Crystal structure and preparation techniques for...

Chapter - 2

Crystal structure

and

preparation techniques for Hexaferrite

This chapter describes crystal structure, molecular

arrangement and magnetic properties of different types of

ferrite like spinel, garnet, ortho and hexaferrite. Particularly

crystal structure of different compositions of barium

hexaferrite; BaFe12O

19, Ba

2Me

2Fe

12O

22, BaMe

2Fe

16O

27, Ba

3Me

2Fe

24O

41,

Ba2Me

2Fe

28O

46, Ba

4Me

2Fe

36O

60 are explained with diagrams.

Magnetic moment at different lattice sits and magnetic

anisotropy of hexaferrite are briefly explained. General

experimental methods used to prepare ferrites and their

composites are also included in this chapter.

Crystal structure and preparation techniques for hexaferrite Chapter - 2

- 26 - Ph.D. Dissertation

2.1 Crystal structure of ferrite

The crystal structure of a ferrite can be regarded as an interlocking network of

positively-charged metal ions (Fe3+

, Me2+

) and negatively charged divalent oxygen

ions (O2-

). The arrangement of the ions or the crystal structure of the ferrite plays a

most important role in determining the magnetic interactions and therefore, the

magnetic properties. According to their different crystal types, ferrites can be

classified into four groups, namely, spinel, garnet, magnetoplumbite or hexaferrite

and orthoferrite [1-7].

2.1.1 Spinel ferrite

Fig. 2.1. Diagrammatic sketch of spinel crystal structure [6]

There is a kind of crystal structure with the same structure as the mineral

spinel (MgAl2O4), which is called spinel structure. Analogous to the mineral spinel,

the spinel has the general formula MeFe2O4 where Me is the divalent metal ion like

Mn2+

, Ni2+

, Cu2+

, Co2+

, Fe2+

or more often, combinations of these. The spinel lattice

is composed of a close-packed oxygen arrangement in which 32 oxygen ions form a

unit cell that is the smallest repeating unit in the crystal network. Between the layers

of oxygen ions, there are interstices that may accommodate the metal ions. Now, the

interstices are not all the same; some which we will call A (tetrahedral) sites are

surrounded by or coordinated with 4 nearest neighboring oxygen ions whose lines

connecting their centers form a tetrahedron.



B (octahedral) sites are coordinated by 6 nearest neighbor oxygen ions whose

center connecting lines describe an octahedron. The unit cell contains eight formula

units MeFe2O4. In a full unit cell there are 64 - A sites, of which 8 are occupied by

divalent metal ions, and 32 - B sites, of which 16 are occupied by trivalent metal ions.

If in the process of preparation, the ratio of metal ions to oxygen ions is too small,

some of the B sites will be unoccupied. These sites are then referred to as vacancies

[2,4,6].

Spinel ferrites can be divided into two types; normal ferrites and inverse

ferrites, depending on the distribution of the divalent ions on A and B sites. In some

spinel ferrites, the divalent ions have a strong preference for the A sites, leaving all

the trivalent Fe3+

ions on the B sites. These ferrites are called normal spinel ferrites.

Other ferrites belong to the class of inverse spinel ferrites, in which the divalent ions

are on B sites, and the trivalent ions are equally divided between A and B sites.

Completely normal or completely inverse spinel ferrites represent extreme cases. In

general, the structure is a mixed spinel with an intermediate structure. The distribution

of cations over A- and B-sites is determined by their ionic radius, electronic

configurations and electrostatic energy in the spinel lattice [2-9].

2.1.2 Garnet ferrite

The crystal structure is that of the garnet mineral, Mn3Al2Si3O12. The magnetic

garnets include Fe3+

instead of Al and Si, and a rare earth cation (R) substitutes Mn, to

give the general formula R3Fe5O12. The crystal structure has cubic symmetry and is

relatively complex. In contrast with spinels, the oxygen sublattice is not a closepacked

arrangement, but it is better described as a polyhedral combination. Three kinds of

cation sites exist in this structure: dodecahedral (eight fold), octahedral (six fold), and

tetrahedral (four fold) sites. Rare earth cations, R, occupy the largest, dodecahedral

sites, while Fe3+

cations distribute among the tetra and octahedral places. There are 16

octahedral, 24 tetrahedral and 16 dodecahedral sites in a unit cell containing 8 formula

units. One formula unit, 3M2O35Fe2O3 is distributed as follows: 3M2O3-dodecahedral,

3Fe2O3-tetrahedral, 2Fe2O3-octahedral [2-5,7,8,10,11].



