EPR of substitutional Fe3+ in TiO2 (Brookite)

J. Phys. Chem.Solids, 1973,Vol. 34, pp. 231-234. PergamonPress. Printedin Great Britain

EPR OF S U B S T I T U T I O N A L

Fe 3+ IN TiO2 (BROOKITE)*

J. A. ROSTWOROWSKI, M. HORN and C. F. SCHWERDTFEGER Department of Physics, Universtiy of British Columbia, Vancouver, Canada (Received 17 April 1972) A b s t r a c t - T h e EPR spectrum of substitutional Fe 3÷ in natural crystals of brooki[e (TiOz) has been analyzed. This represents the first EPR centre to be identified in brookite. The Ka-band data are described by the Hamiltonian parameters: g = 2.002 _ 0.005, D = 0.117 - 0.006 c m - ' and E = 0.033 ___ 0.002 c m - ' .

PAULIr~G and Sturdivant[1] established in 1928 that brookite, a polymorph of TiOz, belonged to the D ~ space group. The constants and crystallographic parameters measured by them have since been improved by Weyl[2]. Brookite has eight molecules per unit cell. The eight Ti 4÷ ions which are surrounded by distorted octahedrons of oxygen ions are crystallographically equivalent. If a paramagnetic impurity substitutes for Ti 4+, one would expect four equivalent EPR spectra since the crystal fields around the Ti 4+ sites are pairwise related through inversion. If the orientations of the magnetic axes of one site are known, the others can be found by reflections on the three principal crystallographic planes, hence each single EPR transition line measured along a crystallographic axis would split into two when the crystal is rotated in a principal crystallographic plane and into four, in any other orientation. For Fe 3+ the E PR spectrum is expected to be characterized by S = 5/2, I = 0 with the approximate spin Hamiltonian

[3]: :::

s +

/

35 \

2

+g). * Research supported by the National Research Council of Canada.

Several crystals of natural brookite from Maderanerthal, Uri, Switzerland and Valser Tal, Graubunden, Switzerland have been analyzed. The samples were yellowish to light brown in colour. They had approximately the same habit; thin flakes parallel to the (010) plane. The EPR spectra were taken at Ka-band frequencies with a balanced bridge design spectrometer. The spectra taken of the crystals from Maderanerthal and Valser Tal were indistinguishable. In the principal crystallographic directions there were some 40 transition lines between 0 and 23 kG. Each of these split into four lines at a random orientation. The line widths as well as their intensities were orientational dependent. There were also lines which were not observed in the principal crystallographic directions but appeared at other orientations. Direct analysis of such a complex spectrum would prove almost impossible, however different relaxation rates for the various centres provided an interesting discrimination mechanism. Previous work on the temperature dependence of the E PR in TiO2: Fe 3+ (anatase) [4, 5] had shown that the substitutional Fe 3+ spectrum could still be observed at temperatures over 1000°K, while the spectra of other Fe 3+ centres associated with an oxygen vacancy disappeared at little over 500°K. Although there was no reason to believe that such a charge compensated paramagnetic centre was present in this case, different impurity centres have in general different 231

J. A. ROSTWOROWSKI, M. HORN and C. F. S C H W E R D T F E G E R

232

and consistency with the extrema of the transition fields in the principal crystallographic planes. T r o u p and Hutton[6] have shown that it is always possible to choose the magnetic axes

relaxation times and hence such a temperature discrimination method might have merit. Its effectiveness in brookite is clearly demonstrated in Fig. 1. Only the typical 5-line spectrum of F e 3+ remains at 200°C.

I

I H .

rolol

I

I

I

_5 - - _3 2 2

3_ ~ 2

L 2

I 2

[ 2

I 2

2

Room T

I

I

I

*,200"C

MAGNETIC FIELD (K/LOGAUSS] 9

10

11

12

13

I"~

I

I

I

I

I

I

Fig. 1. EPR spectra at Ka-band of a natural single crystal of brookite with H parallel to [010] at room temperature and 200°C.

Figure 2 shows the characteristic five line pattern of F e a+ in 3 different planes of the crystal. T h e curves are typical for 'intermediate' crystal field/3]. T h e traditional method of finding the orientations of the magnetic axes by measuring the extremum positions of the transition fields was impractical in the present case because the rotating mechanism was incompatible with the required heating arrangement in the Ka-band cavity. Also a room temperature measurement was hopeless. T h e orientations of the magnetic axes were therefore estimated from crystallographic data assuming F e 3+ replaces the Ti 4+

x, y, z, such that 0 ~ < E / D < ~ 1/3. Rough calculations for the limiting values show that for this case the ratio is nearer to the upper limit. A first estimation of the value of D can be made by using graphs given by Aasa[7], who calculated for S = 5/2 the transition field H as a function of D, using E/D as a parameter. F o r the purpose of the estimation of D, the parameter E/D was set at 0.25. This gives D = 0.11 cm -~ and E = 0.027 cm -1. Since the g-value for F e z+ in most host crystals differs by less than 1per cent from the free electron g-value, an isotropic value of g = 2.002 was assumed.

