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()

Set Plotting Engine¶

In [4]:

project.plotter.engine = 'plotly'

project.plotter.engine = 'plotly'

Add Sample Model¶

In [5]:

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

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

In [6]:

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_from_args(
    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_from_args( 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 [7]:

ed.download_from_repository('ni-q27r100-neutron_from-2.gr', destination='data')

ed.download_from_repository('ni-q27r100-neutron_from-2.gr', destination='data')

Downloading...

File 'ni-q27r100-neutron_from-2.gr' from 'easyscience/diffraction-lib'

In [8]:

project.experiments.add_from_data_path(
    name='pdf',
    data_path='data/ni-q27r100-neutron_from-2.gr',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    scattering_type='total',
)

project.experiments.add_from_data_path( name='pdf', data_path='data/ni-q27r100-neutron_from-2.gr', 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 [9]:

project.experiments['pdf'].linked_phases.add_from_args(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_from_args(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 [10]:

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 [11]:

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 [12]:

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	2334.39
2	9	416.28	82.2% ↓
3	15	210.14	49.5% ↓
4	21	207.13	1.4% ↓
5	45	207.10

🏆 Best goodness-of-fit (reduced χ²) is 207.10 at iteration 44

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 50.55 seconds

📏 Goodness-of-fit (reduced χ²): 207.10

📏 R-factor (Rf): 9.83%

📏 R-factor squared (Rf²): 9.48%

📏 Weighted R-factor (wR): 9.48%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	ni	cell	None	length_a	3.5239	3.5260	0.0000	Å	0.06 % ↑
2	ni	atom_site	Ni	b_iso	0.5000	0.4281	0.0011	Ų	14.39 % ↓
3	pdf	peak	None	broad_q	0.0300	0.0220	0.0001	Å⁻²	26.77 % ↓
4	pdf	peak	None	sharp_delta_2	2.0000	2.5587	0.0444	Ų	27.94 % ↑
5	pdf	linked_phases	ni	scale	1.0000	0.9892	0.0007		1.08 % ↓

Plot Measured vs Calculated¶

In [13]:

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

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