What does the ratio c/a mean in solid state phyiscs

[j-lee00]

What does the ratio c/a mean in solid state physics?

I have attached a table with a an example.

Cheers

 

[DrDu]

It stands for nothing special as long as you don't enlight us what a and c are abbreviations for.
Usually c is the elementary cell extension along the hexagonal axis and a is the dimension along the hexagons.

 

[kanato]

The ratio c/a for a hexagonal elemental system is interesting because there is an ideal c/a ratio where the distance between every atom is the same. If c/a deviates from that value then the distances between nearest neighbor atoms in the basal plane is different than the distances between nearest atoms between planes. The ideal value is something like 1.63; it is a nice exercise to derive it yourself.

 

[DrDu]

Or to say it differently, there is the hcp structure of ideal spheres which a definite ratio of a/c. However, for a general crystal with a hexagonal lattice, group theory does not put any restriction on that ratio.