crystalamorphous 4. STRUCTURE OF AMORPHOUS SOLIDS a) A ; b) A 2 B 3

coordination number z gives some hints: A low coordination number (z = 2, 3, 4) provides evidence for a dominant role of covalent bonding (SiO 2, B 2 O 3 …) 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

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. crystalsamorphous Continuous Random Network (Zachariasen, 1932) a) A ; b) A 2 B 3

Amorphous Morphology.Amorphous Morphology: Continuous Random Network. - coordination number COMMON:- (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.

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 4πr 3 /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  0.1  1 Å Scattering events: Energy transfer: Momentum transfer: Scattering function: