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Magnetic resonance (FMR, EPR) of chromium dioxide supported on titania
Colloids and Surfaces A: Physicochemical and Engineering Aspects 144 (1998) 81–87
Magnetic resonance (FMR, EPR) of chromium dioxide supported on titania K. Ko¨hler a,*1, W. Mo¨rke b, T. Bieruta b a Fritz-Haber-Institut, Max-Planck-Gesellschaft, Faradayweg 4–6, D-14195 Berlin, Germany b Institut fu¨r Analytik und Umweltchemie, Universita¨t Halle-Wittenberg, Geusaer Strasse, D-06217 Merseburg, Germany Received 7 October 1997; accepted 7 July 1998
Abstract Ferromagnetic resonance (FMR) investigations (n=9.5 and 35 GHz) of chromium dioxide, CrIVO , supported on 2 titania for different chromium contents (0.7, 7 and 11 wt% Cr) are reported. CrO particle diameters of 3–4 nm were 2 calculated from the thermomagnetic curves (Griscom’s model ). The temperature dependence of the line widths and simulations of the FMR powder spectra indicate contributions of axial anisotropy and additionally strong interactions of CrO with the TiO surface. In addition to Cr(IV ), varying amounts of Cr( V ) and Cr( VI ) were observed. © 1998 2 2 Elsevier Science B.V. All rights reserved. Keywords: Chromium dioxide; Ferromagnetic resonance
1. Introduction Investigations of chromium and chromium oxides supported on metal oxide surfaces are reported in numerous papers due to their interesting surface chemistry and activity in several catalytic processes. In general, the presence of Cr(III ) and Cr( VI ) and the corresponding oxide phases Cr O and CrO is reported, but also Cr( V ) and 2 3 3 Cr(II ) surface species were proven or proposed. Chromium dioxide, CrO , or Cr(IV ) supported 2 on a metal oxide surface is generally not discussed in the literature. Very recently, a simple and convenient way to prepare CrO supported on titania 2 was reported for higher loaded (7 wt% Cr) * Corresponding author. Fax: +49 89 289 13473; e-mail: [email protected] 1 Present address: Anorganisch-chemisches Institut, Technische Universita¨t Mu¨nchen, Lichtenbergstrasse 4, D-85747 Garching b. Mu¨nchen, Germany.
CrO /TiO systems [1]. The supported chromium x 2 oxide phases CrO , CrOOH and Cr O were pre2 2 3 pared. The distinctive magnetic properties of these three oxides were found to be very suitable for their characterization. CrO is ferromagnetic below 2 its Curie temperature T $390 K [2], a property C never established for any other chromium oxide. CrOOH and Cr O are typical antiferromagnetic 2 3 materials with Ne´el points T $130 K [3] and N 308 K [4], respectively. This paper focuses on the identification and characterization of the chromium dioxide phase supported on titania for different chromium contents (0.7 to 11 wt% Cr) by ferromagnetic resonance.
2. Experimental Supported chromium dioxide was prepared according to ref. [1] by impregnation of TiO (P25, 2
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specific surface area 49 m2/g, rutile:anatase= 30:70, supplier Degussa) with chromium(III ) nitrate, Cr(NO ) · 9H O (Fluka). The supported 33 2 precursor was heated to 573 K in a nitrogen stream (50 ml/min), cooled to room temperature and calcined in an oxygen stream (50 ml/min) at 573 K for 3 or 6 h. Chromium contents of 1.3×10−5, 1.46×10−3 and 2.6×10−3 mol Cr/g TiO (corre2 sponding to about 0.7, 7 and 11.5 wt% Cr or 1, 10 and 16.6 wt% referred to Cr O ) were prepared. 2 3 The acronyms used to designate the samples are derived from their Cr content: CrO -1, CrO -10 2 2 and CrO -16 and CrO -16s (the latter sample is 2 2 singly calcined for 3 h in oxygen, whereas the others were treated twice for 3 h). Ferromagnetic and paramagnetic resonance spectra were recorded on Bruker ESP300 and ESP300E systems at X-band frequency ( Varian E-9 spectrometer at Q-band frequency) at temperatures between 113 and 420 (300) K; microwave frequency about 9.4 (35.5) GHz, microwave power ∏0.5 mW, modulation frequency 100 kHz. The data in parentheses refer to Q-band measurements. The measurements were carried out in a Bruker TE104 double rectangular cavity and a modified Varian E-266 Q-band TE011 (right circular cylinder) cavity, respectively. The g values were determined with an NMR magnetometer and DPPH as g marker. Integration procedure: in order to take into account the different weight of areas in the low and high field part of the FMR spectra (compare Fig. 1), we used the integration method described in refs. [5,6 ] (extrapolation of the baseline of the high field region towards low field ).
