Cation distribution and bond lengths in CoAl2O4 spinel

Solid State Communications 128 (2003) 85–90 www.elsevier.com/locate/ssc

Cation distribution and bond lengths in CoAl2O4 spinel Akihiko Nakatsuka*, Yuya Ikeda, Yuzuru Yamasaki, Noriaki Nakayama, Tadato Mizota Department of Advanced Materials Science and Engineering, Faculty of Engineering, Yamaguchi University, Ube, Yamaguchi 755-8611, Japan Received 15 May 2003; received in revised form 18 June 2003; accepted 30 June 2003 by H. Akai

Abstract It is widely known that CoAl2O4, IV(Co12xAlx) VI[CoxAl22x]O4, is a largely normal spinel ð0 , x , 2=3Þ; but this cation distribution cannot be explained by the effects of cation size, electronegativity and ligand-field of Co2þ. To examine the reason for this peculiar cation distribution, the relationship between the inversion parameters ðxÞ and the interatomic distances was investigated using the Rietveld analysis of X-ray diffraction. On the basis of the results of the structure refinements by Rietveld analysis, the regression equations for the mean bond lengths and O· · ·O distances as a function of x were calculated by a linear least-squares method. The variations of local bond lengths versus x were inferred from the regression equations for the mean bond lengths. With increasing x; the ratio (O· · ·O)shared/(O· · ·O)unshared in VIB-site octahedron increases remarkably and the local bonds on IVA-site are inferred to be abnormally lengthened. These results imply that if CoAl2O4 were a largely inverse spinel, the local bond lengths on IVA-site would become abnormally long and the repulsion between VIB-site cations would become considerably large. Such destabilization factors of the crystal structure can be avoided by the largely normal configuration of cations. q 2003 Elsevier Ltd. All rights reserved. PACS: 61.10.–Nz Keywords: A. CoAl2O4; A. Spinel; C. X-ray scattering; D. Order–disorder effects

1. Introduction Spinels (TM2X4; X ¼ O, S, Se and Te) with transition metals have attracted a great attention in material science field because of their interesting magnetic properties. Since their magnetic properties are very sensitive to the cation distribution in the crystal structure [1– 3], knowledge of the cation distribution is very important for controlling and forecasting the properties. Under the circumstances, the crystallography, including cation distribution, of spinels has been systematized intensively [4,5]. The crystal structure of spinel (space group Fd3¯m) has cations at Wyckoff positions 8a (1/8, 1/8, 1/8) and 16d (1/2, 1/2, 1/2) and oxygens at 32e ðu; u; uÞ; where the positional parameter of oxygen is conventionally called u-parameter. The structural formula is expressed as IV(T12xMx)VI[Tx* Corresponding author. Fax: þ 81-836-85-9651. E-mail address: [email protected] (A. Nakatsuka). 0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00652-5

M22x]X4, where IV ( ) and VI [ ] represent the tetrahedral site (IVA-site; 8a) and the octahedral site (VIB-site; 16d), respectively; x is called the inversion parameter. Two ordered configurations of cations can be adopted at low temperatures; the normal spinel with x ¼ 0; and the inverse spinel with x ¼ 1: A value of x ¼ 2=3 corresponds to a completely random cation distribution between IVA- and VI B-sites. The order –disorder process of cations is sensitive to temperature, and x approaches 2/3 with increasing temperature. In most of actual spinel samples, x is between 0 and 2/3 (largely normal spinel) or between 2/3 and 1 (largely inverse spinel). In general, cation distribution of spinels can be explained in terms of cation size, electronegativity and ligand-field effect of transition metals. However, this is not the case for CoAl2O4 spinel, IV(Co12xAlx)VI[CoxAl22x]O4. CoAl2O4, which is a largely normal spinel [6 – 12], has strong preferences of Al3þ for VIB-site and of Co2þ for IVA-site in contradiction to every effect of cation size ðrAl , rCo [13]),

86

A. Nakatsuka et al. / Solid State Communications 128 (2003) 85–90

electronegativity ðxCo ¼ 1:47 , xAl ¼ 1:54 [14]) and ligandfield of Co2þ. In the present study, we discuss the reason for this peculiar cation distribution of CoAl2O4 spinel from viewpoint of crystal chemistry. For this purpose, CoAl2O4 spinels with different x values are prepared by quenching from various temperatures between 700 and 1350 8C, and the relationship between the cation distributions and the interatomic distances is investigated in these samples using the Rietveld analysis of X-ray diffraction.

