An EPR study of solid solutions of ferric oxide in γ-Al2O3

J. Phys. Chem. Solids, 1974, Vol. 35, pp. 1007-1013.

Pergamon Press.

Printed in Great Britain

AN EPR STUDY OF SOLID SOLUTIONS OF FERRIC OXIDE IN ~/-A1203 F. GESMUNDO and C. DE ASMUNDIS Centro Studi di Chimica e Chimica Fisica Applicata alle Caratteristiche d'Impiego dei Materiali del C.N.R., Piazzale Kennedy, pad. D, Genova, Italy (Received 26 November 1973) Abstract The EPR spectra of solid solutions of ferric oxide in v-alumina have been studied. The dilute samples show two different spectra which are attributed to isolated ferric ions in the A and B sites of the spinel lattice. From the intensity dependence of the spectra on the iron concentration an appr6ximate value of the range of the exchange forces is deduced. The concentrated samples show an isotropic spectrum at g = 2.033 which is attributed to clusters of ferric ions coupled by exchange. The temperature dependence of the intensity of the associated ions spectrum is attributed to the increase of the average spin value of the clusters with T.

1. I N T R O D U C T I O N

In a previous work we studied solid solutions of ferric oxide in a - a l u m i n a by electron paramagnetic resonance [I]. We report here the results of a similar study on solid solutions of ferric oxide in ~/alumina. A different behaviour is expected in the two systems, because of the different structure of the two oxide forms. Pure ferric oxide has very different magnetic properties in the el- and in the 3'-forms, which are isohaorphous with the corresponding aluminum oxides. In fact, while a ferric oxide is antiferromagnetic, */-oxide is ferrimagnetic [2]. The */form of aluminum and iron oxides shows a crystal structure of spinel-type [3, 4], composed of a face-centered cubic lattice of oxygen ions, where the cations occupy a definite fraction of the tetrahedral and octahedral voids. In these oxides a part of the 24 cationic sites usually occupied in the spinels is vacant, so that their correct formula is Ms+l]I--11130,,where [] means a cation vacancy [5, 6]. M o r e o v e r */-alumina has a tetragonal distortion of the cubic cell, depending on the conditions of sample preparation [7]. In the elementary cell of spinels eight tetrahedral ( A ) and sixteen octahedral (B) sites are occupied. The local symmetry of a site A in a perfect spinel is cubic, because it is surrounded by a regular tetrahedron of oxygen ions and cations. On the other hand a B site is surrounded by a regular octahedron of oxygen ions, but the nearest-neighbour B cations form a deformed octahedron and only a sym-

metry axis C3 in t h e [ l 11] direction is left. Therefore a paramagnetic ion in a B site will be s u b j e c t t o an axial crystal field. When the cationic sites of a spinel are occupied by paramagnetic ions, magnetic interactions between neighbours will arise, depending on the reciprocal position of the ions. The strongest interactions are expected between A and B neighbours, while the A - A and B - B interactions are weaker [8]. In */-ferric oxide the resulting magnetic structure is composed of two sublattices, one formed by A and the other by B ions. While all the magnetic moments inside a single sublattice are parallel, the moments of one sublattice are antiparallel to the other one. Therefore ~/-ferric oxide is a ferrimagnetic material, with a Curie temperature of about 858°K [2]. While */-ferric oxide is a very well-known material, due to its technological importance, the solid solutions of ferric oxide in */-alumina have been so far scarcely studied. As far as we know, only two works dealing with their preparation and magnetic properties[9,10] have been published. In these solid solutions the ferric ions can enter both the A and the B sites. At low concentration the ferric ions are far apart from each other so as to b e isolated, and it should be possible to observe the E P R spectrum of the A - and B - type ions. When the iron concentration increases the average distance' between iron ions decreases, magnetic interactions between neighbours occur, and the E P R spectrum is modified. The study of the changes of the E P R

1007

1008

F. GESMUNDO and C. DE ASMUNDIS

spectrum as function of the iron concentration gives a clue on the magnitude and range of the magnetic interactions and on the general magnetic behaviour of the samples. 2. E X P E R I M E N T A L