3. Results 3.1. FMR spectra of supported chromium dioxide Powder spectra of two samples at the frequency n=9.4 GHz are shown in Fig. 1. The spectra of all samples are strongly temperature dependent concerning line width, shape and intensity. Above 390 K (the Curie temperature, T , of CrO ) a C 2 symmetric derivative line is observed: T=400 K: g=1.972, DB =23 mT. {Careful analysis of the pp spectra at different temperatures and the following
Fig. 1. Ferromagnetic resonance spectra of CrO supported on 2 titania for samples CrO -1 (a) and CrO -16 (b) for different 2 2 recording temperatures at X-band (n=9.4 GHz). The arrows indicate where the DB values were taken from. pp
arguments suggest that paramagnetic contributions to the FMR spectra due to paramagnetic impurities can be neglected. (i) The effective anisotropy derived from DBexp exactly reflects the easy pp and hard direction of the FMR powder spectrum (see later). The DBexp values are not influenced by pp other superimposed signals. (ii) There is no indication of a broad superimposed signal in the vicinity of the Curie temperature (which would be expected e.g. for Cr3+ impurities). (iii) Additional analytical methods used especially for the characterization of CrO -10 (e.g. thermoanalytical experiments 2 monitored by mass spectrometry) prove that more than 95% of the total chromium is present as CrO [1]}. Below 390 K the line is broadened, 2 becomes first asymmetric and for T<353 K the low field shoulder (easy direction) appears and is further shifted to lower fields with decreasing temperature. A finite value of absorption is observed at zero field at the lowest temperature investigated in the X-band (T=113 K ). The spectrum of CrO -1 is superimposed by a narrow 2
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signal due to Cr5+ surface species ( g=1.975). The presence of Cr( VI ) surface species in varying amounts is deduced from UV–vis and desorption experiments [1]. To first approximation, the magnetic anisotropies are not frequency dependent. In the FMR spectra at a frequency of 35.5 GHz (T=294 K, not shown), the low field shoulder appears at B= 1.08 T, the corresponding derivative line at 1.26 T ( g=1.975), i.e. the DB value, is practically pp unchanged for both frequencies used.
3.2. Thermomagnetic investigations I exp curves obtained from the temperature rel dependence of the integrated intensity of the FMR spectra are shown in Fig. 2. In comparison to the Brillouin function, a linear or concave curvature is observed. This indicates magnetic properties diverging from bulk crystalline CrO . 2 In the (I exp )2 dependencies of CrO -10 and rel 2 CrO -16, only the high-temperature part is linear. 2 The extrapolation of this part [7] yields Curie temperatures between 390 and 430 K. These values are typical of CrO or doped CrO , respectively 2 2 [8,9]. The mean size of the CrO particles was 2 calculated from the I exp –T curves by Eq. (1) rel
Fig. 2. Temperature dependence of the integrated intensity of the FMR spectra of CrO -1 (open circles), CrO -16 (full circles) 2 2 and CrO -16s (full squares) in comparison to the calculated 2 I values (empty squares, d=4 nm, Griscom’s model ). rel
according to Griscom [10–12]:
G
I cal 1−exp(−2x) M T = S,T [1−exp(−y)] I cal M 1−exp(−2x+y) tT S,tT 1 exp(−y) (x−y)[1−exp(−2)] + 1−exp(−y) x
C
−{1−exp[−2(x−y)]} exp(−y)
DH
(1)
I cal and I cal are the calculated signal intensities at T tT the temperature T of the particular measurement and the lowest temperature measured, respectively. M and M are the spontaneous magneS,T S,tT tization at these temperatures. x and y are the quotients of the Zeeman energy of a crystallite of average volume V or of a Cr(IV ) atom and the thermal energy [ x=M VB/kT or y=gm B/kT, S,T B with B=0.3370 T, k=Boltzmann constant, g=gfactor=1.97 for Cr(IV )]. I cal and I exp are conT T nected by: I cal I exp I cal = T =I exp = T (2) rel I cal rel I exp tT tT The values calculated according to Eq. (1) are presented in Fig. 2 together with the experimental ones for CrO -16. They correspond to a mean 2 particle diameter d=4 nm. For all samples investigated, very similar d values between 4 (CrO -1, 2 CrO -10) and 3 nm (CrO -16s) were obtained, as 2 2 reflected by the very similar thermomagnetic curves shown in Fig. 2. Because the integrated intensity at the lowest temperature measured (tT ) is influenced most by the absorption at zero field (see Fig. 1), the relative intensity is shifted to higher values. The consequence is that the estimated particle size represents an upper limit. To clarify the influence of the absorption at zero field, we calculated the intensity using 230 K as tT (no zero field absorption). This procedure yields a particle diameter of about 4 nm, in good agreement with the results given above. An additional estimation of the error in the integrated intensity introduced by the lack of the absorption at zero field can be done by the analysis of the FMR spectra at tT at Q-band frequencies. In Q-band, the complete spectrum could be recorded for all temperatures.
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Such an estimation confirms the above statement that the determination of the particle size is not remarkably influenced by neglecting the zero field absorption in X-band for the system under investigation. 3.3. Temperature dependence of the line width–magnetic anisotropies Shape and magnetocrystalline anisotropies of the tetragonal CrO can be described by an axial 2 anisotropy. Both types of anisotropy exhibit the same influence of the particle size on the temperature dependence of the experimental line width DB due to superparamagnetic relaxation. We pp calculated the influence of the particle size on DB according to Eq. (3) [13] for uniaxial anisotpp ropy: HKM
=
Fig. 3. Temperature dependence of the experimental peak-topeak line width DB for samples CrO -1 (full squares), pp 2 CrO -16 (full circles) and CrO -16s (empty circles) in compari2 2 son to the calculated values for CrO -16 (empty squares), see 2 text (n=9.4 GHz).
