ATOMIC BONDING ATOMIC BONDING

IN SOLIDSIN SOLIDS

BONDING ENERGY, BONDING ENERGY, INTERATOMIC SPACINGINTERATOMIC SPACING

For two ions to come closer to each For two ions to come closer to each other, two types of forces are in effect.other, two types of forces are in effect.

Attractive Forces Attractive Forces (+)(+) pull atoms togetherpull atoms together

Repulsive Forces Repulsive Forces (-)(-) develop when atoms develop when atoms are brought into close proximity (~nm). are brought into close proximity (~nm). There is mutual electronic repulsion There is mutual electronic repulsion between the two atoms because of the between the two atoms because of the electrons around an atoms. electrons around an atoms.

Fr(x): Repulsive force

Fa(x): Attractive forceFt(x): Total

force

Ten

sile

(+

)C

om

pre

ssiv

e

(-)

x,Interatomic SpacingF

orc

e

x0

When two atoms approach each other When two atoms approach each other they exert forces on one another.they exert forces on one another.

1. Forces of attraction (F1. Forces of attraction (Faa))→Attractive forces b/w atoms →Attractive forces b/w atoms

decrease with interatomic spacing, x. decrease with interatomic spacing, x.

(is inversely proportional with x)(is inversely proportional with x)

2. Forces of repulsion (Fr)→As atoms come closer, →As atoms come closer,

repulsive forces dominate. repulsive forces dominate. (is inversely proportional to a higher power of x than (is inversely proportional to a higher power of x than FFaa))

Total forceTotal force F = FF = Faa+F+Fr r

When When FFaa=F=Frr → Equilibrium point → → Equilibrium point → @@ x=x x=x00

xx00 is also known as equilibrium spacing and is is also known as equilibrium spacing and is a very specific distance for a given pair of a very specific distance for a given pair of atoms or ions. A large amount of force is atoms or ions. A large amount of force is needed to change (stretch or compress) that needed to change (stretch or compress) that distance. Therefore, generally atoms can be distance. Therefore, generally atoms can be assumed as hard balls when atomic assumed as hard balls when atomic arrangements are considered. arrangements are considered.

Sometimes it is more convenient to work with Sometimes it is more convenient to work with the potential energies between two atoms the potential energies between two atoms instead of forces. instead of forces.

ran

x

ran

x

n

EEE

dxFFE

FdxE

FdxE

0

)(

where where EEnn, , EEaa, , EErr are the are the net, attractive and net, attractive and repulsive energies for repulsive energies for two isolated and two isolated and adjacent atoms.adjacent atoms.

For atomic systems

Eb is the bonding energy that represents the energy required to separate two atoms to an infinite separation.

Eb

0

0@x

b FdxE

xx

The magnitude of the bonding energy and The magnitude of the bonding energy and the shape of E-x curve vary from material to the shape of E-x curve vary from material to material and they both depend on the atomic material and they both depend on the atomic bonding.bonding.

Furthermore a number of material properties Furthermore a number of material properties depend on atomic relationships (Edepend on atomic relationships (Ebb, curve , curve

shape and bond type). shape and bond type). Melting pointMelting point HardnessHardness Modulus of ElasticityModulus of Elasticity=dF/dx at x=x=dF/dx at x=x00

Thermal expansionThermal expansion Conductivity of metalsConductivity of metals

Factors Affecting the Atomic Factors Affecting the Atomic RadiusRadius1.1. Temperature: Temperature: As T increases, xAs T increases, x00 also also

increases.increases.

2.2. Ionic Value: Ionic Value: An electropositive atom (FAn electropositive atom (Fee+2+2) has ) has

a smaller radius than a neutral atom (Fa smaller radius than a neutral atom (Fee).).Similarly an Similarly an electronegativelectronegative atom (Oe atom (O-2-2) ) has a higher has a higher radius than a radius than a neutral atom neutral atom (O).(O).

3.3. Surrounding Atoms: Surrounding Atoms: As the number of As the number of surrounding atoms around a bond surrounding atoms around a bond increases, the interatomic distance increases, the interatomic distance increases due to the repulsive forces increases due to the repulsive forces developed by electrons.developed by electrons.

4.4. Covalency: Covalency: As the number of shared As the number of shared electrons increases, atoms will attract electrons increases, atoms will attract each other more and the radius each other more and the radius decreases.decreases.

Example :

Energy is minimum

U = A r-m + B r-n

U = rm

A B+rn

[J]

r: Interatomic distance in nm (*10-

9 m)

A: -7.2 * 10-20 [J (nm)2]

B: 9.4 * 10-25 [J (nm)10]

m = 2, n = 10

Find r0 where the bond is most stable?

Calculate the net energy?

U = r2

+r10

-7.2 * 10-20 9.4 * 10-25

= 0dr

dU

= -m A r-m-1 – n B r-n-1

dr

dU

dr

dU = -2 * (-7.2*10-20) * r-3 – 10*(9.4*10-25)*r-11 = 0

6.53*10-5

r = 0.299 nm

9.4*10-2514.4*10-

20 r3→=

r11r8 =

-6.40*10-19 [J]9.4*10-

25

-7.2*10-

20Umin = =+(0.299)2 (0.299)1

0