO4 Using EDX, ICP for Bulk Analysis, and XPS for Surface Investigations x: Ti/ (Fe3-xTixO4) Fetheo 0.25 0.5 0.75 1
0.09 0.20 0.33 0.50
Ti/ FeICP
Ti/ FeEDX
Ti/ FeXPS
Ti/FeXPS/ Ti/Fetheo
0.09 ( 0.01 0.20 ( 0.01 0.33 ( 0.01 0.52 ( 0.01
0.08 ( 0.02 0.18 ( 0.02 0.29 ( 0.02 0.49 ( 0.02
0.10 ( 0.01 0.14 ( 0.01 0.05 ( 0.01 0.07 ( 0.01
1.11 0.70 0.15 0.14
tion, the partial oxidation observed is also a consequence of the high compressive stresses at the surface of each particle which enhance diffusion kinetics:20 the oxidizing shell involves tensile stresses near the surface of the grains, whereas the stoichiometric bulk leads to compressive stresses (Figure 2b). Diffusion strongly decreases and, in our case, stops at ambient temperature leading to an iron-rich surface. XRD experiments performed in situ show once more, the high reactivity of nanometric powders with the atmosphere. Two experiments were carried out under the following conditions. First, (Fe2.25Ti0.75)1-δO4 powder was reduced in a reaction chamber under appropriate N2/H2/H2O gas mixtures to obtain the stoichiometric state δ ) 0. Second, the powder was quenched under N2 gas. Then, XRD patterns were acquired under a new atmosphere which was established at ambient temperature: (a) N2/H2/H2O mixtures, (b) O2 gas. Figure 3, which represents one peak (line 440) of each whole pattern, clearly shows some asymmetry around high angles for the oxidizing atmosphere (Figure 3b). Since this asymmetry disappears when the sample is studied under an equilibrium atmosphere (Figure 3a), it cannot be attributed to an instrumental aberration and must be due to Fe2+/Fe3+ heterogeneity from the surface to the bulk of each nanoparticle. To perform XRD refinements, a simple model taking into account two phases was used. Indeed, the decomposition of each asymmetric peak can be achieved by means of two symmetrical Pseudo-Voigt functions, as shown Figure 4 for the peak 511 of the (Fe2.25Ti0.75)1-δO4 titanium ferrite studied under O2 atmosphere. This concords with an iron-rich surface where δ ) δmax and a stoichiometric core (δ ) 0). Figure 3b validates that in nanometric materials a disturbance of stoichiometry at the surface, even small, can be revealed by a XRD line profile analysis. Table 4 gives, ∆dhkl/dhkl, the lattice spacings difference between the two constituted phases of each (Fe3-xTix)1-δO4
Figure 3. 440 diffraction peak of (Fe2.25Ti0.75)1-δO4 powder acquires in situ under (a) thermodynamical equilibrium: N2/H2/H2O gas mixture leading to pO2 ) 1.4 10-24 Pa at 460 °C, (b) O2 gas at 25 °C. The circle clearly shows some asymmetry around high angles: under an oxidizing atmosphere, the Fe2+ cations are partially oxidized leading to a γ-Fe2O3 shell and a stoichiometric titanium ferrite bulk inside each particle.
Figure 4. Dessummated example of the 511 diffraction peak of the (Fe2.25Ti0.75)1-δO4 titanium ferrite studied ex situ. The Fe2+ cations are partially oxidized leading to a γ-Fe2O3 shell and a stoichiometric titanium ferrite bulk inside each particle.