1−3x−1 coth x+3x−2
(3) Hm coth x−x−1 K where HKM represents the anisotropy field of a superparamagnet and Hm the anisotropy field of K the bulk material. x is the quotient of magnetic and thermal energy [Eq. (1)]. The experimental line width DBexp consists of the intrinsic part pp (DBint ) and the contribution caused by magnetic pp anisotropies (DBani ). Assuming that (DBint ) is indepp pp pendent of the particle size and small compared to (DBani ) [7], the experimental line width is a pp crude measure for the anisotropy field. The relative temperature dependence of (DBani ) is given by pp Eq. (3). For the comparison of calculated and experimental values, the value calculated for sample CrO -16 at tT was equated to the experi2 mental value. The obtained values are involved in Fig. 3 (empty squares). The difference between calculated and experimental values of DB increases with pp decreasing chromium loading and increasing duration of the thermal treatment. As source for this discrepancy we assume the influence of the titania surface, which strengthens the axial anisotropy. For nanocrystallites, axial and magnetostrictive anisotropies are difficult to distinguish [14]. Probably the observed effects are caused by at least two types of anisotropy.
Accordingly, DB has to be described by an pp effective anisotropy constant, which is composed of shape and/or magnetocrystalline and magnetostrictive interactions. In order to examine these conclusions, the FMR powder spectra were calculated using an effective axial anisotropy constant. Its value was estimated from the experimental DB values as pp 3K /M (vide infra). eff,T S,T 3.4. Simulation of the FMR powder spectra The magnetic dipolar interaction between the CrO particles can be neglected due to the diamag2 netic dilution by the support. In this context ‘‘dilution’’ means that the effective anisotropy energy (K , vide infra) is large compared to the eff magnetic particle–particle interaction. This condition holds if the relation M d3/2r3<2|K |/M S,T eff S,T is fulfilled [15] (where d is the diameter of the chromium oxide particles and r the distance between them). Thus, for CrO at room temper2 ature one calculates r>1.3 nm, which holds for all CrO samples investigated. 2 The ‘‘independent-grain approach’’ [16 ] was used for the simulations. The resonance field was determined according to the Smit–Suhl method [17,18].
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For the case of axial anisotropy the angular dependence of the anisotropy energy, F , is given K by: F =K sin2 H (4) K eff,T The free energy, F, of a ferromagnet consists of and the Zeeman energy {F =−M F K Z S,T B[sin H sin H cos(W−W )+cos H cos H ]} [15]. B B B (H, W) and (H , W ) define the orientation of the B B magnetization and of the external field, respectively, in a given coordinate system. Determining the equilibrium position of the magnetization, by equation to zero F and F give the relationship H W between (H, W) and (H , W ). B B Determining the second derivatives with respect to (H, W) (F , F , F ) at the equilibrium posiWW HH WH tion and inserting the second derivatives in Eq. (5): v/c={F F −F2 }1/2/M sin H (5) HH WW WH S,T yields a relationship of fourth order between the resonance magnetic field B and the (H , W ) orienB B tation [19]. In the case of weak axial anisotropy [15], the angular dependence of the resonance field B(H ) is described by a term K / B eff,T M (3cos2 H −1). This gives a peak-to-peak line S,T B width of 3K /M . eff,T S,T The FMR powder spectra were calculated according to Eq. (6) for an individual Lorentzian line shape with the line width DB [20]:
P
2p (DB)3[B−B(H )] sin H dH B B B (6) {3(DB)2+[B−B(H )]2}2 0 B A simulated and an experimental spectrum of sample CrO -16 (T=294 K ) are compared in 2 Fig. 4. The value K =2.5×104 J m−3 used for eff,T the calculation was obtained from the experimental temperature dependence of DB (see above); DB= pp 15 mT; B represents the point of intersection of 0 the I curve with the B-axis. The agreement of rel the experimental and calculated spectra is satisfactory. It is not possible, however, to improve the fit using only one set of parameters (K /M ; eff,T S,T DB, B ). Nevertheless, the calculation of the 0 spectra additionally confirms the model for the effective anisotropy chosen. However, this model does not explain the shift of the point of intersection of the spectra with the B-axis. Additional I = B
Fig. 4. Experimental (full line) and simulated (dashed line) FMR powder spectra of CrO -16 (n=9.4 GHz, T=294 K ), 2 see text.
information about the interaction of the CrO 2 particles with the support can be deduced from the comparison of the experimentally observed signal position with the calculated one. For the effective axial anisotropy constant one would expect the intersection point with the B-axis at H =90°. Accordingly, we can calculate the correB sponding B value with B(90)=B(g=1.97)+K eff,T /M [19] (neglecting terms of higher order in S,T K ). This (assumed ) isotropic signal shift is eff,T attributed to magnetostrictive interactions in the literature [21]. The isotropic signal shift DB is connected with the stress s acting on the particles by: DB=l s/M [7]. The corresponding pressure S S,T is of the order of magnitude ca. 8×109 Pa, and is large enough to cause the observed influence on DB via the anisotropic magnetostrictive conpp stants (l is the isotropic magnetostriction constant of CrO [22]). The term ‘‘isotropic’’ has, in this 2 context, a two-fold meaning: (i) the most simple approach to describe magnetoelastic influences [21]; and (ii) concerning the fact that an anisotropic magnetoelastic interaction can be decomposed into an anisotropic (change of form of the spectrum) and an ‘‘isotropic’’ part (shift of the crossing point of the FMR spectrum) [23]. In the context of our simple model, we can conclude magnetoelastic interactions from an additional shift of the crossing point only. The discrepancy in the broadness and the ‘‘weight’’ of the resonances in the easy (B#180 mT ) and hard directions (B#350 mT )
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between experimental and simulated spectra can indicate that the individual CrO particles fixed on 2 the titania surface are magnetically not uniform. Reasons for this could be e.g.: (i) particle size distribution; (ii) different mechanical constraints due to CrO –TiO interactions; or (iii) non-uni2 2 form distribution of Cr( V ) or Cr( VI ). Because it is not possible to quantify these sources of line broadening at this point of the investigation, we deliberate on a minimum parameter set. That is why we do not like to achieve a better fit simply by changing the line widths of the envelope.
