Planar Density of (0,-1,1,0) plane in HCP

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SUMMARY

The planar density of the (0,-1,1,0) plane in hexagonal close-packed (HCP) structures can be calculated using the atomic radius (r) and the lattice parameters (a and c). The relationship between these parameters is defined by the equation a = 2r, while the determination of c requires analyzing the arrangement of interior atoms within the hexagonal cell. The planar density is defined as the number of atoms per unit area on the specified plane, necessitating a clear understanding of how many atoms intersect this plane.

PREREQUISITES
  • Understanding of hexagonal close-packed (HCP) crystal structures
  • Knowledge of lattice parameters a and c
  • Familiarity with atomic radius and its significance in crystallography
  • Basic concepts of planar density calculations
NEXT STEPS
  • Research the calculation methods for planar density in HCP structures
  • Study the relationship between lattice parameters and atomic radius in crystalline materials
  • Explore the geometric arrangement of atoms in hexagonal cells
  • Learn about the theoretical c/a ratio in HCP configurations
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Materials scientists, crystallographers, and students studying solid-state physics who are interested in understanding the properties of hexagonal close-packed structures and their atomic arrangements.

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How can I calculate the planar density of the (0,-1,1,0) plane in HCP? (in terms of atomic radius r)
 
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What is the definition of planar density?

Knowing the c and a lattice parameters, how would one calculated the area of the (0,-1,1,0) plane?

How do the c and a lattice parameters relate to the atomic radius?
 
Astronuc said:
What is the definition of planar density?

Knowing the c and a lattice parameters, how would one calculated the area of the (0,-1,1,0) plane?

How do the c and a lattice parameters relate to the atomic radius?

Finding "a" is easy it's equal 2r but finding "c" is more complicated, also determine how many atoms that plane crosses is complicated as well.
 
One should be able to find c as a function of r by looking at the packing of the 3 interior atoms between the top and bottom planes of the hexagonal cell.

Ostensibly, there is a theoretical c/a.
 

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