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

📦 Define Project¶

Create Project¶

In [3]:

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

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

Add Structure¶

In [4]:

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

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

In [5]:

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

Display Structure¶

In [6]:

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¶

In [7]:

data_path = ed.download_data(id=6, destination='data')

data_path = ed.download_data(id=6, destination='data')

Getting data...

Data #6: ni-q27r100-neutron_from-2.gr

✅ Data #6 downloaded to '../../../data/ed-6.gr'

In [8]:

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.

In [9]:

project.experiments['pdf'].linked_phases.create(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.create(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

🚀 Perform Analysis¶

Set Free Parameters¶

In [10]:

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

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.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	1.94	2334.39
2	4	7.69	2322.80
3	7	13.46	2334.46
4	9	16.79	416.28	82.2% ↓
5	13	22.54	416.28
6	15	25.46	210.14	49.5% ↓
7	19	31.34	210.15
8	21	34.28	207.13	1.4% ↓
9	25	40.08	207.13
10	29	45.86	207.10
11	33	51.68	207.10
12	37	57.63	207.10
13	41	63.47	207.10
14	45	69.29	207.10

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

✅ 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)	69.29
4	🔁 Iterations	42
5	📏 Goodness-of-fit (reduced χ²)	207.10
6	📏 R-factor (Rf, %)	9.83
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	Ų	0.5000	0.4281	0.0011	14.39 % ↓
3	pdf	linked_phases	ni	scale		1.0000	0.9892	0.0007	1.08 % ↓
4	pdf	peak		broad_q	Å⁻²	0.0300	0.0220	0.0001	26.77 % ↓
5	pdf	peak		sharp_delta_2	Ų	2.0000	2.5587	0.0444	27.94 % ↑

• 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¶

In [13]:

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

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

Loading plot…

💾 Save Project¶

In [14]:

project.save_as(dir_path='projects/ed_10_ni_pdf')

project.save_as(dir_path='projects/ed_10_ni_pdf')

Saving project 📦 'ni_pdf' to '../../../projects/ed_10_ni_pdf'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 ni.cif

├── 📁 experiments/

│   └── 📄 pdf.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 ni_pdf.html