1Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Ceramic Materials
F. Filser & L.J. Gauckler
ETH-Zrich, Departement Materials
[email protected]
HS 2007
Chapter 3: Bond Energy and Properties
mailto:[email protected]
2Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Goal of this Chapter is
to develop semiquantitative relationships between
the properties of a ceramic material and
the depth and shape of the energy well
3Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Bond Energy and the Physical Properties
Bond forces / energy between ions or atoms composing a
solid determine a lot of its physical properties
Hence we can use the bond energy as a means to predict
physical properties
Examples: melting temperature, modulus of elasticity,
strength, hardness
This prediction works in a lot of cases but not in all.
Refinement is required for crystallized solids, i.e. effect of
Madelung, and for solids made up of mixed ionic-
convalent bondings.
4Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Contents
potential well & bond energy for ionic bonding, the equilibrium distance
bond force as a function of the inter-ionic distance, max. force, inflexion
point.
melting temperature and hardness for ionic bonded compounds
limitation of the prediction by potential well (example of MgO / Al2O3)
-> introduction of covalency (of an ionic bond)
thermal expansion explained with the potential well
elastic modulus
theoretic strength of compounds
5Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Bond Energy for Ionic Type of Bonding
Ions Distance
Potential
Eattraction
E repulsion
Sum
r0
r0 = equilibrium distance
attr
acti
ng
repel
ling
- +
2
1 2
0
2
1 2
0
4
4
net att rep
att
rep n
net n
E E E
z z eE r
r
BE r
r
z z e BE r
r r
2
1 2
0 0
11
4bond
z z eE
r n
8Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Potential and Force
as Function of Inter-Ionic Distance
0 100 200 300 400 500 600 700 800
-40
-20
0
20
40
Fo
rce [
nN
]
Inter-Ionic Distance r [pm]
x1
x2
-150
-100
-50
0
50
100
150
0 100 200 300 400 500 600 700 800
Po
ten
tia
l [e
V]
Inter-Ionic Distance r [pm]
x1x2
2
1 2
04net n
z z e BE r
r r
net
net
dE rF r
dr
9Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Comparison of Potential Inter-Ionic Distance Curves
for NaCl, MgO, LiF
-40
-20
0
20
40
0 0.5 1 1.5 2 2.5 3 3.5 4
NaCl
LiF
MgO
Po
ten
tia
l [e
V]
Relative Inter-Ionic Distance r/r0 [-]
MgO potential well is
much deeper than for LiF
and NaCl (ca 4x deeper)
LiF potential well is a bit
deeper than for NaCl.
Same crystal structure
(Rocksalt)
Inter-Ionic Equilibrium
Distances
- NaCl r0=283 pm
- LiF r0= 209 pm
- MgO r0=212 pm
Valencies are different
2
1 2
0 0
11
4bond
z z eE
r n
r0
10Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Melting Temperature
The Bond strength Ebond-> depends strongly on the valency and the ionic radii/distance (lattice distance).
The bond strength Ebond of ionic bonded compounds is directly proportional the
multiplication of its ionic charges z1 and z2 and inverse proportional the
equilibrium ionic distance r0.
The higher the valency the stronger the bond strength.
The compounds MgO, NaCl and LiF crystallize in same lattice (fcc lattice),
and ionic character of the bond is prevailing (>60 %).
MgO NaCl LiF Crystal Structure
2852C 801C 848C Rocksalt
11Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Melting Temperature of some Compounds
Ionic
Distance []
Melting
Temperature [C]
NaF 2.31 988
NaCl 2.81 801
NaBr 2.98 755
NaI 3.23 651
MgO 2.1 2800
CaO 2.4 2580
SrO 2.57 2430
BaO 2.76 1923
LiF 2.01 824
NaF 2.311 988
KF 2.67 846
RbF 2.82 775
The melting temperature increases as the ionic distance decreases within the lattice.
The melting temperature increases for increasing valency given about same ionic distance
melting temperature
decreasing
inter-ionic distance
increasing due to cation
radius increasing
inter-ionic distance
increasing due to anion
radius increasing
melting temperature
decreasing
inter-ionic distance
increasing due to cation
radius increasing
melting temperature
decreasing
z1=+2, z2=-2
z1=+1, z2=-1
z1=+1, z2=-1
Comparable
!!!decrease
!!!
12Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Compound Ionic Distance
[ ]
Hardness
[Mohs]
BeO 1.65 9
MgO 2.3 6.5
CaO 2.4 4.5
SrO 2.57 3.5
BaO 2.76 3.3
NaF 2.01 3.2
MgO 2.3 6.5
ScN 2.67 7-8
TiC 2.82 8-9
Hardness
as function of the inter-ionic distance and the ionic charge
Compound Ionic Distance
[ ]
Hardness
[Mohs]
BeO 1.65 9
MgO 2.3 6.5
CaO 2.4 4.5
SrO 2.57 3.5
BaO 2.76 3.3
Na+F- 2.01 3.2
Mg2+O2- 2.3 6.5
Sc3+N3- 2.67 7-8
Ti4+C4- 2.82 8-9
inter-ionic distance
increasing due to cation
radius increasinghardness
decreasing
z1=+2, z2=-2
valency of ions
increasing & despite
inter-ionic distance
increasing
hardness
increasing
The hardness increases with decreasing ionic distance, assuming constant ionic charges.
The hardness increases for increasing valency, despite ! increasing ionic distance.
13Ceramics: Bond Energy and Properties, Chap 3
Material Science I
Al2O3: 2054 C
MgO: 2852 C
Ionic Distance
Valency
Bond Energy
Lattice Energy
}
Criteria of Analysis:
Presumption: MgO has the lower melting temperature.
Why?
The Melting Temperature of Al2O3 and MgO
14Ceramics: Bond Energy and Properties, Chap 3
Material Science I
2 3 1.64MgOAl O
bond bondE E
Al2O3: 2054 C
MgO: 2852 C
Ionic Distance
Valency
Bond Energy
Lattice Energy
}
-> r0Al2O3 = 193.5 pm, r0
MgO = 212 pm
-> (z1 x z2)Al2O3= -6, (z1 x z2)
MgO= -4
2 3 23.54MgOAl O
Lattice LatticeE E
Criteria of Analysis:
Presumption: MgO has the lower melting temperature.
Why?
The analysis based on the potential well of an ionic bonded solid is often good and correct,
however not all the time!!!
The Melting Temperature of Al2O3 and MgO
15Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Melting Temperature of Al2O3 and MgO
Al2O3: 2054 C
MgO: 2852 C}
Further Criterium of Analysis:
We need other and better criteria !!!
-> Type of Bond: amount of covalency in the bonds for Al2O3 is higher
than for MgO.
A measure for covalency is, for example, the difference in
electronegativity of the ions. DENAl2O3 = 1.83, DENMgO = 2.13
16Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Covalent Character of a Bond
The covalent character of a bond increases from the left to right.
The network structure of the bonds changes: from a 3D structure of TiO2 (Rutile), to a
layered structure of CdI2, to a molecule lattice of CO2. The melting temperature
decrease in this direction, too.
CO2 molecule lattice
Tm = -57C
MX2 stoichiom., DEN = 0.89
CdI2 layer structure
Tm = 387C
MX2 stoichiom., DEN = 0.97
TiO2 idealized Rutile
Tm = 1857C
MX2 stoichiom., DEN = 1.9
Tm = melting temp.
17Ceramics: Bond Energy and Properties, Chap 3
Material Science I
What issues influence the amount of covalency
in an ionic bond?
Polarizing power of the cation
Polarizibility of the anion
Elektron configuration of the cation
ideal pair of ions
(no polarization)high amount of polarizing sufficient
to form a covalent bond
polarized
pair of ions
fAl3+ = 60 1/nm; fMg2+ = 31 1/nm
aeO2- equal for both cases
MgO vs Al2O3
no d-electrons in both cases
18Ceramics: Bond Energy and Properties, Chap 3
Material Science I
The Thermal Expansion Coefficient
pT
l
l
0
1a
=
X
Pote
nti
al E
ner
gy
r0
energy level of the thermal vibration
rmin rmaxr0rmin rmax
ionic distance r
maximum potential energy
= mean ion density (location) for increasing temperature