4. Discussion The magnetic resonance spectra observed after decomposition and calcination of chromium(III ) nitrate on titania, i.e. the spectral features at Xand Q-band frequencies (Fig. 1) and their characteristic temperature dependence ( Figs. 2 and 3) are doubtless due to collective magnetic properties of a ferromagnetic system. Chromium dioxide, CrO , 2 is the only known chromium oxide that is ferromagnetic at room temperature. Even for loadings as low as 0.7 wt% chromium (CrO -1), the pres2 ence of CrO [besides Cr( V ) and Cr( VI ) surface 2 species] on titania could be proven. Ferromagnetic resonance is shown to be a very sensitive tool to monitor structural changes of supported CrO . 2 Particle diameters of about 4 nm were deduced from the thermomagnetic curves using Griscom’s model. The question remains, however, to what extent this method and the magnetic properties of CrO can be influenced by an interaction of 2 CrO with the surface of TiO or by a partial 2 2 mixing of CrO and TiO . A strong interaction of 2 2 CrO with the titania surface is indicated by experi2 mental observations and magnetic anisotropy considerations. (i) We obtained very similar I /T rel curves ( Fig. 2) and corresponding particle sizes for samples with remarkably differing chromium concentrations. (ii) The sample with the lowest loading, for which an effect due to substrate support interactions is expected to be most significant, actually exhibits the largest DB (Fig. 3). (iii) The pp difference between calculated and experimental values of DB increases with decreasing chromium pp
loading and increasing duration of the thermal treatment. (iv) Magnetostrictive influence is indicated by the differences in experimentally observed and corresponding calculated signal positions ( Fig. 4). (v) The magnetic anisotropy (asymmetric line broadening3T ) depends on slight, more or less influenceable changes of the preparation conditions. In a few cases, especially for lower chromium contents and short calcination times, broad symmetric lines were observed in the full temperature range investigated. Repeated calcination at 573 K, however, always yielded the typical anisotropic features shown in Figs. 1 and 3. This thermal treatment does not cause changes in the composition and of the average chromium oxidation state (temperature programmed reduction, thermoanalytical methods [1]). The additional thermal treatment seems to cause a strong interaction of CrO particles and titania support. 2 An evident formation of mixed oxides under maintaining the rutile structure would take place at temperatures of about 1273 K and higher only [2]. Simultaneously, the Curie temperature and the spontaneous magnetization of CrO are 2 changed [2]. We suggest that also in the case of (epitactical ) interaction of both oxides T and C M are influenced. Further information about S,T the structural and chemical influence of the support could be obtained by studies of the formation and magnetic properties of CrO on other oxides like 2 Al O and SiO . Such investigations are in 2 3 2 progress.
Acknowledgment The authors thank Professor R. Kirmse, University of Leipzig, for the possibility of measuring magnetic resonance spectra at his laboratories. K.K. wishes to thank the Stiftung Stipendienfonds des Verbandes der Chemischen Industrie ( F.R.G.) for a grant (Liebig-Stipendium) and T.B. the VW Stiftung ( F.R.G.) for financial support.
References [1] K. Ko¨hler, M. Maciejewski, H. Schneider, A. Baiker, J. Catal. 157 (1995) 301.
K. Ko¨hler et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 144 (1998) 81–87 [2] B.L. Chamberland, CRC Crit. Rev. Solid State Mater. Sci. 7 (1977) 1. [3] A.N. Christensen, Acta Chem. Scand. A30 (1976) 133. [4] E.S. Dayhoff, Phys. Rev. 107 (1957) 84. [5] R.M. Housley, E.H. Cirlin, I.B. Goldberg, H. Crowe, R.A. Weeks, R. Perhac, Proc. 6th Lunar Science Conf., Houston, TX, 1975, p. 3173. [6 ] W. Mo¨rke, M. Hirschfelder, S. Gehre, K. Doerffel, Chemo. Intell. Lab. Syst. 8 (1990) 87. [7] L. Bonneviot, D. Olivier, in: B. Imellik, J.C. Vedrine ( Eds.), Catalyst Characterization: Physical Techniques for Solid Materials, Plenum Press, New York, 1994, chapter 7. [8] M. Hirschfelder, Models for the ferromagnetic resonance of single-domain particles, Thesis, Merseburg, Germany, 1990. [9] G. Bate, Recording materials, in: E.P. Wohlfahrt ( Ed.), Ferromagnetic Materials 2, North-Holland, Amsterdam, 1980, p. 381. [10] D.L. Griscom, IEEE Trans. Magn. 17 (1981) 2748. [11] A. Chatelain, P. Buffat, P. Stadelmann, R.A. Weeks, J. Non-Cryst. Solids 71 (1985) 335.
