Zachariasen's rules for glass formation

Question 1

First rule

Answer 1

~ Polyhedra should consist of cations with 3-fold (triangular) or 4-fold (tetrahedral) coordination of anions (need SMALL cation!)

Question 2

Second rule

Answer 2

~ No anion links the central cations of more than two other polyhedra (free pivoting, need lots of oxygen and cations with high charge)

Question 3

Third rule

Answer 3

~ Polyhedra share only CORNERS, not faces or edges (cation with high charge)

Question 4

Fourth rule

Answer 4

~ At least 3/4 of polyhedra corner must link/bridge to other polyhedra
~ based on glass making experience, this can be relaxed to 2/4

Question 5

What glasses obey all four rules?

Answer 5

Cristobalite (SiO2), B2O3, P2O5, Sb2O3, As2O3, GeO2

Question 6

What characteristics are needed for rules 3 and 4?

Answer 6

~ cation with high charge and high covalent character

Question 7

What kind of bonds obey rule four?

Answer 7

Na+~O2- bonds are easily sheared in liquid state, tetrahedra easily shift and re-orient

Question 8

What equations govern rule four?

Answer 8

~ R: avg # of oxygens per network former
~ Z: # of oxygens
~ X: non-bridging oxygens
~ Y: bridging oxygens

~ X + Y = Z (plug in X and solve for X)
~ X + 1/2Y = R (plug in X from first eqn)