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Transcript of crystal
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crystal amorphous
4. STRUCTURE OF AMORPHOUS SOLIDS
a) A ; b) A2B3
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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.
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Radial Distribution Function J(r) = 4 r 2 (r)
RDF
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RDF J (r) = 4 r 2 (r)
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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
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Amorphous Morphology: Continuous Random Network.
crystals amorphous
Continuous Random Network (Zachariasen, 1932)
a) A ; b) A2B3
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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
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Review of crystalline close packing.
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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 .
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Amorphous Morphology: Random Close Packing
There is a limited number of local structures.
The volume occupancy is 64%
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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 !!!
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Basic geometry for diffraction experiments:
k = (4 / ) sen
I (k)
= h c / E
= h / (2·m·E)1/2
DIFFRACTION EXPERIMENTS
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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),(
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