**2.3 Cubic ferrites**

Materials which crystallize in the spinel structure, or structures closely related to it, have the general formula AB2O4 in which A and B display tetrahedral and octahedral cation sites, respectively, and O indicates the oxygen anion site (Figure1). Spinel ferrites with the general formula MeO Fe2O3 or MeІІFe2ІІІO4 where MeІІ represents a divalent metal cation such as Mn, Fe, Co, Ni, Cu, Zn, Cd, Mg, or (0.5LiІ + 0.5FeІІІ), and FeІІІ is the trivalent iron cation, have the same crystallographic structure as the mineral spinel (MgAl2O4), which was determined by Bragg [8,9]. The unit cell of spinel ferrite belongs to the cubic structure (space group Oh7-F3dm) and presents itself the cube formed by 8 MeOFe2O3 molecules and consisting of 32 of O2- anions. The oxygene anions form the close face-centered cube (FCC) packing consisting in 64 tetrahedral (A) and 32 octahedral (B) empty spaces partly populated by Fe3+ and Me2+ cations [10].

For the interactions the distances Me-O and Me-O-Me play an important role, ten triangular configurations of Me-O-Me are illustrated in Figure2, where the shortest distance is shown as p and other distances are given by q, r, s and t; these distances are also given in Table1, as a function of the variable δ = u - 3/8 that δ is oxygen parameter [11].

ferrites and to prepare magnetic carriers based on them. Ferrites have three different structural symmetries: garnet, hexagonal and cubic which are determined by the size and charge of the metal ions that balance the charge of the oxygen ions, and their relative amounts [5]. In this review, the focus will be on spinel ferrites nanocrystals because, they are regarded as two of the most important inorganic nanomaterials because of their electronic, optical, electrical, magnetic, and catalytic properties.Moreover, the majority of the important

The general formula for garnets is Me3Fe5O12, where Me is one of the rare earth metal ions, including Y, La and Gd. The cubic unit cell contains 8 formula units or 160 atoms, which can be described as a spatial arrangement of 96 O2- with interstitial cations. Yttrium iron garnet Y3Fe5O12 (YIG) is a well-known garnet. The coordination of the cations is considerably more complex than spinels, with 24 Y3+ in dodecahedral sites, 24 Fe3+ ions in tetrahedral sites and 16 remaining Fe3+ in octahedral sites. Similar to spinels and hexagonal ferrites, a wide range of transition metal cations can substitute Y3+ or Fe3+; especially rare earth ions may replace the ions on octahedral and dodecahedral sites. Each type of lattice site will accept other metal ions at dodecahedral sites, octahedral sites and at tetrahedral sites. Thus pentavalent ions such as V5+ and As5+ can occupy tetrahedral sites, while Ca2+ substitute ions on dodecahedral sites [7].

Hexagonal ferrites are widely used as permanent magnets and are characterized by possesing a high coercivity [4].Their general formula is MeO·6Fe2O3 where Me can be Ba, Sr, or Pb. The hexagonal ferrite lattice is similar to the spinel structure, with the oxygen ions closely packed, but some layers include metal ions, which have practically the same ionic radii as the oxygen ions. This lattice has three different sites occupied by metals: tetrahedral,

Materials which crystallize in the spinel structure, or structures closely related to it, have the general formula AB2O4 in which A and B display tetrahedral and octahedral cation sites, respectively, and O indicates the oxygen anion site (Figure1). Spinel ferrites with the general formula MeO Fe2O3 or MeІІFe2ІІІO4 where MeІІ represents a divalent metal cation such as Mn, Fe, Co, Ni, Cu, Zn, Cd, Mg, or (0.5LiІ + 0.5FeІІІ), and FeІІІ is the trivalent iron cation, have the same crystallographic structure as the mineral spinel (MgAl2O4), which was determined by Bragg [8,9]. The unit cell of spinel ferrite belongs to the cubic structure (space group Oh7-F3dm) and presents itself the cube formed by 8 MeOFe2O3 molecules and consisting of 32 of O2- anions. The oxygene anions form the close face-centered cube (FCC) packing consisting in 64 tetrahedral (A) and 32 octahedral (B) empty spaces partly

For the interactions the distances Me-O and Me-O-Me play an important role, ten triangular configurations of Me-O-Me are illustrated in Figure2, where the shortest distance is shown as p and other distances are given by q, r, s and t; these distances are also given in Table1, as

octahedral, and trigonal bi pyramid (surrounded by five oxygen ions).

a function of the variable δ = u - 3/8 that δ is oxygen parameter [11].

ferrite are spinel ferrite [6].

**2.1 Garnets ferrites** 

**2.2 Hexagonal ferrites** 

**2.3 Cubic ferrites** 

populated by Fe3+ and Me2+ cations [10].

Fig. 1. Schematic of two subcells of a unit cell of the spinel structure, showing octahedral and tetrahedral sites.