Fig. 2.2. Crystal structure of the garnet [12]

2.1.3 Hexagonal ferrite

The group of ferrites possessing hexagonal crystal structure is referred to

hexagonal ferrites. Six types of hexagonal ferrites are distinguished and indicated as

M, W, Y, X, Z and U as shown in the composition diagram in Fig. 2.3. They

correspond to (MO + MeO)/Fe2O3 ratios of 1:6, 3:8, 4:6, 4:14, 5:12 and 6:18

respectively. Where M can be the ions Ba, Sr, Pb, Ca, La, etc. whilst Me is a transition

cation (Zn, Mg, Mn, Co, etc.) or a combination of cations as it would occur in spinels.

Moreover the substitution of Fe3+

ions with other trivalent cations such as Al3+

, Ga3+

,

Sc3+

, In3+

etc. is also possible. One can obtain an extremely large number of

compounds with considerably different magnetic properties. This fact makes the

hexagonal ferrites attractive for different technical applications and interesting for

basic studies on the magnetic interactions in insulators [13].

The crystalline structure of the hexagonal ferrites is the result of a close

packing of oxygen ion layers. The divalent and trivalent metallic cations are located in

interstitial sites of the structure, while the heavy Ba or Sr ions enter substitutionaly the

oxygen layers. All the known hexagonal ferrites have a crystalline structure which can

be described as a superposition of three fundamental structural blocks namely S, R

and T. The S*, R

* and T

* are the rotational symmetry of S, R, and T at 180

o around the

hexagonal c-axis. The repeating unit ‘S’ has composition of either [Me22+

Fe43+

O8]0

(S0) or [Fe6

3+ O8]

2+ (S

2+) with neutral or uncompensated charge of +2 per subunit,

respectively. The ‘R’ sub-unit has the composition [Me2+

Fe63+

O11]2−

whereas the ‘T’



unit is [Ba22+

Fe83+

O14]0. The sub-unit ‘R’ combines with ‘S

2+’ to give the neutral

block (RS), with the total composition MeFe12O19 (M-phase). Similarly, ‘T’ sub-unit

combines with the S0 to give the neutral block (TS), with the total composition

Ba2Me2Fe12O22 (Y-phase). Other stacking sequences of cubic and hexagonal basic

units leading to different compositions such as W, X, Y, Z and U-types hexaferrites

are also known as shown in table 2.1 [3-5,7,13-15].

Fig. 2.3. Ternary diagram showing the composition of the main barium hexagonal ferrites [13]

Table 2.1 Types of hexaferrites [9]

Symbol Composition Crystallographic

build up

No. of

molecules

/unit cell

c-axis

(Å)

M BaFe12O19 RSR*S* (MM*) 2M 23.2

Y Ba2Me2Fe12O22 3TS 3MeY 43.5

W BaMe2Fe16O27 MSM*S* 2MeW 32.8

Z Ba3Me2Fe24O41 MYMY 2MeZ 52.3

X Ba2Me2Fe28O46 MM*S 3MeX 84.0

U Ba4Me2Fe36O60 MM*Y* MeU 38.1



Fig. 2.4. The three fundamental structural blocks S, R and T of the hexagonal ferrites [13]

(i) M-type hexaferrite

M-type hexaferrite is a solid solution written in molecular form MeO·6Fe2O3

or MeFe12O19 and possesses the same structure as the natural mineral

magnetoplumbite [2, 3]. Where, Me can be the divalent ions Ba2+

, Sr2+

or Pb2+

. The

magnetoplumbite structure can be built up from spinel blocks of two oxygen layers

being blocks S and S* which are connected by a block R containing barium or

strontium ion. The layer containing the barium is hexagonally packed with respect to

two oxygen layers at each side. The four oxygen layers between those containing the

barium ion are cubically packed. The basal plane containing the barium ion is a mirror

plane of R block and consequently the block preceding and succeeding the R block

must be rotated over 180o with respect to each other. Five oxygen layers make one

molecule and two molecules make one unit cell. The crystallographic structure can be

described as RSR*S

* and the space group is denoted as P63/mmc (D

46h) [16].



