The document summarizes key aspects of the diamond lattice structure formed by carbon atoms in a diamond crystal. It describes the diamond lattice as being formed by two interpenetrating face-centered cubic (fcc) sublattices offset by 1/4 cube edge. Each carbon atom has four nearest neighbors in a tetrahedral structure, giving the diamond lattice a coordination number of 4. The packing factor of the diamond lattice is 0.34, indicating it is a loosely packed structure.

2. BASIC DIAMOND LATTICE
formed by the carbon atoms in a diamond crysta)

3. DEFINITION
 The diamond lattice can be considered to be formed by
interpenetrating two fcc lattices along the body diagonal by ¼ cube
edge.
 One sublattice has its orgin at the point (0,0,0 )and the order at the
point quarter of the way along the body daigonal (at the point
a/4,a/4,a/4).
 The diamond cubic structure is loosely packed ,since each atom has
four nearest neighbour

4. NUMBER OF ATOMS PER UNIT CELL
 In the eight corner each atom is shared by eight unit cells
1/8 *8=1
 The each 6 faces ever single atom which is shared by 2 unit cells
½*6=3
 And in every unit cell it has 4 atoms inside 4
 1+3+4=8

5. THE FIGURES OF BOTH POSITION AND BASIC
DAIMOND LATTICE

6. ATOMIC RADIUS
 (𝑥𝑧)2
=𝑎2
/8
 (𝑥𝑦)2
= (𝑥𝑧)2
+(𝑦𝑧)2
=𝑎2
/8+𝑎2
/16=3𝑎2
/16
 XY=2r
 (2𝑟)2
= 3𝑎2
/16
 r=√3/8*a
 Or a=

7. COORDINATION NUMBER
 In a diamond crystal, the carbon atom are
linked by the directional covalent bond
 Carbon atoms from covalent bonds with four
other carbon atoms that occupy four corners
of the cube in a tetrehedral structure.
 In the diamond lattice each atom has four
nearest neighbour with which it forms covalent
bonds ,thus the coordination number of
diamond crystal is 4

8. PACKING FACTOR
 Packing factor =volume of all atoms in the unit cell /volume of the unit cell
 = number of the atoms in the unit cell*volume of one
atom
 /volume of the unit cell
 =8*(4/3*π𝒓 𝟑
)/𝒂 𝟑
 =(π√3)/16
 =0.34
 Packing factor =34%
 Thus it islossely packed structure
 Carbon ,silicon ,germanium ,and grey tin crystallize in the diamond stucture

10. Thanking you