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[12] W. Mo¨rke, R. Lamber, U. Schubert, B. Breitscheidel, Chem. Mater. 6 (1994) 1659. [13] R.S. DeBiasi, T.C. Devezas, J. Appl. Phys. 49 (1978) 2466. [14] L. Bonneviot, Thesis, Pierre et Marie Curie University, Paris, 1983. [15] D.L. Griscom, Geochim. Cosmochim. Acta 38 (1974) 1509. [16 ] E. Schlo¨mann, J. Phys. Chem. Solids 6 (1958) 257. [17] J. Smit, H.G. Beljers, Philips Res. Rep. 10 (1955) 113. [18] H. Suhl, Phys. Rev. 97 (1955) 555. [19] I. Onyszkievicz, J. Pietrzak, Phys. Status Solidi A 73 (1982) 641. [20] J.H. Lunsford, Adv. Catal. 22 (1972) 265. [21] G. Suran, A. Stankoff, F. Hoffmann, Phys. Rev. B 8 (1973) 1109. [22] G. Bate, Recording materials, in: E.P. Wohlfahrt (Ed.), Ferromagnetic Materials 2, North-Holland, Amsterdam, 1980, p. 496. [23] Yu. Kotyukov, V. Abrasov, Sov. Phys. J. 15 (1972) 1.
Magnetic resonance (FMR, EPR) of chromium dioxide supported on titania K. Ko¨hler a,*1, W. Mo¨rke b, T. Bieruta b a Fritz-Haber-Institut, Max-Planck-Gesellschaft, Faradayweg 4–6, D-14195 Berlin, Germany b Institut fu¨r Analytik und Umweltchemie, Universita¨t Halle-Wittenberg, Geusaer Strasse, D-06217 Merseburg, Germany Received 7 October 1997; accepted 7 July 1998
Abstract Ferromagnetic resonance (FMR) investigations (n=9.5 and 35 GHz) of chromium dioxide, CrIVO , supported on 2 titania for different chromium contents (0.7, 7 and 11 wt% Cr) are reported. CrO particle diameters of 3–4 nm were 2 calculated from the thermomagnetic curves (Griscom’s model ). The temperature dependence of the line widths and simulations of the FMR powder spectra indicate contributions of axial anisotropy and additionally strong interactions of CrO with the TiO surface. In addition to Cr(IV ), varying amounts of Cr( V ) and Cr( VI ) were observed. © 1998 2 2 Elsevier Science B.V. All rights reserved. Keywords: Chromium dioxide; Ferromagnetic resonance
1. Introduction Investigations of chromium and chromium oxides supported on metal oxide surfaces are reported in numerous papers due to their interesting surface chemistry and activity in several catalytic processes. In general, the presence of Cr(III ) and Cr( VI ) and the corresponding oxide phases Cr O and CrO is reported, but also Cr( V ) and 2 3 3 Cr(II ) surface species were proven or proposed. Chromium dioxide, CrO , or Cr(IV ) supported 2 on a metal oxide surface is generally not discussed in the literature. Very recently, a simple and convenient way to prepare CrO supported on titania 2 was reported for higher loaded (7 wt% Cr) * Corresponding author. Fax: +49 89 289 13473; e-mail: [email protected] 1 Present address: Anorganisch-chemisches Institut, Technische Universita¨t Mu¨nchen, Lichtenbergstrasse 4, D-85747 Garching b. Mu¨nchen, Germany.
CrO /TiO systems [1]. The supported chromium x 2 oxide phases CrO , CrOOH and Cr O were pre2 2 3 pared. The distinctive magnetic properties of these three oxides were found to be very suitable for their characterization. CrO is ferromagnetic below 2 its Curie temperature T $390 K [2], a property C never established for any other chromium oxide. CrOOH and Cr O are typical antiferromagnetic 2 3 materials with Ne´el points T $130 K [3] and N 308 K [4], respectively. This paper focuses on the identification and characterization of the chromium dioxide phase supported on titania for different chromium contents (0.7 to 11 wt% Cr) by ferromagnetic resonance.
2. Experimental Supported chromium dioxide was prepared according to ref. [1] by impregnation of TiO (P25, 2
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specific surface area 49 m2/g, rutile:anatase= 30:70, supplier Degussa) with chromium(III ) nitrate, Cr(NO ) · 9H O (Fluka). The supported 33 2 precursor was heated to 573 K in a nitrogen stream (50 ml/min), cooled to room temperature and calcined in an oxygen stream (50 ml/min) at 573 K for 3 or 6 h. Chromium contents of 1.3×10−5, 1.46×10−3 and 2.6×10−3 mol Cr/g TiO (corre2 sponding to about 0.7, 7 and 11.5 wt% Cr or 1, 10 and 16.6 wt% referred to Cr O ) were prepared. 2 3 The acronyms used to designate the samples are derived from their Cr content: CrO -1, CrO -10 2 2 and CrO -16 and CrO -16s (the latter sample is 2 2 singly calcined for 3 h in oxygen, whereas the others were treated twice for 3 h). Ferromagnetic and paramagnetic resonance spectra were recorded on Bruker ESP300 and ESP300E systems at X-band frequency ( Varian E-9 spectrometer at Q-band frequency) at temperatures between 113 and 420 (300) K; microwave frequency about 9.4 (35.5) GHz, microwave power ∏0.5 mW, modulation frequency 100 kHz. The data in parentheses refer to Q-band measurements. The measurements were carried out in a Bruker TE104 double rectangular cavity and a modified Varian E-266 Q-band TE011 (right circular cylinder) cavity, respectively. The g values were determined with an NMR magnetometer and DPPH as g marker. Integration procedure: in order to take into account the different weight of areas in the low and high field part of the FMR spectra (compare Fig. 1), we used the integration method described in refs. [5,6 ] (extrapolation of the baseline of the high field region towards low field ).