Fig. 2. Interionic distances in the spinel structure for the different types of lattice site interactions

According to the distribution of cations, there are normal, mixed and inversed spinels structures which depended on the fact what kind of ions and in what order A and B take empty spaces. In this review, we will investigate zinc ferrite (ZnFe2O4), manganese ferrites (MnFe2O4) and nickel ferrite (NiFe2O4) from normal, mixed and inverse structures respectively [12].

Crystalization in Spinel Ferrite Nanoparticles 353

Inversed spinel structure, where all Me2+ are in B-positions and Fe3+ ions are equally distributed betweenAand B-sites: structural formula of these ferrites are Fe3+[Me2+Fe3+] O4 <sup>2</sup>−. Magnetite Fe3O4, ferrites NiFe2O4 and CoFe2O4 have inversed spinel structure [12].In the inversed ferrites one half of Fe3+ is placed in A-sites and another half in B-sites. Their magnetic moments are mutually compensated and the resulting moment of the ferrite is due to the magnetic moments of bivalent cations Me2+ in the B-positions. This type spinel ferrite

Domains, which are groups of spins all pointing in the same direction and acting cooperatively are separated by domain walls, which have a characteristic width and energy associated with their formation and existence. The motion of domain walls is a primary means of reversing magnetization. Experimental investigation of the dependence of coercivity on particle size showed a behavior similar to that schematically illustrated in

It was found that the coercivity Hc increases with decreasing grain size D down to values of about 40 nm, independent of the kind of material. The increase of Hc is proportional to 1/D. The reason for this is that in small particles the formation of a closed magnetic flux becomes energetically less favorable so that the magnetic domain size with a uniform magnetization becomes more and more identical with the grain size. This grain size is defined as the first critical size (Dc, which is characteristic of each material) where the multidomain materials

Fig. 4. Cation distribution in mixed spinel ferrites.

**2.3.3 Inversred spinel ferrites** 

are schematically illustrated in Figure5.

**2.4 Domains** 

Figure 6 [13].

Fig. 5. Cation distribution in inversed spinel ferrites.


Table 1. Distances in the spinel lattice as a function of δ=u-3/8

#### **2.3.1 Normal spinel ferrites**

Normal spinel structure, where all Me2+ ions occupy A sites; structural formula of such ferrites is Me2+[Fe2 3+] O4 <sup>2</sup>−. This type of distribution takes place in zinc ferrites Zn2+[Fe2+Fe3+]O4 <sup>2</sup>−. This type spinel ferrite are schematically illustrated in Figure3.

Fig. 3. Cation distribution in normal spinel ferrites.

#### **2.3.2 Mixed spinel ferrites**

Mixed spinel structure, when cations Me2+ and Fe3+ occupy both A and B-positions; structural formula of this ferrite is Me1−δ 2+Fe<sup>δ</sup> 3+ [Me<sup>δ</sup> 2+Fe2−δ 3+] O4 <sup>2</sup>−, where δ is the degree of inversion. MnFe2O4 represent this type of structure and has an inversion degree of δ = 0.2 and its structural formula therefore is Mn0.82+Fe0.23+ [Mn0.22+Fe1.8 3+] O4 <sup>2</sup>−. [12]. This type spinel ferrite are schematically illustrated in Figure4.

**Me-O distance** Me-Me distance

Normal spinel structure, where all Me2+ ions occupy A sites; structural formula of such ferrites is Me2+[Fe2 3+] O4 <sup>2</sup>−. This type of distribution takes place in zinc ferrites

Mixed spinel structure, when cations Me2+ and Fe3+ occupy both A and B-positions; structural formula of this ferrite is Me1−δ 2+Fe<sup>δ</sup> 3+ [Me<sup>δ</sup> 2+Fe2−δ 3+] O4 <sup>2</sup>−, where δ is the degree of inversion. MnFe2O4 represent this type of structure and has an inversion degree of δ = 0.2 and its structural formula therefore is Mn0.82+Fe0.23+ [Mn0.22+Fe1.8 3+] O4 <sup>2</sup>−. [12]. This type

Zn2+[Fe2+Fe3+]O4 <sup>2</sup>−. This type spinel ferrite are schematically illustrated in Figure3.

b = 1 <sup>4</sup> a√2

c = 1 <sup>8</sup> a√11

d = 1 <sup>4</sup> a√3

e = 3 <sup>8</sup> a√3

f = 1 <sup>4</sup> a√6

�=�� �

�=�� �

�=�� �

**2.3.1 Normal spinel ferrites** 

**2.3.2 Mixed spinel ferrites** 

�=��

�� <sup>−</sup> �

�� <sup>+</sup> � � � + ���

�� <sup>+</sup> �

� = �� ��

� + ��� √�

� � + ���

� �� + ���

Table 1. Distances in the spinel lattice as a function of δ=u-3/8

� − �� √�

Fig. 3. Cation distribution in normal spinel ferrites.

spinel ferrite are schematically illustrated in Figure4.

Fig. 4. Cation distribution in mixed spinel ferrites.
