Pair Distribution Function: Si, NPD¶

This example demonstrates a pair distribution function (PDF) analysis of Si, based on data collected from a time-of-flight neutron powder diffraction experiment at NOMAD at SNS.

Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

⚠️ 'pycrysfml' module not found. This calculation engine will not be available.
✅ 'cryspy' calculation engine is successfully imported.
✅ 'pdffit' calculation engine is successfully imported.

Create Project¶

In [3]:

project = ed.Project()

project = ed.Project()

Set Plotting Engine¶

In [4]:

project.plotter.engine = 'plotly'
project.plotter.x_max = 40

project.plotter.engine = 'plotly' project.plotter.x_max = 40

Current plotter changed to
plotly

Add Sample Model¶

In [5]:

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

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

In [6]:

sample_model = project.sample_models['si']
sample_model.space_group.name_h_m.value = 'F d -3 m'
sample_model.space_group.it_coordinate_system_code = '1'
sample_model.cell.length_a = 5.43146
sample_model.atom_sites.add(label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=0.5)

sample_model = project.sample_models['si'] sample_model.space_group.name_h_m.value = 'F d -3 m' sample_model.space_group.it_coordinate_system_code = '1' sample_model.cell.length_a = 5.43146 sample_model.atom_sites.add(label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=0.5)

Add Experiment¶

In [7]:

ed.download_from_repository('NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr', destination='data')

ed.download_from_repository('NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr', destination='data')

⚠️ Warning
File 'data/NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr' already exists and will not be overwritten.

In [8]:

project.experiments.add(
    name='nomad',
    sample_form='powder',
    beam_mode='time-of-flight',
    radiation_probe='neutron',
    scattering_type='total',
    data_path='data/NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr',
)

project.experiments.add( name='nomad', sample_form='powder', beam_mode='time-of-flight', radiation_probe='neutron', scattering_type='total', data_path='data/NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr', )

Loading measured data from ASCII file
/Users/runner/work/diffraction-lib/diffraction-lib/docs/tutorials/data/NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr
Warning: No uncertainty (sy) column provided. Defaulting to 0.03.

Data loaded successfully
Experiment 🔬 'nomad'. Number of data points: 5033

In [9]:

experiment = project.experiments['nomad']
experiment.linked_phases.add(id='si', scale=1.0)
experiment.peak.damp_q = 0.02
experiment.peak.broad_q = 0.03
experiment.peak.cutoff_q = 35.0
experiment.peak.sharp_delta_1 = 0.0
experiment.peak.sharp_delta_2 = 4.0
experiment.peak.damp_particle_diameter = 0

experiment = project.experiments['nomad'] experiment.linked_phases.add(id='si', scale=1.0) experiment.peak.damp_q = 0.02 experiment.peak.broad_q = 0.03 experiment.peak.cutoff_q = 35.0 experiment.peak.sharp_delta_1 = 0.0 experiment.peak.sharp_delta_2 = 4.0 experiment.peak.damp_particle_diameter = 0

Select Fitting Parameters¶

In [10]:

project.sample_models['si'].cell.length_a.free = True
project.sample_models['si'].atom_sites['Si'].b_iso.free = True
experiment.linked_phases['si'].scale.free = True

project.sample_models['si'].cell.length_a.free = True project.sample_models['si'].atom_sites['Si'].b_iso.free = True experiment.linked_phases['si'].scale.free = True

In [11]:

experiment.peak.damp_q.free = True
experiment.peak.broad_q.free = True
experiment.peak.sharp_delta_1.free = True
experiment.peak.sharp_delta_2.free = True

experiment.peak.damp_q.free = True experiment.peak.broad_q.free = True experiment.peak.sharp_delta_1.free = True experiment.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 🔬 'nomad' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	3102.63
11	2177.55	29.8% ↓
19	345.28	84.1% ↓
27	180.23	47.8% ↓
35	170.60	5.3% ↓
68	170.54

🏆 Best goodness-of-fit (reduced χ²) is 170.54 at iteration 67
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 6.95 seconds
📏 Goodness-of-fit (reduced χ²): 170.54
📏 R-factor (Rf): 8.40%
📏 R-factor squared (Rf²): 8.30%
📏 Weighted R-factor (wR): 8.30%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	si	atom_sites	Si	b_iso	0.5000	0.7170	0.0050	Ų	43.40 % ↑
2	si	cell		length_a	5.4315	5.4306	0.0000	Å	0.02 % ↓
3	nomad	linked_phases	si	scale	1.0000	1.2728	0.0014		27.28 % ↑
4	nomad	peak		broad_q	0.0300	0.0183	0.0003	Å⁻²	39.10 % ↓
5	nomad	peak		damp_q	0.0200	0.0251	0.0001	Å⁻¹	25.66 % ↑
6	nomad	peak		sharp_delta_1	0.0000	2.5400	0.0529	Å	N/A
7	nomad	peak		sharp_delta_2	4.0000	-1.7525	0.1244	Ų	143.81 % ↓

Plot Measured vs Calculated¶

In [13]:

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)