DPPH

RESULTS

The solid solutions of ferric oxide in y-alumina have been prepared as previously reported[9, 10], by precipitating with ammonia a mixture of the required volumes of titrated solutions of aluminum and iron nitrates. The precipitate was then washed, dried at 120°C, ground and heated to 800°C for 10 days. Such a long time was required to obtain an EPR spectrum intensity stable on further heating. The crystal structure of the samples was checked by X-ray diffraction. Following this procedure we obtained the ~/-alumina'structure up to a mole fraction of iron f = 0.1, whim samples of higher iron concentrations showed the ~x-alumina structure. The samples will be called AFx, where x = 100f, [ being the mole fraction of iron. The EPR spectra have been measured with a spectrometer Varian V-4502-12 working at X - b a n d frequency (v ~ 9.52 kMHz) with a 100 k H z modulation. The sample temperature could be changed in the range 100-573°K with a commercial variable temperature unit. The g values have been obtained by comparison with polycrystalline DPPH. The E P R spectrum of solid solutions of ferric oxide in y-alumina is strongly affected by the iron concentration. In Fig. 1 the spectra of some samples are shown. The spectrum of the dilute sample A F 0.1 (curve a) shows an absorption at low fields ( H ~ 1600 G) and a very broad one (AH ~ 800 G) at higher fields ( H ~2450 G). The spectrum of the more concentrated sample A F 2 (curve b) shows again the low-field absorption, but instead of the 2540 G component it has a strong absorption centered at about 3350 G. In even more concentrated samples ( A F 5 , c u r v e c ) the low-field absorption decreases progressively partially overlapping the central absorption, until in the most concentrated sample ( A F 10) only the central absorption is observed. In the present paper the three absorptions will be called /3 spectrum (1600G), ~x spectrum (2540 G) and ~ spectrum (3350 G) respectively. We also measured the relative intensity at room temperature of the three spectra. The intensity values have been obtained by computation of the first moment of the /3 and ~ s p e c t r a [ I l l . For ~x spectrum we used the approximate expression I h A H 2, being h the height and A H the peak-to-peak linewidth of the spectrum[12], assuming that the form of the spectrum does not vary from sample to

C

Fig. 1 EPR spectra of solid solutions of ferric oxide in 3,-AI203: (a) AF 0-I ; (b) AF 2; (c) AF 5.

I

I

I

I

I

I

I

I

I

I

\ \ 1 0.5

o! I

/ I

"\. I

I 0.04

I

I o.O6

f r-~o3

I

•/ ~ O.Oe

9 "'.--,t 071

Fig. 2. Relative intensity at room temperature of the EPR spectra ~ (O), /3(O), and @(,t) in function of the iron concentration.

An EPR study of solid solutions of ferric oxide i

i

i

i

i

/"

1

/°~e~

e ~o.~,

,,~1 m

~m

o

°"~ ° ~°'~°"~

I ~

I 3O0

o

O~o~o~o~O--O

I

TEMPERATURE

OK

I 500

I

Fig. 3. Dependence o f / T on T of • spectrum for different samples: © AF 2; • AF 5; • AF 7; • AF 10. sample. In fact the method of the first moment is not satisfactory in this case, because of the broadness of the spectrum and of a large base-line drift. The values so obtained and normalized to unity are shown in Fig. 2. In Fig. 3 the value of the product IT, w h e r e . / i s the relative intensity of d9 spectrum and T the absolute temperature, is shown as a function of T for some samples.

3. D I S C U S S I O N

3.1 Spectra of the isolated ions (a) Interpretation of the spectra. The ~ and /3 spectra are the only absorptions shown by diluted samples. When f > 0 - 0 1 5 a spectrum disappears hidden b y the stronger qb spectrum, while/3 spectrum, being well separated from • absorption, is observed up to much higher concentration (f = 0.09), but with decreasing intensity. Therefore they must be assigned to ferric ions isolated in 7alumina. The/3 spectrum shows one absorption only, centered at about 1600 G, with a small displacement depending on iron concentration. Assuming that the g value of this spectrum is 2-001, as measured for ferric ions in the spinel MgAI204[13], a value of H/Ho = 0.470 (where Ho = by~g~3) is obtained. This value is very close to 0.467, typical of the unique absorption shown in the E P R spectrum of powders with ferric ions in sites of rhombic symmetry, with zero field splitting parameters fulfilling the conditions: D > hv[2 and E / D = 1/3[14]. Therefore, at

