NEET Chemistry Notes Solid State – Packing Efficiency
Packing Efficiency
Packing Efficiency
It is the ratio of volumes occupied by atoms in unit cell to the total volume of the unit cell. It is also known as packing fraction or density ofrpacking.
Packing fraction 
volume occupied by particles of unit cell total volume of unit cell The density of packing gives idea about how closely the atoms are packed in a unit cell. For the primitive cubic lattices, it follows the following order
fcc (74%) > bcc (68%) > simple cubic lattice (52%) > diamond (32%)
VOIDS
In closely packed structures, the empty space is called interstitial site or void. The
void can be a simple triangular space in the case of two dimensional packing and called the trigonal void.
In three dimensional close packing patterns, the voids can be of two types:
- Tetrahedral Void A tetrahedral void is a simple 3 triangular space surrounded by 4 spheres as shown below Octahedral Void An octahedral void is a double triangular void surrounded by 6 spheres as shown below:
- Increasing order of void size
Trigonal < Tetrahedral < Octahedral In CCP structure, number of octahedral voids =4, number of tetrahedral voids = 8 - . In general, if in a closed packed (ccp or hep) there are N sphere (atoms or ions) in the packing then
- Number of octahedral voids = N
- Number of tetrahedral voids =2 N
Calculations Involving Unit Cell Parameters
- Relation between Edge Length and Radius of Sphere
- Simple cubic r = a/2
- Percentage of packing fraction =52%.
- Face centred cubic r = \(\frac{a}{2 \sqrt{2}}\)
- Percentage of packing fraction = 74%
- Body centred cubic r = \(\frac{\sqrt{3}}{4} a\)
- Percentage of packing fraction = 68%
Calculation of Density of Unit Cell
where, d = density
M = molecular weight
Z = number of atoms per unit cell
NA = Avogadro number
a = edge length of unit cell
Structures of Some Ionic Solids
Coordination Number
The number of atoms in a crystal which- surrounds particular atoms as its nearest atoms in its neighbour is called its coordination number.
Shape from Radius Ratio