Fig. 2.5(a). The crystal structure of hexagonal M-type Strontium hexaferrite [17]

Fig. 2. 5(b). Five Fe sites with their surroundings [17]

The M-type hexaferrite crystallizes in a hexagonal structure with 64 ions per

unit cell on 11 different symmetry sites. The unit cell contains 38 oxygen ions, 24

ferric ions and 2 Me ions (Me = Ba2+

, Sr2+

, Pb2+

and La3+

). The 24 ferric ions are

distributed over five distinct sites i.e. 2a, 2b, 4f1, 4f2 and 12k. Out of these five, 2a, 4f2



and 12k are octahedral, 4f1 is tetrahedral and the last in which the ferric ion is

surrounded by five oxygen atoms forming a trigonal bipyramid (2b) site. The oxygen

ions occupy 4e, 4f, 6h, and 12k sites form a closed pack lattice. The Me ions

(Me = Ba, Sr, Pb and La) occupy 2d sites. The 12 Fe3+

are arranged as: 6 Fe3+

are in

12k site having the spin up, 2 ions in 4f2 and 4f1 having spin down and 1 ion in 2a and

2b site having spin up. So the 8 Fe3+

are in the upward direction and 4 in the

downward direction. So 4 upward and downward cancel each other and the net

moment is obtained of 4 Fe3+

per formula units. According to the configuration of

Fe3+

, there are 5 unpaired electrons in the 3d orbital, each Fe3+

ion has the magnetic

moment of 5 μB and the total moment is 20 μB per formula unit [13,18,19].

Table 2.2 Number of Fe3+

ions in sublattices of hexaferrites and their spin [18]

Site Geometry No. of Fe3+

ions Spin

12K Octahedral 6 Up

2a Octahedral 1 Up

4f1 Tetrahedral 2 Down

4f2 Octahedral 2 Down

2b Trigonal

bipyramidal

1 Up

(ii) W-type hexaferrite

Fig. 2.6. Crystal structure of W-type hexferrite (BaMe2Fe16O27) [7]



The molecular unit of W ferrite is composed of two S blocks and one R block,

so it is similar to the M structure but not identical. There are now two S blocks above

and below the R block, but again there is a mirror plane in the R block and the unit

cell consists of two molecular W units to give SSRS*S

*R

*. The cell length of Fe2W is

32.84 Å, it is a member of the space group P63/mmc, and the structure is shown in

Fig. 2.6 [7,13,20,21].

(iii) Y-type hexaferrite

The molecular unit of Y-type hexaferrite is one S and one T unit, with a total

of six layers, the unit cell consists of three of these units, with the length of the c-axis

being 43.56 Å, and is a member of the space group R3m [20]. The T block does not

have a mirror plane, and therefore a series of three T blocks is required to

accommodate the overlap of hexagonal and cubic close packed layers, with the

relative positions of the barium atoms repeating every three T blocks. This gives the

unit cell formula as simply 3(ST), and the structure is shown in Fig. 2.7 [13, 21-24].

Fig. 2.7. Cross section view of Y-type hexaferrite (Ba2Me2Fe12O22) structure [7]



(iv) X-type hexaferrite

Fig. 2.8. Cross section view of the X-type hexaferrite (Ba2Me2Fe28O46) structure [7]

The crystal structure of X-type hexaferrite is similar to that of W-type

hexaferrite, being composed of one M and one W molecular units (Fig. 2.8), to give

the structure SRS*S

*R

*, with the blocks of the W section rotated through 180

o relative

to the M section. The unit cell is constructed from three identical units to give the

crystal structure 3(SRS*S

*R

*), c = 84.11 Å, and it is a member of the R3m space group

[13,20,21].

