Class 4

Class 4 – Primary Bonds
READING
•Chapter 2 in DeGraef and McHenry, pp.38-48.
•REFERENCES: Ch. 13 in W.F. Hosford, Materials Science An Intermediate Text,
(Cambridge University Press, 2007); Chs. 6-9 in Rohrer.
Prof. M.L. Weaver
Types
yp
• Covalent
• Ionic
• Metallic
Prof. M.L. Weaver
Covalent Bonding Model
• Covalent - there is valence electron sharing
between two adjacent
j
atoms such that each
atom assumes a stable electron configuration.
C: has 4 valence e-, needs 4 more
H hhas 1 valence
H:
l
e-, needs
d 1 more
Example is methane:
• Each atom contributes at least one electron
to the bond and the shared electrons may be
considered to belong to both atoms.
• For methane each H atom can acquire a He
electron configuration, when one of four
carbon sp3 valence electrons is shared for total of
8 valence electrons (Ne electron configuration), octet rule.
Prof. M.L. Weaver
Adapted from Fig. 2.10, Callister & Rethwisch 3e.
Covalent Bonding Model
• How many covalent bonds are possible for a particular atom?
• The number of covalent bonds possible for a particular atom is determined
by the number of valence electrons. For N
N' valence electrons, an atom can
covalently bond with at most 8-N′ other atoms.
Examples:
• Cl atom has valence electron structure of 3s23p5
• C and Si have 2s22p2 and 3s23p2 structures, respectively.
• f ≤ 0.5
0 5 (small EN) metallic-nonmetallic
metallic nonmetallic elements and in crystals with
nonmetallic elements.
• Bonds are directional in nature: they exist only in the direction between
atoms that
h participate
i i
in
i electron
l
sharing.
h i
• Covalently bonded materials are generally less dense than ionically or
metallicallyy bonded ones (non-directional);
(
); when bonds are directional,, the
atoms cannot pack together in as dense a manner, thus yielding a lower
mass density.
Prof. M.L. Weaver
Examples of Covalent Bonding
H2
H
2.1
Li
1.0
Be
1.5
Na
0.9
Mg
1.2
K
0.8
Ca
1.0
Rb
0.8
Sr
1.0
Cs
0.7
Ba
0.9
Fr
0.7
Ra
0.9
•
•
•
•
column
n IVA
H2O
C(diamond)
SiC
F2
He
O
2.0
C
2.5
Si
1.8
Ti
1.5
Cr
1.6
Fe
1.8
Ni
1.8
Zn
1.8
Ga
1.6
Ge
1.8
As
2.0
Sn
1.8
Pb
1.8
F
4.0
Ne
-
Cl
3.0
Ar
-
Br
2.8
Kr
-
I
2.5
Xe
-
At
2.2
Rn
-
Cl2
G A
GaAs
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is
adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright
1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
Molecules with nonmetals, e.g. Cl2, F2, O2
Molecules with metals and nonmetals
Elemental solids (RHS of Periodic Table)
Compound solids (about column IVA)
Chapter 2 -
Simple Bonding Models – Covalent (continued)
There is a covalently bonded path
between any two atoms.
The molecular solid has covalent
bonds (dark lines) only within
individual molecules. Thus, there is
no covalently bonded path between
the atom labeled 1 and the atom
labeled 2; the molecules are bonded
to one another only by weak
secondary forces.
Covalently bonded 33-D
D network such as Si,
SiC, BN, etc.
•All atoms are linked by covalent bonds, i.e.,
there is a covalently bonded path between any
2 atoms
t
in
i the
th solid.
lid
Molecular solids or polymeric solids such as
crystalline materials C60, H2O, and
macromolecular solids polyethylene.
•Atoms within each molecule are linked by
covalent
l bonds,
b d but
b t the
th molecules
l l that
th t make
k up
the crystal are held together only by the
weak interactions known collectively as intermolecular forces or secondary bonds (including van
), dipolar,
p
, and hydrogen
y g bond).
)
der Waals ((VDW),
•In such solids, not all atoms are connected by a path of strong covalent bonds.
•Rule of Thumb: if more than two thirds of the components in a covalently bonded compound are
H C
H,
C, O
O, N
N, or a halogen
halogen, then it is likely to be a molecular solid.
solid
•However, diamond is a noteworthy example illustrating that this guideline should be applied
with caution.
Prof. M.L. Weaver
Covalent Bonding Model (continued)
•Simple
i l model
d l assumes that
h electrons
l
are shared
h d
between atoms and that electron charge density
accumulates between relatively positive atomic cores.
•Defining characteristic of a covalent bond is the
existence of a local maximum in the valence electron
density in the regions between the atomic cores. For
example, experimentally measured charged density in
Si is shown:
•The p
peak in electron densityy at the midpoint
p
connecting the two Si nuclei is signature of the
covalent bond.
•Concentrating the valence electrons in the spaces
between the atomic cores is clearly distinct from the
ionic bonding model, where the valence electrons are
centered on the anion positions, and the metallic
bonding model where the valence electrons are
uniformly distributed in the free electron sea.
Prof. M.L. Weaver
Fig. Valence electron density map in the {110} plane of Si. Contours are at 0.1 e/Å3. The shape of the peaks are theoretically predicted and also found in many III‐V
predicted and also found in many III
V semiconductors, e.g. GaAs.
