Material Engineering - Lecture - structures, Lecture notes of Material Engineering

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Structures of Metals & Ceramics

Structures

• (^) The properties of some materials are

directly related to their crystal

structures.

• (^) Significant property differences exist

between crystalline and noncrystalline

materials having the same composition.

• atoms pack in periodic, 3D arrays

Crystalline materials...

-metals

-many ceramics

-some polymers

• atoms have no periodic packing

Noncrystalline materials...

-complex structures

-rapid cooling

crystalline SiO 2

"Amorphous" = Noncrystalline^ noncrystalline SiO^2

Materials and Packing

Si Oxygen

• typical of:
  • occurs for:

Metallic Crystal Structures

• (^) How can we stack metal atoms to minimize

empty space?

2-dimensions

vs.

• Rare due to low packing density (only Po has this structure)
• Close-packed directions are cube edges.
  • Coordination # = 6

(# nearest neighbors)

Simple Cubic Structure (SC)

• APF for a simple cubic structure = 0.

APF =

a

(0.5 a )

atoms

unit cell

atom

volume

unit cell

volume

Atomic Packing Factor (APF)

APF =

Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

close-packed directions

a

R =0.5 a

contains 8 x 1/8 =

1 atom/unit cell

Atomic Packing Factor: BCC

a

APF =

 (^) ( 3 a /4)

atoms

unit cell atom

volume

a

unit cell

volume

length = 4 R =

Close-packed directions:

3 a

• APF for a body-centered cubic structure = 0.

a

R

2 a

3^ a

• Coordination # = 12
  • Atoms touch each other along face diagonals.

--Note: All atoms are identical; the face-centered atoms are shaded

differently only for ease of viewing.

Face Centered Cubic Structure (FCC)

ex: Al, Cu, Au, Pb, Ni, Pt, Ag

4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/

• APF for a face-centered cubic structure = 0.

Atomic Packing Factor: FCC

maximum achievable APF

APF =

( 2 a /4)

atoms

unit cell atom

volume

a

unit cell

volume

Close-packed directions:

length = 4 R = 2 a

Unit cell contains:

6 x 1/2 + 8 x 1/

= 4 atoms/unit cell a

2 a

Hexagonal Close-Packed Structure

(HCP – another view)

ABAB... Stacking Sequence

X-Ray Diffraction

Theoretical Density, 

where n = number of atoms/unit cell

A = atomic weight

V

C

= Volume of unit cell = a

3 for cubic

N

A

= Avogadro’s number

= 6.022 x 10

23 atoms/mol

Density =  =

V

C

N

A

n A  =

Total Volume of Unit Cell

Massof AtomsinUnit Cell