(v) Z-type hexaferrite

The Z - unit is composed of Y + M, and therefore consists of ST + SR, with a

mirror plane in the R block and a repeat distance of 11 oxygen layers. Therefore, two

molecular units are required to form a single unit cell of Z - ferrite, one rotated 180o

around the c-axis relative to the other, to give STSRS*T

*S

*R

*, with a c axis length of

52.30 Å, and it is a member of the space group P63/mmc. Perspective views of the

unit cell are also shown in Fig. 2.9 [13,21,25,26].



Fig. 2.9. Crystal structure of Z-type Barium hexaferrite [27]

(vi) U-type hexaferrite

Fig. 2.10. Cross section view of U-type hexaferrite (Ba4Me2Fe36O60) [7]



The unit cell of the U-type compound formed by three molecules possesses the

rhombohedral structure belonging to space group R3m. The structure is built up by the

superposition of two M-blocks and one Y-block along the c-axis, which gives the

block structure as SRS*R

*S

*T. Cross section view of U-type ferrite is shown in Fig.

2.10 [28-30].

2.1.4 Orthoferrite

Orthoferrites are the component with formula RFeO3, where R represents rare

earth or transition metal. They have perovskite structure with a general form ABO,

where A is an twelve-coordinated oxygen site occupied commonly by magnetic ions

of the lanthanide (rare-earth) series, and B houses a transition metal ion, usually Fe3+

.

The ideal perovskite structure is simple cubic. The mineral perovskite is CaTiO3 and

is actually orthorhombic at room temperature, becoming cubic only at temperatures

above 900°C. Other ceramics with the perovskite structure include BaTiO3, SrTiO3,

and KNbO3. The unique magneto-optical properties of orthoferrites are a direct

consequence of their structure. The speciality of orthoferrites is that their unit cell is

slightly orthorhombic instead of cubic like BaTiO3. Indeed, the orthoferrite unit cell is

very nearly cubic, but instead the angle between the c-axis and the a-b plane is

slightly greater than 90o. This orthorhombic cell manifests itself as a slight canting in

the unit cell of the orthoferrite usually in the order of 0.6o [31].

Fig. 2.11. Representation of YFeO3 unit cell [32]



An example of a common orthoferrite is YFeO3. It crystallizes in a distorted

perovskite structure with an orthorhombic unit cell. The distortion from the ideal

perovskite is mainly in the position of the yttrium ions, whereas the Fe3+

ions are

present in an essentially octahedral environment. The structure can be visualized as a

three-dimensional network of strings of FeO6 octahedra. One of the anions (O2-

)

forms the common apex of the two adjacent octahedra and provides the super-

exchange bond (Fe-O-Fe) between two iron ions. Thus each iron ion is coupled by

super-exchange to six nearest (iron) neighbours. Because the spin alignment of Fe is

not strictly antiparallel but slightly canted, a small net magnetization results, giving

rise to a weak ferromagnetic behavior [2, 3, 32].

2.2 Magnetism in hexaferrite

2.2.1 Magnetic moment

Magnetic moment depends on the electronic configuration and the distribution

of the substituted ions at different sites in the crystal structure [33]. In hexaferrite,

each S block consists of two layers of four oxygen atoms with three cations between

each layer, in octahedral and tetrahedral sites having opposing magnetic spins. There

are four octahedral magnetic moments and two opposing tetrahedral moments, giving

a net total of two moments. The R block has five octahedral moments, but due to the

effects of the large barium atom two of them are really distorted tetrahedral sites and

so they oppose the other three octahedral sites. The moment of the five-coordinate

trigonal bipyramidal site is aligned with three of the octahedral moments as it is a

distorted octahedral site, and so the total also results in a net of two moments. The T

section has six octahedral and two tetrahedral moments, but again two of the

octahedral moments are aligned with the tetrahedral, giving a net of zero magnetic

moments. The tetrahedral sites are formed by the two barium atoms distorting two

trigonal bipyramidal sites [7,9].