particle: γ-Fe2O3 shell and stoichiometric titanium ferrite bulk. This analysis carried out on each diffraction line (hkl), provides a check for whether the partial oxidation is isotropic or not. For all (Fe3-xTix)1-δO4 powders, whose diffractograms were recorded under air atmosphere, the angular difference denoted ∆θ which exists between the two “dessummated” peaks of each line was measured. This allows the determination of the lattice spacings difference, ∆dhkl, existing between the bulk and the shell of the grains by the use of the following relation:
∆dhkl ∆θ ) dhkl tan θ First, we can notice that in the case of the composition x ) 0.5 the segregation phenomenon is not perceptible. The peaks
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Figure 5. (a) 57Fe room-temperature Mo¨ssbauer spectra of (Fe2.5Ti0.5)1-δO4 studied in room conditions, (b) room-temperature hyperfine field of the outer sextuplet S1 of titanomagnetite Mo¨ssbauer spectra as a function of Ti content: refs •,28 9.29
TABLE 4: ∆dhkl/dhkl, the Lattice Spacings Difference between the Two Constituted Phases of Each (Fe3-xTix)1-δO4 Particle: γ-Fe2O3 Shell and Stoichiometric Titanium Ferrite Bulk. In the Case of the Composition x ) 0.5, the Segregation Phenomenon Is Not Perceptible. The Peaks Broadening Due to Size Effects Is So Important That It Hides a Potential Asymmetry 220 311 400 422 511 440
xTi)0.25
xTi)0.5
xTi)0.75
xTi)1
0.56% 0.41% 0.17% -
-
0.20% 0.20% 0.39% 0.19% 0.25% 0.25%
0.17% 0.40% 0.34% 0.48% 0.17% 0.13%
broadening due to size effects is so important that it hides a potential asymmetry. Second, the oxidation phenomenon, leading to chemical segregation, is isotropic and no privileged direction is detected. X-ray diffraction appears to be an original technique for studying the segregation phenomenon which occurs when nanometric powders are studied under oxidizing atmosphere. To see if this phenomenon can be investigated by another technique, Mo¨ssbauer spectrometry has been also utilized. Figure 5a shows Mo¨ssbauer spectra of (Fe2.5Ti0.5)1-δO4. Clear differences exist with the spectrum published for a titanoferrite of the same composition.29,30 In particular, the hyperfine field of the outer sextet is much larger in our case (H1 ) 486 kG) than it is for the titanomagnetite investigated by Melzer (H1 ) 447 kG).29 The field value determined by Melzer is consistent with the results of Tanaka and Kono for Fe3-xTixO4 (0 < x < 0.33)28 which show that the latter hyperfine field decreases with
Ti content (Figure 5b). A reasonable range of values for the hyperfine field H1 of the titanium composition x ) 0.50 is 431(Q)-452(L) kG (calculated from a linear, L, and from a quadratic, Q, extrapolation of the published values). We must conclude that the outer sextet S1 observed in Figure 5a cannot be associated with a titanomagnetite whose Ti content is x ) 0.50. The x dependence of the hyperfine field (Figure 5b) is mainly associated with a titanoferrite whose Ti content is less than at most x ) 0.10. Mo¨ssbauer characteristics can therefore be accounted for by chemical composition heterogeneities. The measured field H1 is consistent, once more, with a γ-Fe2O3 surface layer. The subspectrum S2 with broad lines has an average field H2 of 455 kG. The total spectrum results then from the superposition of two contributions: a γ-Fe2O3 shell and a stoichiometric titanium ferrite bulk. To confirm the previous observations, the local structure of the powders was investigated using HRTEM. Results for a characteristic analysis is shown in Figure 6. The image of a particle was digitized (Figure 6a) and the Fourier transform calculated (Figure 6b). The phase image corresponding to the (220) lattice fringes was then determined (Figure 6c). A sudden change in the gradient of the phase at about 2 nm from the grain surface is observed (Figure 6d) and is directly related, as previously explained, to a lattice parameter discontinuity inside the grain. The related ∆g b, is ascribed to a lattice rotation of 2° of the surface phase with respect to the bulk reference. It is important to note that this change is uniform for the surface layer. On the left side of the grain (region A), a lattice parameter difference of about 1% (in compression for the surface) is also detected. The magnitude of the misfit here is however approximate given the high degree of noise present in the image and the fact that the surface material is most likely tilted with respect to a perfect zone axis. Nevertheless, the sudden and significant change in the crystal lattice for the surface layer provides evidence for a heterogeneous core-shell structure for the particle. The case described by Figure 6 corresponds to an extreme case which we voluntarily sought on high resolution micrographs, it does not exclude a mean heterogeneity of about 0.5% determined by X-ray diffraction. This grain may be one of the most exposed during oxidation, i.e., on the top of the amassed powder. For other grains, undoubtedly more in the bulk of the agglomerate, this phenomenon is less clear. The lattice parameter variations observed in Figure 6c are consistent with an Fe2Ti04 bulk (a ) 8.53 Å) and a γ-Fe2O3 shell in the surface (a ) 8.34 Å) and highlights clearly the great difference in mobility existing between Ti4+ and Fe2+ cations, phenomenon which leads to compressive stresses in the bulk of the grains. The diffusion strongly decreases and, in our case, stops at the ambient temperature leading to the coexistence of two compositions inside each particle: a γ-Fe2O3 shell and a titanium ferrite bulk. Given the nature of HREM experiments it is not, however, possible to analyze a statistically significant number of grains. The analysis should therefore be considered as a complement to the X-ray and Mo¨ssbauer experiments providing evidence that chemical inhomogeneity can exist in the powders consistent with the core-shell model. 4. Conclusions Dynamic Fe-Ti segregation related to Fe2+ oxidation in Ti ferrites has been explained by difference of mobility of Ti and Fe in the spinel structure. During incorporation of oxygen in the lattice, movement of the more mobile cations toward the surface is observed. XPS, Mo¨ssbauer spectrometry, XRD, and
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Figure 6. HRTEM image analysis of a (Fe2.5Ti0.5)1-δO4 titanium ferrite powder: (a) digitized image of a particle; (b) Fourier transform of this image. The circle shows the filtering of the 220 lattice fringes; (c) 220 phase image calculated by Fourier filtering: P220(r), black ) 0 white ) 2π; (d) horizontal phase profile averaged over box shown in (c). For this grain (region B), the phase gradient, ∇Pg(rb) ) 2π ∆g b, is ascribed to a lattice rotation of 2° of the surface phase with respect to the bulk reference (∆g b/2g bref ) sin(θ/2)). On the left side of the grain (region A), a lattice parameter difference of about 1% (in compression for the surface) is also detected.
