1. coordination numbers
A coordination number CN =6 is widely come across in ionic compounds. Silicon in SiO2 on the other hand has a CN = 4 because Si4+ ion is too small to accommodate 6 oxygen ions. r/R for silicon is approximately 0.3.
To calculate r/R ratio for a four-fold coordination (i.e. when CN = 4)
The larger atoms are located at the four corners of a regular tetrahedron. The small atoms sits in the body centre of the tetrahedron and touches each of the four atoms at the corners. The distance between any two corner atoms = 2R
See below

2. The four corner atoms may be visualized as occupying the corners of a cube

3. Hence, it may be written that the body diagonal
d = 2R + 2r, also d = a √3
But a √2 = 2R or a = 2R/√2
2(R+r) = a √3 = 2R/√2
Or R+r/R = √3/2
Hence, 1 + r/R = 1.224
And r/R = 0.224

4. Coordination of 12:
all the atoms are the same size,
each atom have 12 immediate neighbors.
Solid circles: four neighbors in the same plane as the central atom. Dashed circles: four neighbors above, and four neighbors below. Each neighbor also will be coordinated with 12 neighbors.

5. Metallic Bonding
Unlike ionic and covalent solids where the valence electrons are localized
The nature of bonding is different from both types.
like the bi electrons in benzene valence electrons are delocalized, it can easily move under the effect of electric field.
it is best described as positive ions surrounded by a sea of delocalized electrons.
CN can be >12 it can exceed 100

8. Properties and atomic bonding
Density: determined at at. Wt., at. Radius and the coordination number (Sig)
Melting & boiling: depth of the energy well = bond energy
Hardness: the height of the total force curve
Elasticity: the slope of the sum curve, where the net force is zero. It s also related to the bond energy.
Thermal expansion: inversely related to the melting temperature. See Figure

12. Conductivity of Metals
Electrical conductivity depends on the nature of atomic bons.
Ionic and covalent materials are poor conductors in the solid state.
In metals the delocalized electrons can free move along potential gradient.
Thermal conductivity is high in metallic bonds, due to the delocalized electrons are efficient carriers of thermal as well as electrical energy.