S block = 2↓ tetrahedral and 4↑ octahedral = 2↑

R block = 1↑ trigonal bipyramidal and 3↑ 2↓ octahedral = 2↑

T block = 2↓ tetrahedral and 4↑ 2↓ octahedral = 0



In case of M-type barium hexaferrite, The magnetic moments of the Fe3+

ions

are arranged parallel to the hexagonal c-axis, but with opposite spin directions of the

sublattices. The iron ions in the 12k, 2a and 2b sites have their spins aligned parallel

to each other and the crystallographic c-axis, whereas those of 4f2 and 4f1 point in the

opposite direction. The resulting magnetization (M) at a temperature (T) of BaFe12O19

per formula unit can be approximated by simple summation according to the formula

(2.1)

Where, σi stands for the magnetic moment of the i-Fe3+

ion. Assuming a magnetic

moment of 5 μB per Fe3+

ion at 0K (μB is the Bohr magneton) the net magnetization

is of 20 μB per formula unit of barium hexaferrite [3,7,34,35].

In ferrites other than M type hexaferrite, and in doped M type hexaferrites,

some of the cations are other metals with different magnetic moments, which may

occupy different sites depending upon composition and temperature, and may occupy

on a fraction of the total number of a certain site. The opposing spins of the T block,

which is antiferromagnetic if all the ions are identical, lead to the lower magnetic

saturation values for the Y-ferrites compared to the other hexagonal ferrites. This

explains the many variations seen in the magnetic properties of the hexagonal ferrites

with temperature and composition, but it also means that to calculate the magnetic

moment of a compound the exact positions of all the cations must first be known.

However, the contribution towards the moment of each site in a compound can still be

summed up as [7,9]:

M = 1↑ trigonal bipyramidal + 7↑ 2↓ octahedral + 2↓ tetragonal = 4↑

W=1↑ trigonal bipyramidal + 11↑ 2↓ octahedral + 4↓ tetragonal = 6↑

X = 2↑ trigonal bipyramidal + 10↑ 4↓ octahedral + 2↓ tetragonal = 6↑

Y = 8↑ 2↓ octahedral + 4↓ tetrahedral = 2↑

Z = 1↑ trigonal bipyramidal + 15↑ 4↓ octahedral + 6↓ tetragonal = 6↑

U = 2↑ trigonal bipyramidal + 22↑ 6↓ octahedral + 8↓ tetragonal = 10↑



2.2.2 Magnetic anisotropy and coercivity

The energy of a magnetic material depends on the orientation of the

magnetization with respect to the crystal axes, which is known as magnetic

anisotropy. The magnetic anisotropy affects strongly the hysteresis loop shape and the

values of the coercivity and the remanence. The magneto-crystalline anisotropy is an

intrinsic property of the ferrimagnetic materials which does not depend on the

particles’ shape and size. For a single crystal, it is the energy necessary to re-orient

the magnetic moment of the crystal from the easy magnetization axis of to the hard

magnetization axis. The existence of these two axes of magnetization arises from the

interaction between the spin magnetic moment and the crystal lattice (spin–orbital

coupling).

Generally, ferrites with hexagonal structure have two types of anisotropy,

namely c-axis anisotropy and c-plane anisotropy, which are associated with the easy

magnetization along the c-axis and in the c- plane, respectively. In the barium ferrite

family, only the Y-type barium ferrite has c-plane anisotropy, while the others have

c-axis anisotropy. The BaFe12O19 exhibits one of the highest values of the magneto-

crystalline anisotropy constant - K1 = 3.3 ×105 Jm−3 [33]. The energy Ek per unit

volume of the magneto-crystalline anisotropy for uniaxial anisotropy can be written as

follows:

(2.2)

Where, θ is the angle between the magnetization and the c-axis. K1 and K2 are the first

and the second anisotropy constant. The direction along which Ek has an absolute

minimum is called the easy magnetization axis [36-38].

