# Have I missed something? "Aluminum is even simpler than Silicon: one atom per unit cell in a fcc lattic"?

In this tutorial page 17, it says: "Aluminum is even simpler than Silicon: one atom per unit cell in a fcc lattic".

If it is FCC, then it should be the same as Silicon, two atoms per unit cell, ibrav=2.

• Silicon is diamond cubic. Space group Fd3m (227) while aluminium is Fm3m (225). For primitive unit cell, we need one atom for aluminium while you need atleast two in Silicon. Commented Mar 26 at 9:17
• @Pranavkumar Thanks for the explanation. Commented Mar 26 at 9:28
• @Pranavkumar can you expand that into an answer? Commented Mar 26 at 11:56

Silicon is diamond cubic in its most stable phase, with a space group of $$Fd\bar{3}m$$ (227), whereas aluminum is face-centered cubic with a crystal symmetry of $$Fm\bar{3}m$$ (225). The conventional unit cell of aluminum has four atoms, whereas silicon has eight atoms. However, the diamond cubic structure can be seen as the interlocking of two FCC systems translated by $$(0.25, 0.25, 0.25)$$ of the lattice parameter, as shown in the figure below:

The primitive unit cell of silicon is same as aluminium with additional motif at $$(0.25,0.25,0.25)$$.

Sample example of Silicon primitive and conventional unit cell

ATOMIC_POSITIONS crystal
Si           0.0000000000       0.0000000000       0.0000000000
Si           0.2500000000       0.2500000000       0.2500000000

CELL_PARAMETERS angstrom
2.7154800000       2.7154800000       0.0000000000
2.7154800000       0.0000000000       2.7154800000
0.0000000000       2.7154800000       2.7154800000

ATOMIC_POSITIONS crystal
Si           0.0000000000       0.0000000000       0.0000000000
Si           0.2500000000       0.7500000000       0.7500000000
Si           0.0000000000       0.5000000000       0.5000000000
Si           0.2500000000       0.2500000000       0.2500000000
Si           0.5000000000       0.0000000000       0.5000000000
Si           0.7500000000       0.7500000000       0.2500000000
Si           0.5000000000       0.5000000000       0.0000000000
Si           0.7500000000       0.2500000000       0.7500000000
CELL_PARAMETERS angstrom
5.4309600000       0.0000000000       0.0000000000
0.0000000000       5.4309600000       0.0000000000
0.0000000000       0.0000000000       5.4309600000


Sample example of Aluminium primitive and conventional unit cell

ATOMIC_POSITIONS crystal
Al           0.0000000000       0.0000000000       0.0000000000

CELL_PARAMETERS angstrom
2.0200000000       2.0200000000       0.0000000000
2.0200000000       0.0000000000       2.0200000000
0.0000000000       2.0200000000       2.0200000000

ATOMIC_POSITIONS crystal
Al           0.0000000000       0.0000000000       0.0000000000
Al           0.0000000000       0.5000000000       0.5000000000
Al           0.5000000000       0.0000000000       0.5000000000
Al           0.5000000000       0.5000000000       0.0000000000
CELL_PARAMETERS angstrom
4.0400000000       0.0000000000       0.0000000000
0.0000000000       4.0400000000       0.0000000000
0.0000000000       0.0000000000       4.0400000000