**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**