IMPURITY CONDUCTION IN MAGNETITE BELOW THE VERWEY TEMPERATURE

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IMPURITY CONDUCTION IN MAGNETITE

BELOW THE VERWEY TEMPERATURE

A. Kuipers, V. Brabers

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C1, suppliment au no 4, Tome 38, Avril 1977, page C1-233

IMPURITY CONDUCTION

IN MAGNETITE BELOW

THE VERWEY TEMPERATURE

A. J. M. KUIPERS and V. A. M. BRABERS

Department of Physics, Eindhoven University of Technology, Eindhoven, The Netherlands

Rkumb. - Le pouvoir thermoClectrique a ete mesure de 70 A 240 K sur des monocristaux synthetiques de magnetite dopks avec differentes teneurs en Ti, jusqu'k 8 000 ppm. Dans 1'Ctat ordonne les resultats sont compatibles avec un modhle de conduction mixte A deux niveaux.

Abstract. - Thermoelectric-power has been measured in the temperature range 70-240 K on synthetic single crystals of magnetite doped with different amounts of Ti up to 8 000 ppm. In the ordered state the results are compatible with a model of mixed conduction over two levels.

1. Introduction.

-

Until recently, thermoelectric and HalCeffect measurements on magnetite reported in literature [I-41 were not unanimous about the sign of the charge carriers below the Verwey transition ;

electrons as well as holes were reported to be the majority charge carriers. In a recent article [5], the present authors showed that deviations from oxygen stoichiometry have a decisive influence whether p or n type conduction is observed in the ordered state. To explain these results, it was assumed that below the Verwey transition conduction takes place by charge transport on two levels, which are separated by an energy gap of about 0.1 1 eV. This gap arises from the electron ordering. Within this model it is also possible that a small amount of impurities, influencing the Fe2+/Fe3+ ratio can establish a change of sign of the majority charge carriers. To check this model and to get more quantitative insight ip the different para- meters involved, we doped the samples with titanium in the range from 100 to 8 000 ppm (ppm with respect to formula units Fe,04). In this paper the results of thermoelectric measurements on these doped samples are given.

2. Theory. - Below the Verwey transition charge

carriers are supposed to be created by excitation of an electron across an energy gap [ 6 ] . If the gap width is denoted as 2 A , the distribution of the electrons over the two energy levels is given by :

In these equations n, and n, are the numbers of electrons below and above the energy gap, respectively, while N , and N2 are the total numbers of available sites in the levels, which both are taken equal to half

the number of octahedral sites occupied by an iron ion. Then the number of ~egative charge carriers is

n = n2 and the number of positive charge carriers is

p = N,

-

n,. The Ferrni level 8, is measured from the

middle of the gap and can be calculated from the equation :

The total number of electrons n, equals the number of Fez+ ions ; if we write the formula for non-stoichiometric magnetite (characterized by the vacancy concentration y ) doped with an amount of x Ti-ions per formula unit as

then n, = N ( l

-

3 y

+

x), in which N is the number of formula units per cm3. Ignoring the kinetic term [7],

the Seebeck coefficient can be expressed as :

In this equation pp and pn are the mobilities of the p- and n-type charge carriers, respectively, which are assumed to be thermally activated [8] ( I )

3. Experimental. - Single crystals of the compound

Fe3-,Ti,O, with x = 0, loF4, 4 x 3 x

and 8 x were prepared from spec. pure Fe,03 and TiO, by means of a floating zone technique in an

( I ) Actually a better choice would be :

However, for the sake of simplicity and because an other choice only causes a very small difference in the Seebeck coefficient calculations, the preexponential factors were put equal.

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C1-234 A. J. M. KUIPERS AND V. A. M. BRABERS

optical furnace [9]. After the crystallization the crystals were annealed for 70 h at 1130 OC in a C0,-H, mixture with a partial oxygen pressure of 10-lo atm. During cooling to loom temperature the C0,-H, ratio was changed in such a way that the slope of the Po, - 1/T

curve was the same as that proposed by Smiltens [lo] for growing stoichiometric magnetite crystals.

In the temperature range from 70

K

to 240 K thermoelectric measurements were made on cylindrical crystals with typical dimensions of 3 cm length and

0.5 cm diameter. The [I101 direction was parallel to the axis of the samples. No precautions were taken to prevent twinning of the crystals, so that below the Verwey transition all the measurements were carried out on twinned specimens. Details of the measuring method have been described elsewhere [5].

