Structure Refinement: Co2SiO4, D20 (T-scan)¶

This example demonstrates a Rietveld refinement of the Co2SiO4 crystal structure using constant-wavelength neutron powder diffraction data from D20 at ILL. A sequential refinement of the same structure against a temperature scan is performed to show how to manage multiple experiments in a project.

Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Step 1: Define Project¶

The project object manages structures, experiments, and analysis.

In [3]:

project = ed.Project()

project = ed.Project()

Set output verbosity level to "short" to show only one-line status messages during the analysis process.

In [4]:

project.verbosity = 'short'

project.verbosity = 'short'

Step 2: Define Crystal Structure¶

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

Create Structure¶

In [5]:

project.structures.create(name='cosio')
structure = project.structures['cosio']

project.structures.create(name='cosio') structure = project.structures['cosio']

Set Space Group¶

In [6]:

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

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

Set Unit Cell¶

In [7]:

structure.cell.length_a = 10.31
structure.cell.length_b = 6.0
structure.cell.length_c = 4.79

structure.cell.length_a = 10.31 structure.cell.length_b = 6.0 structure.cell.length_c = 4.79

Set Atom Sites¶

In [8]:

structure.atom_sites.create(
    label='Co1',
    type_symbol='Co',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.3,
)
structure.atom_sites.create(
    label='Co2',
    type_symbol='Co',
    fract_x=0.279,
    fract_y=0.25,
    fract_z=0.985,
    wyckoff_letter='c',
    b_iso=0.3,
)
structure.atom_sites.create(
    label='Si',
    type_symbol='Si',
    fract_x=0.094,
    fract_y=0.25,
    fract_z=0.429,
    wyckoff_letter='c',
    b_iso=0.34,
)
structure.atom_sites.create(
    label='O1',
    type_symbol='O',
    fract_x=0.091,
    fract_y=0.25,
    fract_z=0.771,
    wyckoff_letter='c',
    b_iso=0.63,
)
structure.atom_sites.create(
    label='O2',
    type_symbol='O',
    fract_x=0.448,
    fract_y=0.25,
    fract_z=0.217,
    wyckoff_letter='c',
    b_iso=0.59,
)
structure.atom_sites.create(
    label='O3',
    type_symbol='O',
    fract_x=0.164,
    fract_y=0.032,
    fract_z=0.28,
    wyckoff_letter='d',
    b_iso=0.83,
)

structure.atom_sites.create( label='Co1', type_symbol='Co', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=0.3, ) structure.atom_sites.create( label='Co2', type_symbol='Co', fract_x=0.279, fract_y=0.25, fract_z=0.985, wyckoff_letter='c', b_iso=0.3, ) structure.atom_sites.create( label='Si', type_symbol='Si', fract_x=0.094, fract_y=0.25, fract_z=0.429, wyckoff_letter='c', b_iso=0.34, ) structure.atom_sites.create( label='O1', type_symbol='O', fract_x=0.091, fract_y=0.25, fract_z=0.771, wyckoff_letter='c', b_iso=0.63, ) structure.atom_sites.create( label='O2', type_symbol='O', fract_x=0.448, fract_y=0.25, fract_z=0.217, wyckoff_letter='c', b_iso=0.59, ) structure.atom_sites.create( label='O3', type_symbol='O', fract_x=0.164, fract_y=0.032, fract_z=0.28, wyckoff_letter='d', b_iso=0.83, )

Step 3: Define Experiments¶

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

Download Measured Data¶

In [9]:

file_path = ed.download_data(id=27, destination='data')

file_path = ed.download_data(id=27, destination='data')

Getting data...