2. Experiments 2.1. Sample preparation It is indispensable for accurate Rietveld analyses to control the preferred orientation and make the grain size uniform. For this purpose, CoAl2O4 spinel was prepared by a chelate gel method with anhydrous citric acid. Stoichiometric amounts of metallic Co (99.9%) and Al (99.99%) (molar ratio Co:Al ¼ 1:2) were dissolved in nitric acid (conc. 69%) at 100 8C. Anhydrous citric acid (C6H8O7) was added to this solution, in molar ratio (Co þ Al):C6H8O7 ¼ 1:5. This mixed solution was heated at 230 8C with stirring on a hot-plate in order to promote gelation, and then the citrate amorphous precursor obtained by this heattreatment was decomposed at 1000 8C for 24 h in a furnace. The crystalline products obtained as a consequent of the thermal decomposition have an attractive royal blue color, and a powder X-ray diffraction ascertained that they are single phase of CoAl2O4 spinel without any impurities. These indicate that trivalent Co ions are not present in the samples. The quenching experiments were performed in a vertical tube furnace. In each experiment, the initially obtained CoAl2O4 spinel was enclosed in a Pt capsule and suspended on a thin Pt wire next to a Pt/Pt – Rh thermocouple. The samples were annealed at various temperatures between 700 and 1350 8C. After being annealed for desired periods, the samples were dropped into ice water. The quenching time was estimated to be below 0.2 s. The annealing time for each sample is summarized in Table 1. There was no change in color of the samples before and after annealing, and the powder X-ray diffraction ascertained that the annealed samples are single phase of CoAl2O4 spinel as well as the initially synthesized ones. These indicate that Co ions in the spinel showed no valence-change from 2 þ to 3 þ during the annealing treatments.

 was monochromatized Cu Ka radiation ðl ¼ 1:54184 AÞ used for the measurements. The diffraction data were collected in 208 , 2u , 1208 by u 2 2u symmetric stepscan at 0.0208 step with fixed counting time of 10.0 s. The Rietveld analyses were carried out using a program RIETAN [15]. The occupancy parameters of the cations on IV A- and VIB-sites were constrained to keep the chemical composition. Consequently, the variable occupancy parameter was only that of Al3þ on IVA-site, i.e. the inversion parameter ðxÞ: In the final structure refinements, the following parameters were refined: background, zeropoint, half-width, pseudo-Voigt, asymmetry, preferred orientation, scale, positional, isotropic displacement, occupancy and lattice parameters. Reliability indices ðRwp ; Rp ; Re ; RI and RF Þ obtained by the refinements using the ionized scattering factors were slightly improved compared with those using the scattering factors for neutral atoms, and accordingly the scattering factors of Co2þ, Al3þ and O22 were used in the final refinements. Reliability indices on refinements are summarized in Table 1. Refined structural parameters are listed in Table 2. A typical result of the Rietveld analysis on the measured powder X-ray diffraction pattern is shown in Fig. 1.

3. Results and discussion Fig. 2 shows the annealing temperature dependence of inversion parameter ðxÞ: The x values increase smoothly from 700 to 1100 8C. On the other hand, above 1100 8C, the values are kept at a nearly constant value of x < 0:23 much smaller than 2/3, which corresponds to a completely random cation distribution between IVA- and VIB-sites, in spite of the increase in annealing temperature. Here, in order to assess whether our quenched samples maintain the equilibrium cation distributions at the annealing temperatures, the parameter x was fitted by the following O’Neill –Navrotsky thermodynamic equation [16], using a multiple non-linear

2.2. X-ray measurements and Rietveld analyses For the quenched samples, the powder X-ray diffraction data for the Rietveld analyses were measured at room temperature (23 8C) with a Rigaku RINT2200 diffractometer operated at 40 kV and 30 mA. The graphite-

Fig. 1. Observed (dots) and calculated (upper solid line) powder Xray diffraction patters of the sample annealed at 1050 8C. The lower solid line shows the difference between the observed and calculated intensities. Vertical bars represent the positions of the diffraction peaks.

