Nutan junior college,wavi Tal – sinner

Prof :- Mrs. VIDHATE G.B. (M.Sc.B.Ed)

Simple cubic unit cell

BODY CENTRED CUBIC UNIT CELL

•Body centred cubic

unit cell is a

modification of simple

cubic unit cell.( bcc

•in which one particle

is at the center of the

unit cell & 8 particles

at the corner , each

corner attached

particle size is 1/8 of

the particle.

•Total number of

sphere = no.of unit

cell at the corner x

size of unit cell + 1

•Total number of unit

cell = = 8 x 1/8 +1

•= 1 + 1

•= 2

•face centred cubic

unit cell is a

modification of simple

cubic unit cell.( fcc)

•in which four particle

is at the center of the

unit cell & 8 particles

at the corner , each

corner attached

particle size is 1/8 of

the particle.

•Total number of

sphere = no.of unit

cell at the corner x

size of unit cell +

Total no.of half

sphere x size of half

sphere

•Total number of unit

cell/sphere = 8 x 1/8

+6 x ½

•=1+3

•= 4

Face centered cubic unit cell

REPRESENTATION OF CRYSTAL LATTICE

•The participating particles atoms,ions or

molecules touche each other and form three

diamentional network .

•This three diamentional structure can draw

with help of small circles are participating

particles & connecting neighbouring particles

with the help of straight line.

PACKING IN SOLIDS

In case of a crystal lattice formed by simple cubic unit cell the occupied space by constituents particles is to the extent of 52.4 % and 47.6 % space is unoccupied empty space is called void.

In case of body centered cubic str. the space occupied is 68 % and void is 32 %.

In face centered cubic str. The space occupied is 74 % & void is 26 %.

Closest packing is most efficient arrangement because most space occupied by particles & minimum space remains for void space.

There are three types of arrangement for unit cell.

1) linear packing in one direction

2) planar packing arrangement of sphere

3) three dimensional packing

1) Stage I-linear packing in one

direction

• The constituent particles of the crystalline solids are represented by

Sphere of equal size.

• The linear arrangement of sphere in one dimension can be made by

arranging the sphere in one row in which each sphere is attached to

two neighboring sphere ,except two ends sphere.

• The co-ordination number of the particles in one dimension is two.

Stage II-planar packing arrangement of spheres

AAAA TYPE ARRANGEMENT

ABAB -TYPE PACKING

ARRANGEMENT

ITS CLOSEST PACKING ARRANGEMENT

Three dimensional packing

Three dimensional str. are made by /with the help of two dimensional

AAAA/ABAB Type of crystal str.

Three dimensional crystalline str. Are prepared by placing two dimensinal

crystal str. One over another.

There are also two types

1) AAAA type simple cubic str.

2) ABAB type Hexagonal closed packed str.

AAAA Type simple cubic str.

AAAA Type of two dimensional crystal layers are placed over one another in such

A way that all the sphere of each layer are exactly above the sphere of lower layer.

All the sphere of different layers are aligned horizontally & also vertically.

It is evident from fig. each sphere are surrounded by six sphere out of which 4 are

Onded to sphere & one are above & one are below.

Co-ordination is six. there are more empty space in the simple cubic str.

ABAB type Hexagonal closed

packed str.

ABAB Type of two dimensional crystal layers are placed over one another by such

A way that empty space Is reduced & packing is made most efficient.

In both the str. The central sphere are surrouded by six sphere in each layer. The

sphere of second layer are packed into depressions between the sphere of first

Layer due to this packing is made most efficient & reduce empty space.

• Evidence from fig.

• Only half the no. of triangular open spaces of lower layer A are completely

covered

• By sphere of upper layer B .this consists a tetrahedral hole in the lower

layer A

• Formed four sphere, three in the lower layer A & one sphere in the upper

layer B.

• Simultaneously new tetrahedral holes are also created by three

neighboring sphere

• Of the top layer & one sphere of the lower layer.

• The remaining half of triangular open spaces of the lower layer are

partially covered by three neighboring spheres of upper layer & a new type

of open space

• Is formed by total six sphere open space known as octahedral void.

Tetrahedral void

Octahedral void

If the no. Of closed packed sphere are N , the no. of

octahedral void are N & the no. of tetrahedral void are 2N

1) Placing the spheres of the third

layer into the tetrahedral voids