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

Create Project¶

In [3]:

project = ed.Project()

project = ed.Project()

Set Plotting Engine¶

In [4]:

# Keep the auto-selected engine. Alternatively, you can uncomment the
# line below to explicitly set the engine to the required one.
# project.plotter.engine = 'plotly'

# Keep the auto-selected engine. Alternatively, you can uncomment the # line below to explicitly set the engine to the required one. # project.plotter.engine = 'plotly'

In [5]:

# Set global plot range for plots
project.plotter.x_max = 40

# Set global plot range for plots project.plotter.x_max = 40

Add Structure¶

In [6]:

project.structures.create(name='si')

project.structures.create(name='si')

In [7]:

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

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

Add Experiment¶

In [8]:

data_path = ed.download_data(id=5, destination='data')

data_path = ed.download_data(id=5, destination='data')

Getting data...

Data #5: NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr

✅ Data #5 downloaded to 'data/ed-5.gr'

In [9]:

project.experiments.add_from_data_path(
    name='nomad',
    data_path=data_path,
    sample_form='powder',
    beam_mode='time-of-flight',
    radiation_probe='neutron',
    scattering_type='total',
)

project.experiments.add_from_data_path( name='nomad', data_path=data_path, sample_form='powder', beam_mode='time-of-flight', radiation_probe='neutron', scattering_type='total', )

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

Data loaded successfully

Experiment 🔬 'nomad'. Number of data points: 5033.

In [10]:

experiment = project.experiments['nomad']
experiment.linked_phases.create(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.create(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 [11]:

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

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

In [12]:

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 [13]:

project.analysis.fit()
project.analysis.show_fit_results()

project.analysis.fit() project.analysis.show_fit_results()

Using experiment 🔬 'nomad' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	3102.63
2	11	2177.55	29.8% ↓
3	19	345.28	84.1% ↓
4	27	180.23	47.8% ↓
5	35	170.60	5.3% ↓
6	68	170.54

🏆 Best goodness-of-fit (reduced χ²) is 170.54 at iteration 67

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 16.42 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	cell		length_a	5.4315	5.4306	0.0000	Å	0.02 % ↓
2	si	atom_site	Si	b_iso	0.5000	0.7170	0.0055	Ų	43.40 % ↑
3	nomad	linked_phases	si	scale	1.0000	1.2728	0.0014		27.28 % ↑
4	nomad	peak		damp_q	0.0200	0.0251	0.0001	Å⁻¹	25.66 % ↑
5	nomad	peak		broad_q	0.0300	0.0183	0.0003	Å⁻²	39.10 % ↓
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 [14]:

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

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