3. Results 3.1. FMR spectra of supported chromium dioxide Powder spectra of two samples at the frequency n=9.4 GHz are shown in Fig. 1. The spectra of all samples are strongly temperature dependent concerning line width, shape and intensity. Above 390 K (the Curie temperature, T , of CrO ) a C 2 symmetric derivative line is observed: T=400 K: g=1.972, DB =23 mT. {Careful analysis of the pp spectra at different temperatures and the following
Fig. 1. Ferromagnetic resonance spectra of CrO supported on 2 titania for samples CrO -1 (a) and CrO -16 (b) for different 2 2 recording temperatures at X-band (n=9.4 GHz). The arrows indicate where the DB values were taken from. pp
arguments suggest that paramagnetic contributions to the FMR spectra due to paramagnetic impurities can be neglected. (i) The effective anisotropy derived from DBexp exactly reflects the easy pp and hard direction of the FMR powder spectrum (see later). The DBexp values are not influenced by pp other superimposed signals. (ii) There is no indication of a broad superimposed signal in the vicinity of the Curie temperature (which would be expected e.g. for Cr3+ impurities). (iii) Additional analytical methods used especially for the characterization of CrO -10 (e.g. thermoanalytical experiments 2 monitored by mass spectrometry) prove that more than 95% of the total chromium is present as CrO [1]}. Below 390 K the line is broadened, 2 becomes first asymmetric and for T<353 K the low field shoulder (easy direction) appears and is further shifted to lower fields with decreasing temperature. A finite value of absorption is observed at zero field at the lowest temperature investigated in the X-band (T=113 K ). The spectrum of CrO -1 is superimposed by a narrow 2
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signal due to Cr5+ surface species ( g=1.975). The presence of Cr( VI ) surface species in varying amounts is deduced from UV–vis and desorption experiments [1]. To first approximation, the magnetic anisotropies are not frequency dependent. In the FMR spectra at a frequency of 35.5 GHz (T=294 K, not shown), the low field shoulder appears at B= 1.08 T, the corresponding derivative line at 1.26 T ( g=1.975), i.e. the DB value, is practically pp unchanged for both frequencies used.
3.2. Thermomagnetic investigations I exp curves obtained from the temperature rel dependence of the integrated intensity of the FMR spectra are shown in Fig. 2. In comparison to the Brillouin function, a linear or concave curvature is observed. This indicates magnetic properties diverging from bulk crystalline CrO . 2 In the (I exp )2 dependencies of CrO -10 and rel 2 CrO -16, only the high-temperature part is linear. 2 The extrapolation of this part [7] yields Curie temperatures between 390 and 430 K. These values are typical of CrO or doped CrO , respectively 2 2 [8,9]. The mean size of the CrO particles was 2 calculated from the I exp –T curves by Eq. (1) rel
Fig. 2. Temperature dependence of the integrated intensity of the FMR spectra of CrO -1 (open circles), CrO -16 (full circles) 2 2 and CrO -16s (full squares) in comparison to the calculated 2 I values (empty squares, d=4 nm, Griscom’s model ). rel
according to Griscom [10–12]:
G
I cal 1−exp(−2x) M T = S,T [1−exp(−y)] I cal M 1−exp(−2x+y) tT S,tT 1 exp(−y) (x−y)[1−exp(−2)] + 1−exp(−y) x
C
−{1−exp[−2(x−y)]} exp(−y)
DH
(1)
I cal and I cal are the calculated signal intensities at T tT the temperature T of the particular measurement and the lowest temperature measured, respectively. M and M are the spontaneous magneS,T S,tT tization at these temperatures. x and y are the quotients of the Zeeman energy of a crystallite of average volume V or of a Cr(IV ) atom and the thermal energy [ x=M VB/kT or y=gm B/kT, S,T B with B=0.3370 T, k=Boltzmann constant, g=gfactor=1.97 for Cr(IV )]. I cal and I exp are conT T nected by: I cal I exp I cal = T =I exp = T (2) rel I cal rel I exp tT tT The values calculated according to Eq. (1) are presented in Fig. 2 together with the experimental ones for CrO -16. They correspond to a mean 2 particle diameter d=4 nm. For all samples investigated, very similar d values between 4 (CrO -1, 2 CrO -10) and 3 nm (CrO -16s) were obtained, as 2 2 reflected by the very similar thermomagnetic curves shown in Fig. 2. Because the integrated intensity at the lowest temperature measured (tT ) is influenced most by the absorption at zero field (see Fig. 1), the relative intensity is shifted to higher values. The consequence is that the estimated particle size represents an upper limit. To clarify the influence of the absorption at zero field, we calculated the intensity using 230 K as tT (no zero field absorption). This procedure yields a particle diameter of about 4 nm, in good agreement with the results given above. An additional estimation of the error in the integrated intensity introduced by the lack of the absorption at zero field can be done by the analysis of the FMR spectra at tT at Q-band frequencies. In Q-band, the complete spectrum could be recorded for all temperatures.
