# Surface density diamond structure [1 1 1]

• Ulumab
In summary, the surface density of the silicon diamond structure in the [1 0 0] and [1 1 0] planes is 2/a^2 and 4/sqrt(2)*a^2 respectively. For the [1 1 1] plane, the surface density is 2/(sqrt(3)/2*a^2), but the hint provided in the description can be ignored if one is familiar with the structure of the diamond lattice.
Ulumab

## 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.

## 1. What is the surface density of a diamond with a [1 1 1] structure?

The surface density of a diamond with a [1 1 1] structure is approximately 4.07 x 10^14 atoms/cm^2.

## 2. How does the surface density of a diamond with a [1 1 1] structure compare to other diamond structures?

The [1 1 1] diamond structure has the highest surface density among all diamond structures.

## 3. What is the significance of the [1 1 1] diamond structure?

The [1 1 1] diamond structure is considered the most stable and strongest crystal structure, making it ideal for industrial and technological applications.

## 4. How is the surface density of a diamond with a [1 1 1] structure calculated?

The surface density of a diamond with a [1 1 1] structure is calculated by dividing the number of atoms in one layer of the structure by the area of that layer.

## 5. Can the surface density of a diamond with a [1 1 1] structure vary?

Yes, the surface density of a diamond with a [1 1 1] structure can vary depending on factors such as impurities, defects, and temperature.

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