Refine lattice from 3 reflections

NOTE: work-in-progress

The lattice parameters of a sample can be computed from a set of 3 or more reflections if the solver provides such a method. The hkl_soleil solver uses a simplex. The computed lattice is likely the lowest symmetry since the parameters are refined to meet best the observed reflections.

Create a diffractometer object

First, create a diffractometer object that uses the "hkl_soleil" solver with the "hkl" computation engine. This solver provides support for many diffractometer geometries. This example will use the simulated 4-circle geometry from the solver’s "E4CV".

from hklpy2 import SimulatedE4CV

diffractometer = SimulatedE4CV(name="diffractometer")

Defaults

The diffractometer object starts with a default sample. The structure is cubic (\(a=b=c\), 90 degree corners).

diffractometer.sample

Sample(name='sample', lattice=Lattice(a=1, system='cubic'))

Add 3 reflections

At least three reflections are needed to refine the lattice parameters. Since we do not specify the wavelength, the support assumes the diffractometer’s current wavelength.

diffractometer.wavelength.get()

1.0

Add three non-parallel reflections. Here, just the values of the pseudos and reals are specified as Python tuples, in the exact order expected by the solver geometry.

r100 = diffractometer.add_reflection((1, 0, 0), (-145.451, 5, -5, 69.0966), name="(100)")
r010 = diffractometer.add_reflection((0, 1, 0), (-145.451, 5, 85, 69.0966), name="(010)")
r001 = diffractometer.add_reflection((0, 0, 1), (-145.451, -85, -95, 69.0966), name="(001)")

Compute refined lattice

Compute the lattice refined with these three reflections. Notice that the refined lattice is triclinic and not the original cubic symmetry.

lattice = diffractometer.operator.refine_lattice([r100, r010, r001])
lattice

Lattice(a=0.885, b=0.8953, c=0.8987, alpha=79.9999, beta=85.0196, gamma=89.5632, system='triclinic')

The refine_lattice() method returns the refined lattice but does not actually change the sample lattice:

diffractometer.sample.lattice

Lattice(a=1, system='cubic')

Change the sample lattice

The sample lattice can be changed with the refined lattice:

diffractometer.sample.lattice = lattice
diffractometer.sample.lattice

Lattice(a=0.885, b=0.8953, c=0.8987, alpha=79.9999, beta=85.0196, gamma=89.5632, system='triclinic')