source : Slide serve

In ionic crystals the positive and negative ions are held together with coulombic forces . A crystal structure is determined by the ratio of ionic radii of its components . This ratio coordinates the coordination number of the smaller ions. In ionic crystals each ion is surrounded by definite number of the oppositely charged  ions. The number of the nearest neighbour is the coordination number  of the central ion. This number depends upon the radii of the ions and radius ratio of the two ions.

The  ratio of the radii of the positive and negative ions is called the limiting radius ratio.

### Limiting radius ratio = Radius of cation /  Radius of anion = r + / r –

#### ‘ The effect of radius ratio in determining the coordination number and shape of the ionic crystal is known as radius ratio effect.’

On the basis of  Limiting radius ratio ,we can say about coordination number and shape of the ionic crystal.

#### 0 – 0.155                                                 2                              Linear                        –

0.155 – 0.225                                             3                        Trigonal planar                B2O3

0.225 – 0.414                                             4                          Tetrahedral                 ZnO, CuCl

0.414 – 0.732                                             6                            Octahedral                   NaCl , MgO

0.732 – 1.000                                             8                            Body centred cubic     CsCl, NH4Br

For radius ratio greater than 0.155 , the compound may be stable.

#### For Ex.-

The radius of Na+ is 0.95 Angstrom and that of Cl is 187 Angstrom. Hence ,

#### Radius  ratio in NaCl  = rNa+ / r Cl– = 0.95 / 0.81 = 0.524

Limiting radius ratio is 0.524 , therefore coordination number is six and shape is octahedral. It is proved by X-ray study of NaCl crystal that each Na+ is surrounded by six Cl which are arranged octahedrally . Each Cl is surrounded by six Na+.