82
L. A. Frolova et al.
Table 5.1 Composition of the samples obtained
Code of the sample
1
2
3
4
¸ in the formula Co x Fe 3-x O 4 1.0
0.75
0.5
0.25
Gross formula
CoFe 2 O 4 Co 0.75 Fe 2.25 O 4 Co 0.5 Fe 2 . 5 O 4 Co 0.25 Fe 2.75 O 4
Table 5.2 Average cation-oxygen distances in tetrahedral (d Td ) and octahedral (d Oh ) sites
d(Me-O) bond lengths (A ◦ )
Fe 3+
Co 2+
Co 3+
Fe 2+
In tetrahedral site (Td) nm
0.1858
0.1974
0.2003
In octahedral site(Oh) nm
0.2020
0.2123
0.1892
0.215
0.2240
a is the lattice constant (nm)
Table 5.3 Structural
parameters at room
temperature for the samples
Co x Fe 3-x O 4
Ø
Ã, nm
L 1 , A M, %
D, sm −2
0.25 0.83373 418
4.66·10 −4 40.55·10 10
0.5
0.83154 481
526·10 −4
30.5·10 10
0.75 0.83382 460
2.93·10 −4 33.3·10 10
1.0
0.83401 350
8.64·10 −4
8.64·10 10
ferrites. This suggests that the spinels formed in the system have a defect structure
similar to that of maghemite. Using this approach, a cationic distribution can be
suggested, for x less than 1, in the form of the following structural formula:
F e
3+
1−x+xω
Co
2+
x F e
3+
5/3+x/3−xω 1/3−x/3
O 4 0 ≤ x ≤ 1, 1 ≤ ω
ω is the degree of inversion (the fraction of divalent cations in the octahedral position
or trivalent ones in tetrahedral)
– vacancies in the crystal lattice
The dependences of the cation distribution and the crystal-chemical parameters
of cobalt ferrites on the cobalt content in the samples calculated from the diffractograms are presented in Table 5.2. The lattice constant of the spinel phases was
calculated by the equation:
a = 2.0995d T d +
5, 8182
d ˆ
I h
2 − 1, 4107d
2
T d
1/2
(5.1)
where d Td and d Oh are the average distances of the oxygen cation in tetrahedral and
octahedral sites, respectively (Table 5.2) (nm).
Table 5.3 shows the results of X-ray phase analysis, where L 1 is the crystallite
size, A; M is the degree of micro-stresses, %; D is the dislocation density, sm −2 .
Ion-atom tetrahedral and octahedral distances are more often attributed to a
fictitious cation and are a weighted mean value of ion-atom distances of cations
contained in certain positions. With this determining method of the cation distribution over the sublattice, we minimized the difference between the experimentally
L. A. Frolova et al.
Table 5.1 Composition of the samples obtained
Code of the sample
1
2
3
4
¸ in the formula Co x Fe 3-x O 4 1.0
0.75
0.5
0.25
Gross formula
CoFe 2 O 4 Co 0.75 Fe 2.25 O 4 Co 0.5 Fe 2 . 5 O 4 Co 0.25 Fe 2.75 O 4
Table 5.2 Average cation-oxygen distances in tetrahedral (d Td ) and octahedral (d Oh ) sites
d(Me-O) bond lengths (A ◦ )
Fe 3+
Co 2+
Co 3+
Fe 2+
In tetrahedral site (Td) nm
0.1858
0.1974
0.2003
In octahedral site(Oh) nm
0.2020
0.2123
0.1892
0.215
0.2240
a is the lattice constant (nm)
Table 5.3 Structural
parameters at room
temperature for the samples
Co x Fe 3-x O 4
Ø
Ã, nm
L 1 , A M, %
D, sm −2
0.25 0.83373 418
4.66·10 −4 40.55·10 10
0.5
0.83154 481
526·10 −4
30.5·10 10
0.75 0.83382 460
2.93·10 −4 33.3·10 10
1.0
0.83401 350
8.64·10 −4
8.64·10 10
ferrites. This suggests that the spinels formed in the system have a defect structure
similar to that of maghemite. Using this approach, a cationic distribution can be
suggested, for x less than 1, in the form of the following structural formula:
F e
3+
1−x+xω
Co
2+
x F e
3+
5/3+x/3−xω 1/3−x/3
O 4 0 ≤ x ≤ 1, 1 ≤ ω
ω is the degree of inversion (the fraction of divalent cations in the octahedral position
or trivalent ones in tetrahedral)
– vacancies in the crystal lattice
The dependences of the cation distribution and the crystal-chemical parameters
of cobalt ferrites on the cobalt content in the samples calculated from the diffractograms are presented in Table 5.2. The lattice constant of the spinel phases was
calculated by the equation:
a = 2.0995d T d +
5, 8182
d ˆ
I h
2 − 1, 4107d
2
T d
1/2
(5.1)
where d Td and d Oh are the average distances of the oxygen cation in tetrahedral and
octahedral sites, respectively (Table 5.2) (nm).
Table 5.3 shows the results of X-ray phase analysis, where L 1 is the crystallite
size, A; M is the degree of micro-stresses, %; D is the dislocation density, sm −2 .
Ion-atom tetrahedral and octahedral distances are more often attributed to a
fictitious cation and are a weighted mean value of ion-atom distances of cations
contained in certain positions. With this determining method of the cation distribution over the sublattice, we minimized the difference between the experimentally