1009

the frequency v = 9.521 kMHz, the parameters of/3 spectrum are D > 0.159 cm-', E > 0.053 cm-L The spectrum is to be assigned to ferric ions subject to a strong crystal field with rhombic symmetry. The a spectrum is c o m p o s e d of a single broad absorption, approximately symmetrical, centered at H = 2540 G, corresponding to g = 2.68. It cannot be considered a component of /3 spectrum, since this is dominated by the strong absorption at H/Ho = 0-467 [15].The o~ spectrum must then originate from a different source. It cannot be assigned to ferric ions in a cubic environment because its g value (g =2.68) is too high for ferric ions[16]. Therefore a spectrum must be due to ferric ions in sites of symmetry lower than cubic, with a crystal field such as to produce the observed shift of its center from the Ho = hv/g/3 value. The values of the D and E parameters cannot be obtained from the spectrum since this is not well resolved, but, since the shift from Ho is small, they should be small too. The presence of two different spectra due to isolated ferric ions in dilute solutions is in agreement with the existence of two sorts of sites in 7alumina. Yet their assignment to the ions in the A and B sites is not straightforward. In fact in the spinel structure the A and B sites have respectively cubic and axial symmetry, while both the observed spectra point to a symmetry lower than cubic. The most likely attribution is to assign a spectrum, which corresponds to a lower local distorsion, to A - t y p e ions, and/3 spectrum to B - t y p e ions. In any case the E P R spectrum shows a decrease of symmetry of the cationic sites, which may be due to the presence of the cation vacancies as well as to the tetragonal distortion of y-alumina. (b) Intensity of the spectra. The relative intensity of/y and/3 spectra measured at room temperature as a function of the mole fraction of iron is shown in Fig. 2. The/3 spectrum reaches its maximum intensity for f ~0-015, while for a spectrum it is not possible to assess the position of the maximum, because when f > 0.015 a spectrum is no longer observed, being obscured by the much stronger d~ spectrum. One can only state that its maximum intensity does not fall at f < 0-015. The knowledge of the f value at the maximum intensity of/3 spectrum is important because it gives an indication on the distance to which the exchange interactions between ferric ions can be transmitted in 7-alumina. The determination of the corresponding value for a spectrum would also allow to have an indication on the distribution of ferric ions between A and B sites of v-alumina. Since this is

I010

F. GESMUNDOand C. DE ASMUNDIS

unknown we will assume that the ferric ions have no tendency to go into neither of the two sites. To express completely the composition of a given sample, not only the total mole fraction of iron f, but also the mole fraction of iron in octahedral sites fo and in tetrahedral sites f, must be known. We call f, = 3"f, fo= 8f, and therefore 3" + 8 = 1, since f, + fo = f. Moreover, if we assume that ferric ions have no preference for one kind of sites, fo = 2f,, and 3' = 1/3, 8 = 2/3. The ferric ions in solution will give the EPR spectrum of isolated ions (a or/3) only if they have no strong magnetic exchange interaction with neighbours [1]. If the ions are randomly distributed among the cationic sites available, the probability that a site A is occupied by a ferric ion in a sample with a mole fraction of iron f is f, = 3'f, while for a site B the probability will be fo = 8f[l]. Let us assume that a ferric ion behaves as isolated only if it has no ferric ion neighbour in the cationic sites included in a sphere of radius r. The sphere will contain on the average m sites A and 2m sites B, according to their ratio. By means of statistical considerations already developed in a similar case [1], we can give the mole fraction of isolated ferric ions in the sites A ~°) and in the sites B (fo°) as:

forms, although in y-alumina this is somewhat larger than in c~-alumina. 3.2 Spectrum of the associated ions (a) Assignment of the spectrum. The qb spectrum appears together with/3 spectrum in dilute samples (f->0-02), and is the strongest absorption in the more concentrated samples. Its intensity increases regularly with the iron concentration (Fig. 2), as it is expected for the spectrum of associated ions. In fact the increase of the iron concentration makes more and more probable the presence of clusters of two or more ferric ions coupled by exchange interactions strong enough to modify the EPR spectrum with respect to the isolated ions spectrum. The simplest group of associated ferric ions is the pair. It behaves as a system having different energy levels corresponding to the allowed values of the total spin S, varying between zero and 2s, where s is the single ion spin. The EPR spectrum for each level of the pair may be computed using the spin Hamiltonian of the system [17], knowing the values of the zero field splitting parameters of the pair, given by the contribution of the crystal field and the magnetic interactions according to the expressions:

