ARTICLE IN PRESS
N. Bagrets et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 1565–1567
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experimental and
theoretical loops
600
400
200
0
0.05
0.04
0.03
0.02
0.01
0.00
superparamagnetic
particles
superparamagnetic
particles
single domain particles
single domain particles
-200
-400
-600
-6000 -3000
0
3000 6000
0
20
40
60
80
100
Magnetic field, Oe
diameter of particle, Å
Fig. 1. Typical experimental and calculated hysteresis loops for fine Co particle system and calculated particle size distribution (at
room temperature).
experimental set-up was described earlier [2].
The analysis of the hysteresis loops (typical example
is shown in Fig. 1) allowed us to conclude that two
0.40
0.36
0.32
0.28
0.24
types of nanoparticles are present in the silica gel
matrix; namely superparamagnetic particles with
small grain sizes and single-domain particles having
larger grain sizes. This conclusion is based on
the observations that (i) hysteresis loops are non-
saturated in large magnetic fields (upto 8000 Oe) which
is a typical behavior for systems consisting super-
paramagnetic particles, and (ii) the hysteresis loops have
residual magnetization, thus not all particles are super-
paramagnetic.
250 300 350 400 450 500 550
Temperature of reduction, ˚C
To evaluate the particle size distribution, we assumed
that both ‘‘small’’ and ‘‘large’’ particles have the
spherical form and considering that two fractions
of particles are independent subsystems, we presented
the particle size distribution PðdÞ as a sum of two
log-normal distributions f1ðdÞ and f2ðdÞ: The contri-
bution of the small superparamagnetic particles to
the hysteresis loopis described by the Langevin
function averaged over distribution f1ðdÞ [3]. We
describe the second fraction (large particles) by
the Stoner–Wohlfarth model [4] for non-interacting
single-domain particles with uniaxial magneto-crystal-
line anisotropy and easy axis oriented randomly
in space. The dependence of coercivity HcBd6 on
the grain size d was taken into account as it was
predicted by the random anisotropy model [5,6].
Parameters describing two log-normal distributions are
determined using the numerical procedure of minimiza-
tion of a root-mean-square deviation between the
theoretical and experimental loops. The typical experi-
mental and calculated fitting hysteresis loops are shown
in Fig. 1a. The corresponding particle size distribution
(Fig. 1b) has two peaks that reflect the non-homo-
geneous structure of the samples, so that the first peak
corresponds to subsystem of the superparamagnetic
particles and the second one corresponds to the single-
domain particles.
Fig. 2. The ratio Vsp=Vsd of volume fraction of superparamag-
netic and single-domain particles vs. temperature of reduction.
4. Results and discussion
One of our aims was to find such technological
conditions that would allow getting samples containing
larger quantity of superparamegnetic particles, because
small Co particles serve as catalysts of chemical
reactions. For this goal first the series of samples
reduced from Co oxide in hydrogen atmosphere at
different temperatures (270–550ꢀC) was prepared. We
observed that the ratio of volume fraction of super-
paramagnetic and single-domain particles increases
while the temperature of reduction process increases
(Fig. 2). At the first stepof the reduction the impurity
centers (small Co clusters) appear in the Co oxide. The
subsequent growth of the Co particles takes place
around impurity centers. The velocity of this process is
weakly dependent on the temperature. However, the
increase of temperature leads to the more active
formation of the impurity centers thus leading to the
growth of the volume fraction of the small super-
paramagnetic particles.
Bagrets
