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Submitted on 1 Jan 1977

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KINETICS OF THE CATION REDISTRIBUTION IN

MAGNESIUM FERRITES

V. Brabers, J. Klerk

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C1, suppliment au no 4, Tome 38, Avril 1977, page C1-207

KINETICS OF THE CATION REDISTRIBUTION

IN MAGNESIUM FERRITES

V. A. M. BRABERS and J. KLERK

Department of Physics, Eindhoven University of Technology, Den Dolech, Eindhoven, Netherlands

RhumC. - La cinetique de la distribution des ions Mg2+ et Fe3+ sur les sites tetrakdriques et octakdriques de ferrites de magnesium est CtudiCe par mesure de dilatation. L'arrangement des ions se produit par la diffusion des lacunes de cations ; la reaction M ~ A

+

Vn

z

M ~ F I

+

VA determine la vitesse d'echange des cations. Deux energies d'activation sont dCgagees : celle correspondant

A

1'6quilibre thermodynamique (0,2 eV) et celle correspondant it la constante de temps de mise en equilibre (1,3 eV).

Abstract. - The kinetics of the cation ordening over octahedral and tetrahedral sites in Mg ferrites has been studied with dilatometric measurements. The ordering takes place by the diffusion of cation vacancies and the rate determining step was found to be Mga

+

VB FT Mgn

+

VA.

Two energies were determined, one (0.2 eV) corresponding to the thermodynamic equilibrium, the other (1.3 eV) being the activation energy of the time constant of the diffusion.

1 . Introduction.

-

The distribution of cations over octahedral and tetrahedral sites determines t o a great extent the physical properties of ferrites. The cation distribution in magnesium ferrite has been studied by various authors and was found to be strongly temperature dependent 11-61. Comparison of the cation distributions determined at room tempe- rature on quenched samples and those found at high temperature in equilibrated samples revealed that the high temperature distributions are not completely retained by quenching techniques [7, 81 ; the kinetics of the redistribution turned out to be very important if ferrites with definite inversion -degrees are needed.

In the case of magnesium ferrite, literature on the redistribution kinetics is meagre. Reynen [9] studied the phase relations in the Mg-Fe-0 system with thermogravimetry and found that stiochiometric MgFe,04 exists, in contradiction with earlier papers [lo, 111. From saturation magnetization data of Mg ferrites with small excess of MgO [9, 121, he concluded that the mobility of the cations increases by the presence of cation vacancies.

Luca et al. [13] found also an enhancement of the

redistribution rate of the cations by the presence of cation vacancies in Mg,.,Fe,,,04, but their analysis of the kinetics based on magnetization measurements was not quantitative. Walters et nl. [14] followed the redistribution on quenched and annealed magnesium ferrite by T,,,i,-measurements and suggested the process to be a kind of nucleation and growth trans- formation.

In this paper we report on the kinetics of the redis- tribution process in magnesium ferrites, which was studied by means of thermal expansion and isothermal dilation measurements.

2. Experiments and results. - The method to study the kinetics of the cation redistribution by iso- thermal dilatation has been described in 1151. If a specimen of Mg ferrite is quenched from high tempe- rature, the high temperature distribution will be more or less retained at room temperature. When raising the temperature again, the redistribution becomes noticeable in the temperature region where the ionic mobility is large enough. As the lattice parameter of magnesium ferrite depends on the cation distribution, it is possible to follow the variation of the inversion degree by means of the variations of the lattice cons- tant as a function of the annealing time. Because of the isotropic thermal expansion and the absence of sinter- ing effects, the change of the macroscopic dimensions of a polycrystalline specimen of Mg ferrite is linearly related to the change of the lattice constant ; conse- quently, the redistribution rate of the cations can be determined from the isothermal dilatation during annealing, if the relation between lattice parameter and inversion degree is known. Since in literature the values of the lattice constant as function of the distri- bution showed substantially spread [3, 7, 16-18], we determined this relation with X-ray techniques on MgFe,O, samples, quenched from annealing tempe- ratures of 1200, 1000, 800 and 600 O C , respectively.

