# An easy way to generate the unit cell

## Main Question or Discussion Point

If I have the fractional coordinates of asymmetric unit and I know the space group of certain material, is there an easy way to generate the fractional coordinates of the atoms in the conventional unit cell?

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You can use PCW software.

If I have the fractional coordinates of asymmetric unit and I know the space group of certain material, is there an easy way to generate the fractional coordinates of the atoms in the conventional unit cell?
Could you define the terms in red?

Thank you, abhi2005singh!

* Fractional coordinates: are the coordinates of the atoms in a box with respect to the vectors that define the box.Thus, they should range between 0 and 1. If a cubic box has edge length of 4 A and an atom has fractional coordinates 1/4 1/4 1/2 then (assuming the origin at (0,0,0), the Cartesian coordinates of this atom is (1,1,2)

* Conventional unit cell: Is the building block of a crystal structure that is not necessarily the most primitive one, but more important that it has more symmetry compared to the primitive cell.

*fractional coordinates of asymmetric unit: By which I mean the fractional coordinates of the atoms that are enough to form the smallest building block of a conventional unit cell. These fractions are with respect to the conventional cell vectors. The rest of atoms coordinates in the conventional cell can be evaluated based on the symmetry operations of the space group to which the structure belongs.

Better explanation can be found in Ashcroft and Mermine, Solid State Physics, Chapters 4,5,6,7

What is a primitive cell?

It is the volume of space that when translated through all vectors in a Bravais lattice , fills the space without overlapping or leaving voids.

I think that is the definition of any unit cell, not just a primitive one.

I think that is the definition of any unit cell, not just a primitive one.
A primitive cell is a unit cell, but not all unit cells are primitive. A primitive unit cell is the smallest unit cell that can reproduce the entire crystal structure.

FCC unit cell: not primitive
1st Brillouin zone: primitive (in reciprocal space)

All the terms that Useful nucleus used in the OP are standard solid state/crystallography terms. They don't really need to be explained. They can be looked up easily.

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