EPR O F S U B S T I T U T I O N A L

plane010

Fe z+ IN TiO2 ( B R O O K I T E )

planelO0

233

plane 001

i

I

Co

17-

o

15-

c~

13-

11-

~:~

9

.-o

9,o z,5 6p ~,5 3,o 1,s q

,,..~

....,i''"

i~ ~, ~ 6,o ~ ~ ~s ~o ~ 3o ~5 o

Fig. 2. Angular dependence of the EPR spectrum of brookite at 200"C and Ka-band frequencies with H rotated in the three principal crystallographic planes.

T h e observed E P R transition fields measured along the principal crystallographic axes were fit to the truncated spin Hamiltonian (equation (1) neglecting terms in a and F) with a trial and error method varying D, E and the orientation of the magnetic axes using a computer programme given by Byfleet et al [8]. This computer programme calculates the transition fields and probabilities and plots the energy levels. ~ does not however include a and F. Several arguments can be drawn from the results of the E P R measurements which show that the contribution of these terms in the transition field can not be neglected. Thus the contribution of these terms to the transition fields was calculated by first order perturbation theory taking the Z e e m a n term as the unperturbed Hamiltonian. This contribution is proportional to p a + (1 / 12)qF = R where p = 5/2(14 + m 4 + n 4 -- 3/5) with l, m, n being the direction cosines of the magnetic field H along the cubic axes ~:, "0, ~, and q = 3 5 c o s 4 0 - - 3 0 c o s ~ 0 + 3 where 0 is the angle between H and Z. T h e proportionality factor being 2,--2.5, 0, 2.5,--2 depending on what transition one actually considered

[3]. Since from the avilable d a t a p is unknown, we can only give the value for R for any measured direction. Finally a least square fit for the parameters D, E, or, /3, y, Rio,, R01o, Ro01 where ct,/3, 3' are the Euler angles which give the orientation of the magnetic axes, was made with aid of a computer programme[9] for all E P R transition fields along the principal Table 1. Hamiltonian parameters. g = 2.002 ___0.005 D = (1170---30) x 10-4 cm - ' E = ( 3 3 0 ± 2 0 ) x 10-4 cm -~ [pa+ (l/12)qF]olo = (13--- 10) x I0-4 cm -I [pa+ (1/12)qF]loo = (-- 13-----5) x l0 -4 cm -~ [pa+ (l/12)qF]oo, = ( - - 6 6 ± 4 ) x 10-4 cm -~ Polar angles for one of the eight substitutional sites ( ± 3")*: Magnetic axes z y x

0 81 ° 149" 60 °

ck 55 ° 231" 210 °

*The direction approximately along the longest and shortest T i - O bond, which are nearly opposite, corresponds to the z magnetic axis. Polar angles for the other seven substitutional sites are easily calculated from symmetry considerations.

234

J.A.

ROSTWOROWSKI, M. HORN and C. F. S C H W E R D T F E G E R

crystallographic axes. The results of this fit are shown in Table 1. These results are consistent with the assumption that Fe 3+ substitutes Ti 4+. Furthermore the Fe 3+ occupies any of the eight substitutional sites within the unit cell with equal probability. Measurements at liquid Helium temperatures were made for the determination of the absolute sign of the fine structure parameters. This measurement also indicated that the low temperature Hamiltonian parameters are the same as those at room temperature to within the experimental error. A comparison with the other natural polymorphic forms of titanium dioxide makes this behaviour of brookite similar to rutile[10] and completely different from anatase [4]. Additional spectra have been observed at and below liquid nitrogen temperatures. To date no positive identification of these

or the other observed lines at room temperature has been made. Acknowledgements-The authors express their thanks to A. Harnik of the Crystallographic Institute of E.T.H., Zurich for the gift of severai brookite samples. REFERENCES 1. P A U L I N G L. and S T U R D I V A N T J. H., Z. KristaUogr. 611,239 (1928). 2. WEYL R., Z. KristaUogr. 111, 401 (1959). 3. A B R A G A M A. and B L E A N E Y B., Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford (1970). 4. HORN M. and S C H W E R D T F E G E R C. F.,J. Phys. Chem. Solids 32, 2529 ( 1971 ). 5. HORN M. and S C H W E R D T F E G E R C. F., Solid State Commun. 8, 1741 (1970). 6. T R O U P G. and H U T T O N D., Brit. J. appl. Phys. 15, 1493 (1964). 7. AASA R.,J. chem. Phys. 52, 3919 (1970). 8. BYFLEET C., C H O N G D., H E B D E N J. and M C D O W E L L J.,J. Magn. Res. 2, 69 (1970). 9. This programme uses mainly the Scientific Subroutine Package (Subroutine LLSQ), IBM Corp. Publ. Division (1968). I0. C A R T E R D. and O K A Y A A., Phys. Rev. 118, 1485 (1960).