Data #27: Co2SiO4, D20 (ILL), 23 files, T from ~60K to ~500K

✅ Data #27 downloaded to 'data/ed-27.zip'

Create Experiments and Set Temperature¶

In [10]:

data_paths = ed.extract_data_paths_from_zip(file_path)
for i, data_path in enumerate(data_paths, start=1):
    name = f'd20_{i}'
    project.experiments.add_from_data_path(
        name=name,
        data_path=data_path,
    )
    expt = project.experiments[name]
    expt.diffrn.ambient_temperature = ed.extract_metadata(
        file_path=data_path,
        pattern=r'^TEMP\s+([0-9.]+)',
    )

data_paths = ed.extract_data_paths_from_zip(file_path) for i, data_path in enumerate(data_paths, start=1): name = f'd20_{i}' project.experiments.add_from_data_path( name=name, data_path=data_path, ) expt = project.experiments[name] expt.diffrn.ambient_temperature = ed.extract_metadata( file_path=data_path, pattern=r'^TEMP\s+([0-9.]+)', )

✅ Data loaded: Experiment 🔬 'd20_1'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_2'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_3'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_4'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_5'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_6'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_7'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_8'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_9'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_10'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_11'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_12'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_13'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_14'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_15'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_16'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_17'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_18'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_19'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_20'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_21'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_22'. 1507 points.

✅ Data loaded: Experiment 🔬 'd20_23'. 1507 points.

Set Instrument¶

In [11]:

for expt in project.experiments:
    expt.instrument.setup_wavelength = 1.87
    expt.instrument.calib_twotheta_offset = 0.29

for expt in project.experiments: expt.instrument.setup_wavelength = 1.87 expt.instrument.calib_twotheta_offset = 0.29

Set Peak Profile¶

In [12]:

for expt in project.experiments:
    expt.peak.broad_gauss_u = 0.24
    expt.peak.broad_gauss_v = -0.53
    expt.peak.broad_gauss_w = 0.38
    expt.peak.broad_lorentz_y = 0.02

for expt in project.experiments: expt.peak.broad_gauss_u = 0.24 expt.peak.broad_gauss_v = -0.53 expt.peak.broad_gauss_w = 0.38 expt.peak.broad_lorentz_y = 0.02

Set Excluded Regions¶

In [13]:

for expt in project.experiments:
    expt.excluded_regions.create(id='1', start=0, end=8)
    expt.excluded_regions.create(id='2', start=150, end=180)

for expt in project.experiments: expt.excluded_regions.create(id='1', start=0, end=8) expt.excluded_regions.create(id='2', start=150, end=180)

Set Background¶

In [14]:

for expt in project.experiments:
    expt.background.create(id='1', x=8, y=609)
    expt.background.create(id='2', x=9, y=581)
    expt.background.create(id='3', x=10, y=563)
    expt.background.create(id='4', x=11, y=540)
    expt.background.create(id='5', x=12, y=520)
    expt.background.create(id='6', x=15, y=507)
    expt.background.create(id='7', x=25, y=463)
    expt.background.create(id='8', x=30, y=434)
    expt.background.create(id='9', x=50, y=451)
    expt.background.create(id='10', x=70, y=431)
    expt.background.create(id='11', x=90, y=414)
    expt.background.create(id='12', x=110, y=361)
    expt.background.create(id='13', x=130, y=292)
    expt.background.create(id='14', x=150, y=241)

for expt in project.experiments: expt.background.create(id='1', x=8, y=609) expt.background.create(id='2', x=9, y=581) expt.background.create(id='3', x=10, y=563) expt.background.create(id='4', x=11, y=540) expt.background.create(id='5', x=12, y=520) expt.background.create(id='6', x=15, y=507) expt.background.create(id='7', x=25, y=463) expt.background.create(id='8', x=30, y=434) expt.background.create(id='9', x=50, y=451) expt.background.create(id='10', x=70, y=431) expt.background.create(id='11', x=90, y=414) expt.background.create(id='12', x=110, y=361) expt.background.create(id='13', x=130, y=292) expt.background.create(id='14', x=150, y=241)

Set Linked Phases¶

In [15]:

for expt in project.experiments:
    expt.linked_phases.create(id='cosio', scale=1.2)

for expt in project.experiments: expt.linked_phases.create(id='cosio', scale=1.2)

Step 4: Perform Analysis¶

This section shows how to set free parameters, define constraints, and run the refinement.

