Bonding in Solids

Bonding in Solids
•
Bonding in Solids
There are four types of solid:
1. Molecular (formed from molecules) - usually soft
with low melting points and poor conductivity.
2. Covalent network - very hard with very high
melting points and poor conductivity.
3. Ionic (formed form ions) - hard, brittle, high melting
points and poor conductivity.
4. Metallic (formed from metal atoms) - soft or hard,
high melting points, good conductivity, malleable
and ductile.
– NB: A solid with only one type of atom is also called
‘atomic’
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16a–1
16a–2
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Bonding in Solids
Bonding in Solids
Covalent Network Solids
Covalent Network Solids
• Intermolecular forces: dipole-dipole, London dispersion and Hbonds.
• Atoms held together in large networks.
• Examples: diamond, graphite, quartz (SiO2), silicon carbide (SiC),
and boron nitride (BN).
• In diamond:
– each C atom has a coordination number of 4;
– each C atom is tetrahedral;
– there is a three-dimensional array of atoms.
– Diamond is hard, and has a high melting point (3550 C).
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16a–3
16a–4
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Diamond
-Hard Structure
- Tetrahedral atomic
arrangement
What hybrid state
do you think the
carbon has?
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16a–5
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16a–6
1
Bonding in Solids
Covalent Network Solids
• In graphite
– each C atom is arranged in a planar hexagonal ring;
– layers of interconnected rings are placed on top of
each other;
– the distance between C atoms is close to benzene (1.42
Å vs. 1.395 Å in benzene);
– the distance between layers is large (3.41 Å);
– electrons move in delocalized orbitals (good
conductor).
16a–7
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Fullerene-C60
•Closely Related to
Graphite Structure
Graphite
- Form planar sheets
- actuallyy more stable than
diamond
•Both Six-membered and
Five-membered Rings of
Carbon are Found in the
Fullerenes
What hybrid state do you
think the carbon has?
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16a–9
Artists carbon nanotubes, multiwalled
MWCNT
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16a–10
Forming Carbon Nanotubes
16a–11
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16a–12
2
Real carbon nanotubes
Examples of Three Types of Crystalline Solids
16a–13
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16a–14
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16a–16
Cubic Unit Cells
There are 7 basic crystal systems, but we are
only concerned with CUBIC.
All sides
equal length
All angles
are 90 degrees
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16a–15
X-rays scattered from two different
atoms may reinforce (constructive interference) or
cancel (destructive interference) one another.
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16a–17
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3
Figure 16.11: Reflection of X rays of
wavelength
Reflection of X rays: Bragg equation
n λ = 2 d sin θ
Father and son Bragg – Nobel prize 1915
16a–19
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Crystal Lattices
16a–20
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Cubic Unit Cells of Metals
Simple
cubic (SC)
• Regular 33--D arrangements of equivalent LATTICE
POINTS in space.
• Lattice points define UNIT CELLS
– smallest repeating internal unit that has the symmetry
characteristic of the solid.
1 atom/unit cell
BodyBodycentered
cubic (BCC)
2 atoms/unit cell
FaceFacecentered
cubic ((FCC))
4 atoms/unit cell
16a–21
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16a–22
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Atom Sharing
at Cube Faces and Corners
Atoms in unit cell
1
½
¼
Atom shared in corner
--> 1/8 inside each unit cell
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Atom shared in face
--> 1/2 inside each unit cell
1/8
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4
Number of Atoms per Unit Cell
Unit Cell Type
SC
BCC
FCC
Simple Ionic Compounds
Net Number Atoms
1
2
4
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16a–25
Two Views of CsCl Unit Cell
16a–26
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Simple Ionic Compounds
Either arrangement leads to formula of 1 Cs+ and 1 Cl- per unit cell
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CsCl has a SC lattice of
Cs+ ions with Cl- in the
center.
1 unit cell has 1 Cl- ion
plus
(8 corners)(1/8 Cs+ per
corner)
= 1 net Cs+ ion.
Salts with formula
MX can have SC
structure
t t
— but
b t
not salts with
formula MX2 or
M2 X
16a–27
16a–28
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NaCl Construction
FCC lattice of Cl- with
Na+ in holes
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16a–29
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Na+ in
octahedral
holes
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5
The Sodium Chloride Lattice
Your eyes “see” 14 Cl- ions and 13 Na+
ions in the figure
Many common salts have FCC arrangements of anions with
cations in OCTAHEDRAL HOLES — e.g., salts such as CA
= NaCl
• FCC lattice of anions ---->
----> 4 A-/unit cell
• C+ in octahedral holes ----->
> 1 C+ at center
+
+ [12 edges • 1/4 C per edge]
= 4 C+ per unit cell
Ion Count for the Unit Cell: 4 Na+ and 4 Cl- Na4Cl4 = NaCl
Can you see how this formula comes from the unit cell?
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16a–32
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Bonding in Solids
Comparing NaCl and CsCl
Ionic Solids
– NaCl Structure
• Even though their formulas have one
cation and one anion, the lattices of CsCl
and NaCl are different.
• The different lattices arise from the fact
that a Cs+ ion is much larger than a Na+
ion.
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The CsCl and NaCl Structures
•
•
•
•
Each ion has a coordination number of 6.
Face-centered cubic lattice.
Cation to anion ratio is 1:1.
Examples: LiF, KCl, AgCl and CaO.
– CsCl Structure
• Cs+ has a coordination number of 8.
• Different from the NaCl structure (Cs+ is larger than
Na+).
• Cation to anion ratio is 1:1.
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fcc
Volume :
Density :
R 8
3
4 x mass
R 8
3
4
 R3
3
 0.74
3
R 8
4x
fraction :
CsCl
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

NaCl
16a–35
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16a–36
6
bcc
sc
 4R 
Volume : 

 3
D i :
Density
3
Volume :
2 x mass
ass
 4R 


 3
Density :
3
16a–37
Figure 16.13: The closet packing
arrangement of uniform spheres.
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3
1 x mass
 2R 
3
4
 R3
3
 0.524
3
 2R 
1x
4
2 x  R3
3
 0.68
fraction :
Volume
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 2R 
fraction :
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16a–38
Figure 16.14: When spheres are closest packed so that the spheres
in the third layer are directlly over those in the first layer (aba),
the unit cell is the hexagonal prism illustrated here in red.
16a–39
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16a–40
Figure 16.36:
The holes that
exist among
closest packed
uniform
spheres
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16a–41
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7
Figure 16.37: (a) The octahedral hole (shown in yellow)
lies at the center of six spheres that touch along the edge
(e) of the square.
Figure 16.37: (a) The octahedral hole (shown in yellow)
lies at the center of six spheres that touch along the edge
(e) of the square.
d = 2R√2
2r = 2R√2 – 2R
r = R(√2
(√ – 1))
= R(0.414)
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16a–43
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16a–44
(a) A simple cubic array with X- ions,
with an M+ ion in the center (in the cubic hole).
(b) The body diagonal b equals 2r + R
Figure 16.38:
(a) The
tetrahedral
hole
((b)) The body
y
diagonal b
equals r + R
r = R(0.225)
r = R(0.732)
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16a–45
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16a–47
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