Ds = 3asD, +/3sDc ; Es = asE, + ~3sEe

(2)

ff = f,(1 - f,)~ (I _ fo)2m = 3"f(l - 3'f)~ (I - 8f)2~ (I) and fo °

= fo(l -ft)m(l --fo) 2m

m

8f(l - y/)m (I - 8f)".

The functions fo° and ff will have a maximum for a given value of jr, which can be found by differentiating the equations (1) and equating to zero. The conditions for the maximum of .)co°and ff are found to be the same. They represent at the same time the conditions of maximum intensity of a and /3 spectra. Using the f value corresponding to the maximum intensity of/3 spectrum as found experimentally, and taking 3' = 1/3 and 8 = 2/3, the values m = 40 and 3m = 120 are found. Assuming a continuous distribution of cations in the spinel lattice, the radius of a sphere containing 120 cations is r = 1-06a, where a is the cubic cell edge. For 3"alumina a = 7.9 ,~,[6], and so we obtain that the exchange interactions between ferric ions in 3'alumina are strong up to a distance of about 8.4,~,. For solid solutions of ferric oxide in a-alumina the range of the exchange forces was found to be about 7.4~[1]. It seems therefore that the exchange interactions have a long range in both alumina

where the symbols have the usual significance[17]. In our case the exact computation of the spectrum of the pairs is impossible because the values of the parameters D and E for the isolated ions are not known. In these conditions only a rough estimate of the spectrum of the pairs is possible, taking into account only the contribution from the dipolar magnetic interaction in the equation (2). This calculation, performed as in a previous work [18], shows that the strongest absorptions due to the pairs spectrum fall far from • spectrum, at least for the short-distance pairs, as already found for other systems [1, 18]. Therefore even for the solutions of ferric oxide in 3'-alumina the spectrum of the associated ions must be attributed not to the pairs, but to larger clusters of iron ions. (b) Features of the spectrum. The relative intensity of qb spectrum, measured at room temperature, is shown in Fig. 2 as function of iron concentration f. The intensity increases up to f = 0.07, and then decreases up to f = 0.1. The initial increase is related to the increase of the concentration of iron taking part of clusters with .f. On the contrary the existence of a maximum at [ = 0.07 is unexpected. It seems that a fraction of the iron present in sam-

An EPR study of solid solutions of ferric oxide pies more concentrated than A F 7 is not detected by the E P R spectrum. The possibility that this effect is caused by the presence of a second phase seems to be ruled out, since the X-ray diffraction does not show any other phase than y-alumina, unless an ill-crystallized phase, like one of the towtemperature forms of alumina, is present. In the absence of other data, this aspect of the spectrum of the associated ions cannot be explained. More interesting is on the contrary the dependence of I T on T for qb spectrum, shown in Fig. 3. This is of the kind already observed for pure antiferromagnetic compounds [19] as well as for their concentrated solutions in diamagnetic substances [18, 20-23]. Since pure y-ferric oxide is ferrimagnetic, this result is at first sight surprising and requires some comment. In a cluster of ferric ions coupled by exchange in ,/-alumina, there will be on the average twice as many F e 3+ ions in B sites than in A sites: if n is the number of ferric ions in A sites, 2n will be the number of those in B sites, 3n being the total number of ions in the cluster. The exchange interactions will couple all the ions of the cluster, giving a total spin S which may have all the values differing by integers from the maximum value Smax = 3ns (s = spin of a single ion) down to the minimum value zero (for n even) or 1/2 (for n odd). The same S value may pertain to many states, and as a rule every state will have its own energy. A calculation of the energy values of all the allowed states for clusters has only been performed for triads of ions with spin 1/2124] or 3/2125], coupled by antiferromagnetic interactions and with various geometrical configurations. The calculation requires the knowledge of all the exchange interaction constants of the pairs formed inside the cluster, not known in this case, and anyway would be extremely laborious for groups of many ions. However the lowest energy state of a cluster should have a relatively low value of the total spin S. In fact the spin configuration of this state should approach the structure of pure ,/-ferric oxide, that is the spins of the A ions should be parallel to each other, like those of the B ions, but the former antiparallel to the latter. The value of the spin S for this configuration should be close to the difference between the sum of the spins of B ions and that of A ions, that is S(Em~n)~ ns. This value is intermediate between the highest and the lowest allowed values for S. If this is true, the number of substates of states having a spin S > S(Em~o) is much higher than the corresponding number pertaining to states with spin S < S(Em~,). This can be shown referring

