Calculating the F-Fingerprint to compare crystal structures¶

The F-Fingerprint was introduced by Oganov and Valle in doi:10.1063/1.3079326 and doi:10.1107/S0108767310026395. The definition is based on the pair-wise partial radial distribution function.

First we create two crystals with ase:

[1]:

from ase.spacegroup import crystal

### GaAs
a = 4.066 * 2.0
GaAs_prim = crystal(
    ("Ga", "As"),
    basis=((0.0, 0.0, 0.0), (0.75, 0.75, 0.75)),
    spacegroup=216,
    cellpar=[a, a, a, 90, 90, 90],
    primitive_cell=True,
)
GaAs_conv = crystal(
    ("Ga", "As"),
    basis=((0.0, 0.0, 0.0), (0.75, 0.75, 0.75)),
    spacegroup=216,
    cellpar=[a, a, a, 90, 90, 90],
    primitive_cell=False,
)

We have created two times the same materials, but using different unit cells. GaAs_prim is the crystal structure with the primitive unit cell and GaAs_conv is uses conventional unit cell. We can print the crystal structures to visualize them with e.g. VESTA:

[2]:

from ase.io import write

write("GaAs_prim.xsf", GaAs_prim)
write("GaAs_conv.xsf", GaAs_conv)

Now, to compare both structures (they should be identical), we import the FFingerPrint class and load the structures into the object.

[3]:

from aim2dat.strct import StructureCollection

strct_collection = StructureCollection()
strct_collection.append_from_ase_atoms("GaAs 216 prim", GaAs_prim)
strct_collection.append_from_ase_atoms("GaAs 216 conv", GaAs_conv)

Now we can calculate the f-fingerprint and compare the elemental contributions:

[4]:

from aim2dat.plots import PartialRDFPlot

plot = PartialRDFPlot()
plot.ratio = (10, 4)
plot.show_legend = True
plot.y_label = "F-Fingerprint"
element_fingerprints, atomic_fingerprints = strct_collection[
    "GaAs 216 conv"
].calculate_ffingerprint()
plot.import_ffingerprint("GaAs 216 conv", **element_fingerprints, x_unit="ang")
element_fingerprints, atomic_fingerprints = strct_collection[
    "GaAs 216 prim"
].calculate_ffingerprint()
plot.import_ffingerprint("GaAs 216 prim", **element_fingerprints, x_unit="ang")
plot.plot(["GaAs 216 conv", "GaAs 216 prim"])

[4]:

We can already see that both structures have the same fingerprints. Now we can also calculate the similarity of the two structures based on the cosine-distance:

[5]:

from aim2dat.strct import StructureOperations

strct_op = StructureOperations(structures=strct_collection)
strct_op.compare_structures_via_ffingerprint("GaAs 216 prim", "GaAs 216 conv", use_weights=True)

[5]:

1.1102230246251565e-16