ME 381R Fall 2003

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ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid
Science and Technology Lecture
3 Microstructure of Solids
Dr. Li Shi Department of Mechanical Engineering
The University of Texas at Austin Austin, TX
78712 www.me.utexas.edu/lishi lishi_at_mail.utexas.
edu
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Outline

• Kinetic Theory
• Crystalline Structure of Solids
• Crystal Bonding
• Reading Kittel Ch1

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Heat Conduction in Gases

• Heat conducted by gas molecules. K is determined
  by inter-molecular collisions, and can be
  predicted using kinetic theory

Thermal Conductivity
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Heat Conduction in Solids

• Heat is conducted by electrons and phonons.
• k is determined by electron-electron,
  phonon-phonon, and electron-phonon collisions.

Hot
Hot
Cold
p
-
Cold

• Kinetic theory is valid for particles can
  electrons and
• crystal vibrations be considered particles?

• If so, what are C, v, ? for electrons and
  crystal vibrations?

• We will use the next 4 lectures to figure out C,
  v, ? and k of crystal vibrations, i.e. phonons.

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Crystal Structure

• The building blocks of these two are identical,
  but different crystal faces are developed

• Kittel pg. 2

• Cleaving a crystal of rocksalt

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Crystal Periodic Arrays of Atoms
a3
Translation Vectors
a2
a1, a2 ,a3
Atom
a1

• Primitive Cell
• Smallest building block for
• the crystal structure.
• Repetition of the primitive cell
• ? crystal structure

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Common Lattice Types

• There are 14 lattice types
• Most common types (Kittel Table 3)
• Cubic
• Li, Na, Al, K, Cr, Fe, Ir, Pt, Au
  etc.
• Hexagonal Closed Pack (HCP)
• Mg, Co, Zn, Y, Zr, etc.
• Diamond
• C, Si, Ge, Sn (only four)

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Three Cubic Lattices
1. Simple Cubic (SC)
a1 a2 a3 a1 ? a2 ? a3
Conventional Cell Primitive Cell
a3
a2
a1
Conventional Cell ? Primitive Cell
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Primitive Cell of BCC

• Kittel, p. 13

• Rhombohedron primitive cell

0.5?3a
109o28
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Primitive Cell of FCC

• Kittel, P. 13

• Angle between a1, a2, a3 60o

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Kittel p. 12
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Diamond Structure
C, Si, Ge, a-Sn

• Add 4 atoms to a FCC
• Tetrahedral bond arrangement
• Each atom has 4 nearest neighbors and
• 12 next nearest neighbors

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Hexagonal Close Packing (hcp)
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Crystal Structures of Elements
Kittel, pg. 23
Notice hcp vs. fcc in same column
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Index System for Crystal Planes (Miller Indices)
1) Find the intercepts on the axes in terms of
the lattice constants a1, a2, a3. The axes may
be those of a primitive or nonprimitive unit
cell. 2) Take the reciprocals of these numbers
and then reduce to three integers having the same
ratio, usually the smallest three integers. The
reulst enclosed in parethesis (hkl), is called
the index of the plane.
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Crystal Planes
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Types of Microstructures

• Single Crystalline
• Polycrystalline
• Amorphous

TEM images of nanobelts by Prof. Z. L. Wang
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Crystal Bonding

• van der Waals bond
• Ionic bond
• Hydrogen bond
• Metallic bond
• Covalence bond

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van der Waals bond

• Bonding energy
• 0.01 eV (weak)
• Compared to thermal
• vibration energy kBT
• 0.026 eV at T 300 K
• Examples inert gases

Ar
Ar
Ar -
Ar -
Dipole-dipole interaction
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Ionic Bond

• The electron of the Na atom is
• removed and attached to the Cl atom
• Bonding energy 1-10 eV (strong)

Cl-
Cl-
Na
Cl-
Na
Na
Cl-
Cl-
Na
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Hydrogen bond

• The electron of the H atom is
• pulled toward the other atom
• Ionic in nature
• Bonding energy kBT (weak)
• Examples DNA
• intermolecular bond between
• water and ice

F-
F-
H
HF2- molecule
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Metallic Bond
Positive ions in a sea of electrons
Na
Na
Electron sea
Na
Na
Na

• Bonding energy
• 1-10 eV (strong)

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H

H
H
H
Covalence bond
C
C

• Two atoms share a pair of electrons
• Bonding energy 1-10 eV (strong)
• Examples C, Ge, Si, H2

C
C
C
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Bonding Energy vs. Inter-atomic Distance
1-D Array of Spring Mass System