Joint Refinement: Si, Bragg + PDF¶

This example demonstrates a joint refinement of the Si crystal structure combining Bragg diffraction and pair distribution function (PDF) analysis. The Bragg experiment uses time-of-flight neutron powder diffraction data from SEPD at Argonne, while the PDF experiment uses data from NOMAD at SNS. A single shared Si structure is refined simultaneously against both datasets.

Import Library¶

In [2]:

from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import StructureFactory
from easydiffraction import download_data

from easydiffraction import ExperimentFactory from easydiffraction import Project from easydiffraction import StructureFactory from easydiffraction import download_data

Define Structure¶

A single Si structure is shared between the Bragg and PDF experiments. Structural parameters refined against both datasets simultaneously.

Create Structure¶

In [3]:

structure = StructureFactory.from_scratch(name='si')

structure = StructureFactory.from_scratch(name='si')

Set Space Group¶

In [4]:

structure.space_group.name_h_m = 'F d -3 m'
structure.space_group.it_coordinate_system_code = '1'

structure.space_group.name_h_m = 'F d -3 m' structure.space_group.it_coordinate_system_code = '1'

Set Unit Cell¶

In [5]:

structure.cell.length_a = 5.42

structure.cell.length_a = 5.42

Set Atom Sites¶

In [6]:

structure.atom_sites.create(
    label='Si',
    type_symbol='Si',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.2,
)

structure.atom_sites.create( label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, wyckoff_letter='a', b_iso=0.2, )

Define Experiments¶

Two experiments are defined: one for Bragg diffraction and one for PDF analysis. Both are linked to the same Si structure.

Experiment 1: Bragg (SEPD, TOF)¶

Download Data¶

In [7]:

bragg_data_path = download_data(id=7, destination='data')

bragg_data_path = download_data(id=7, destination='data')

Getting data...

Data #7: Si, SEPD (Argonne)

✅ Data #7 downloaded to 'data/ed-7.xye'

Create Experiment¶

In [8]:

bragg_expt = ExperimentFactory.from_data_path(
    name='sepd', data_path=bragg_data_path, beam_mode='time-of-flight'
)

bragg_expt = ExperimentFactory.from_data_path( name='sepd', data_path=bragg_data_path, beam_mode='time-of-flight' )

Data loaded successfully

Experiment 🔬 'sepd'. Number of data points: 5600.

Set Instrument¶

In [9]:

bragg_expt.instrument.setup_twotheta_bank = 144.845
bragg_expt.instrument.calib_d_to_tof_offset = -9.2
bragg_expt.instrument.calib_d_to_tof_linear = 7476.91
bragg_expt.instrument.calib_d_to_tof_quad = -1.54

bragg_expt.instrument.setup_twotheta_bank = 144.845 bragg_expt.instrument.calib_d_to_tof_offset = -9.2 bragg_expt.instrument.calib_d_to_tof_linear = 7476.91 bragg_expt.instrument.calib_d_to_tof_quad = -1.54

Set Peak Profile¶

In [10]:

bragg_expt.peak_profile_type = 'pseudo-voigt * ikeda-carpenter'
bragg_expt.peak.broad_gauss_sigma_0 = 5.0
bragg_expt.peak.broad_gauss_sigma_1 = 45.0
bragg_expt.peak.broad_gauss_sigma_2 = 1.0
bragg_expt.peak.broad_mix_beta_0 = 0.04221
bragg_expt.peak.broad_mix_beta_1 = 0.00946
bragg_expt.peak.asym_alpha_0 = 0.0
bragg_expt.peak.asym_alpha_1 = 0.5971

bragg_expt.peak_profile_type = 'pseudo-voigt * ikeda-carpenter' bragg_expt.peak.broad_gauss_sigma_0 = 5.0 bragg_expt.peak.broad_gauss_sigma_1 = 45.0 bragg_expt.peak.broad_gauss_sigma_2 = 1.0 bragg_expt.peak.broad_mix_beta_0 = 0.04221 bragg_expt.peak.broad_mix_beta_1 = 0.00946 bragg_expt.peak.asym_alpha_0 = 0.0 bragg_expt.peak.asym_alpha_1 = 0.5971

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

Peak profile type for experiment 'sepd' changed to

pseudo-voigt * ikeda-carpenter

Set Background¶

In [11]:

bragg_expt.background_type = 'line-segment'
for x in range(0, 35000, 5000):
    bragg_expt.background.create(id=str(x), x=x, y=200)

bragg_expt.background_type = 'line-segment' for x in range(0, 35000, 5000): bragg_expt.background.create(id=str(x), x=x, y=200)

Background type for experiment 'sepd' already set to

line-segment

Set Linked Phases¶

In [12]:

bragg_expt.linked_phases.create(id='si', scale=13.0)

bragg_expt.linked_phases.create(id='si', scale=13.0)

Experiment 2: PDF (NOMAD, TOF)¶

Download Data¶

In [13]:

pdf_data_path = download_data(id=5, destination='data')

pdf_data_path = download_data(id=5, destination='data')

Getting data...