HRTEM analysis all point to an iron enrichment of particle surface. Fe cations therefore have higher mobility than Ti, which is in agreement with both measurements of cationic diffusion coefficient obtained at high temperature on micrometric titanomagnetites and with the respective Ti and Fe oxygen-cation bond length. This study also demonstrates that in nanometric materials a disturbance of stoichiometry in surface layers, even slight, can be detected by classical techniques such as XRD or Mo¨ssbauer spectrometry. To study homogeneous stoichiometric ferrites in the nanometric range two solutions can then be proposed: studying materials in situ under appropriate N2/H2/H2O gazes mixtures, or studying materials with cations thermodynamically stable in room conditions. Acknowledgment. The authors thank S. Collin for XPS experiments and G. Le Cae¨r for helpful discussions about Mo¨ssbauer investigations.
References and Notes (1) Readman, P. W.; O’Reilly, W. J. Geomagn. Geoelectr. 1972, 24, 69. (2) Ozima, M.; Ozima, M. Phys. Earth Planet. Interiors 1972, 5, 87. (3) Nishitani, M. Kono. J. Geomagn. Geoelectr. 1989, 41, 19. (4) O’Reilly, W. J. Magn. Magn. Pater. 1994, 137, 167. (5) Dieckmann, R.; Schmalzried, H. Ber. Bunsen-Ges. 1977, 81, 344. (6) Ayyub, P.; Multani, M.; Barma, M.; Palkar, V. R.; Vijayaraghavan, R. J. Phys. C: Solid State Phys. 1988, 21, 2229. (7) Verwey, E. J.; Heilman, E. L. J. Chem. Phys. 1947, 15, 174. (8) Akimoto, S. J. Geomagn. Geoelectr. 1954, 61, 1. (9) Ne´el, L. AdV. Phys. 1955, 4, 191. (10) Chevalier, R.; Bolfa, J.; Mathiew, S. Bull. Soc. Franc. Min. Crist. 1955, 78, 307. (11) O’Reilly, W.; Banerjee, S. K. Phys. Lett. 1965, 17, 237. (12) Trestman-Matts, A.; Dorris, S. E.; Kumarakrishnan, S.; Mason, T. O. J. Am. Ceram. Soc. 1983, 66, 829. (13) O’Neill, H. S. C.; Navrotsky, A. Am. Mineral. 1983, 68, 181. (14) Perriat, P.; Fries, E.; Millot, N.; Domenichini, B. Solid State Ionics 1999, 117, 175. (15) Millot, N.; Be´gin-Colin, S.; Perriat, P.; Le Cae¨r, G. J. Solid State Chem. 1998, 139, 66.
7132 J. Phys. Chem. B, Vol. 105, No. 29, 2001 (16) Aymes, D.; Millot, N.; Nivoix, V.; Perriat, P.; Gillot, B. Solid State Ionics 1997, 101-103, 261. (17) Petersen, N. Phys. Earth Planet. Inter. 1970, 2, 175. (18) Freer, R.; Hauptman, Z. Phys. Earth Planet. Inter. 1978, 16, 223. (19) Gillot, B. J. Solid State Chem. 1994, 113, 163. (20) Perriat, P.; Domenichini, B.; Gillot, B. J. Phys. Chem. Solids 1996, 57, 1641. (21) Hy¨ tch, M. J.; Snoeck, E.; Kilaas, R. Microstruct. Ultramicrosc. 1998, 874, 131. (22) Langford, J. I. National Institute of Standards and Technology, Special Publication 1992, 846, 145. (23) Halder, N. C.; Wagner, C. N. J. AdV. X-ray Anal. 1966, 9, 91. (24) Le Cae¨r, G.; Brand, R. A.; J. Phys. Condens. Matter 1998, 10, 10715.
Guigue-Millot et al. (25) Poix, P. Liaisons interatomiques et proprie´ te´ s physiques des compose´ s mine´ raux; Suchet: Paris, 1966; p 88. (26) Poix, P.; Basile, F.; Djega-Mariadassou, C. Ann. Chim. 1975, 3, 159. (27) El Guendouzi, M.; Sbai, K.; Perriat, P.; Gillot, B. Mater. Chem. Phys. 1990, 25, 429. (28) Tanaka, H.; Kono, M. J. Geomagn. Geoelectr. 1987, 39, 463. (29) Melzer, K.; Simsa, Z.; Lukaslak, M.; Suwalski, J. Cryst. Res. Technol. 1987, 22, 132. (30) In-house software taking into account the effect of sample gap. (31) Available in the PC software package DIFFRACT AT supplied by SIEMENS.