The results are plotted in figure I , together with some

literature data, from which a linear aproximation was made for the relation between the distribution para- meter A (MgAFe, -,[Mg, -,Fe,

+,lo,)

and the lattice constant a :

The redistribution was studied on three different compositions with x = 0.95, 0.97 and 0.99, respecti-

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C1-208 V. A. M. BRABER IS AND J. KLERK

FIG. 1. - Lattice constant as function of distribution parameter 1. ( 0 ) present investigation, (----) Kriessman et al. (3), ($.)

Faller et al. (7), (-) Mozzi et al. (16) on Mg 1.06Fel. !3403$7, (O) Vishvenskii et al. (17) and (0) de Grave et al. (18).

vely. Polycrystalline rods (1.5 x 1.5 x 30 mm3) were prepared with the usual ceramic techniques, sintered in oxygen at 1 250 OC and quenched in water. The thermal dilatation of the quenched samples was measured with a dilatometer described elsewhere [19]. The results of these measurements, given in figure 2,

-

temperature I'c)

FIG. 2.

-

Thermal expansion of MgzFe3-204 samples, quench- ed from 1 250 OC.

show anomalous behaviour in the range of 450 to 600 OC. The difference between the lattice parameters of the specimens before and after the measurements amounts about 0.015

A,

which is just compatible with the total effect of the shrinkage during the thermal expansion measurement (A111

z

1.8 x and which indicates that the anomaly is entirely due to the variation of the lattice parameter, or in other words to the cation migration. Further, the remarkable effect, that the anomaly shifts to lower temperatures with decreasing x points to the influence of the cation vacancies on the redistribution rate. The specimens

were prepared in an oxidizing atmosphere at 1 250 OC and turned out to be single phase spinels, which was checked with X-ray diffraction and microscopic investigation. As the analysed ferrous content of the specimens was neglectably small, the composition of the three materials can be given by the formulas M~0.944Fe2.037v0.01904~ M~0.972Fe2.019v0.00904 and Mg, ~9,,Fe,~oo7Vo .oo404, respectively. With decreasing Mg content, the cation vacancy concentra- tion [V] increases. The expansion measurements were carried out in air by heating the specimens 3 OC/minute and by comparing the results for the different composi- tions one can conclude that the cation vacancies enhance the cation migration.

To follow the kinetics of the redistribution, thermal expansion of quenched samples was measured up to a temperature where the migration did not yet proceed

(+ 4300C) and then the temperature was stepwise increased up to a fixed temperature between 460 and 560 OC. This temperature was reached and stabilized within a few minutes and after that, the negative dilatation was continuously measured as function of time at constant temperature. Typical examples of these measurements are given in figure 3 for the

0 5 0 100

t ~ m e (rn~nl

FIG. 3.

-

Relative shrinkage of quenched Mgo.9sFe2.0s04.0~s as function of the annealing time.

composition x = 0.95. From these curves the deriva- tive of the length after time (dlldt) was determined, and by using the relation a = 8.370

+

0.009 75

A

A

(1) with minor corrections for the variation of x, the rate of the cation migration dA/dt could be calculated as a function of

A.

The effect of the shrinkage during the annealing was in the order of 1.3 O/oo but during the

stabilization of the temperature a shrinkage of 0.5 o/,,

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KINETICS OF THE CATION REDISTRIBUTION IN MAGNESIUM FERRITES Cl-209 3. Analysis of the results. - The process of the and

cation redistribution will be the exchange via cation b k - , = B exp - (EJkT)

.

vacancies according to the equations : (5)

The activation energies E, and E, amount 1.3 and

k l

MgA

+

V, Mg,

+

VA (1) 1.5 eV respectively ; the difference of 0.2 eV being

k - 1

and I I 1

" Mg0.g22Fe2.037 v0.019 '4 (x-0.95)

k z

(2) Mg0.97Z Fe2.019 V0.0094°4 'x=0'975)

VA

+

FeB

s

VB

+

FeA

.

M g ~ w Fe2.C07 VQ0039 OL [x -0.991

k- 2

from which it is clear that the migration rate is pro- portional to the octahedral vacancy concentration. From the curves of dlldt versus 1 obtained as described in section 2, k , and b k - , could be calculated by taking the cation vacancy concentration z equal to the total concentration of vacancies as given in section 2. The concentration of vacancies due to intrinsic disorder can be ignored in proportion to the large concentration due to non-stoichiometry. The plots of k , and b k - , versus reciprocal temperature (Fig. 4) can be analysed with the equations

k,

= A exp

-

( E l / k T ) (4)

Take y and z being the concentration of vacancies on

A and B sites, one can introduce the ratio b = y/z,

the distribution parameter of the cation vacancies. lo1

Introducing further a quasistationair situation as was proposed by NicoIas [201, the ratio b will be constant.

