Lecture 56 The Solid State I

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Lecture 56 - The Solid State I
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Look around...

• How many gases are you familiar with?
• Liquids?
• Solids?
• Most familiar objects are solids!

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The Solid State

• - relatively hard
• - may be brittle
• - may conduct electricity or heat
• - particles close together
• - little relative movement of particles

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Solids may be...

• crystalline - long range 3D order in arrangement
  of particles
• amorphous - random arrangement of particles

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Particles in solids may be...

• 1. separate ions (Na, Cl-)
• 2. separate molecules (H2O, CO2)
• 3. covalently bound networks of atoms (C,
  SiO2) or molecules
• 4. metal atoms (Cu, Ag, Fe)

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Intermolecular Forces in Solids

• Solid Force Properties
• Ionic ion-ion hard, brittle, high
  Tm
• Molecular dispersion, soft, low Tm,
• H-bond, non-conducting
• dipole-dipole
• Covalent covalent bonds hard, high Tm,
• network non-conducting
• Metallic metallic bonds conducting

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X-ray Diffraction
x-rays in
to detector
q
d
d sin(q)
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X-ray Diffraction

destructive interference
constructive interference

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X-ray Diffraction

• constructive interference only when

nl
d
2 sin (q)
n an integer
(The Bragg equation)
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The Unit Cell...

• the smallest repeating unit in a crystal
• repeats in x, y or z directions

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The Crystal Lattice
The Unit Cell
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The Crystal Lattice
or
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The Unit Cell...

• the smallest repeating unit in a crystal
• repeats in x, y or z directions
• 14 known geometries
• 3 are cubic

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The Cubic Crystal Lattice
Lattice Points (atoms, ions or molecules)
Unit Cell
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Simple Cubic Lattices
simple cubic
8 x 1/8 1 atom/unit cell
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Simple Cubic Lattices
unit cell volume (2r)3 8r3
r
space used 8 (1/8) (4/3pr3) 4/3pr3
space used
4/3pr3

x 100 52
8r3
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Coordination Number
6 for simple cubic structures
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for example,

• Po metal crystallizes in a simple cubic
  structure, r 9.4 g/cm3
• Find
• 1. The radius of a Po atom
• 2. The length of the unit cell (d)

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for example,

• Strategy
• 1. Find mass of one Po atom
• 2. Find volume of unit cell
• 3. Find r
• 4. Find length of unit cell

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for example,
210.05 g/mol
1. mass
6.022 x 1023 atom/mol
3.49 x 10-22 g/atom
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for example,

• 2. unit cell (8 x 1/8 atoms) 1 atom

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for example,

• 2. unit cell (8 x 1/8 atoms) 1 atom

mass
unit cell volume
density
3.49 x 10-22 g/atom x 1 atom

9.4 g cm-3
3.71 x 10-23 cm3
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for example,

• 3. unit cell volume 8r3

8r3 3.71 x 10-23 cm3
or, r 1.67 x 10-8 cm
1.67 x 10-10 m
167 x 10-12 m
167 pm
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for example,

• 4. Unit cell length 2r

334 pm
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Body Centred Cubic Lattices
(8 x 1/8) 1 2 atoms/unit cell
body centered cubic
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Body Centred Cubic Lattices

• Coordination number 8
• Space used 68

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for example,

• U crystallizes in a body centred cubic lattice
  with an edge d 346 pm
• Find the density of U

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for example,
1. volume of unit cell d3
(3.46 x 10-8 cm)3
4.15 x 10-23 cm3
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for example,
2. unit cell 2 atoms
mass of unit cell
238.0 g/mol
2 atoms x
6.02 x 1023 atoms/mol
7.90 x 10-22 g
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for example,
mass
3. density
volume
7.90 x 10-22 g

4.15 x 10-23 cm3
19.04 g/cm3
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Face Centred Cubic Lattices
8 x 1/8 6 x 1/2 4 atoms/unit cell
face centered cubic
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Face Centred Cubic Lattices

• coordination number 12
• space used 74

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Hexagonal Lattice
Top View
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Hexagonal Lattice

• coordination number 12
• space used 74

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Closest Packing...

• face centred cubic
• and hexagonal unit cells