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

Create Project¶

In [3]:

project = ed.Project()

project = ed.Project()

Set Plotting Engine¶

In [4]:

project.plotter.engine = 'plotly'
project.plotter.x_min = 2.0
project.plotter.x_max = 30.0

project.plotter.engine = 'plotly' project.plotter.x_min = 2.0 project.plotter.x_max = 30.0

Add Sample Model¶

In [5]:

project.sample_models.add_minimal(name='nacl')

project.sample_models.add_minimal(name='nacl')

In [6]:

project.sample_models['nacl'].space_group.name_h_m = 'F m -3 m'
project.sample_models['nacl'].space_group.it_coordinate_system_code = '1'
project.sample_models['nacl'].cell.length_a = 5.62
project.sample_models['nacl'].atom_sites.add_from_args(
    label='Na', type_symbol='Na', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=1.0
)
project.sample_models['nacl'].atom_sites.add_from_args(
    label='Cl',
    type_symbol='Cl',
    fract_x=0.5,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='b',
    b_iso=1.0,
)

project.sample_models['nacl'].space_group.name_h_m = 'F m -3 m' project.sample_models['nacl'].space_group.it_coordinate_system_code = '1' project.sample_models['nacl'].cell.length_a = 5.62 project.sample_models['nacl'].atom_sites.add_from_args( label='Na', type_symbol='Na', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=1.0 ) project.sample_models['nacl'].atom_sites.add_from_args( label='Cl', type_symbol='Cl', fract_x=0.5, fract_y=0.5, fract_z=0.5, wyckoff_letter='b', b_iso=1.0, )

Add Experiment¶

In [7]:

ed.download_from_repository('NaCl.gr', destination='data')

ed.download_from_repository('NaCl.gr', destination='data')

Downloading...

File 'NaCl.gr' from 'easyscience/diffraction-lib'

In [8]:

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

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

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

In [9]:

project.experiments['xray_pdf'].show_supported_peak_profile_types()

project.experiments['xray_pdf'].show_supported_peak_profile_types()

Supported peak profile types

	Peak profile type	Description
1	gaussian-damped-sinc	Gaussian-damped sinc profile for pair distribution function (PDF) analysis.

In [10]:

project.experiments['xray_pdf'].show_current_peak_profile_type()

project.experiments['xray_pdf'].show_current_peak_profile_type()

Current peak profile type

PeakProfileTypeEnum.GAUSSIAN_DAMPED_SINC

In [11]:

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

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

Peak profile type for experiment 'xray_pdf' changed to

gaussian-damped-sinc

In [12]:

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 [13]:

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

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

Select Fitting Parameters¶

In [14]:

project.sample_models['nacl'].cell.length_a.free = True
project.sample_models['nacl'].atom_sites['Na'].b_iso.free = True
project.sample_models['nacl'].atom_sites['Cl'].b_iso.free = True

project.sample_models['nacl'].cell.length_a.free = True project.sample_models['nacl'].atom_sites['Na'].b_iso.free = True project.sample_models['nacl'].atom_sites['Cl'].b_iso.free = True

In [15]:

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 [16]:

project.analysis.current_calculator = 'pdffit'
project.analysis.fit()

project.analysis.current_calculator = 'pdffit' project.analysis.fit()

Current calculator changed to

pdffit

Using experiment 🔬 'xray_pdf' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	163.09
2	10	17.06	89.5% ↓
3	17	2.27	86.7% ↓
4	24	1.48	34.6% ↓
5	53	1.48

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

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 11.07 seconds

📏 Goodness-of-fit (reduced χ²): 1.48

📏 R-factor (Rf): 11.02%

📏 R-factor squared (Rf²): 11.38%

📏 Weighted R-factor (wR): 11.38%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	nacl	cell	None	length_a	5.6200	5.6018	0.0001	Å	0.32 % ↓
2	nacl	atom_site	Na	b_iso	1.0000	1.1053	0.0077	Ų	10.53 % ↑
3	nacl	atom_site	Cl	b_iso	1.0000	0.5707	0.0028	Ų	42.93 % ↓
4	xray_pdf	peak	None	damp_q	0.0300	0.0606	0.0001	Å⁻¹	102.13 % ↑
5	xray_pdf	peak	None	sharp_delta_2	5.0000	3.5041	0.0667	Ų	29.92 % ↓
6	xray_pdf	linked_phases	nacl	scale	0.5000	0.4254	0.0006		14.93 % ↓

Plot Measured vs Calculated¶

In [17]:

project.plot_meas_vs_calc(expt_name='xray_pdf')

project.plot_meas_vs_calc(expt_name='xray_pdf')