Pair Distribution Function: Ni, NPD¶

This example demonstrates a pair distribution function (PDF) analysis of Ni, based on data collected from a constant wavelength neutron powder diffraction experiment.

The dataset is taken from: https://github.com/diffpy/cmi_exchange/tree/main/cmi_scripts/fitNiPDF

Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Create Project¶

In [3]:

project = ed.Project()

project = ed.Project()

Add Sample Model¶

In [4]:

project.sample_models.add(name='ni')

project.sample_models.add(name='ni')

In [5]:

project.sample_models['ni'].space_group.name_h_m = 'F m -3 m'
project.sample_models['ni'].space_group.it_coordinate_system_code = '1'
project.sample_models['ni'].cell.length_a = 3.52387
project.sample_models['ni'].atom_sites.add(
    label='Ni',
    type_symbol='Ni',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    wyckoff_letter='a',
    b_iso=0.5,
)

project.sample_models['ni'].space_group.name_h_m = 'F m -3 m' project.sample_models['ni'].space_group.it_coordinate_system_code = '1' project.sample_models['ni'].cell.length_a = 3.52387 project.sample_models['ni'].atom_sites.add( label='Ni', type_symbol='Ni', fract_x=0.0, fract_y=0.0, fract_z=0.0, wyckoff_letter='a', b_iso=0.5, )

Add Experiment¶

In [6]:

data_path = ed.download_data(id=6, destination='data')

data_path = ed.download_data(id=6, destination='data')

Getting data...

Data #6: ni-q27r100-neutron_from-2.gr

✅ Data #6 downloaded to 'data/ed-6.gr'

In [7]:

project.experiments.add(
    name='pdf',
    data_path=data_path,
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    scattering_type='total',
)

project.experiments.add( name='pdf', data_path=data_path, sample_form='powder', beam_mode='constant wavelength', radiation_probe='neutron', scattering_type='total', )

Warning: No uncertainty (sy) column provided. Defaulting to 0.03.

Data loaded successfully

Experiment 🔬 'pdf'. Number of data points: 9801

In [8]:

project.experiments['pdf'].linked_phases.add(id='ni', scale=1.0)
project.experiments['pdf'].peak.damp_q = 0
project.experiments['pdf'].peak.broad_q = 0.03
project.experiments['pdf'].peak.cutoff_q = 27.0
project.experiments['pdf'].peak.sharp_delta_1 = 0.0
project.experiments['pdf'].peak.sharp_delta_2 = 2.0
project.experiments['pdf'].peak.damp_particle_diameter = 0

project.experiments['pdf'].linked_phases.add(id='ni', scale=1.0) project.experiments['pdf'].peak.damp_q = 0 project.experiments['pdf'].peak.broad_q = 0.03 project.experiments['pdf'].peak.cutoff_q = 27.0 project.experiments['pdf'].peak.sharp_delta_1 = 0.0 project.experiments['pdf'].peak.sharp_delta_2 = 2.0 project.experiments['pdf'].peak.damp_particle_diameter = 0

Select Fitting Parameters¶

In [9]:

project.sample_models['ni'].cell.length_a.free = True
project.sample_models['ni'].atom_sites['Ni'].b_iso.free = True

project.sample_models['ni'].cell.length_a.free = True project.sample_models['ni'].atom_sites['Ni'].b_iso.free = True

In [10]:

project.experiments['pdf'].linked_phases['ni'].scale.free = True
project.experiments['pdf'].peak.broad_q.free = True
project.experiments['pdf'].peak.sharp_delta_2.free = True

project.experiments['pdf'].linked_phases['ni'].scale.free = True project.experiments['pdf'].peak.broad_q.free = True project.experiments['pdf'].peak.sharp_delta_2.free = True

Run Fitting¶

In [11]:

project.analysis.current_calculator = 'pdffit'
project.analysis.fit()

project.analysis.current_calculator = 'pdffit' project.analysis.fit()

Current calculator changed to

pdffit

Using experiment 🔬 'pdf' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	2324.45
2	9	921.68	60.3% ↓
3	15	887.03	3.8% ↓
4	56	886.39

🏆 Best goodness-of-fit (reduced χ²) is 886.39 at iteration 55

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 70.05 seconds

📏 Goodness-of-fit (reduced χ²): 886.39

📏 R-factor (Rf): 20.00%

📏 R-factor squared (Rf²): 19.61%

📏 Weighted R-factor (wR): 19.61%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	ni	cell		length_a	3.5239	3.5239	N/A	Å	0.00 % ↓
2	ni	atom_site	Ni	b_iso	0.5000	0.5000	N/A	Ų	0.00 % ↓
3	pdf	linked_phases	ni	scale	1.0000	1.0088	N/A		0.88 % ↑
4	pdf	peak		broad_q	0.0300	0.0204	N/A	Å⁻²	31.99 % ↓
5	pdf	peak		sharp_delta_2	2.0000	3.1153	N/A	Ų	55.76 % ↑

Plot Measured vs Calculated¶

In [12]:

project.plot_meas_vs_calc(expt_name='pdf', show_residual=True)

project.plot_meas_vs_calc(expt_name='pdf', show_residual=True)