A Rietveld refinement on your own data¶

A template: change the cells marked ✏️ and run the notebook top to bottom. As shipped it runs on the fluorapatite example from notebooks 01 and 02, so you can see every output before you change anything.

In Colab, upload your files with the folder icon in the left sidebar. Right-click a file and choose Copy path to get its path, which starts /content/. Files there are deleted when the runtime stops, so download what the last cell writes.

%pip install rietx

Your files and instrument ✏️¶

from pathlib import Path

import numpy as np

import rietx as rx
from rietx.examples import examples_dir

PATTERN = examples_dir() / "FAP.XRA"            # ✏️ your pattern
CIFS = [examples_dir() / "fluorapatite.cif"]    # ✏️ one CIF per crystalline phase
RADIATION = "CuKa"                              # ✏️ the anode: "CuKa", "CoKa", "MoKa", ...
TWO_THETA_LIMITS = (15, 130)                    # ✏️ the range to fit, in degrees 2θ; None fits all of it
OUTPUT = Path("rietx_output")                   # where the last cell writes

rx.read_pattern reads the format from the file. rx.capabilities().reader_formats lists every format it opens.

data = rx.read_pattern(PATTERN)
data.plot()

Check the data before modelling it. Fewer than about five steps across a peak’s width limits what the peak shape can tell you. A contaminating line, such as Kβ or tungsten Lα from an old tube, needs its range excluded or a line added to the source.

diag = rx.diagnose(data)
print(f"steps across a peak's FWHM: {diag.steps_per_fwhm:.1f}")
print(f"signal over background:     {diag.signal_to_background:.0f}")
print(f"contaminating lines:        {diag.contamination or 'none'}")
print(f"dead channels:              {diag.dead_channels or 'none'}")

The model, checked before fitting¶

For a capillary or a synchrotron pattern, replace the instrument with rx.Instrument.debye_scherrer(wavelength=...), the wavelength in Å.

phases = [phase for cif in CIFS for phase in rx.Structure.from_cif(cif).phases]
structure = rx.Structure(phases=phases)

instrument = rx.Instrument.bragg_brentano(radiation=RADIATION)
instrument.background = rx.BackgroundChebyshev.with_terms(6)
instrument.background.coefficients[0].value = float(np.percentile(data.intensity, 5))

ref = rx.Refinement(structure, instrument)
low = TWO_THETA_LIMITS[0] if TWO_THETA_LIMITS else min(data.two_theta)
data.plot(model=ref, two_theta_range=(low, low + 10))  # ✏️ any 10° with strong peaks

Every observed peak in the window should have a tick under it. Ticks offset by the same amount everywhere point to the cell or the zero shift. Peaks with no tick point to a phase you have not given a CIF for.

Le Bail: does the cell index the pattern?¶

Le Bail fits the cell and the peak shapes with free intensities. If it cannot fit the pattern, a Rietveld fit will not either. It runs on a copy of the model, so the Rietveld fit below starts from the CIF.

lebail = rx.Refinement(structure, instrument).fit(
    data, mode="lebail", plan="profile_only", two_theta_limits=TWO_THETA_LIMITS)
lebail.plot()

A flat difference curve here means the cell and the peak shapes are right. Keep its Rwp: a Rietveld Rwp well above it points at the structure model rather than the cell or the peaks. It is not a floor: this Le Bail plan frees fewer instrument terms than the Rietveld one, so a Rietveld Rwp a little below it is normal.

Rietveld¶

mccusker_structural frees background and scale first, then the cell and peak widths, then the atoms. rx.PLAN_INFO lists the other plans and what each is for.

result = ref.fit(data, plan="mccusker_structural", two_theta_limits=TWO_THETA_LIMITS)
print(f"Le Bail Rwp {lebail.statistics.rwp:.4f}, Rietveld Rwp {result.statistics.rwp:.4f}")
result.plot()

What the fit says about itself¶

Read every diagnostic before quoting a number. deliverable picks the rows that decide whether the fit is done for one purpose: "structure", "qpa", "phase_id" or "series".

print(ref.summary(deliverable="structure"))

The refined structure¶

The default view is oblique. view takes "a", "b", "c", a direction [u, v, w], a plane normal {"hkl": (h, k, l)}, or "auto", which picks the low-index direction that hides the fewest atoms. A view down a symmetry axis is often the one a reader recognises. turn="-15x" tips the view, and atom_labels=True names the sites.

rx.viz.render_structure(ref.structure)  # ✏️ view=, turn=, phase=1 for a second phase

Save the results¶

The CIF carries the refined structure with its esds, the R factors and the pattern. The project directory starts from the refined model with these settings, and rietx gui opens it. It does not hold this fit’s stages: a fit run through rx.Project would record them.

OUTPUT.mkdir(exist_ok=True)
rx.write_refinement_cif(result, ref.fitted_structure, ref.instrument,
                        OUTPUT / "refined.cif", pattern=data)
result.plot(path=OUTPUT / "fit.png")
rex = OUTPUT / "refinement.rex"
if rex.exists():
    print(f"{rex} exists and was kept: delete or rename it to save this fit as a project")
else:
    rx.Project.create(rex, pattern=PATTERN, structure=ref.structure, instrument=ref.instrument,
                      plan="mccusker_structural", two_theta_limits=TWO_THETA_LIMITS).save()
print(sorted(item.name for item in OUTPUT.iterdir()))