4. Results and discussion. - In figure 1 the abso-

lute thermopower of the six samples is plotted versus

temperature (K)

FIG. 1. - Absolute thermoelectric-power vs temperature of

Fe3-%Tiz04. The lines are only meant as a guide to the eye.

temperature. Except for the specimen with x = 8 x lop3,

the values of the Seebeck coefficient above the Verwey transition are equal within experimental error and they are also in agreement with the values reported before [5]. At the Verwey transition a sharp decrease of the Seebeck coefficient occurs for all the specimens. In the ordered state the influence of Ti dope is consi- derable. At decreasing temperature the specimens with x = 0 and x = show a strongly increasing Seebeck coefficient reaching a value of about

+

250 pV/K at 70 K. This behaviour is analogous to that of most of the specimens in ref. [5]. The thermo- power of the samples with x = 4 x increases

with decreasing temperature until T = 85 K and then

decreases. The specimens with x

<

4 x l o w 4 all show below

T,

a steep decrease of the Seebeck coefficient with a value of about - 500 pV/K at 70 K. Within the model described in section 2 sign reversal of the Seebeck coefficient at low temperature occurs at

x = 513 y. The fact that in the experimental data a sign reversal occurs between x = and x = 4 x

implies that the possible values of y within this model are restricted to : 6 x l o w 5

<

y < 2.4 x In figure 2a the calculated Seebeck coefficients for

temperature ( K )

FIG. 2. - Seebeck coefficient calculated according to formula (2)

vs. temperature with a) y = 2 x 10-4, A = 0.067 eV,

q p - q n = 0.007 eV ; b) y = 5 x 10-4, A = 0.060 eV, q p

-

qn = 0.008 eV.

y = 2 x which give the best fit with experiment are plotted. It appears that over the whole range, except for x = 4 x at low temperatures, a better fit is obtained for a value of y of about 5 x lou4.

The results for y = 5 x A = 0.060 eV and

q, - q, = 0.008 eV are plotted in figure 2b. The rather peculiar behaviour of the sample with

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IMPURITY CONDUCTION IN MAGNETITE BELOW THE VERWEY TEMPERATURE Cl-235

The slightly deviating curve of the most Ti rich specimen can be explained in the same way as was done for the most oxidized sample A in ref. [5] ;

the rather large concentration of foreign ions will interfere with the ordering phenomenon. This view is supported by preliminary conductivity measurements ;

the jump in the conductivity of the sample with

x = 8 x is smaller and less pronounced and the transition temperature is lower than for the more pure specimens.

5. Conclusions. - Although some uncertainty about the exact values of the different quantities still remains, the present results show that the basic features

of the proposed model are correct. In the ordered state of magnetite an energy gap of about 0.1 1-0.14 eV exists between two kinds of states. In the stoichiometric case at T = 0 the lower Ievels are completely filled while the upper levels are empty. At T # 0 and in non-stoichiometric specimens a mixed conduction of p and n type charge carriers occurs ; the concentration of impurities and the non-stiochiometry of the specimens determine the sign of the majority carriers.

Acknowledgments. - The authors would like to thank J. Klerk for the assistance with the sample preparation and 0. Manche for carrying out the measurements.

References

(11 LAVINE, J. M., Phys. Rev. 114 (1959) 482. [5] KUIPERS, A. J. M. and BRAHERS. V. A. M., Phys. Rev. B.

[2] FENG, J. S., PASHLAY, R. D. and NICOLET, M. A., J. P11y.r. 14 (1976) 1401.

C 8 (1975) 1010. [6] CULLEN, J. R. and CALLEN, E. R., Phys. Rev. B 7 (1973) 397.

[7] AUSTIN, I. G . and MOTT, N. F., Adv. Phys. 18 (1969) 41.

[3] SIEMONS, W. J., IBM. J. Res. Dev. 14 (1970) 245. ₁₈₁_KLINGEK,_{M. I.,}_{J. Phys. C}₈_{(1975) 3595.}

[4] CONSTANTIN, C. and ROSENDERG, M., SoIidState Commun. 9 [9] BRARERS, V. A. M., J. Cryst. Growth 8 (1971) 26.