As in a number of ferrites the cation vacancies are lo2-

located dominantly on octahedral sites [21] reaction ( I )

in the right magnitude of 0.15 eV, which is the work needed for the cation exchange between the sublat- tices [2]. The pre-exponential factors A and B are in the order of lo9 s-', which deviates strongly from the expected Debye frequency : lOI3 s-l. An explanation of this deviation may be searched in the approxima- tions we have made i. e. the temperature independent distribution of the vacancies and the use of concentra- tions instead of the chemical activities of the cations. The nucleation process, which was proposed by Wal- ters et al. [14] for the kinetics can also be explained with the influence of cation vacancies, especially with the inhomogeneities due to oxygen non-stoichiometry.

I \

-<\

$\

:it

=1.3ev kl. b EXt =1.5eV 1 I I I References

will be the rate determining step and the migration 1.20 1.25 130 135

-

1.20 1 0 ~ 1 ~ K-1

rate can be approximated by FIG. 4. -Values of kl and bk-I calculated from isothermal d 1 dilatation curves and plotted versus reciprocal temperature.

- - =

dt

{

kl

A

-

k-l(x

-

A)

b } z (3)

[I] NEEL, L., C. R. Hebd. Sian. Acad. Sc. 230 (1950) 190. [2] PAUTHENET, R., and BOCHIROL, L., J. Physique Rad. 12

(1951) 249.

[3] KRIESSMAN, C. J. and HARRISON, S. E., Phys. Rev. 103

(1956) 857.

[4] EPSTEIN, D. J. and FRACKIEWICZ, B., J. Appl. Phys. 29

(1958) 376.

[5] M o z z ~ , R. L. and PALEDINO, A. E., J. Chem. Phys. 39 (1963) 435.

[6] ALLEN, W. C., J. Am. Ceram. Soc. 49 (1966) 257.

[7] FALLER, J. G. and BIRCHENALL, C. E., J. Appl. Crystallogr. 3

(1970) 496.

[8] JIRAK, Z., SIMSA, Z., SIM~OVA, J., ROSKOVEE, V., VRATIS-

LAV, S., and BRABERS, V., Proc. I. C. M . Moscow 1973,

Nauka 5 (1974) 260.

[9] REYNEN, P., Plrilips Res. Repts. 23 (1968) 151. [lo] PALEDINO, A. E., J. Am. Ceram. Soc. 43 (1960) 183. [ l l ] SCHMALZRIFD, H. and TRETJAKOW, J. D., Ber. Buns.

Phys. Chem. 70 (1966) 180.

[12] BLACKMAN, L., Trans. Faraday Soc. 55 (1959) 391. 1131 LUCA, E., MAXIM, G. L. and CRAUS, M. L., Phys. Stat.

Sol. (a) 14 (1972) K 153.

[14] WALTERS, D. S. and WIRTZ, G. P., J. Am. Ceram. Soc. 54

(1971) 563.

[15] KLERK, J. and BRABERS, V. A. M., Phys. Stat. Sol. a 23

(1974) K 107.

[16] Mozzr, R. L. and PALEDINO, A. E . , J . Chem. Phys. 39

(1963) 435.

[17] VISHNEVSKII, L., ALAPIN, B., AKSEL'ROD, E. and SUKHA-

REVSKII, B., IZV. A. N. SSSR, Neorgan. Mat 6 (1979)

1479.

[I81 DE GRAVE, E., DE SITTER, J. and VANDENBERGHE, R., Appl.

Phys. 7 (1975) 77.

[19] BRABERS, V. A. M., Thesis Eindhoven University of Tech- nology, (1970) p. 42.

1201 NICOLAS, J., J. Phys. Chem. Solids 28 (1967) 847.

[21] KRONMWLLER, H., SCHWTZENAUER, R., WALZ, F., Phys.

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