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Periodic table
0
IA
IIA
transition metals
IIIB IVB VB VIBVIIB
VIIIB
postIIIA IVA VA VIA VIIA
transition
metals
IB IIB
Bonding in Solids
e
repulsive Coulomb interaction
between ions
e
repulsive Coulomb interaction
between electrons
attractive Coulomb interaction
between ions and electrons
Stable Solids :
EK  EP  energy of neutral atoms
kinetic energy of electrons
2
EK ~
2m( x)2
Molecular (van der Waals) bond
Crystals of “inert” gases of group 0: Ar, Kr, Xe, Rn
e
e
m1
m2
Electric field in the visinity
of the second atom : E ~
2 m1
40 R 3
Induced dipole moment
in the second atom : m2 ~ E 
R
2m1
40 R 3
Potential energy between two dipoles :
2
 2  m12
C
2

: V ( R ) ~ - m2 E  E   


6
R6
 40  R
Van-der Waals, London
or fluctuating dipole
interaction
Molecular (van der Waals) bond
atom1
atom2
electron charge distribution
Electron charge distributi on overlaps. Repulsive interactio n
arises due to Pauli exclusion principle : VRepalsive( R ) ~
Lennard - Jones potential : V ( R ) ~ -
C
B


R 6 R12
B
,B0
12
R
V (R )
4
  12   6 
 4      , 4 6  C , 4 12  B 
 R  
 R 
6
-1/4
2
R
 
 
IONIC bond
Crystals: NaCl, CsCl, CaCl2
Na
+
Na+
Cl
Cl-
cohesive
energy
+ 7.9eV
Na  5.1eV  Na   free electron
Energy
balance
Cl  free electron  Cl   3.6eV
Coulomb interactio n between Na  and Cl  :
V ( R)  
e2
40 R

 5eV , R  2.81 
IONIC bond: Madelung
constant
Vi  V ji   
i j
i j

40 Rij
R
Rij  pij R , where R  nearest
40 R
A,
A
i j



separation in the crystal
then Vi 

q2
  for like charge

 for unlike charge
q2

 
pij
Madelung constant
A
1
1
1

 2 

 ......  
R
 R 2 R 3R

2
 ln 2
R
IONIC bond: Madelung
constant
Rij  pij R , where R  nearest
separation in the crystal
then Vi 
q2
40 R
Madelung constant
A,
A
i j
 
pij
NaCl~ 1.75
CsCl~1.76
ZnS (cubic)~1.64
For 2 N ions (  N pairs of ions)
Nq2
V  NVi  
A
40 R
Covalent bond
Crystals: C, Si, Ge, H
Covalent bond is formed by two electrons, one
from each atom, localised in the region
between the atoms (spins of electrons are
anti-parallel )
Example: Carbon 1S2 2S2 2p2
C
C
3D
Diamond:
tetrahedron,
cohesive energy 7.3eV
2D
Covalent bond
Energy
Hydrogen
molecule
H4
1S
1S
H atom
Methane
molecule
H atom
H2
molecule
C
H1
H3
H2
Covalent bond
Atoms in group III, IV,V,&VI tend to form
covalent bond
Filling factor
T. :0.34
F.C.C :0.74
Metallic bond
Atoms in group IA-IIB let electrons to roam in
a crystal. Free electrons glue the crystal
Attract
eAttract
Repel
Repel
Na+
Na+
Attract
Attract
e-
Additional binding due to interaction of partially filled d – electron shells
takes place in transitional metals: IIIB - VIIIB
The Hydrogen bond
Hydrogen bond is formed between the most electronegative
atoms: F,O and N. Bonding energy is ~ 0.1ev
Bonding in DNA molecule
F-
N
H+
C
N
sugar
N
C
H
C
H
C
H
C
N
C
C
H
adenine
O
C
N
N
H
C
C
H
H
H
F-
N
sugar
thymine
Bonding in Solids
Melting
point
(K)
Molecular
crystals
Metals
Ionic
crystals
W(3683)
C(<3500)
BN(3270)
3000
Mo(2883)
Pt(2034)
Fe(1808)
2000
1000
organic
crystals
0
Covalent
crystals
Cu(1336)
Al(933)
Pb(600)
Na(371)
Hg(234)
SiO2(2001)
LiF(1143)
KCl(1063)
Si(1683)
Ge(1240)