crystal amorphous

4. STRUCTURE OF AMORPHOUS SOLIDS

a) A ; b) A2B3

coordination number z gives some hints:

• A low coordination number (z = 2, 3, 4) provides evidence for a dominant role of covalent bonding (SiO2, B2O3…)

• More “closed-packed” structures are symptomatic of non-directional forces (ionic, van der Waals, metallic bonding…): z(NaCl)=6, z(Ca)=8, z(F)=4 …

• fcc or hcp structures are typical of metallic crystals AB forming a close-packed lattice with z=12, the extreme of maximum occupation.

Radial Distribution Function J(r) = 4 r 2 (r)

RDF

RDF J (r) = 4 r 2 (r)

3 main kinds of atomic-scale structure (models) of amorphous solids:

Continuous Random Network covalent glasses

Random Close Packing simple metallic glasses

Random Coil Model polymeric organic glasses

Amorphous Morphology: Continuous Random Network.

crystals amorphous

Continuous Random Network (Zachariasen, 1932)

a) A ; b) A2B3

Amorphous Morphology.Amorphous Morphology: Continuous Random Network.

- coordination numberCOMMON: - (approx.) constant bond lengths

- ideal structures (no dangling bonds…)

DIFFERENT: - significant spread in bond angles- long-range order is absent

Review of crystalline close packing.

Review of crystalline close packing.

74.018)2/4(

)34

(4)( Factor Packing

24r / cells,unit FCCfor Since,

)34

)(atoms/cell (4 Factor Packing

3

3

0

30

3

r

r

r

aa

Calculate the packing factor for the FCC cell:

In a FCC cell, there are four lattice points per cell; if there is one atom per lattice point, there are also four atoms per cell. The volume of one atom is 4πr3/3 and the volume of the unit cell is .

Amorphous Morphology: Random Close Packing

There is a limited number of local structures.

The volume occupancy is 64%

Amorphous Morphology: Random Coil Model

RCM is the most satisfactory model for polymers, based upon ideas developed by Flory (1949, …, 1975).

Each individual chain is regarded as adopting a RC configuration (describable as a 3-D random walk).

The glass consists of interpenetrating random coils, which are substantially intermeshed – like spaghetti !!!

Basic geometry for diffraction experiments:

k = (4 / ) sen

I (k)

= h c / E

= h / (2·m·E)1/2

DIFFRACTION EXPERIMENTS

Neutron scattering

It allows to take data to higher values of k (using smaller wavelengths) and hence reduce “termination errors” in the Fourier transform.

Neutrons emerge from a nuclear reactor pile with 0.11 Å

Scattering events:

Energy transfer:

Momentum transfer:

EE 0

kkQ

0

Scattering function:

dtrdetrGQS trQi

0 0

)(),(2

1),(