# Deviation from ideal behaviour , FAJAN’S RULE

Still now we have discussed all about those compounds which are either 100 percent ionic or covalent from the Lewis theory .
i.e. the formation of the compound from the respective elements takes place either by mutual sharing or by complete transfer of electrons resulting either covalent species or ionic species.

Now we know that NaBr is an ionic crystal. Similarly AlBr3 is also an ionic crystal as its formation takes place by complete transfer of electrons.

So as both are ionic compounds and as it is a well known fact that ionic compounds have high melting points, so we should expect a high melting point for both.

But contrary to our expectations the melting point of NaBr is 775°C and that of AlBr3 is 97.5°C .

Similarly CaF2 has got a melting point of 1400° C while that of CaI2 is 575° C.

This fact indicates that all those compounds which are ionic from the concept of transfer of electrons are not 100% ionic but have some percent of covalent character induced in it.

So it is better to say a compound to be more of ionic rather than totally ionic.

### Transition from Ionic to Covalent Character

In an ideal ionic lattice, the ions are supposed to be hard inelastic spheres just touching each other at equilibrium.
But properties of most ionic solids deviate from ideal ionic character because lattice may undergo some distortion.
Cations are usually smaller than anions and have higher effective nuclear charge than the latter.

The outer electron cloud in a cation is more firmly held than in an anion. Electron cloud in an anion is rather loosely held and may be attracted by the neighbouring cation in the lattice.

Hence the anion may not retain its spherical symmetry and may be distorted. Such a phenomenon is known as polarisability of the anion and the capacity of the cation to distort the electron cloud of anion is known as polarization power of the cation.

As the anion shift’s slightly its electrons towards cation, the positive charge over cation decreases and negative charge over anion also decreases imparting partial ionic character to the bond.

In other words a completely ionic bond becomes partial ionic bond and shifting of electrons towards cation imparts covalent nature to the bond i.e. bond starts behaving like polar covalent bond

The polarising power of a cation is expressed by an index, Φ defined as

$\large \phi = \frac{Cationic \; Charge}{Cationic \; radius}$

where Φ is called ionic potential.

Again the extent to which an anion is polarised is given by its polarisability. This is governed by the charge and size of the anion.

### FAJAN’S RULE

Factors Governing Polarization & Polarisability ( FAJAN’S RULE ):

### Cation Size:

Smaller is the cation more is the value of φ and hence more its polarising power. As a result more covalent character will develop.

Let us take the example of the chlorides of the alkaline earth metals. As we go down from Be to Ba the cation size increases and the value of φ decreases which indicates that BaCl2 is less covalent i.e. more ionic.

This is well reflected in their melting points. Melting points of BeCl2 = 405° C and BaCl2 = 960° C.

### Cationic Charge:

More is the charge on the cation, the higher is the value of φ and higher is the polarising power. This can be well illustrated by the example already given, NaBr and AlBr3.

Here the charge on Na is +1 while that of Al is +3, hence polarising power of Al is higher which in turn means a higher degree of covalency resulting in a lowering of melting point of AlBr3 as compared to NaBr.

##### Noble Gas vs Pseudo Noble Gas Cation:

A Pseudo noble gas cation consists of a noble gas core surrounded by electron cloud due to filled d-sub shell.

Since d-electrons provide inadequate shielding from the nuclei charge due to relatively less penetration of orbitals into the inner electron core, the effective nuclear charge (ENC) is relatively larger than that of a noble gas cation of the same period.

NaCl has got a melting point of 800°C while CuCl has got melting point of 425°C. The configuration of Cu+ = [Ar] 3d10 while that Na+ = [Ne].
Due to presence of d electrons ENC is more and therefore Cl is more polarised in CuCl leading to a higher degree of covalency and lower melting point.

### Anion Size:

Larger is the anion, more is the polarisability and hence more covalent character is expected. An e.g. of this is CaF2 and CaI2, the former has meltingpoint of 1400° C and latter has 575° C. The larger size of I ion compared to F causes more polarization of the molecule leading to a lowering of covalency and increasing in melting point

### Anionic Charge:

Larger is the anionic charge, the more is the polarisability. A well illustrated example is the much higher degree of covalency in magnesium nitride ( 3 Mg++ N3- ) compared to magnesium fluoride ( Mg++ 2F ). This is due to higher charge of nitride compare to fluoride.
These five factors are collectively known as Fajan’s Rule.