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

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SUMMARY

The ratio c/a in solid state physics refers to the relationship between the hexagonal axis extension (c) and the dimension along the hexagons (a) in hexagonal crystal structures. An ideal c/a ratio of approximately 1.63 ensures uniform distances between atoms, maintaining consistent atomic spacing in both the basal plane and between planes. Deviations from this ideal ratio lead to variations in atomic distances, impacting the crystal's properties. Understanding this ratio is essential for analyzing hexagonal close-packed (hcp) structures and their behavior.

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  • Understanding of hexagonal crystal structures
  • Familiarity with solid state physics terminology
  • Basic knowledge of atomic spacing and lattice structures
  • Experience with group theory in crystallography
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  • Research the derivation of the ideal c/a ratio for hexagonal close-packed structures
  • Explore the implications of atomic spacing variations in solid state materials
  • Study group theory applications in crystallography
  • Investigate the properties of materials with varying c/a ratios
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Solid state physicists, materials scientists, and researchers studying crystal structures and their atomic arrangements will benefit from this discussion.

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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