Set Free Parameters¶

In [16]:

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

structure.atom_sites['Co2'].fract_x.free = True
structure.atom_sites['Co2'].fract_z.free = True
structure.atom_sites['Si'].fract_x.free = True
structure.atom_sites['Si'].fract_z.free = True
structure.atom_sites['O1'].fract_x.free = True
structure.atom_sites['O1'].fract_z.free = True
structure.atom_sites['O2'].fract_x.free = True
structure.atom_sites['O2'].fract_z.free = True
structure.atom_sites['O3'].fract_x.free = True
structure.atom_sites['O3'].fract_y.free = True
structure.atom_sites['O3'].fract_z.free = True

structure.atom_sites['Co1'].b_iso.free = True
structure.atom_sites['Co2'].b_iso.free = True
structure.atom_sites['Si'].b_iso.free = True
structure.atom_sites['O1'].b_iso.free = True
structure.atom_sites['O2'].b_iso.free = True
structure.atom_sites['O3'].b_iso.free = True

structure.cell.length_a.free = True structure.cell.length_b.free = True structure.cell.length_c.free = True structure.atom_sites['Co2'].fract_x.free = True structure.atom_sites['Co2'].fract_z.free = True structure.atom_sites['Si'].fract_x.free = True structure.atom_sites['Si'].fract_z.free = True structure.atom_sites['O1'].fract_x.free = True structure.atom_sites['O1'].fract_z.free = True structure.atom_sites['O2'].fract_x.free = True structure.atom_sites['O2'].fract_z.free = True structure.atom_sites['O3'].fract_x.free = True structure.atom_sites['O3'].fract_y.free = True structure.atom_sites['O3'].fract_z.free = True structure.atom_sites['Co1'].b_iso.free = True structure.atom_sites['Co2'].b_iso.free = True structure.atom_sites['Si'].b_iso.free = True structure.atom_sites['O1'].b_iso.free = True structure.atom_sites['O2'].b_iso.free = True structure.atom_sites['O3'].b_iso.free = True

In [17]:

for expt in project.experiments:
    expt.linked_phases['cosio'].scale.free = True

    expt.instrument.calib_twotheta_offset.free = True

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

    for point in expt.background:
        point.y.free = True

for expt in project.experiments: expt.linked_phases['cosio'].scale.free = True expt.instrument.calib_twotheta_offset.free = True expt.peak.broad_gauss_u.free = True expt.peak.broad_gauss_v.free = True expt.peak.broad_gauss_w.free = True expt.peak.broad_lorentz_y.free = True for point in expt.background: point.y.free = True

Set Constraints¶

Set aliases for parameters.

In [18]:

project.analysis.aliases.create(
    label='biso_Co1',
    param_uid=structure.atom_sites['Co1'].b_iso.uid,
)
project.analysis.aliases.create(
    label='biso_Co2',
    param_uid=structure.atom_sites['Co2'].b_iso.uid,
)

project.analysis.aliases.create( label='biso_Co1', param_uid=structure.atom_sites['Co1'].b_iso.uid, ) project.analysis.aliases.create( label='biso_Co2', param_uid=structure.atom_sites['Co2'].b_iso.uid, )

Set constraints.

In [19]:

project.analysis.constraints.create(
    expression='biso_Co2 = biso_Co1',
)

project.analysis.constraints.create( expression='biso_Co2 = biso_Co1', )

Apply constraints.

In [20]:

project.analysis.apply_constraints()

project.analysis.apply_constraints()

Set Fit Mode¶

In [21]:

project.analysis.fit_mode.mode = 'single'

project.analysis.fit_mode.mode = 'single'

Run Fitting¶

In [22]:

project.analysis.fit()

project.analysis.fit()

Using 23 experiments 🔬 from 'd20_1' to 'd20_23' for 'single' fitting

🚀 Starting fit process with 'lmfit'...

