Solid State Palladium: 27 Atoms in a Unit Cell?

[PHY-101]

Dear all,

I am trying to reproduce the results from a paper in computational physics and it says that for their simulation, they used a computational supercell of palladium of 27 atoms in a periodic system.

How can there be 27 atoms considering that in solid state, the palladium has a fcc structure and hence, that there is supposed to be 4 atoms per unit cell?

Anyone can help me with this?

 

[kanato]

An fcc structure has one atom per primitive unit cell, with lattice vectors a1 = a/2(1,1,0), a2 = a/2(1,0,1), a3 = a/2(0,1,1). Probably they have a 3x3x3 supercell where the lattice vectors are just 3 times those.

 

[PHY-101]

Hum... isn't it the simple cubic structure that contains only one atom per unit cell?

 

[kanato]

fcc, bcc and sc all have a primitive unit cell with only one atom. You're confusing the conventional cell (which has 4 atoms for fcc) as being the primitive unit cell, and often times they are different cells. The primitive cell for fcc is not cubic (look at the vectors I gave you; they are not orthogonal) but it has the same symmetry of the cubic groups, so the conventional cell is to be cubic so you can see the symmetry.

Try writing down the atomic positions in a conventional fcc unit cell, and then use the lattice vectors I gave you to locate atomic positions from the primitive cell, and you will see that you get all the same atoms either way, but for the primitive cell you have only one atom per cell.

 

[PHY-101]

Thank you so much, now it is crystal clear ;0)

 

[malawi_glenn]

In fact, the definition of 'primitive cell' IS one atom/lattice point.

 

[PHY-101]

Yeah thanks Malawi, I sort of figured that out now!

But in the paper they never mentionned a "primitive" cell, that's where I got confused. Up until now, I had only worked with conventional cells and never would have thought there could me something smaller...