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

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Discussion Overview

The discussion centers on the meaning and implications of the ratio c/a in solid state physics, particularly in relation to hexagonal crystal structures. Participants explore its significance in terms of atomic distances and structural characteristics.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the meaning of the ratio c/a without clarification on what a and c represent.
  • Another participant explains that c typically refers to the cell extension along the hexagonal axis, while a refers to the dimension along the hexagons.
  • A different viewpoint highlights that there exists an ideal c/a ratio for hexagonal systems, where atomic distances are uniform, suggesting an ideal value around 1.63.
  • Another participant notes that while the hcp structure has a specific c/a ratio, group theory does not impose restrictions on this ratio for general hexagonal lattices.

Areas of Agreement / Disagreement

Participants express differing views on the significance and implications of the c/a ratio, indicating that multiple competing perspectives exist without a clear consensus.

Contextual Notes

There are assumptions regarding the definitions of a and c that may not be universally understood, and the discussion does not resolve the implications of varying c/a ratios in different contexts.

j-lee00
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What does the ratio c/a mean in solid state physics?

I have attached a table with a an example.

Cheers
 

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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.
 
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.
 
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.
 

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