# Primitive unit cell (Diamond)

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• Porkaborg
In summary, the conversation discusses the construction of a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbon atoms. There are two variants of the unit cell, one occupying 1/4 of the conventional-cell volume and the other occupying 1/8 of the conventional-cell volume. Both versions are listed as primitive unit cells for diamond, but the difference in appearance is confusing. The conversation also mentions the difficulty in filling space with translated copies of a tetrahedron and the need for a single lattice point in the tetrahedron to fulfill the definition of a primitive unit cell.
Porkaborg
TL;DR Summary
Primitive unit cell of diamond, great confusion.
Hi guys , I want to construct a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbons atoms. I know that a primitive unit cell isn't unique but the two variants I get are drastically different . As far as I can see they both include 2 whole atoms/points in the lattice, however one of them occupies 1/4 of the conventional-cell volume, and the other occupies 1/8 of the conventional-cell volume.

When I couldn't get further in reasoning, I tried googling it and found both versions listed as primitive unit cells for diamond. But I am still confused why they look so very different.
(The left picture doesn't include rest of the atoms for some reason but they are there before creating the primitive unit cell)

I hope someone can point out the difference , or pinpoint why I may be confused, please comment if I need to add some additional info.

How do you want to fill space with only translated copies of a tetrahedron?

Porkaborg
I guess I can't , which is needed to fulfill the definition of a unitcell. Thanks a lot DrDu!. Upon looking some more at it , the tetrahedron also doesn't include a single lattice point which it is supposed to do to be a primitive unit cell.

## What is a primitive unit cell?

A primitive unit cell is the smallest repeating unit of a crystal lattice that contains one lattice point. It is the most basic unit that can be used to describe the structure of a crystal.

## What is the shape of a primitive unit cell in diamond?

The primitive unit cell in diamond is a cube with edges of equal length. This is because the carbon atoms in diamond are arranged in a face-centered cubic lattice, where each atom is bonded to four other atoms in a tetrahedral arrangement.

## How many atoms are in a primitive unit cell of diamond?

There are 8 atoms in a primitive unit cell of diamond. Each corner of the cube contains one-eighth of an atom, and each face contains one-half of an atom. Therefore, there are 8 atoms in total.

## What is the volume of a primitive unit cell of diamond?

The volume of a primitive unit cell of diamond is equal to the cube of the edge length. This is because the unit cell is a cube, and the volume of a cube is calculated by multiplying the length of one edge by itself three times.

## How is the primitive unit cell of diamond related to the crystal structure?

The primitive unit cell of diamond is the basic building block of the crystal structure. By repeating the primitive unit cell in three dimensions, the entire crystal structure can be constructed. This allows scientists to understand and predict the properties of diamond based on its unit cell structure.

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