1) The document discusses different types of unit cell structures in crystalline solids, including simple cubic, body centered cubic, and face centered cubic unit cells. 2) It also describes the packing efficiency of each unit cell structure, with face centered cubic being the most efficient with 74% of space occupied by particles. 3) The document outlines the three stages of packing - linear packing in one dimension, planar packing arrangements, and three-dimensional packing. It provides examples of AAAA and ABAB planar arrangements and how they correspond to simple cubic and hexagonal close packed 3D structures.

1. Nutan junior college,wavi Tal – sinner
Prof :- Mrs. VIDHATE G.B.

2. Simple cubic unit cell

4. 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

5. •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

6. 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.

7. 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

8. 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.

9. Stage II-planar packing arrangement of spheres
AAAA TYPE ARRANGEMENT

10. ABAB -TYPE PACKING
ARRANGEMENT
ITS CLOSEST PACKING ARRANGEMENT

11. 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.

12. AAAA Type simple cubic str.
AAAA Type of two dimensional crystal layers are placed over one another in suc
A way that all the sphere of each layer are exactly above the sphere of lower lay
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 a
Onded to sphere & one are above & one are below.
Co-ordination is six. there are more empty space in the simple cubic str.

13. ABAB type Hexagonal closed
packed str.
ABAB Type of two dimensional crystal layers are placed over one another by
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.
sphere of second layer are packed into depressions between the sphere of
Layer due to this packing is made most efficient & reduce empty space.

14. • 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.

15. Tetrahedral void

16. 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

17. 1) Placing the spheres of the third
layer into the tetrahedral voids