Ionic bond – metal +
donates
electrons
nonmetal
accepts
electrons
Dissimilar electronegati
electronegativities
ities
eex:: MgO
gO
Mgg 1ss2 2ss2 2pp6 3s2
[Ne] 3s2
Mg2+ 1s2 2s2 2p6
[Ne] O
1ss2 2ss2 2pp4
O2‐ 1s2 2s2 2p6
[Ne] 91
Prof. M.L. Weaver
Ionic Bonding
• Occurs between + and ‐ ions.
• Requires electron transfer.
• Large difference in electronegativity required.
L
diff
i l t
ti it
i d
• Example: NaCl
Na (metal) unstable
Cl (nonmetal) unstable
electron Na (cation) Na
(cation)
stable
-
+
Coulombic
Attraction
Cl (anion) Cl
( i )
stable
92
Prof. M.L. Weaver
Ionic Bondingg
• Energy – minimum energy most stable
– Energy balance of attractive and repulsive terms
EN = EA + ER = 
A
r

B
rn
Repulsive energy ER
Interatomic separation r
Net energy EN
Net energy E
Adapted from Fig. 2.8(b), Callister & Rethwisch 8e.
Attractive energy EA
93
Prof. M.L. Weaver
Review: Ionic Bonding Model
•Ionic
I i – charge
h
i transferred
is
t
f
d from
f
th
the more metallic
t lli (low
(l EN) atom
t
to
t the
th non-metallic
t lli (high
(hi h
EN) atom forming oppositely charged species, the cation (+) and anion (-).
•The electrostatic interaction between the two ions, F12, forms the bond, and increases with
increasingg charge
g ((e)) and decreases with increasingg separation,
p
, r12, accordingg to Coulomb’s Law:
FA  
k o Z1eZ 2 e
r122
ko  1
4
Na (metal)
unstable
Cl (nonmetal)
unstable
•The attractive bonding forces are
electron
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.
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.
8
EN (net) potential energy is sum of EA + ER or the net potential energy between 2 adjacent ions.
Prof. M.L. Weaver
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 directions.
• Ionic bonding occurs
when f >0.5;
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?
Prof. M.L. Weaver
Relationship between Melting Point and
Elastic Modulus and Lattice Energy (Force)
13.3. The melting points of AB ionic crystals increase with z2/d.
13.4. The correlation between z2/d and the elastic modulus C44, for
various AB compounds
p
with a NaCl structure. Data from J.J.
Gilman, Progress in Ceramic Science 1 (1961) 146-194.
From Materials Science – an Intermediate Text by William F. Hosford Prof. M.L. Weaver
Examples of Ionic Bonding
• Predominant bonding in Ceramics
H
2.1
Li
10
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Fr
0.7
NaCl
M O
MgO
CaF2
CsCl
Be
15
1.5
O
F
35 4
3.5
4.0
0
Cl
3.0
Mg
1.2
Ca
1.0
Sr
1.0
Ti
1.5
Cr
1.6
Ba
0.9
Fe
1.8
Ni
1.8
Zn
1.8
As
2.0
Br
2.8
I
2.5
At
2.2
He
Ne
Ar
Kr
Xe
Rn
-
Ra
0.9
Give up electrons
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.
Chapter 2 -
Take Ionic Bonding Model a Step Further
pp y it to Crystal
y
Structures
and Apply
•Compute the total electrostatic contribution to the lattice energy, E. Sum both the attractive and
repulsive interactions between all of the ions of nearest neighbor distance (ro):
where M is the Madelungg constant,, which is a relationship
p of the distance of
ke 2
EA   M ro the ions from one another due to a specific type of crystal. It depends on the
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
structures, it is common to use a reduced Madelung constant,
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
ke 2 ( n1  n2 ) Z1 Z 2
constant:
EA  
2 ro
(3)
•1.25≤
•1
25≤ ≤1.76,
≤1 76  generally increases with the coordination number of the structure,
structure e.g.
eg
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.
We still need to include the repulsive energy contribution, we will return to this later since we
need to discuss the Lennard-Jones portion of the energy.
Prof. M.L. Weaver
Metallic Bonds
 Valence atoms in electrons behave as a delocalized sea of electrons
 The behavior, illustrated in the picture on the right, the picture on the right
allows for high conductivity
 A slightly more detailed explanation can be found on the next page.
p g
Electron Sea
Metallic Bonding Model
•Metallic - Metallic materials have one,, two,, or at most
three valence electrons.
•With this scheme, these electrons are not bound to any
pparticular atom in the solid and are more or less free to drift
throughout the entire metal sharing electrons.
•The remaining non-valence electrons and atomic nuclei
g equal
q
form ion cores,, which ppossess a net ppositive charge
in magnitude to total valence electron charge per atom.
•The ion cores arranged periodically are shielded from one
g
together
g
by
y the sea of valence
another,, and also "glued"
(free) electrons or electron clouds.
•In other words, the free electrons shield the positively
g ion cores from mutuallyy repulsive
p
electrostatic
charged
forces, which they would otherwise exert upon one other,
thus metallic bond is non-directional.
g number of freelyy movingg electrons,, metals are
•Due to large
good thermal (conduction of heat by free electrons) and
electrical conductors.
Prof. M.L. Weaver
METALLIC