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

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Discussion Overview

The discussion revolves around calculating the planar density of the (0,-1,1,0) plane in hexagonal close-packed (HCP) structures, focusing on the relationship between lattice parameters and atomic radius.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the method to calculate the planar density in terms of atomic radius r.
  • Several participants seek clarification on the definition of planar density and how to calculate the area of the (0,-1,1,0) plane using the c and a lattice parameters.
  • There is a mention that while finding "a" is straightforward as it equals 2r, determining "c" is more complex, and the number of atoms the plane intersects is also complicated.
  • Another participant suggests that "c" can be expressed as a function of r by examining the packing of the three interior atoms between the top and bottom planes of the hexagonal cell, introducing the concept of a theoretical c/a ratio.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the calculation of the lattice parameters and their relationship to atomic radius, indicating that multiple viewpoints and uncertainties exist in the discussion.

Contextual Notes

Limitations include the complexity in determining the c lattice parameter and the number of atoms intersected by the plane, which are not fully resolved in the discussion.

Eliad_Ay
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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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