crystallography hexagonal closed packed structure -coordination number,number of atoms -atomic radius -packing factor

1. CYSTALLOGRAPHY

2. Amorphous solids
Irregularly arranged
Eg : glass ,wood
Crystalline solids
Regularly arranged
Eg : quartz , diamond
TYPES OF SOLIDS

3. KEY WORDS TO UNDERSTAND
Faces
Form
Edges and interfacial angles
The crystal lattice
Basis
The crystal structure
Unit cell
Primitive lattice cell
BCC
FCC
Coordination number
Packing factor
Atomic radius
Nearest neighbor distance

4. EXPLANATIONS
COORDINATION NUMBER: the number of atoms or ions immediately
surrounding a central atom in a crystal.
PACKING FACTOR : atomic packing factor is the ratio of the volume of
the atom in the unit cell to the volume of the unit cell
Higher the value of the P.F indicates that the atoms are closely packed in
the unit cell
ATOMIC RADIUS : Half the distance between the two nearest
neighboring distance atoms (r).
NEAREST NEIGHBOURING DISTANCE :The distance between the
Centre’s of the nearest neighboring distance (2r)

5. HEXAGONAL CLOSE PACKED
STURUCTURE
(HCP)

6. a=b ≠ c
α=β= 90º
Γ=120º
ARRANGEMENT

9. At the bottom layer , central atom has six nearest atoms in the same plane
Top layer has the same atomic arrangement as the bottom layer
At c/2 distance from the bottom layer there is middle layer containing
three atoms
THREE LAYERS OF THE ATOM IN
UNIT CELL

10. Top layer contains 6 atoms at the corner
and one in the center
The corner atom is shared by 6 unit cells
6*1/6=1
The central atom is shared by 2 unit cells
1/2
Similarly for the top and bottom layer
3/2+3/2
There are 3 atoms in the center layer it is
within the cell hence it wholly inside 3
3/2+3/2+3=6
NUMBER OF THE ATOMS

11. Atoms are in contact along the edges
of the hexagon
2r=a
A=r/2
ATOMIC RADIUS

12. In the top layer of the HCP it
touches 6 atoms in its plane
3 atoms in the plane just below it
3 atoms in the just above it
Hence the coordination number
is 12
COORDINATION NUMBER

13. It is dertermined by computing the area of the base into the height of
the cell
Area of the base (hexagon) which is divided into 6 equilateral triangle
whose side is equal to ‘a’
Area of the base= 6 (1/2*a *a sin 60)=3√3/2 a*a
Volume of the unit cell= (3√3/2 a*a) c
VOLUME OF THE UNIT CELL

14. Let c be the height of the unit cell and a be the its edge also a=2r
2𝑟2 = 𝑥2 + (
𝑐
2
)2
X=2/3(a √3/2)=a/√3
𝑎2= 𝑎2/3+
𝑐2
4
𝑐2/4=2𝑎2/3
𝑐2/𝑎2=8/3
c/a=√(3/2)
c/a=1.633
CALCULATION OF C/A RATIO

15. Packing factor =volume of all atoms in the unit cell/volume of the unit cell
= no of the atoms in unit cell*volume of one atom
/volume of the unit cell
=(6*4/3𝜋𝑟3)/(3√3𝑎2c)
=П/3√2
=0.74
Packing factor =74%
Since the density of the packing is 74%, it is a close packed structure
Magnesium ,zinc ,cadmium crystalize in this structure
CALCULATION OF PACKING
FACTOR

16. Modern physics by R. murugeshan
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REFERENCES

17. THANK ING YOU
Presented by gaayathiri