Good refinement practice#

Warning

PowderLine does not judge your refinement PowderLine checks that a recipe is well-formed and consistent with its symmetry. It does not decide whether your choices make sense for your data.

A recipe can validate, run, converge and report a low Rwp, and still be a poor model. One example: refining crystallite size and microstrain together when the data can’t tell them apart. Which parameters to refine, in what order, and whether the result is physically reasonable are your decisions.

This page collects widely used rules of thumb, each with a source. It is a starting point, not a substitute for the references at the end.

Judge a fit by looking at it#

Plot the observed, calculated and difference curves. The most important test of a Rietveld fit is to look at it and check that the model is chemically plausible. R-factors alone can mislead (Toby 2006).
Read Rwp next to Rexp. Rexp is the Rwp expected from the noise alone, as the weights describe it. Rwp near Rexp (GoF ≈ 1) means the misfit is at the noise level; Rwp well above it means a misfit the model does not explain. Rwp well below it (GoF < 1) usually means the weights overstate the noise. A pattern dominated by background can give a low Rwp with a wrong structural model, and counting longer can raise χ² for the same model, because the smaller noise exposes its systematic errors (Toby 2006).
Compare models on the same points. PowderLine’s uniform Rwp, Rexp and GoF use the same points for every engine, so two models of the same data can be compared directly. Comparing Rwp across different datasets says little.

Refine in stages#

Start with the parameters the data determine best, and add others one group at a time, checking the fit at each step (McCusker et al. 1999). A common order is scale and background, then cell and instrument corrections, then peak shape, then atomic coordinates, then displacement parameters.
Calibrate the instrument on a standard, and hold it for your samples. Then sample broadening isn’t confused with instrument broadening. See Calibrate the instrument.
Keep the high-angle data. Excluding it limited accuracy in the IUCr round robin, as did peak-shape and background functions that were too inflexible (Hill 1992).

Know which parameters fight each other#

Some parameters change the pattern in nearly the same way, so the data can pin down only a combination of them. Refining such parameters together gives large, correlated uncertainties and values that can drift to unphysical ones.

Parameters	Why they correlate	What helps
Crystallite size and microstrain	Both broaden peaks. They differ only in how the broadening changes with angle: size as 1/cos θ, strain as tan θ.	A wide angular range with well-resolved peaks. Otherwise refine one and hold the other. In the IUCr size–strain round robin, many Rietveld refinements wrongly attributed size broadening to strain (Balzar et al. 2004).
Occupancy and displacement parameter of a site	Both scale how strongly the site scatters.	Refine one at a time, or fix one from chemistry. Releasing both for oxygen limited accuracy with X-ray data in the IUCr round robin (Hill 1992).
Scale, background and displacement parameters	All change the overall intensity or its fall-off with angle.	A sensible number of background terms; check the correlation after the fit.
Light atoms with X-rays (Li, B, H)	They scatter weakly next to heavy atoms.	Expect large uncertainties; consider holding their parameters.

Check the result is physical#

Sizes are positive, occupancies lie between 0 and 1, displacement parameters are positive (or positive definite), and bond lengths and angles are chemically reasonable (McCusker et al. 1999).
Least-squares uncertainties from a Rietveld refinement usually underestimate the true uncertainty (McCusker et al. 1999).
The same data analyzed by different people can give different answers, and the refinement strategy is a large part of why (Hill 1992; Madsen et al. 2001). Recording the strategy matters. A chain of recipes records it exactly.

Signals PowderLine gives you#

PowderLine doesn’t judge the model, but it reports what it sees:

Signal	Where	What it suggests
`output_recipe_valid: false` with `output_recipe_not_valid`	result, warnings	The engine returned a value the schema refuses, e.g. a negative size or an occupancy above 1
`at_limit`	`parameter_dispositions`	A value ended on a bound
`requested_not_varied`	`parameter_dispositions`	You asked to refine it, but the engine did not vary it
`converged: false`	result	The engine did not reach its convergence criterion
`uaniso_not_positive_definite`	warnings	A displacement tensor that is not physical

The teaching examples show several of these on real data.