NaCl &DIAMOND STRUCTURE

NAME:-Ruman Ansari

Branch:-MEBatch:-2015

1

RELATION BETWEEN LATTICE CONSTANT AND DENSITY

Consider a cubic crystal of lattice constant ‘a’.

Density of the crystal = ρ

Volume of the unit cell =V = a3

Number of atoms per unit cell = n

Atomic weight of the material = M

Avagadro number = N

In M gram of material there are ‘N’ atoms i.e., mass of N atoms is ‘M’ gram.

Mass of 1 atom =

Mass of ‘n’ molecules i.e., mass of an unit cell = (1) Density ‘ρ’=

i.e. ρ =

MN

nMN

massvolume

mV

RELATION BETWEEN LATTICE CONSTANT AND DENSITY

ρ =

mass ‘m’ = ρ a3 (2)

Equating (1) and (2), we get,

ρ a3 =

ρ =

3

ma

nMN

3

nMNa

RELATION BETWEEN LATTICE CONSTANT AND DENSITY

RELATION BETWEEN LATTICE CONSTANT AND DENSITY

Number of atoms per unit cell Atomic weightAvagadro number (Lattice constant)

3

NaCl STRUCTURE

Nacl having fcc structure so, n=4 & the co- ordinate no. N=6Atomic weight of Nacl =23+35.45=58.45Density of Nacl =2180 kg/Lattice constant for Nacl structure

a=

NaCl STRUCTURE

3m

31

Nanm

NaCl STRUCTURE

a=

a=5.625Inter atomic distance is a/2 hence Inter atomic distance is = 5.625/2 = 2.8125A

31

2610023.6218045.584

DIAMOND CUBIC STRUCTURE

a

a/4

Z

YY

2r

a/4W

a/4

X

DIAMOND CUBIC STRUCTURE

DIAMOND CUBIC STRUCTURE

It is formed by carbon atoms. Every carbon atom is surrounded by four other carbon atoms

situated at the corners of regular tetrahedral by the covalent linkages.

The diamond cubic structure is a combination of two interpenetrating FCC sub lattices displaced along the body diagonal of the cubic cell by 1/4th length of that diagonal.

DIAMOND CUBIC STRUCTURE

In the diamond cubic unit cell, there are eight corner atoms, six face centred atoms and four more atoms.

No. of atoms contributed by the corner atoms to an unit cell is 1/8×8 =1.

No. of atoms contributed by the face centred atoms to the unit cell is 1/2 × 6 = 3• There are four more atoms inside the structure.

DIAMOND CUBIC STRUCTURE

No.of atoms present in a diamond cubic unit cell is 1 + 3 + 4 = 8. Since each carbon atom is surrounded by four more carbon atoms,

the co-ordination number is 4.

ATOMIC RADIUS(R)From the figure,in the triangle WXY,

XY2 = XW2 + WY2

=

2 2a a4 4

DIAMOND CUBIC STRUCTURE

XY2 =

Also in the triangle XYZ,

XZ2 = XY2 + YZ2

=

XZ2 =

2a8

22a a8 4

23a16

DIAMOND CUBIC STRUCTURE

But XZ = 2r

(2r)2 =

4r2 =

r2=

Atomic radius r =

23a16

23a16

23a64

3 a8

DIAMOND CUBIC STRUCTURE

Atomic packing factor (APF)

APF =

v =

i.e. v =

APF =

vV

348 r3

3

4 3a83 8

3

3 3

8 4 3 3 a3 8 a

DIAMOND CUBIC STRUCTURE

APF =

i.e. APF = 34%

Thus it is a loosely packed structure.

3 0.3416