A. Nakatsuka et al. / Solid State Communications 128 (2003) 85–90

87

Table 1 Reliability indices on Rietveld refinements Annealing temperature (8C) 700

700

700

750

750

800

900

1000

1050

1100

1150

Annealing time (h) 240 120 48 336 120 48 24 24 24 24 24 10.43 10.48 10.43 10.61 10.54 10.45 10.35 10.20 10.23 10.29 10.46 Rwp (%) Rp (%) 7.11 7.16 6.95 7.33 7.16 6.89 7.04 6.87 7.04 6.98 7.12 Re (%) 8.06 8.12 8.24 8.17 8.13 8.11 8.03 8.07 8.10 8.18 8.13 1.97 2.00 1.80 1.86 1.92 1.94 2.07 1.67 1.90 1.48 1.95 RI (%) RF (%) 1.67 1.79 1.48 1.59 1.66 1.74 1.89 1.54 1.68 1.74 1.91

21

21

2RT lnx ð1 2 xÞ ð2 2 xÞ

¼ a þ 2bx;

1250

1300

1350

24 24 24 24 14.75 11.26 14.08 14.48 10.14 8.01 10.09 10.60 11.73 8.25 8.51 8.35 2.25 2.27 1.84 1.89 3.00 2.37 1.63 1.70

Fig. 3 shows the variations of the mean interatomic distances versus x: To extrapolate these variations to the unobservable x range, their regression equations were calculated using a least-squares method. The best fits to 33 data, including the previous data [10,12], are expressed by the following liner equations:

least squares procedure (Fig. 2): 2

1200

ð1Þ

where R is gas constant and T is absolute temperature. The fit of Eq. (1) to all the data in the annealing-temperature range from 700 to 1350 8C does not adequately fit the data (dotted curve in Fig. 2). Whereas the fit to the data from 700 to 1100 8C agrees well with the data in this annealingtemperature range (solid curve in Fig. 2). These show that the samples quenched from temperatures between 700 and 1100 8C keep the equilibrium cation distributions at the annealing temperatures, but those from temperatures above 1100 8C do not maintain the equilibrium cation distributions at the annealing temperatures. As pointed out in other spinels [17 – 19], this is because the kinetics of cation ordering in spinels under high-temperature is rapid enough to allow some degree of cation redistribution between IVAand VIB-sites during quenching. Because of such kinetics, it is next to impossible to freeze the cation distribution of CoAl2O4 spinel to the x values above 0.23 by quenching methods.

R½A – O ¼ 20:1253x þ 1:9615;

ð2Þ

R½B – O ¼ 0:0722x þ 1:9130;

ð3Þ

ðO· · ·OÞtetra ¼ 20:2046x þ 3:2031;

ð4Þ

ðO· · ·OÞunshared ¼ 20:0032x þ 2:8742;

ð5Þ

ðO· · ·OÞshared ¼ 0:2206x þ 2:5255;

ð6Þ

where R[A– O] and R[B – O] are the mean cation– oxygen bond lengths on IV A- and VI B-sites, respectively; (O· · ·O)tetra is the edge length of tetrahedron about IVAsite; (O· · ·O)unshared and (O· · ·O)shared are the unshared and shared edge lengths of octahedron about VIB-site, respectively. The mean bond lengths estimated at x ¼ 0 are R[A– ˚ from Eq. (2) and R[B – O] ¼ 1.913 A ˚ from O] ¼ 1.962 A Eq. (3). These R[A– O] and R[B – O] correspond to IVCo – O

Table 2 Refined structural parameters Annealing temperature (8C)

Annealing time (h)

a0 ˚) (A

u

x

Biso ˚ 2) (A IV ( A-site)

Biso ˚ 2) (A VI ( B-site)

Biso ˚ 2) (A (oxygen)

700 700 700 750 750 800 900 1000 1050 1100 1150 1200 1250 1300 1350

240 120 48 336 120 48 24 24 24 24 24 24 24 24 24

8.10298(5) 8.10276(5) 8.10268(5) 8.10294(5) 8.10296(5) 8.10319(5) 8.10391(5) 8.10452(5) 8.10560(5) 8.10609(5) 8.10630(5) 8.10644(6) 8.10659(4) 8.10652(3) 8.10657(3)

0.2639(3) 0.2640(3) 0.2640(3) 0.2639(4) 0.2638(4) 0.2636(3) 0.2636(3) 0.2630(3) 0.2630(4) 0.2625(4) 0.2627(4) 0.2624(6) 0.2623(4) 0.2629(6) 0.2628(6)

0.078(8) 0.081(9) 0.091(7) 0.109(9) 0.087(9) 0.097(8) 0.145(7) 0.190(7) 0.197(7) 0.221(7) 0.225(8) 0.229(11) 0.231(9) 0.228(13) 0.225(13)

0.42(4) 0.41(5) 0.36(4) 0.38(5) 0.45(5) 0.40(5) 0.46(4) 0.45(4) 0.46(4) 0.46(4) 0.53(4) 0.47(6) 0.46(5) 0.28(7) 0.34(7)

