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¶

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import easydiffraction as edi
import easydiffraction as edi

📦 Define Project¶

Create Project¶

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project = edi.Project(name='ni_pdf')
project = edi.Project(name='ni_pdf')

Add Structure¶

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

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project.structures['ni'].space_group.name_h_m = 'F m -3 m'
project.structures['ni'].space_group.coord_system_code = '1'
project.structures['ni'].cell.length_a = 3.52387
project.structures['ni'].atom_sites.create(
    id='Ni',
    type_symbol='Ni',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    adp_iso=0.5,
)
project.structures['ni'].space_group.name_h_m = 'F m -3 m'
project.structures['ni'].space_group.coord_system_code = '1'
project.structures['ni'].cell.length_a = 3.52387
project.structures['ni'].atom_sites.create(
    id='Ni',
    type_symbol='Ni',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    adp_iso=0.5,
)

Display Structure¶

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

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

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Add Experiment¶

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data_path = edi.download_data('meas-ni-pdf', destination='data')
data_path = edi.download_data('meas-ni-pdf', destination='data')

Getting data...

Data 'meas-ni-pdf': Ni, PDF

✅ Data 'meas-ni-pdf' downloaded to '../../../data/meas-ni-pdf.gr'

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

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

Data loaded successfully

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

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project.experiments['pdf'].linked_structures.create(structure_id='ni', scale=1.0)
project.experiments['pdf'].peak.damp_q = 0
project.experiments['pdf'].peak.broad_q = 0.02
project.experiments['pdf'].peak.cutoff_q = 27.0
project.experiments['pdf'].peak.sharp_delta_1 = 0.0
project.experiments['pdf'].peak.sharp_delta_2 = 2.8
project.experiments['pdf'].peak.damp_particle_diameter = 0
project.experiments['pdf'].linked_structures.create(structure_id='ni', scale=1.0)
project.experiments['pdf'].peak.damp_q = 0
project.experiments['pdf'].peak.broad_q = 0.02
project.experiments['pdf'].peak.cutoff_q = 27.0
project.experiments['pdf'].peak.sharp_delta_1 = 0.0
project.experiments['pdf'].peak.sharp_delta_2 = 2.8
project.experiments['pdf'].peak.damp_particle_diameter = 0

🚀 Perform Analysis¶

Set Free Parameters¶

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project.structures['ni'].cell.length_a.free = True
project.structures['ni'].atom_sites['Ni'].adp_iso.free = True
project.structures['ni'].cell.length_a.free = True
project.structures['ni'].atom_sites['Ni'].adp_iso.free = True

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

Run Fitting¶

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project.analysis.fit()
project.display.fit.results()
project.display.fit.correlations(threshold=0.75)
project.analysis.fit()
project.display.fit.results()
project.display.fit.correlations(threshold=0.75)

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	1.70	911.16
2	4	6.68	890.92	2.2% ↓
3	8	13.30	911.16
4	9	15.01	220.45	75.3% ↓
5	12	20.05	220.44
6	15	25.12	207.23	6.0% ↓
7	18	30.17	207.23
8	22	36.76	207.29
9	26	43.38	207.10
10	30	49.71	207.10
11	34	56.39	207.28
12	37	63.71	207.10
13	39	68.74	207.10
14	42	76.21	207.10
15	44	81.35	207.10
16	47	87.00	207.10
17	50	92.51	207.10
18	53	98.15	207.10
19	54	100.05	207.10

🏆 Best goodness-of-fit (reduced χ²) is 207.10 at iteration 45

✅ 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)	100.05
4	🔁 Iterations	51
5	📏 Goodness-of-fit (reduced χ²)	207.10
6	📏 R-factor (Rf, %)	9.85
7	📏 R-factor squared (Rf², %)	9.48
8	📏 Weighted R-factor (wR, %)	9.48

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	ni	cell		length_a	Å	3.5239	3.5260	0.0000	0.06 % ↑
2	ni	atom_site	Ni	adp_iso	Å²	0.5000	0.4281	0.0013	14.39 % ↓
3	pdf	linked_structure	ni	scale		1.0000	0.9785	0.0014	2.15 % ↓
4	pdf	peak		broad_q	Å⁻²	0.0200	0.0220	0.0001	9.84 % ↑
5	pdf	peak		sharp_delta_2	Å²	2.8000	2.5589	0.0444	8.61 % ↓

  • 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

⚠️ No parameter pairs with |correlation| >= 0.75 were found.

Display Pattern¶

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

Loading plot…

💾 Save Project¶

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project.save_as(dir_path='projects/pdf-ni-npd')
project.save_as(dir_path='projects/pdf-ni-npd')

Saving project 📦 'ni_pdf' to '../../../projects/pdf-ni-npd'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 ni.edi

├── 📁 experiments/

│   └── 📄 pdf.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 ni_pdf.html