Structure Refinement: PbSO4, NPD + XRD¶

This example demonstrates a more advanced use of the EasyDiffraction library by explicitly creating and configuring structures and experiments before adding them to a project. It could be more suitable for users who are interested in creating custom workflows. This tutorial provides minimal explanation and is intended for users already familiar with EasyDiffraction.

The tutorial covers a Rietveld refinement of PbSO4 crystal structure based on the joint fit of both X-ray and neutron diffraction data.

Import Library¶

In [2]:

from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import StructureFactory
from easydiffraction import download_data

from easydiffraction import ExperimentFactory from easydiffraction import Project from easydiffraction import StructureFactory from easydiffraction import download_data

Define Structure¶

This section shows how to add structures and modify their parameters.

Create Structure¶

In [3]:

structure = StructureFactory.from_scratch(name='pbso4')

structure = StructureFactory.from_scratch(name='pbso4')

Set Space Group¶

In [4]:

structure.space_group.name_h_m = 'P n m a'

structure.space_group.name_h_m = 'P n m a'

Set Unit Cell¶

In [5]:

structure.cell.length_a = 8.47
structure.cell.length_b = 5.39
structure.cell.length_c = 6.95

structure.cell.length_a = 8.47 structure.cell.length_b = 5.39 structure.cell.length_c = 6.95

Set Atom Sites¶

In [6]:

structure.atom_sites.create(
    label='Pb',
    type_symbol='Pb',
    fract_x=0.1876,
    fract_y=0.25,
    fract_z=0.167,
    wyckoff_letter='c',
    adp_iso=1.37,
)
structure.atom_sites.create(
    label='S',
    type_symbol='S',
    fract_x=0.0654,
    fract_y=0.25,
    fract_z=0.684,
    wyckoff_letter='c',
    adp_iso=0.3777,
)
structure.atom_sites.create(
    label='O1',
    type_symbol='O',
    fract_x=0.9082,
    fract_y=0.25,
    fract_z=0.5954,
    wyckoff_letter='c',
    adp_iso=1.9764,
)
structure.atom_sites.create(
    label='O2',
    type_symbol='O',
    fract_x=0.1935,
    fract_y=0.25,
    fract_z=0.5432,
    wyckoff_letter='c',
    adp_iso=1.4456,
)
structure.atom_sites.create(
    label='O3',
    type_symbol='O',
    fract_x=0.0811,
    fract_y=0.0272,
    fract_z=0.8086,
    wyckoff_letter='d',
    adp_iso=1.2822,
)

structure.atom_sites.create( label='Pb', type_symbol='Pb', fract_x=0.1876, fract_y=0.25, fract_z=0.167, wyckoff_letter='c', adp_iso=1.37, ) structure.atom_sites.create( label='S', type_symbol='S', fract_x=0.0654, fract_y=0.25, fract_z=0.684, wyckoff_letter='c', adp_iso=0.3777, ) structure.atom_sites.create( label='O1', type_symbol='O', fract_x=0.9082, fract_y=0.25, fract_z=0.5954, wyckoff_letter='c', adp_iso=1.9764, ) structure.atom_sites.create( label='O2', type_symbol='O', fract_x=0.1935, fract_y=0.25, fract_z=0.5432, wyckoff_letter='c', adp_iso=1.4456, ) structure.atom_sites.create( label='O3', type_symbol='O', fract_x=0.0811, fract_y=0.0272, fract_z=0.8086, wyckoff_letter='d', adp_iso=1.2822, )

Define Experiments¶

This section shows how to add experiments, configure their parameters, and link the structures defined in the previous step.

Experiment 1: npd¶

Download Data¶

In [7]:

data_path1 = download_data(id=13, destination='data')

data_path1 = download_data(id=13, destination='data')

Getting data...

Data #13: PbSO4, D1A (ILL)

✅ Data #13 downloaded to 'data/ed-13.dat'

Create Experiment¶

In [8]:

expt1 = ExperimentFactory.from_data_path(
    name='npd',
    data_path=data_path1,
    radiation_probe='neutron',
)

expt1 = ExperimentFactory.from_data_path( name='npd', data_path=data_path1, radiation_probe='neutron', )

Set Instrument¶

In [9]:

expt1.instrument.setup_wavelength = 1.91
expt1.instrument.calib_twotheta_offset = -0.1406

expt1.instrument.setup_wavelength = 1.91 expt1.instrument.calib_twotheta_offset = -0.1406

Set Peak Profile¶

In [10]:

expt1.peak.broad_gauss_u = 0.139
expt1.peak.broad_gauss_v = -0.412
expt1.peak.broad_gauss_w = 0.386
expt1.peak.broad_lorentz_x = 0
expt1.peak.broad_lorentz_y = 0.088

expt1.peak.broad_gauss_u = 0.139 expt1.peak.broad_gauss_v = -0.412 expt1.peak.broad_gauss_w = 0.386 expt1.peak.broad_lorentz_x = 0 expt1.peak.broad_lorentz_y = 0.088

Set Background¶

Select the background type.

In [11]:

expt1.background_type = 'line-segment'

expt1.background_type = 'line-segment'

Background type for experiment 'npd' already set to

line-segment

Add background points.

In [12]:

for id, x, y in [
    ('1', 11.0, 206.1624),
    ('2', 15.0, 194.75),
    ('3', 20.0, 194.505),
    ('4', 30.0, 188.4375),
    ('5', 50.0, 207.7633),
    ('6', 70.0, 201.7002),
    ('7', 120.0, 244.4525),
    ('8', 153.0, 226.0595),
]:
    expt1.background.create(id=id, x=x, y=y)

for id, x, y in [ ('1', 11.0, 206.1624), ('2', 15.0, 194.75), ('3', 20.0, 194.505), ('4', 30.0, 188.4375), ('5', 50.0, 207.7633), ('6', 70.0, 201.7002), ('7', 120.0, 244.4525), ('8', 153.0, 226.0595), ]: expt1.background.create(id=id, x=x, y=y)

Set Linked Phases¶

In [13]:

expt1.linked_phases.create(id='pbso4', scale=1.5)

expt1.linked_phases.create(id='pbso4', scale=1.5)

Experiment 2: xrd¶

Download Data¶

In [14]:

data_path2 = download_data(id=16, destination='data')

data_path2 = download_data(id=16, destination='data')

Getting data...