📈 Goodness-of-fit (reduced χ²) per experiment:

	experiment	χ²	iterations	status
1	d20_1	4.74	323	✅
2	d20_2	4.59	187	✅
3	d20_3	4.84	187	✅
4	d20_4	4.71	184	✅
5	d20_5	4.66	203	✅
6	d20_6	4.84	187	✅
7	d20_7	4.79	187	✅
8	d20_8	4.56	187	✅
9	d20_9	4.75	187	✅
10	d20_10	4.81	243	✅
11	d20_11	4.66	283	✅
12	d20_12	4.56	283	✅
13	d20_13	4.80	283	✅
14	d20_14	4.61	203	✅
15	d20_15	4.62	323	✅
16	d20_16	4.60	283	✅
17	d20_17	4.81	323	✅
18	d20_18	4.66	323	✅
19	d20_19	4.64	283	✅
20	d20_20	4.74	323	✅
21	d20_21	4.69	323	✅
22	d20_22	4.85	323	✅
23	d20_23	3.87	323	✅

Plot Measured vs Calculated¶

In [23]:

last_expt_name = project.experiments.names[-1]
project.plot_meas_vs_calc(expt_name=last_expt_name, show_residual=True)

last_expt_name = project.experiments.names[-1] project.plot_meas_vs_calc(expt_name=last_expt_name, show_residual=True)

Plot Parameter Evolution¶

Define the quantity to use as the x-axis in the following plots.

In [24]:

temperature = project.experiments[0].diffrn.ambient_temperature

temperature = project.experiments[0].diffrn.ambient_temperature

Plot unit cell parameters vs. temperature.

In [25]:

project.plot_param_series(structure.cell.length_a, versus=temperature)
project.plot_param_series(structure.cell.length_b, versus=temperature)
project.plot_param_series(structure.cell.length_c, versus=temperature)

project.plot_param_series(structure.cell.length_a, versus=temperature) project.plot_param_series(structure.cell.length_b, versus=temperature) project.plot_param_series(structure.cell.length_c, versus=temperature)

Plot isotropic displacement parameters vs. temperature.

In [26]:

project.plot_param_series(structure.atom_sites['Co1'].b_iso, versus=temperature)
project.plot_param_series(structure.atom_sites['Si'].b_iso, versus=temperature)
project.plot_param_series(structure.atom_sites['O1'].b_iso, versus=temperature)
project.plot_param_series(structure.atom_sites['O2'].b_iso, versus=temperature)
project.plot_param_series(structure.atom_sites['O3'].b_iso, versus=temperature)

project.plot_param_series(structure.atom_sites['Co1'].b_iso, versus=temperature) project.plot_param_series(structure.atom_sites['Si'].b_iso, versus=temperature) project.plot_param_series(structure.atom_sites['O1'].b_iso, versus=temperature) project.plot_param_series(structure.atom_sites['O2'].b_iso, versus=temperature) project.plot_param_series(structure.atom_sites['O3'].b_iso, versus=temperature)

Plot selected fractional coordinates vs. temperature.

In [27]:

project.plot_param_series(structure.atom_sites['Co2'].fract_x, versus=temperature)
project.plot_param_series(structure.atom_sites['Co2'].fract_z, versus=temperature)
project.plot_param_series(structure.atom_sites['O1'].fract_z, versus=temperature)
project.plot_param_series(structure.atom_sites['O2'].fract_z, versus=temperature)
project.plot_param_series(structure.atom_sites['O3'].fract_z, versus=temperature)

project.plot_param_series(structure.atom_sites['Co2'].fract_x, versus=temperature) project.plot_param_series(structure.atom_sites['Co2'].fract_z, versus=temperature) project.plot_param_series(structure.atom_sites['O1'].fract_z, versus=temperature) project.plot_param_series(structure.atom_sites['O2'].fract_z, versus=temperature) project.plot_param_series(structure.atom_sites['O3'].fract_z, versus=temperature)