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Introduction to voids in FCC unit cell

In the close packed crystals (FCC, HCP) there are two types of voidstetrahedraland octahedral.

OCTAHEDRAL VOIDS IN FCC UNIT CELLThe octahedral void has a coordination number 6.The positions of

octahedral voids are as follows.

1. BODY CENTER - 12. EDGE CENTERS 123. NUMBER OF OCTAHEDRAL VOIDS PER UNIT CELL = (12/4)+1 = 44. NUMBER OF OCTAHEDRAL VOIDS PER ATOM = 1

FIGURE SHOWING THE VOID AT THE CENTER OF THE BODY SURROUNDED BY SIX ATOMS

FIGURE SHOWING THE VOID AT THE EDGE CENTERS SURROUNDED BY SIX ATOMS

TETRAHEDRAL VOIDS IN FCC UNIT CELL

FIGURE SHOWING EIGHT TETRAGONAL VOIDS SURROUNDED BY FOUR ATOMS

POSITION OF OCTAHEDRAL VOIDS:

(1/4)th WAY FROM EACH VORTEX / CORNER OF THE CUBE ALONG THE

BODY DIAGONAL

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SPINEL AND INVERSE SPINEL STRUCTURES OF FERRITE

Spinel is an important class of mixed-metal oxides, which has the

general chemical composition of AB2O4. Normally A is a divalent metal atom

of radius between 80 and 110pm, such as Mg, Fe, Mn, Zn, and Cu and B is atrivalent metal atom of radius between 75 and 90pm, such as Ti, Fe, Al, and Co.

There are 8 FCC sub cells. One FCC sub cell has 8 equivalent tetrahedral and 4octahedral sites. The structure consists of a cubic closed-packed array of 32oxygen ions, which occupy 64 cubic corners and 48 face centers in one unit cell

(containing eight formula units (AB2O4)8). In general totally there are 64

tetrahedral interstitial sites and 32 octahedral interstitial sites available in a

spinel ferrite unit cell. But (1/8)th

of tetrahedral interstitial sites (8 sites) and halfof the total octahedral interstitial sites (16 sites) are occupied. There are two

types of sub-cells commonly described for the spinel structure, (i) Structure-A

and Structure-B as shown in Figures (1-a) and (1-b) respectively. Structure-Ashows the filling of 2 tetrahedral sites within one-eighth of the unit cell and

structure-B shows a filled octahedral site. The arrangement of these two cubic

sub-cells in one unit cell is shown in Figure 2. In a normal spinel structure, allthe 8 divalent cations occupy 8 tetrahedral sites while all the 16 trivalent cations

are located in 16 octahedral sites.

Figure-2 shows an arrangement of structure - A and structure - B in oneunit cell. The shaded cube represents structure - A, while white one representsstructure - B.Figure-3 shows an example spinel MgAl2O4. Notice the red

oxygen atoms, the green magnesium atoms in the tetrahral voids, and the gray

aluminum atoms in the octahedral voids. The pattern of structure -A andstructure - B can also be seen in Figure 3. Figure-3 shows arrangement of atoms

within the MgAl2O4 unit cell. Mg is in green, Al is in gray, and O is in red.

Figure 3

FIG.1A FIG.1BFIGURE-2

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Cobalt ferrite

CoFe2O4 has an inverse spinel crystal structure. In general totally there are

64 tetrahedral interstitial sites and 32 octahedral interstitial sites available in aninverse spinel ferrite unit cell like in spinel ferrite unit cell. But (1/8) th of

tetrahedral interstitial sites (8 sites) and half of the total octahedral interstitial

sites (16 sites) are occupied. In the case of an inverse spinel such as CoFe 2O4,the divalent 8 Co cations occupy 8 octahedral coordination sites and 8 Fe3+

cations occupy the other half of the octahedral 8 coordination sites. Theremaining 8 Fe

3+cations occupy the 8 tetrahedral coordination sites. The

magnetic moments of the octahedral and tetrahedral sites oppose and cancel

each other. As in the case of spinel ferrite unit cell oxygen anions occupy 64

cubic corners and 48 face centers in one unit cell (containing eight formula units

(AB2O4)8). The crystal structure of CoFe2O4 is shown in Figure 4.

Figure-4

Ferrous ferrite (FeO.Fe2O3)

IonAtomicNumber

Electronic configuration of 3d orbital

Magneticmoment in

Bohrmagneton

Fe 2+ 24

1s2, 2s2 2p6, 3s2 3p6 3d6

4

Fe 3+ 231s2, 2s2 2p6, 3s2 3p6 3d5

5

CompositionInterstitial

sites

No.

availableNo. Occupied

Net magnetic

moment per

sub cell in

Bohr

magneton

Octahedral 32 16 (8 Fe

3+

, 8 Fe

2+

)FeO.Fe2O3

Inverse spinelTetrahedral 64

8 Fe 3+

4

The magnetic moment due to 8 Fe 3+ ions in 8 octahedral interstitial sites and 8

Fe 3+ ions in 8 tetrahedral interstitial sites oppose and cancel each other. But 8 Fe 2+

ions in 8 octahedral interstitial sites are left in one inverse spinel ferrite unit cell. The

number of Fe2+

ion per FCC sub cell is one. This one Fe2+

ion gives rise to magnetic

moment of 4 Bohr magnetons. The magnetic moment due to 8 Fe2+

ions in one

complete ferrous ferrite inverse spinel unit cell is 32 Bohr magnetons. Materials having

inverse spinel ferrite structure are soft ferrite.