The document discusses properties of a face centered cubic (FCC) crystal structure. An FCC crystal has: 1) A unit cell with 4 atoms located at the corners and face centers of the cube. 2) An atomic radius of a/√22 where a is the lattice parameter. 3) A nearest neighbor distance of a/2 between adjacent atoms. 4) A coordination number of 12, atomic packing fraction of 0.74, and void space of 26%.

1. Properties of FCC CRYSTAL

2.  The constituent particles of a crystalline solid are arranged in a definite
fashion in the three dimensional space. Such a regular arrangement of
the constituent particles of a crystal in a three dimensional space is called
crystal lattice or space lattice.
Crystal Structure

3. TYPES OF CUBIC CRYSTAL

4. UNIT CELL CHARACTERISTICS
Volume of Unit Cell
No of atoms per unit cell
Atomic radius
Nearest neighbour distance
Coordination number
Atomic Packing Fraction
Void space
Density

5. 1) Volume of the unit cell :
V= a3
FACE CENTRED CUBIC (FCC) CELL

6. 2) Effective Number of Atoms per unit Cell (Z):
Z = 4
3) Atomic Radius (r) :
In face centered unit cubic cell, atoms
situated at the corners are not in contact
with each other. They are in contact with
the atom situated at the face centered
atom of the cell.
r = a/ 22
FACE CENTRED CUBIC (FCC) CELL

7. 4) Nearest Neighbor Distance, 2r :
The centre to centre distance between any two adjacent neighbor atoms is
called ‘Nearest Neighbor Distance’.
In case of Face Centered Cubic Unit Cell,
NND = a/ 2
5) Coordination Number, CN :
CN= 12
FACE CENTRED CUBIC (FCC) CELL

8. 6) Atomic Packing Fraction (APF):
The fraction of actual volume of the unit cell occupied by the atoms is
called ‘atomic packing fraction’.
FACE CENTRED CUBIC (FCC) CELL

9. 7) Void Space= (1-APF)X100%
Void Space = 26 %
8) Volume mass Density ( r ):
The ratio of mass to volume is called
volume mass density of the cell.
Therefore it is given by-
W=M/NA
Z (W)
V
Z (M/NA)
a3
4M
NA a3
r =
r =
r =
FACE CENTRED CUBIC (FCC) CELL