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

• osc_wildly
In summary, to calculate the surface atom density of an fcc(111) surface expressed in terms of a, the lengths can be found using the quadratic formula and the angles can be determined as 60 degrees. The height of the triangle can then be found using geometry and the area can be calculated. From there, the amount of atoms enclosed by the plane can be determined to find the surface atom density.
osc_wildly
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!

bernardyves sosa
vincent_vega said:
nevermind

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.

## 1. What is the formula for calculating the surface atom density of an fcc(111) surface?

The formula for calculating the surface atom density of an fcc(111) surface is ρ = n/(√3a2), where ρ is the surface atom density, n is the number of atoms in the surface unit cell, and a is the lattice constant.

## 2. How do I determine the number of atoms in the surface unit cell?

The number of atoms in the surface unit cell can be determined by counting the number of atoms present in the unit cell in the (111) plane. For fcc structures, there are 4 atoms in the unit cell in the (111) plane.

## 3. What is the lattice constant for an fcc(111) surface?

The lattice constant for an fcc(111) surface is equal to the distance between the (111) planes, which can be calculated using the equation a = d/(√3/2), where a is the lattice constant and d is the interplanar spacing.

## 4. Can the surface atom density of an fcc(111) surface change?

Yes, the surface atom density of an fcc(111) surface can change depending on external factors such as temperature, pressure, and surface modifications. However, the surface atom density will remain constant as long as the crystal structure and lattice constant remain unchanged.

## 5. How is the surface atom density of an fcc(111) surface related to its surface energy?

The surface atom density of an fcc(111) surface is directly proportional to its surface energy. This means that as the surface atom density increases, so does the surface energy. This relationship is known as the Gibbs-Thomson equation and is important in understanding the behavior of materials at surfaces and interfaces.

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