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Such an estimation confirms the above statement that the determination of the particle size is not remarkably influenced by neglecting the zero field absorption in X-band for the system under investigation. 3.3. Temperature dependence of the line width–magnetic anisotropies Shape and magnetocrystalline anisotropies of the tetragonal CrO can be described by an axial 2 anisotropy. Both types of anisotropy exhibit the same influence of the particle size on the temperature dependence of the experimental line width DB due to superparamagnetic relaxation. We pp calculated the influence of the particle size on DB according to Eq. (3) [13] for uniaxial anisotpp ropy: HKM
=
Fig. 3. Temperature dependence of the experimental peak-topeak line width DB for samples CrO -1 (full squares), pp 2 CrO -16 (full circles) and CrO -16s (empty circles) in compari2 2 son to the calculated values for CrO -16 (empty squares), see 2 text (n=9.4 GHz).
1−3x−1 coth x+3x−2
(3) Hm coth x−x−1 K where HKM represents the anisotropy field of a superparamagnet and Hm the anisotropy field of K the bulk material. x is the quotient of magnetic and thermal energy [Eq. (1)]. The experimental line width DBexp consists of the intrinsic part pp (DBint ) and the contribution caused by magnetic pp anisotropies (DBani ). Assuming that (DBint ) is indepp pp pendent of the particle size and small compared to (DBani ) [7], the experimental line width is a pp crude measure for the anisotropy field. The relative temperature dependence of (DBani ) is given by pp Eq. (3). For the comparison of calculated and experimental values, the value calculated for sample CrO -16 at tT was equated to the experi2 mental value. The obtained values are involved in Fig. 3 (empty squares). The difference between calculated and experimental values of DB increases with pp decreasing chromium loading and increasing duration of the thermal treatment. As source for this discrepancy we assume the influence of the titania surface, which strengthens the axial anisotropy. For nanocrystallites, axial and magnetostrictive anisotropies are difficult to distinguish [14]. Probably the observed effects are caused by at least two types of anisotropy.
Accordingly, DB has to be described by an pp effective anisotropy constant, which is composed of shape and/or magnetocrystalline and magnetostrictive interactions. In order to examine these conclusions, the FMR powder spectra were calculated using an effective axial anisotropy constant. Its value was estimated from the experimental DB values as pp 3K /M (vide infra). eff,T S,T 3.4. Simulation of the FMR powder spectra The magnetic dipolar interaction between the CrO particles can be neglected due to the diamag2 netic dilution by the support. In this context ‘‘dilution’’ means that the effective anisotropy energy (K , vide infra) is large compared to the eff magnetic particle–particle interaction. This condition holds if the relation M d3/2r3<2|K |/M S,T eff S,T is fulfilled [15] (where d is the diameter of the chromium oxide particles and r the distance between them). Thus, for CrO at room temper2 ature one calculates r>1.3 nm, which holds for all CrO samples investigated. 2 The ‘‘independent-grain approach’’ [16 ] was used for the simulations. The resonance field was determined according to the Smit–Suhl method [17,18].
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For the case of axial anisotropy the angular dependence of the anisotropy energy, F , is given K by: F =K sin2 H (4) K eff,T The free energy, F, of a ferromagnet consists of and the Zeeman energy {F =−M F K Z S,T B[sin H sin H cos(W−W )+cos H cos H ]} [15]. B B B (H, W) and (H , W ) define the orientation of the B B magnetization and of the external field, respectively, in a given coordinate system. Determining the equilibrium position of the magnetization, by equation to zero F and F give the relationship H W between (H, W) and (H , W ). B B Determining the second derivatives with respect to (H, W) (F , F , F ) at the equilibrium posiWW HH WH tion and inserting the second derivatives in Eq. (5): v/c={F F −F2 }1/2/M sin H (5) HH WW WH S,T yields a relationship of fourth order between the resonance magnetic field B and the (H , W ) orienB B tation [19]. In the case of weak axial anisotropy [15], the angular dependence of the resonance field B(H ) is described by a term K / B eff,T M (3cos2 H −1). This gives a peak-to-peak line S,T B width of 3K /M . eff,T S,T The FMR powder spectra were calculated according to Eq. (6) for an individual Lorentzian line shape with the line width DB [20]:
P
2p (DB)3[B−B(H )] sin H dH B B B (6) {3(DB)2+[B−B(H )]2}2 0 B A simulated and an experimental spectrum of sample CrO -16 (T=294 K ) are compared in 2 Fig. 4. The value K =2.5×104 J m−3 used for eff,T the calculation was obtained from the experimental temperature dependence of DB (see above); DB= pp 15 mT; B represents the point of intersection of 0 the I curve with the B-axis. The agreement of rel the experimental and calculated spectra is satisfactory. It is not possible, however, to improve the fit using only one set of parameters (K /M ; eff,T S,T DB, B ). Nevertheless, the calculation of the 0 spectra additionally confirms the model for the effective anisotropy chosen. However, this model does not explain the shift of the point of intersection of the spectra with the B-axis. Additional I = B
Fig. 4. Experimental (full line) and simulated (dashed line) FMR powder spectra of CrO -16 (n=9.4 GHz, T=294 K ), 2 see text.
