How to calculate the surface atom density of an fcc(111) surface?

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SUMMARY

The surface atom density of an fcc(111) surface can be calculated using geometric principles and the quadratic formula. The fcc(111) surface is triangular, with all angles measuring 60 degrees. By determining the height of the triangle and the area it encloses, one can accurately compute the number of atoms per unit area. This method builds on the calculations previously established for fcc(100) and fcc(110) surfaces.

PREREQUISITES
  • Understanding of face-centered cubic (fcc) crystal structures
  • Knowledge of geometric principles, particularly triangle properties
  • Familiarity with the quadratic formula
  • Basic concepts of surface atom density calculations
NEXT STEPS
  • Research the geometric properties of fcc crystal structures
  • Study the application of the quadratic formula in solid-state physics
  • Learn about surface atom density calculations for different crystal planes
  • Explore advanced topics in crystallography and material science
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Material scientists, crystallographers, and students studying solid-state physics who are interested in surface properties of crystalline materials.

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How do you calculate the surface atom density of an fcc(111) surface expressed in terms of a?

I've managed to do it for fcc(100) and fcc(110), but I can't seem to figure it out for fcc(111).

Any help would be greatly appreciated!
 
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vincent_vega said:
nevermind

Not very helpful...
 
well all of the lengths are going to be diagonals right? (since the plane is a triangle) just use the quadratic formula to the the lengths. Then since all the lengths are the same all the angles are 60 deg. so use geometry to find the height of the triangle. With that you can find the area. Then just find how much of the atoms are enclosed by the plane.
 

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