Review: Ionic Bonding Model
•Ionic – charge is transferred from the more metallic (low EN) atom to the non-metallic (high
EN) atom forming oppositely charged species, the cation (+) and anion (-).
•The electrostatic interaction between the two ions, F12, forms the bond, and increases with
increasing ion charge (Ze) and decreases with increasing separation, r12, according to Coulomb’s
Law:
k o Z1eZ 2 e ko  1
Cl (nonmetal)
4 Na (metal)
FA   r 2
unstable
unstable
12
electron
•The attractive bonding forces are
coulombic that is positive and
negative ions attract one another.
Na (cation) +
Cl (anion)
FA increases as ions approach.
stable
stable
Coulombic
•However bond length is never zero
Attraction
because FR counteracts, due to
overlapping of similarly charged (-ve) electric fields from each ion, as well as an attempt to bring
(+ve) nuclei together.
 r /  where  and  are experimentally determined constants.
FR  e
•For two ions the attractive energy EA is a function of the interatomic distance:
EA 
A
r
where A  ko( Z1e )( Z 2e ) and repulsive energy ER is
ER 
B
rn
n is ~8.
EN (net) potential energy is sum of EA + ER or the net potential energy between 2 adjacent ions.
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Ionic Bonding Model (continued)
Calculate force of attraction (FA) between Ca2+ and O2- ions with their centers separated by 1.25 nm
•Crystals such as
salts and ceramics
are ionically bound.
•Non-directional, Na+ will
attract any adjacent Clequally in all 3 directions.
•Ionic bonding occurs
when f >0.5; large EN
difference (far L and R
columns on Periodic table.)
Na: 1s22s22p63s1  Na+: give up 1 eCl: 1s22s22p63s23p5  Cl-: picks it up
This transfer results in a long-range
coulombic attraction between oppositely
charged ions.
•Why is melting point of CaF2 > CaCl2 > CaBr2?
•The lattice energy, similar to bond energy, is the energy required to separate all of the ions
(cation and anion) in a crystal to infinity. Thus, it’s a measure of the crystal’s bond strength.
•Why would LiCl (ro=2.57Å) and SrO (ro=2.58Å) have approximately the same interionic
spacing and the same crystal structure (rocksalt), but have different lattice energies of
Eo=9eV and Eo=33eV, respectively?
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Relationship between Melting Point &
Elastic Modulus and Lattice Energy (Force)
From Materials Science – an Intermediate Text by William F. Hosford
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Examples of Ionic Bonding
• Predominant bonding in Ceramics
NaCl
MgO
CaF2
CsCl
H
2.1
Li
1.0
Be
1.5
Na
0.9
Mg
1.2
K
0.8
Ca
1.0
Rb
0.8
He
O
F
3.5 4.0
Ne
-
Cl
3.0
Ar
-
Br
2.8
Kr
-
Sr
1.0
I
2.5
Xe
-
Cs
0.7
Ba
0.9
At
2.2
Rn
-
Fr
0.7
Ra
0.9
Ti
1.5
Cr
1.6
Give up electrons
Fe
1.8
Ni
1.8
Zn
1.8
As
2.0
Acquire electrons
Adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and
1940, 3rd edition. Copyright 1960 by Cornell University.
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Take Ionic Bonding Model a Step Further
and Apply it to Crystal Structures
•To compute the total electrostatic contribution to the lattice energy, E, we must sum both the
attractive and repulsive interactions between all of the ions of nearest neighbor distance (ro):
where M is the Madelung constant, which is a relationship of the distance of
ke 2
the ions from one another due to a specific type of crystal. It depends on the
A
ro
geometric arrangement of the constituent ions in the crystal structure. “See
(1) class handout and Table 7.9 in Rohrer for values.”
  ( n  n2 M) Z Z
1
2
1 2
•For binary structures, it is common to use a reduced Madelung constant, :
where n1 and n2 are stoichiometry of cation and anion. For NaCl, n1=n2=Z1=Z2=1
(2)
•The reduced Madelung constant leads to a convenient expression for the total electrostatic
energy which separates the chemical parameters such as charge (Z), stoichiometry (n) and ionic
distance/sizes (ro) from the structural information in the Madelung constant:
2
E  M
EA  
ke  ( n1  n2 ) Z1 Z 2
2 ro
•1.25≤ ≤1.76,  generally increases with increasing coordination number of the structure, e.g.(3)
CsCl > NaCl > ZnS. Also, compounds with layered structures (more directional bonding),
e.g. CdCl2 and V2O5 have lower ’s which implies the electrostatic
contribution to the bonding is diminished while the covalent
contribution is increased. [SiF4: =1.25 since low CN & covalent.]
We still need to include the repulsive energy (ER) contribution, we will return to this later
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since we need to discuss the Lennard-Jones portion of the energy.
Example Calculation of Madelung Constant
For NaCl (Rocksalt crystal structure):
From Handout “Materials Science – an Intermediate Text by William F. Hosford”
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