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

AI Thread Summary
To calculate the surface atom density of an fcc(111) surface in terms of the lattice parameter 'a', one must recognize that the fcc(111) plane forms a triangular arrangement of atoms. The lengths of the triangle's sides correspond to the diagonals, and since all angles are 60 degrees, geometry can be applied to determine the height of the triangle. By calculating the area of the triangle and determining how many atoms are enclosed within that area, the surface atom density can be derived. This method effectively utilizes both geometric principles and the properties of the fcc structure. Accurate calculations will yield the desired surface atom density for the fcc(111) surface.
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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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