Surface density diamond structure [1 1 1]

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SUMMARY

The discussion focuses on calculating the surface density of the Silicon diamond structure in the [1 0 0], [1 1 0], and [1 1 1] planes, using a lattice constant of a = 5.431 Å. The calculated surface densities are 2/a² for the [1 0 0] plane, 4/sqrt(2)*a² for the [1 1 0] plane, and 2/(sqrt(3)/2*a²) for the [1 1 1] plane. The hint regarding the visualization of the diamond lattice as two interpenetrating FCC lattices is crucial for understanding the [1 1 1] plane but can be bypassed by those familiar with the structure.

PREREQUISITES
  • Understanding of planar density calculations
  • Familiarity with the diamond crystal structure
  • Knowledge of face-centered cubic (FCC) lattices
  • Basic proficiency in crystallography concepts
NEXT STEPS
  • Study the derivation of surface density for different crystal planes
  • Learn about the properties of diamond cubic structures
  • Explore the implications of interpenetrating lattices in crystallography
  • Investigate the significance of lattice constants in material properties
USEFUL FOR

Students and professionals in materials science, crystallography, and solid-state physics who are focused on understanding the properties of silicon and its crystal structures.

Ulumab
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Homework Statement


Calculate the surface density (planar density) of the Silicon diamond structure in the [1 0 0],[1 1 0],[1 1 1] planes.
Given a = 5.431 A (latice constant)

Hint: For the (111) plane, it should help you to think of the diamond lattice as two interpenetrating FCC lattices.2. The attempt at a solution
I managed to solve [1 0 0] and [1 1 0](2/a^2 and 4/sqrt(2)*a^2) I have also got a result for [1 1 1](2/(sqrt(3)/2*a^2)) but I completely ignored the hint in the description.
 
Ulumab said:
2. The attempt at a solution
I managed to solve [1 0 0] and [1 1 0](2/a^2 and 4/sqrt(2)*a^2) I have also got a result for [1 1 1](2/(sqrt(3)/2*a^2)) but I completely ignored the hint in the description.
The hint helps to imagine the diamond structure. You do not need it if you know how it looks like.
 

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