1011

to the simplest system of this kind, formed by three ferric ions, two being in B sites and one in an A site. The number of the independent states with spin S can be deduced following the procedure already used for similar cases [26]. Each state of spin S has a manifold of 2S + 1 substates: the number of states with spin S, the multiplicity of a single state, and the total multiplicity of the states with spin S are reported in Table 1. F r o m Table 1 it can be seen that the number of states with S > 5/2 is 15, with S = 5/2 is 6 and with S < 5/2 is 6, while the number of substates pertaining to states with S > 5 / 2 is 160, to states with S = 5/2 is 36 and to states with S < 5/2 is 20. Table 1. Classification of the states S of a triad of ferric ions (s = 5/2) coupled by exchange Values of S 15/2 13/2

Frequency of Degeneracy Total occurence of a state degeneracy 1 2

11/2

3

9/2 7/2 5/2 312 1/2

4 5 6 4 2

16 14 12 10 8 6 4 2

16 28 36 40 40 36 16 4

At the temperature of 0°K only the lowest energy state will be occupied (one of the states with S = 5•2). If the temperature increases, the population of the triad will move towards higher energy levels, according to the Boltzmann distribution law. An exact calculation of the distribution of the triads among the allowed levels requires the knowledge of their energy. However, even without this information, it can be assumed that, when the temperature increases, the triads will occupy states with S > 5/2 rather than states with S < 5•2, because the former have a larger number of substates than the latter. In fact, being equal the energy, the population of a state will be proportional to the number of its substates. Therefore an increase of the temperature in the system will produce an increase of the average value of the total spin of the triads. The same consideration can be applied to more complex systems. The increase of the average value of the spin for each kind of clusters of iron ions with the temperature can be connected to a parallel increase of the product I T in the following way. Consider a system whose average spin value increases with the temperature. The simplest system of this kind is composed of a pair of identical ions

1012

F. GESMUNDO and C. DE ASMUNDIS

coupled by a strong antiferromagnetic exchange. For a pair o f ferric ions the spin S of the allowed states may have all the integer values between 5 and zero, and the corresponding energies are Es = ½JS(S + 1). The intensity of a transition between two substates M and M + 1 of a state S is given by [27]: Iu.s =

h 2u 2NM.sWM.s kT

i

r

I

10

15

(3)

where NM.s is the population of a substate of the state with spin S, and is given by the Boltzmann law: Nu.s = Nr exp [ - J S ( S + 1)/2kT] Z

(4)

(Nr is the total number of pairs, Z is the partition function for the system), while Wu.s is the probability of the transition, and has the form [28, 29]: Wu.s oc (S + M ) ( S - M + 1).

(5)

Introducing the equations (4) and (5) into the equation (3), one gets: IM.sT ~ exp [ - J S ( S + l)/2kT] (S + M ) Z x (S - M + 1).

