The equivalent space groups

We can find the same space group with different settings but only one of the different is the standard one. We will present some cases.

Case 01:
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The orthorhombic space groupe which has the number 62 has 6 different settings but the standard setting is Pnma. We can find find the space group with the setting Pbnm. The equivalence between these two settings are as follows:

we take the standard setting as reference.

Pnma with lattice parameters a,b,c  -----> the lattice parameters will be c,a,b with Pbnm.


We take the following example of the Barium sulfide BaS with lattice parameters:

a=8.85 Å, b=5.43 Å, c=7.13 Å, α=β=γ=90°   in Pnma setting

We can see that in this setting, the bigger value is that of "a" parameter and after the value of "c" parameter.


Now, we get the lattice parameters in the Pbnm setting

a=7.13 Å, b=8.85 Å, c=5.43 Å , α=β=γ=90°


Case 02:
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The monoclinic space group which has the number 15 has two settings:

C2/c and B2/b and the only setting accepted by the code wien2k is the C2/c.

For that, if we have data in the setting B2/b we have to transform them to the setting B2/b.

We take the following example of the Copper Oxide CuO with lattice parameters in the B2/b setting:

a= 4.7 Å ,  b=3.4 Å ,  c=5.1 Å     alpha=gamma=90°  ,   beta=99.54°


The equivalent data in the setting C2/c are the following:

a= 3.4 Å ,  b=4.7 Å ,  c=5.1 Å     alpha=beta=90°  ,   gamma=99.54°

Good Luck