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

📦 Define Project¶

Create Project¶

In [3]:

project = ed.Project(name='si_nomad_pdf')

project = ed.Project(name='si_nomad_pdf')

Set Plotting Engine¶

In [4]:

project.rendering_plot.show_supported()

project.rendering_plot.show_supported()

Rendering Plot types

		Type	Description
1	*	auto	Environment default rendering_plot engine
2		asciichartpy	Console ASCII line charts
3		plotly	Interactive browser-based graphing library

In [5]:

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

# Set global plot range for plots project.rendering_plot.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,
    adp_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, adp_iso=0.5, )

Display Structure¶

In [8]:

project.display.structure(struct_name='si')

project.display.structure(struct_name='si')

Structure 🧩 'si' (Atom view type: 'covalent')

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Add Experiment¶

In [9]:

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 [10]:

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', )

⚠️ No uncertainty (sy) column provided. Defaulting to 0.03.                                                                       

Data loaded successfully

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

In [11]:

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

🚀 Perform Analysis¶

Set Free Parameters¶

In [12]:

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

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

In [13]:

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 [14]:

project.analysis.fit()
project.display.fit.results()
project.display.fit.correlations()

project.analysis.fit() project.display.fit.results() project.display.fit.correlations()

Standard fitting

📋 Using experiment 🔬 'nomad' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.24	3102.63
2	11	2.47	2177.55	29.8% ↓
3	19	4.09	345.28	84.1% ↓
4	27	5.75	180.23	47.8% ↓
5	35	7.42	170.60	5.3% ↓
6	59	12.56	170.54
7	68	14.54	170.54

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

✅ Fitting complete.

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	14.54
4	🔁 Iterations	65
5	📏 Goodness-of-fit (reduced χ²)	170.54
6	📏 R-factor (Rf, %)	8.40
7	📏 R-factor squared (Rf², %)	8.30
8	📏 Weighted R-factor (wR, %)	8.30

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4315	5.4306	0.0000	0.02 % ↓
2	si	atom_site	Si	adp_iso	Ų	0.5000	0.7170	0.0055	43.40 % ↑
3	nomad	linked_phases	si	scale		1.0000	1.2728	0.0014	27.28 % ↑
4	nomad	peak		damp_q	Å⁻¹	0.0200	0.0251	0.0001	25.66 % ↑
5	nomad	peak		broad_q	Å⁻²	0.0300	0.0183	0.0003	39.10 % ↓
6	nomad	peak		sharp_delta_1	Å	0.0000	2.5400	0.0529	N/A
7	nomad	peak		sharp_delta_2	Ų	4.0000	-1.7525	0.1244	143.81 % ↓

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Loading plot…

Display Pattern¶

In [15]:

project.display.pattern(expt_name='nomad')

project.display.pattern(expt_name='nomad')

Loading plot…

💾 Save Project¶

In [16]:

project.save_as(dir_path='projects/ed_11_si_nomad_pdf')

project.save_as(dir_path='projects/ed_11_si_nomad_pdf')

Saving project 📦 'si_nomad_pdf' to '../../../projects/ed_11_si_nomad_pdf'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 si.cif

├── 📁 experiments/

│   └── 📄 nomad.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 si_nomad_pdf.html