16. NUMBER
OF
ATOMS
PER UNIT
CELL
16
• Determine the number of lattice points per cell in the cubic crystal
systems. If there is only one atom located at each lattice point,
calculate the number of atoms per unit cell.
• Example 3.1 SOLUTION
• In the SC unit cell: lattice point / unit cell = (8 corners)1/8 = 1
• In BCC unit cells: lattice point / unit cell= (8 corners)1/8 + (1
center)(1) = 2
• In FCC unit cells: lattice point / unit cell = (8 corners)1/8 + (6
faces)(1/2) = 4
• The number of atoms per unit cell would be 1, 2, and 4, for the
simple cubic, body-centered cubic, and face-centered cubic, unit
cells, respectively.
17. COORDINATION NUMBER
Number of nearest neighbours or touching atoms
around an atom
17
Coordination number
(SC)=6
BCC=8
FCC=12
The primitive, body-centred and face-centred cubic unit cells.mp4
30. 30
Determine the density of BCC iron, which has a lattice
parameter of 0.2866 nm.
Example 3.4 SOLUTION
Atoms/cell = 2, a0 = 0.2866 nm = 2.866 10-8 cm
Atomic mass = 55.847 g/mol
Volume of unit cell = = (2.866 10-8 cm)3 = 23.54 10-24
cm3/cell
Avogadro’s number NA = 6.02 1023 atoms/mol
3
0
a
3
23
24
/
882
.
7
)
10
02
.
6
)(
10
54
.
23
(
)
847
.
55
)(
2
(
number)
s
adro'
cell)(Avog
unit
of
(volume
iron)
of
mass
)(atomic
atoms/cell
of
(number
Density
cm
g
=
=
=
−
51. LINEAR AND PLANAR ATOMIC DENSITIES
Linear Density:
Directional equivalency is related to the atomic linear density in the sense that
equivalent directions have identical linear densities.
The direction vector is positioned so as to pass through atom centers.
The fraction of line length intersected by these atoms is equal to the linear
density.
Planar Density:
Crystallographic planes that are equivalent have the same atomic planar
density. The plane of interest is positioned so as to pass through atom
centers.
Planar density is the fraction of total crystallographic plane area that is
occupied by atoms.
52. 52
FCC: LINEAR DENSITY
• Linear Density of Atoms LD =
Unit length of direction vector
Number of atoms
𝐿𝐷110 =
2𝑎𝑡𝑜𝑚𝑠
4𝑅
=
1
2𝑅
