Crystalline Structure

Crystalline materials...

Noncrystalline materials...

crystalline SiO2

noncrystalline SiO2 Amorphous = Noncrystalline

Si Oxygen

random packing

regular packing

Packing, energy, and density

7 crystal systems

14 crystal lattices

Unit cell

lattice parameters

Unit Cell, Crystal Systems, Crystal Lattices

The 7 crystal systems

14 Crystal (Bravais) lattices: arrangement of atoms/molecules

within a unit cell

(1) Coordination # = ? (# nearest neighbors)

Simple cubic structure

(2) Number of lattice points in a cubic unit cell?

(3) What are the close-packed directions?

Atoms/unit cell

APF for a simple cubic structure = ?

Atomic packing factor

Rare due to poor packing (only Po has this structure)

(1) Coordination # ?

(2) Close-packed directions)?

--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

(3) atoms/unit cell?

APF for a face-centered cubic structure = ?

Atomic Packing Factor: FCC

maximum achievable APF

a

2 a

--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

Body Centered Cubic Structure (BCC)

BCC

(1) Coordination # = ?

(2) Close-packed directions)? (3) ? atoms/unit cell

aR

APF for a body-centered cubic structure = ?

BCC

Coordination # = 12

ABAB... Stacking Sequence

APF = 0.74

3D Projection 2D Projection

Hexagonal Close-Packed Structure

N: 6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

c/a = 1.633

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

HCP

Example: theoretical density of copper

crystal structure = FCC: atomic weight = 63.55 g/mol (1 amu = 1 g/mol) atomic radius R = 0.128 nm (1 nm = 10 cm) -7

Theoretical density

s

(g

/cm

3 )

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers Polymers

1

2

2 0 30

10

3 4 5

0.3 0.4 0.5

Magnesium

Aluminum

Steels

Titanium

Cu,Ni Tin, Zinc

Silver, Mo

Tantalum Gold, W Platinum

G raphite Silicon Glass - soda Concrete Si nitride Diamond Al oxide Zirconia

H DPE, PS PP, LDPE PC

PTFE

PET PVC Silicone

Wood

AFRE * CFRE * GFRE* Glass fibers Carbon fibers A ramid fibers

Density of material classes

Polymorphism Example: carbon

diamond graphite Fullerene (bucky ball)

Carbon nanotube