0.37(5) 0.38(6) 0.29(4) 0.28(6) 0.37(6) 0.39(6) 0.40(4) 0.41(4) 0.48(4) 0.39(4) 0.49(4) 0.34(6) 0.36(5) 0.31(7) 0.34(7)

0.31(9) 0.31(10) 0.27(9) 0.32(10) 0.30(10) 0.41(9) 0.50(9) 0.63(8) 0.66(9) 0.64(9) 0.77(9) 0.81(13) 0.78(10) 0.67(15) 0.69(15)

88

A. Nakatsuka et al. / Solid State Communications 128 (2003) 85–90

Fig. 2. Variation of inversion parameter ðxÞ as a function of annealing temperature. Dotted curve is the fit of O’Neill–Navrotsky model [16] to all the data. Solid curve is the best fit to equilibrium data from 700 to 1100 8C.

length on IVA-site and VIAl – O length on VIB-site estimated in the case of a completely normal spinel IV (Co)VI[Al Al]O4, respectively. These lengths agree excel˚ for IVCo– O on IVA-site, 1.915 A ˚ lently with those (1.96 A VI VI for Al – O on B-site) expected from the Shannon’s effective ionic radii [13]. ˚ estimated at x ¼ On the other hand, R[A– O] of 1.836 A 1 from Eq. (2), which corresponds to IVAl – O length on IVAsite estimated in the case of a completely inverse spinel IV ˚ longer than the expected (Al)VI[Co Al]O4, is about 0.07 A IV IV ˚ [13]). The VICo– O Al – O length on A-site (1.77 A length on VI B-site in the case that VI Co 2þ would imaginatively full occupy VIB-site (VI[Co Co]) can be estimated by the extrapolation of R[B – O] to the imaginary inversion parameter of x ¼ 2; and the estimated length is ˚ from Eq. (3). This length is about 0.07 A ˚ shorter 2.057 A ˚ [13]) for VICo2þ on VIB-site, than the expected one (2.125 A whose electron configuration can be concluded to be high5 2 spin ðt2g eg Þ from the variations of the site-distributions of Co2þ and the effective magnetic moments with Ga3þ content in CoAl22cGacO4 spinel solid solution ð0 # c # 2Þ [11]. Thus, the IVAl – O length on IVA-site estimated at x ¼ 1 and the VICo– O length on VIB-site estimated at the imaginary inversion parameter of x ¼ 2 deviate considerably from each expected length. The local IVAl – O length on IVA-site and the local VICo– O length on VIB-site in actual CoAl2O4 spinels, which are largely normal spinel, should be close to the lengths expected from the effective ionic radii [13], as well as IV Co– O length on IVA-site and VIAl –O length on VIB-site estimated at x ¼ 0: If we base on this speculation, these

Fig. 3. Variations of (a) the mean bond lengths and (b) the edge lengths of polyhedra as a function of inversion parameter ðxÞ: Solid symbols are used for both the mean bond lengths on IVA-site (R[A– O]) and the edge lengths of polyhedra. Open symbols are used for the mean bond lengths on VIB-site (R[B –O]). Circles, squares and triangles are from the present study and Refs. [10,12], respectively. Solid lines show linear least-squares fits for these interatomic distances.

local bond lengths will show the variations such as dashedand-dotted lines in Fig. 4 based on lever rule. In particular, the local bond lengths on IVA-site are inferred to increase remarkably with increasing x; and the difference of about ˚ between the local bond lengths on IVA-site estimated 0.07 A

A. Nakatsuka et al. / Solid State Communications 128 (2003) 85–90

89

in the case of a completely inverse spinel ðx ¼ 1Þ and their expected ones [13] seems to be large enough to destabilize the crystal structure. Moreover, from Eqs. (5) and (6), the ratio (O· · ·O)shared/(O· · ·O)unshared in VIB-site octahedron increases remarkably with increasing x; and the ratio would increase up to 0.96 if x increased up to unity. The increment of (O· · ·O)shared/(O· · ·O)unshared increases the repulsion between VIB-site cations across the octahedral shared edge because the shielding effect of oxygens for the repulsion weakens (refer to Refs. [20 – 24] for a discussion of the shielding effect). The large (O· · ·O)shared/(O· · ·O)unshared ratio of 0.96 estimated at x ¼ 1 seems to be insufficient to relax the repulsion between VIB-site cations by the shielding effect because the value is close to unity. Consequently, if CoAl2O4 were a largely inverse spinel, the local bond lengths on IVA-site would become abnormally long and the repulsion between VIB-site cations would become considerably large. Thus, we conclude that CoAl2O4 spinel adopts a largely normal configuration of cations in order to avoid these two energetic destabilization factors occurring in the case that it would be a largely inverse spinel.