information about the interaction of the CrO 2 particles with the support can be deduced from the comparison of the experimentally observed signal position with the calculated one. For the effective axial anisotropy constant one would expect the intersection point with the B-axis at H =90°. Accordingly, we can calculate the correB sponding B value with B(90)=B(g=1.97)+K eff,T /M [19] (neglecting terms of higher order in S,T K ). This (assumed ) isotropic signal shift is eff,T attributed to magnetostrictive interactions in the literature [21]. The isotropic signal shift DB is connected with the stress s acting on the particles by: DB=l s/M [7]. The corresponding pressure S S,T is of the order of magnitude ca. 8×109 Pa, and is large enough to cause the observed influence on DB via the anisotropic magnetostrictive conpp stants (l is the isotropic magnetostriction constant of CrO [22]). The term ‘‘isotropic’’ has, in this 2 context, a two-fold meaning: (i) the most simple approach to describe magnetoelastic influences [21]; and (ii) concerning the fact that an anisotropic magnetoelastic interaction can be decomposed into an anisotropic (change of form of the spectrum) and an ‘‘isotropic’’ part (shift of the crossing point of the FMR spectrum) [23]. In the context of our simple model, we can conclude magnetoelastic interactions from an additional shift of the crossing point only. The discrepancy in the broadness and the ‘‘weight’’ of the resonances in the easy (B#180 mT ) and hard directions (B#350 mT )
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between experimental and simulated spectra can indicate that the individual CrO particles fixed on 2 the titania surface are magnetically not uniform. Reasons for this could be e.g.: (i) particle size distribution; (ii) different mechanical constraints due to CrO –TiO interactions; or (iii) non-uni2 2 form distribution of Cr( V ) or Cr( VI ). Because it is not possible to quantify these sources of line broadening at this point of the investigation, we deliberate on a minimum parameter set. That is why we do not like to achieve a better fit simply by changing the line widths of the envelope.
4. Discussion The magnetic resonance spectra observed after decomposition and calcination of chromium(III ) nitrate on titania, i.e. the spectral features at Xand Q-band frequencies (Fig. 1) and their characteristic temperature dependence ( Figs. 2 and 3) are doubtless due to collective magnetic properties of a ferromagnetic system. Chromium dioxide, CrO , 2 is the only known chromium oxide that is ferromagnetic at room temperature. Even for loadings as low as 0.7 wt% chromium (CrO -1), the pres2 ence of CrO [besides Cr( V ) and Cr( VI ) surface 2 species] on titania could be proven. Ferromagnetic resonance is shown to be a very sensitive tool to monitor structural changes of supported CrO . 2 Particle diameters of about 4 nm were deduced from the thermomagnetic curves using Griscom’s model. The question remains, however, to what extent this method and the magnetic properties of CrO can be influenced by an interaction of 2 CrO with the surface of TiO or by a partial 2 2 mixing of CrO and TiO . A strong interaction of 2 2 CrO with the titania surface is indicated by experi2 mental observations and magnetic anisotropy considerations. (i) We obtained very similar I /T rel curves ( Fig. 2) and corresponding particle sizes for samples with remarkably differing chromium concentrations. (ii) The sample with the lowest loading, for which an effect due to substrate support interactions is expected to be most significant, actually exhibits the largest DB (Fig. 3). (iii) The pp difference between calculated and experimental values of DB increases with decreasing chromium pp
loading and increasing duration of the thermal treatment. (iv) Magnetostrictive influence is indicated by the differences in experimentally observed and corresponding calculated signal positions ( Fig. 4). (v) The magnetic anisotropy (asymmetric line broadening3T ) depends on slight, more or less influenceable changes of the preparation conditions. In a few cases, especially for lower chromium contents and short calcination times, broad symmetric lines were observed in the full temperature range investigated. Repeated calcination at 573 K, however, always yielded the typical anisotropic features shown in Figs. 1 and 3. This thermal treatment does not cause changes in the composition and of the average chromium oxidation state (temperature programmed reduction, thermoanalytical methods [1]). The additional thermal treatment seems to cause a strong interaction of CrO particles and titania support. 2 An evident formation of mixed oxides under maintaining the rutile structure would take place at temperatures of about 1273 K and higher only [2]. Simultaneously, the Curie temperature and the spontaneous magnetization of CrO are 2 changed [2]. We suggest that also in the case of (epitactical ) interaction of both oxides T and C M are influenced. Further information about S,T the structural and chemical influence of the support could be obtained by studies of the formation and magnetic properties of CrO on other oxides like 2 Al O and SiO . Such investigations are in 2 3 2 progress.
Acknowledgment The authors thank Professor R. Kirmse, University of Leipzig, for the possibility of measuring magnetic resonance spectra at his laboratories. K.K. wishes to thank the Stiftung Stipendienfonds des Verbandes der Chemischen Industrie ( F.R.G.) for a grant (Liebig-Stipendium) and T.B. the VW Stiftung ( F.R.G.) for financial support.
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