Pair Distribution Function: NaCl, XRD¶

This example demonstrates a pair distribution function (PDF) analysis of NaCl, based on data collected from an X-ray powder diffraction experiment.

The dataset is taken from: https://github.com/diffpy/add2019-diffpy-cmi/tree/master

🛠️ Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

📦 Define Project¶

Create Project¶

In [3]:

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

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

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.rendering_plot.type = 'plotly'

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

In [5]:

# Set global plot range for plots
project.rendering_plot.plotter.x_min = 2.0
project.rendering_plot.plotter.x_max = 30.0

# Set global plot range for plots project.rendering_plot.plotter.x_min = 2.0 project.rendering_plot.plotter.x_max = 30.0

Add Structure¶

In [6]:

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

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

In [7]:

project.structures['nacl'].space_group.name_h_m = 'F m -3 m'
project.structures['nacl'].space_group.it_coordinate_system_code = '1'
project.structures['nacl'].cell.length_a = 5.62
project.structures['nacl'].atom_sites.create(
    label='Na',
    type_symbol='Na',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    adp_iso=1.0,
)
project.structures['nacl'].atom_sites.create(
    label='Cl',
    type_symbol='Cl',
    fract_x=0.5,
    fract_y=0.5,
    fract_z=0.5,
    adp_iso=1.0,
)

project.structures['nacl'].space_group.name_h_m = 'F m -3 m' project.structures['nacl'].space_group.it_coordinate_system_code = '1' project.structures['nacl'].cell.length_a = 5.62 project.structures['nacl'].atom_sites.create( label='Na', type_symbol='Na', fract_x=0, fract_y=0, fract_z=0, adp_iso=1.0, ) project.structures['nacl'].atom_sites.create( label='Cl', type_symbol='Cl', fract_x=0.5, fract_y=0.5, fract_z=0.5, adp_iso=1.0, )

Display Structure¶

In [8]:

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

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

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

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Add Experiment¶

In [9]:

data_path = ed.download_data(id=4, destination='data')

data_path = ed.download_data(id=4, destination='data')

Getting data...

Data #4: NaCl.gr

✅ Data #4 downloaded to '../../../data/ed-4.gr'

In [10]:

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

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

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

Data loaded successfully

Experiment 🔬 'xray_pdf'. Number of data points: 5000.

In [11]:

project.experiments['xray_pdf'].peak.show_supported()

project.experiments['xray_pdf'].peak.show_supported()

Peak types

		Type	Description
1	*	gaussian-damped-sinc	Total-scattering Gaussian-damped sinc profile for PDF analysis.

In [12]:

project.experiments['xray_pdf'].peak.type = 'gaussian-damped-sinc'

project.experiments['xray_pdf'].peak.type = 'gaussian-damped-sinc'

Peak profile type for experiment 'xray_pdf' changed to

gaussian-damped-sinc

In [13]:

project.experiments['xray_pdf'].peak.damp_q = 0.03
project.experiments['xray_pdf'].peak.broad_q = 0
project.experiments['xray_pdf'].peak.cutoff_q = 21
project.experiments['xray_pdf'].peak.sharp_delta_1 = 0
project.experiments['xray_pdf'].peak.sharp_delta_2 = 5
project.experiments['xray_pdf'].peak.damp_particle_diameter = 0

project.experiments['xray_pdf'].peak.damp_q = 0.03 project.experiments['xray_pdf'].peak.broad_q = 0 project.experiments['xray_pdf'].peak.cutoff_q = 21 project.experiments['xray_pdf'].peak.sharp_delta_1 = 0 project.experiments['xray_pdf'].peak.sharp_delta_2 = 5 project.experiments['xray_pdf'].peak.damp_particle_diameter = 0

In [14]:

project.experiments['xray_pdf'].linked_phases.create(id='nacl', scale=0.5)

project.experiments['xray_pdf'].linked_phases.create(id='nacl', scale=0.5)

🚀 Perform Analysis¶

Set Free Parameters¶

In [15]:

project.structures['nacl'].cell.length_a.free = True
project.structures['nacl'].atom_sites['Na'].adp_iso.free = True
project.structures['nacl'].atom_sites['Cl'].adp_iso.free = True

project.structures['nacl'].cell.length_a.free = True project.structures['nacl'].atom_sites['Na'].adp_iso.free = True project.structures['nacl'].atom_sites['Cl'].adp_iso.free = True

In [16]:

project.experiments['xray_pdf'].linked_phases['nacl'].scale.free = True
project.experiments['xray_pdf'].peak.damp_q.free = True
project.experiments['xray_pdf'].peak.sharp_delta_2.free = True

project.experiments['xray_pdf'].linked_phases['nacl'].scale.free = True project.experiments['xray_pdf'].peak.damp_q.free = True project.experiments['xray_pdf'].peak.sharp_delta_2.free = True

Run Fitting¶

In [17]:

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 🔬 'xray_pdf' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.31	163.09
2	10	2.19	17.06	89.5% ↓
3	17	3.65	2.27	86.7% ↓
4	24	5.08	1.48	34.6% ↓
5	50	10.23	1.48
6	53	10.87	1.48

🏆 Best goodness-of-fit (reduced χ²) is 1.48 at iteration 52

✅ 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)	10.87
4	🔁 Iterations	50
5	📏 Goodness-of-fit (reduced χ²)	1.48
6	📏 R-factor (Rf, %)	11.02
7	📏 R-factor squared (Rf², %)	11.38
8	📏 Weighted R-factor (wR, %)	11.38

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	nacl	cell		length_a	Å	5.6200	5.6018	0.0001	0.32 % ↓
2	nacl	atom_site	Na	adp_iso	Ų	1.0000	1.1053	0.0077	10.53 % ↑
3	nacl	atom_site	Cl	adp_iso	Ų	1.0000	0.5707	0.0028	42.93 % ↓
4	xray_pdf	linked_phases	nacl	scale		0.5000	0.4254	0.0006	14.93 % ↓
5	xray_pdf	peak		damp_q	Å⁻¹	0.0300	0.0606	0.0001	102.13 % ↑
6	xray_pdf	peak		sharp_delta_2	Ų	5.0000	3.5041	0.0667	29.92 % ↓

• 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 [18]:

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

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

Loading plot…

💾 Save Project¶

In [19]:

project.save_as(dir_path='projects/ed_12_nacl_xray_pdf')

project.save_as(dir_path='projects/ed_12_nacl_xray_pdf')

Saving project 📦 'nacl_xray_pdf' to '../../../projects/ed_12_nacl_xray_pdf'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 nacl.cif

├── 📁 experiments/

│   └── 📄 xray_pdf.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 nacl_xray_pdf.html