Coercivity is one of the most important characteristics of the hexaferrites in

what concerns their potential applications. It describes the stability of the remanent

state and gives rise to the classification of magnets into hard magnetic materials. The

fundamental characteristic of the coercivity is its dependence on the particles’ size,

which explains the unceasing development of techniques for preparation of

hexaferrite powders with high homogeneity and ever smaller particles’ size. Below a

certain critical size (Dcritical) the particle become monodomain; due to the



hexaferrites’ magneto-crystalline anisotropy, this size is significantly higher than

that of ferrites with a spinel structures.

2.3 Preparation techniques of ferrites

It is known that the electrical, optical and magnetic properties of ferrites are

very sensitive to the particle sizes, shape and degree of crystallinity. At present,

tremendous efforts have been made in improving their magnetic capabilities by using

different synthesis methods [34]. At the same time, the research on their structural and

physical properties has continued [39, 40]. Recent studies have shown that physical

properties of nanoparticles are influenced significantly by the processing techniques

[41]. Since crystallite size, particle size distribution and inter particle spacing have the

greatest impact on magnetic properties, the ideal synthesis technique must provide

superior control over these parameters.

Table 2.3 Comparison between the wet methods and the conventional ceramic method [42]

No. Wet chemical methods Conventional ceramic method

1 Chemical of mixing of the raw

materials results in a homogeneous

mixture.

Mechanical mixing of raw materials;

difficult to get complete homogeneity.

2 Single phase ferrite formation and

small grain size can be easily

obtained.

Possibility of some phase segregation

cannot be ruled out

3 No impurity pick-up or material loss

during processing.

There is a possibility of impurity pick-

ups and loss of material during the

grinding process.

4 Lower temperature processing,

shorter sintering duration required

and no specific heating and or

cooling rate is required.

Processing requires a higher

temperature and longer durations due to

lower reactivity of the starting oxides,

the heating and/or cooling rates control

the particle size.

5 The raw materials are in the form

nitrate, citrate, acetates and

chlorides.

The raw materials are always in the

form of oxides or carbonates



A typical method of obtaining ferrimagnetic hexagonal oxide particles in

general is the solid-state reaction, which involve physical mixing of hydroxide,

oxide, carbonate, or sulphate raw materials followed by high temperature treatment,

approximately 1100°C, for a lengthy period to enable the formation of the target

compound. This method results in powders with coarse-grained, agglomerated

structures with very low surface area. High temperatures needed for solid state

compound formation, give rise to poor sintering behavior, inhomogeneous

microstructures, possibly abnormal grain growth and lack of control of cation

stoichiometry. [7,43]

The conventional solid-state method for preparing BaFe12O19 is to fire an

appropriate mixture of α-Fe2O3 and BaCO3 at very high temperatures (1150 – 1250

oC). The resulting powder is then ground to reduce the particles’ size. Although

high-temperature firing assures the formation of the required ferrite phase, larger

particles (>1 μm) are often obtained in this firing process. It has been shown that the

theoretical intrinsic coercivities of ferrites can be approached only when the particle

sizes are below 1 μm [43]. On the other hand, grinding may introduce impurities into

the powder and cause strains in the crystal lattices, which has unfavourable effect on

the magnetic properties [44, 45]. To overcome these problems, various soft chemical

methods have been developed in order to reduce the particle size and obtain highly

homogeneous ultra fine single-domain particles of barium hexaferrite. Most common

chemical methods: hydrothermal processes [46], chemical co-precipitation [47,48,49],

micro emulsion [50], sol-gel [51,52,53], pyrolisis of aerosol [54], mechanochemical

method [55], sol-gel auto combustion [56,57,58], microwave combustion method

[59], ionic coordination reaction technique [60], solvothermal method [61],

sonochemical method [62], glass-ceramic processing[63], spray pyrolysis [64], pulsed

laser ablation [65], cryochemical method [66], colloidal synthesis [67], reverse

micelle technique [68], sparkplasma sintering [69], novel chitosan method [70]. In all

these processes, precursors are used that have ultra-fine size and high surface area;

thus conventional restrictions of phase equilibrium and kinetics can be easily

overcome, which leads to lowering of sintering and solid-state reaction temperatures

and increased sintering rate.



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