(6)

The total intensity of the spectrum relative to all the transitions within a state S will be given by: IsT = ~ IMsT ~ exp [ - J S ( S + 1)/2kT] ~, (S + M ) M

"

Z

M

x (S - M + 1)

(7)

because all the substates of a given state S have the same population. Finally, the total intensity of the spectrum of the pair will be obtained by adding the intensities of the transitions of all the allowed states. This will be given by:

kT/J

I00

Fig. 4. Value of / T for the EPR spectrum of a pair of ferric ions with an antiferromagnetic exchange interaction (a) and average value of the spin of the pair S (b) in

function of kT/J.

that an increase of the temperature in the system causes a simultaneous increase of S and of IT. In the case of clusters of ferric ions in v-alumina, the increase in the value of ,~ for each kind of clusters with T can produce an increase of the value of I T in the same way as for the pair of ferric ions, except for greater complexity of the systems involved. Therefore the observed behaviour of the associated ions spectrum is not in disagreement with the ferrimagnetic properties of y-ferric oxide. Acknowledgement--The authors wish to thank Professor V. Lorenzelli for his kind interest in the present work.

i r = Y~ I s T S

4e-" + 20e -3x + 56e -6. + 120e -~°" + 220e -~s~ 1 + 3 e -x + 5 e -3x + 7 e -6" + 9 e -10" + l i e -~5~

(8) where x = J/kT. The second member of equation (8) is shown in Fig. 4 as function of kT/J, with J > 0 (curve a). In the same figure the average value of the spin of the pair ,~ is reported as function of k T / J (curve b). This is given by the expression:

gwhere

E NsS SNr

Ns = ~ NM.s = (2S + 1) Nu.s

(9) is the

total

M

population of a state with spin S. The Fig. 4 shows

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2. Aharoni A., Frei E. H. and Schieber M., Phys. Rev. 127, 3 (1962). 3. Verwey E. J. W., J. chem. Phys. 3, 592 (1935). 4. Van Oosterhout G. W. and Rooijmans C. J. M., Nature, Lond. 181, 44 (1958). 5. Ferguson G. A., Jr. and Hass M., Phys. Rev. 112, 1130 (1958). 6. Brindley G. W. and Nakahira M., Nature, Lond. 183, 1620 (1959). 7. Yanagida H. and Yamaguchi G., Bull. (?him. Soc. Japan 37, 1229 (1964). 8. Gorter E. W., Philips Res. Rept. 9, 295 (1954). 9. Cirilli V., Gazz. Chim. Ital. 77, 255 (1947). 10. Cirilli V., Gazz. Chim. Ital. 80, 347 (1950). I I. Wyard S. J., J. Sci. lnstrum 42, 769 (1965).

An EPR study of solid solutions of ferric oxide 12. Poole C. P., In: Electron Spin Resonance, p. 798. Interscience, New York (1967). 13. Brun E., Loelinger H. and Valdner F., Arch. Sci. (Geneva) 14, 167 (1961). 14. Barry T. I., 3. Mater. Sci. 4, 485 (1969). 15. Barry T. I., N P L Report, IMU Ex6 0967). 16. Abragam A. and Bleaney B., In: Electron Paramagnetic Resonance of Transitions Ions, p. 440. Clarendon Press, Oxford (1970). 17. See Ref. [16], p. 533. 18. Gesmundo F. and De Asmundis C., J. Phys. Chem. Solids 34, 637 (1973). 19. Maxwell L. R. and McGuire T. R., Rev. rood. Phys. 25, 279 (1953). 20. Poole C. P., Jr. and Itzel J. F., Jr., J. chem. Phys. 41, 287 0964).

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21. Stone F. S. and Vickerman J. C., Trans. Faraday Soc. 67, 316 (1971). 22. Vickerman J. C., Trans. Faraday Soc. 67, 665 (1971). 23. Gesmundo F. and Rossi P. F., J. Solid State Chem. 8, 287 (1973). 24. Harris E. A. and Owen J., Proc. R. Soc. Lond. A289, 122 (1965). 25. Bates C. A. and Jasper R. F., J. Phys. C; SolidSt. Phys. 4, 2330 (1971). 26. Perrin C. L. and Sanderson J. E., Mol. Phys. 14, 395 (1968). 27. Garifullina R. L., Zaripov M. M. and Stepanov V. G., Soviet Phys.-solid State 12, 43 (1970). 28. See Ref. [16], p. 159. 29. Fournier J. T. and Landry R. J., J. chem. Phys. 55, 2522 (1971).