Acknowledgements The authors would like to thank Dr O. Ohtaka of Osaka University for critical reading of the manuscript and Dr H. Fujimori of Yamaguchi University for useful advices about the sample preparation. This work was partly supported by Grant-in-Aid for Scientific Research (No 12740299) from the Ministry of Education, Culture, Sports, Science and Technology of the Japanese Government.

References

Fig. 4. Possible relationships among the mean bond lengths (solid line extrapolated by dotted line), the local Co –O lengths (upper dashed-and-dotted line) and the local Al–O lengths (lower dashedand-dotted line) on (a) IVA- and (b) VIB-sites. These relationships are based on lever rule, R[A – O] ¼ (1 2 x)·d(IV Co – O) þ and R[B – O] ¼ (x/2)·d(VI Co – O) þ (1 2 x·d(IV Al – O) VI IV x/2)·d( Al–O), where d( Co–O) and d(VICo –O) are the local Co –O lengths on IVA- and VIB-sites, respectively; d(IVAl–O) and d(VIAl–O) are the local Al –O lengths on IVA- and VIB-sites, respectively; x is the inversion parameter. The symbols denoting the mean bond lengths are the same as those in Fig. 3. Large open inverse-triangles and large open diamonds represent the Co–O and Al – O lengths expected from the effective ionic radii [13], respectively.

[1] E.W. Gorter, Nature 165 (1950) 798. [2] J.A. Schulkes, G. Blasse, J. Phys. Chem. Solids 24 (1963) 1651. [3] G. Blasse, J. Phys. Chem. Solids 27 (1966) 383. [4] R.J. Hill, J.R. Craig, G.V. Gibbs, Phys. Chem. Mineral. 4 (1979) 317. [5] K.E. Sickafus, J.M. Wills, J. Am. Ceram. Soc. 82 (1999) 3279. [6] S. Greenwald, S.J. Pickart, F.H. Grannis, J. Chem. Phys. 22 (1954) 1597. [7] H. Schmalzried, Z. Phys. Chemie. 28 (1961) 203. [8] H. Furuhashi, M. Inagaki, S. Naka, J. Inorg. Nucl. Chem. 35 (1973) 3707. [9] F. Pepe, P. Porta, M. Schiavello, in: J. Wood et al. (Eds.), Proceedings of the 8th International Symposium on the Reactivity of Solids, Gothenburg, Plenum Press, New York, 1976. p. 183. [10] K. Toriumi, M. Ozima, M. Akaogi, Y. Saito, Acta Crystallogr. B34 (1978) 1093. [11] P. Porta, A. Anichini, J. C. S. Faraday I 76 (1980) 2448. [12] H.St.C. O’Neill, Eur. J. Mineral. 6 (1994) 603. [13] R.D. Shannon, Acta Crystallogr. A32 (1976) 751.

90

A. Nakatsuka et al. / Solid State Communications 128 (2003) 85–90

[14] R.T. Sanderson, Inorganic Chemistry, Van Nostrand-Reinhold, New York, 1967. [15] F. Izumi, The Rietveld Method, Oxford University Press, Oxford, 1993. [16] H.St.C. O’Neill, A. Navrotsky, Am. Mineral. 68 (1983) 181. [17] B.J. Wood, R.J. Kirkpatrick, B. Montez, Am. Mineral. 71 (1986) 999. [18] A. Navrotsky, Am. Mineral. 71 (1986) 1160. [19] H.St.C. O’Neill, W.A. Dollase, C.R. Ross II, Phys. Chem. Mineral. 18 (1991) 302.

[20] J.A. Tossell, G.V. Gibbs, Phys. Chem. Mineral. 2 (1977) 21. [21] R.J. Hill, M.D. Newton, G.V. Gibbs, J. Solid State Chem. 47 (1983) 185. [22] A. Nakatsuka, A. Yoshiasa, S. Takeno, Acta Crystallogr. B51 (1995) 737. [23] A. Nakatsuka, A. Yoshiasa, T. Yamanaka, Acta Crystallogr. B55 (1999) 266. [24] A. Nakatsuka, A. Yoshiasa, T. Yamanaka, O. Ohtaka, T. Katsura, E. Ito, Am. Mineral. 84 (1999) 1135.