Data #16: PbSO4, laboratory X-ray

✅ Data #16 downloaded to 'data/ed-16.dat'

Create Experiment¶

In [15]:

expt2 = ExperimentFactory.from_data_path(
    name='xrd',
    data_path=data_path2,
    radiation_probe='xray',
)

expt2 = ExperimentFactory.from_data_path( name='xrd', data_path=data_path2, radiation_probe='xray', )

Set Instrument¶

In [16]:

expt2.instrument.setup_wavelength = 1.540567
expt2.instrument.calib_twotheta_offset = -0.05181

expt2.instrument.setup_wavelength = 1.540567 expt2.instrument.calib_twotheta_offset = -0.05181

Set Peak Profile¶

In [17]:

expt2.peak.broad_gauss_u = 0.304138
expt2.peak.broad_gauss_v = -0.112622
expt2.peak.broad_gauss_w = 0.021272
expt2.peak.broad_lorentz_x = 0
expt2.peak.broad_lorentz_y = 0.057691

expt2.peak.broad_gauss_u = 0.304138 expt2.peak.broad_gauss_v = -0.112622 expt2.peak.broad_gauss_w = 0.021272 expt2.peak.broad_lorentz_x = 0 expt2.peak.broad_lorentz_y = 0.057691

Set Background¶

Select background type.

In [18]:

expt2.background_type = 'chebyshev'

expt2.background_type = 'chebyshev'

Background type for experiment 'xrd' changed to

chebyshev

Add background points.

In [19]:

for id, x, y in [
    ('1', 0, 119.195),
    ('2', 1, 6.221),
    ('3', 2, -45.725),
    ('4', 3, 8.119),
    ('5', 4, 54.552),
    ('6', 5, -20.661),
]:
    expt2.background.create(id=id, order=x, coef=y)

for id, x, y in [ ('1', 0, 119.195), ('2', 1, 6.221), ('3', 2, -45.725), ('4', 3, 8.119), ('5', 4, 54.552), ('6', 5, -20.661), ]: expt2.background.create(id=id, order=x, coef=y)

Set Linked Phases¶

In [20]:

expt2.linked_phases.create(id='pbso4', scale=0.001)

expt2.linked_phases.create(id='pbso4', scale=0.001)

Define Project¶

The project object is used to manage structures, experiments, and analysis.

Create Project¶

In [21]:

project = Project()

project = Project()

Add Structure¶

In [22]:

project.structures.add(structure)

project.structures.add(structure)

Add Experiments¶

In [23]:

project.experiments.add(expt1)
project.experiments.add(expt2)

project.experiments.add(expt1) project.experiments.add(expt2)

Perform Analysis¶

This section outlines the analysis process, including how to configure calculation and fitting engines.

Set Fit Mode¶

In [24]:

project.analysis.fit_mode.mode = 'joint'

project.analysis.fit_mode.mode = 'joint'

Set Minimizer¶

In [25]:

project.analysis.current_minimizer = 'lmfit'

project.analysis.current_minimizer = 'lmfit'

Current minimizer changed to

lmfit

Set Fitting Parameters¶

Set structure parameters to be optimized.

In [26]:

structure.cell.length_a.free = True
structure.cell.length_b.free = True
structure.cell.length_c.free = True

structure.cell.length_a.free = True structure.cell.length_b.free = True structure.cell.length_c.free = True

Set experiment parameters to be optimized.

In [27]:

expt1.linked_phases['pbso4'].scale.free = True

expt1.instrument.calib_twotheta_offset.free = True

expt1.peak.broad_gauss_u.free = True
expt1.peak.broad_gauss_v.free = True
expt1.peak.broad_gauss_w.free = True
expt1.peak.broad_lorentz_y.free = True

expt1.linked_phases['pbso4'].scale.free = True expt1.instrument.calib_twotheta_offset.free = True expt1.peak.broad_gauss_u.free = True expt1.peak.broad_gauss_v.free = True expt1.peak.broad_gauss_w.free = True expt1.peak.broad_lorentz_y.free = True

In [28]:

expt2.linked_phases['pbso4'].scale.free = True

expt2.instrument.calib_twotheta_offset.free = True

expt2.peak.broad_gauss_u.free = True
expt2.peak.broad_gauss_v.free = True
expt2.peak.broad_gauss_w.free = True
expt2.peak.broad_lorentz_y.free = True

for term in expt2.background:
    term.coef.free = True

expt2.linked_phases['pbso4'].scale.free = True expt2.instrument.calib_twotheta_offset.free = True expt2.peak.broad_gauss_u.free = True expt2.peak.broad_gauss_v.free = True expt2.peak.broad_gauss_w.free = True expt2.peak.broad_lorentz_y.free = True for term in expt2.background: term.coef.free = True

Perform Fit¶

Plot Measured vs Calculated¶

In [29]:

project.plotter.plot_meas_vs_calc(expt_name='npd', x_min=35.5, x_max=38.3, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='npd', x_min=35.5, x_max=38.3, show_residual=True)

In [30]:

project.plotter.plot_meas_vs_calc(expt_name='xrd', x_min=29.0, x_max=30.4, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='xrd', x_min=29.0, x_max=30.4, show_residual=True)