CH 3 Atomic Bonding in Solidhhjs (2).pdf

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1. ATOMIC BONDING
IN SOLIDS

Interatomic Distances, Forces and
Energy Relations

2. Chapter Outline
•Bonding Energy and Forces
Interatomic Distances, Forces and
Energy Relations

•Factors Affecting the Interatomic
Distances
–Temperature,
–İonic Value,
–Surrounding Atoms and
–Covalency
•Coordination Number (CN)

3. Bonding Energies and Forces
For two ions to come closer to each other,
two types of forces are in effect.
Attractive Forces (+) pull atoms together
Repulsive Forces (-) develop when atoms
are brought into close proximity (~nm).
There is mutual electronic repulsion
between the two atoms because of the
electrons around atoms.

4. Bonding Energies and Forces

5. Bonding Energies and Forces
The Force necessary to break a bond is called the
cohesive force (F
m) and the corresponding
strength is called the cohesive strength or
theoretical strength.
The energy (or work) necessary to increase the
interatomic distance by dx is,
The energy necessary to break a bond is named
as bond energy.

F = - (dU/dx)

6. Example :
Energy is minimum
U = A r
-m
+ B r
-n
U =
r
m
A B
+
r
n
[J]
Find r
0 where the bond is most stable?
Calculate the net energy?
U =
r
2
+
r
10
dU
= -m A r
-m-1
– n B r
-n-1
dr
dU
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
= 0
dr
-
-7.2 * 10-20 9.4 * 10-25

7. 6.53*10
-5
r = 0.299 nm
10
-24
*9.414.4*10
-20
r
3
→ =
r
11
r
8
=
-6.40*10
-19
[J]
9.4*10
-25
-7.2*10
-20
U
min = = +
(0.299)
2
(0.299)
10
dU
dr
-
= {-2 * (-7.2*10-20) * r-3 – 10*(9.4*10-25)*r-11}= 0
-

9. Net Energy is
minimum when the
ions are at their
equilibrium seperation
distance r
o (a
o).
At the minimum
energy, the force
between the ions is
zero.
At r = r
o (a
o);
U = U
min
F
net = F
attr+F
rep = o

10. Furthermore a number of material properties
depend on atomic relationships (E
b, curve
shape and bond type).
Melting point
Hardness
Modulus of Elasticity=dF/dx at x=x
0
Thermal expansion
Conductivity of metals
The magnitude of the bonding energy and
the shape of E-x curve vary from material to
material and they both depend on the atomic
bonding. -

12. Factors Affecting the Interatomic Distances
1)Temperature: The interatomic distances
increase with temperature. The externally
applied thermal energy results in the vibration
of the atoms and the distance increases upon
thermal expansion.
2)İonic Value: The radius of a (+ve) ion is smaller
than that of the corresponding neutral atom
and the radius of a (-ve) ion is larger.

13. 3)Surrounding Atoms: As the number of
surrounding atoms around an atom increases,
interatomic distances increase a little due to
the repulsive effect of interacting electrons.
4)Covalency: As the # of shared electrons in a
covalent body increases, atoms will attract
each other more and thus the interatomic
distance decreases.

14. Coordination Number (CN)
Number of the first nearest neighbours surrounding
any one atom, ion or molecule. Radius ratio = r /R
•In the gases which are composed of individual
atoms CN is accepted to be zero.
•In a covalent substances, the covalency (# of shared
electrons) affect CN.
•Group VII (e.g. F
9
) form only one bond CN=1
•Group VI (e.g O
8
) molecule with two bonds CN= 2
•Group V (e.g N
7
) ‘’ with three bonds CN= 3
•Group IV (e.g C
6
) ‘’ four bonds CN= 4

15. •Ionic and Mettalic substances have a
tendency of having high CN. As the number
of closest neighbours increase, the energy
of the system decreases and thus it attains a
more STABLE structure.
•CN depends directly on the relative sizes of
the oppositely charged ions and is
characterized by the radius (r/R) Where,
•r = radius of the smaller ion.
•R = radius of the larger ion

16. Cordination Number CN

17. Calculation of CN

18. CNs for
different radius
ratios r /R

21. 9