Data #5: NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-50.gr

✅ Data #5 already present at 'data/ed-5.gr'. Keeping existing file.

Create Experiment¶

In [14]:

pdf_expt = ExperimentFactory.from_data_path(
    name='nomad',
    data_path=pdf_data_path,
    beam_mode='time-of-flight',
    scattering_type='total',
)

pdf_expt = ExperimentFactory.from_data_path( name='nomad', data_path=pdf_data_path, beam_mode='time-of-flight', scattering_type='total', )

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

Data loaded successfully

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

Set Peak Profile (PDF Parameters)¶

In [15]:

pdf_expt.peak.damp_q = 0.02
pdf_expt.peak.broad_q = 0.02
pdf_expt.peak.cutoff_q = 35.0
pdf_expt.peak.sharp_delta_1 = 0.001
pdf_expt.peak.sharp_delta_2 = 4.0
pdf_expt.peak.damp_particle_diameter = 0

pdf_expt.peak.damp_q = 0.02 pdf_expt.peak.broad_q = 0.02 pdf_expt.peak.cutoff_q = 35.0 pdf_expt.peak.sharp_delta_1 = 0.001 pdf_expt.peak.sharp_delta_2 = 4.0 pdf_expt.peak.damp_particle_diameter = 0

Set Linked Phases¶

In [16]:

pdf_expt.linked_phases.create(id='si', scale=1.0)

pdf_expt.linked_phases.create(id='si', scale=1.0)

Define Project¶

The project object manages the shared structure, both experiments, and the analysis.

Create Project¶

In [17]:

project = Project()

project = Project()

Add Structure¶

In [18]:

project.structures.add(structure)

project.structures.add(structure)

Add Experiments¶

In [19]:

project.experiments.add(bragg_expt)
project.experiments.add(pdf_expt)

project.experiments.add(bragg_expt) project.experiments.add(pdf_expt)

Perform Analysis¶

This section shows the joint analysis process. The calculator is auto-resolved per experiment: CrysPy for Bragg, PDFfit for PDF.

Set Fit Mode and Weights¶

In [20]:

project.analysis.fit_mode.mode = 'joint'
project.analysis.joint_fit_experiments.create(id='sepd', weight=0.7)
project.analysis.joint_fit_experiments.create(id='nomad', weight=0.3)

project.analysis.fit_mode.mode = 'joint' project.analysis.joint_fit_experiments.create(id='sepd', weight=0.7) project.analysis.joint_fit_experiments.create(id='nomad', weight=0.3)

Set Minimizer¶

In [21]:

project.analysis.current_minimizer = 'lmfit'

project.analysis.current_minimizer = 'lmfit'

Current minimizer changed to

lmfit

Plot Measured vs Calculated (Before Fit)¶

In [22]:

project.plot_meas_vs_calc(expt_name='sepd', show_residual=False)

project.plot_meas_vs_calc(expt_name='sepd', show_residual=False)

In [23]:

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)

Set Fitting Parameters¶

Shared structural parameters are refined against both datasets simultaneously.

In [24]:

structure.cell.length_a.free = True
structure.atom_sites['Si'].b_iso.free = True

structure.cell.length_a.free = True structure.atom_sites['Si'].b_iso.free = True

Bragg experiment parameters.

In [25]:

bragg_expt.linked_phases['si'].scale.free = True
bragg_expt.instrument.calib_d_to_tof_offset.free = True
bragg_expt.peak.broad_gauss_sigma_0.free = True
bragg_expt.peak.broad_gauss_sigma_1.free = True
bragg_expt.peak.broad_gauss_sigma_2.free = True
for point in bragg_expt.background:
    point.y.free = True

bragg_expt.linked_phases['si'].scale.free = True bragg_expt.instrument.calib_d_to_tof_offset.free = True bragg_expt.peak.broad_gauss_sigma_0.free = True bragg_expt.peak.broad_gauss_sigma_1.free = True bragg_expt.peak.broad_gauss_sigma_2.free = True for point in bragg_expt.background: point.y.free = True

PDF experiment parameters.

In [26]:

pdf_expt.linked_phases['si'].scale.free = True
pdf_expt.peak.damp_q.free = True
pdf_expt.peak.broad_q.free = True
pdf_expt.peak.sharp_delta_1.free = True
pdf_expt.peak.sharp_delta_2.free = True

pdf_expt.linked_phases['si'].scale.free = True pdf_expt.peak.damp_q.free = True pdf_expt.peak.broad_q.free = True pdf_expt.peak.sharp_delta_1.free = True pdf_expt.peak.sharp_delta_2.free = True

Show Free Parameters¶

In [27]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	si	cell		length_a	5.42000		-inf	inf	Å
2	si	atom_site	Si	b_iso	0.20000		-inf	inf	Ų
3	sepd	linked_phases	si	scale	13.00000		-inf	inf
4	sepd	peak		gauss_sigma_0	5.00000		-inf	inf	µs²
5	sepd	peak		gauss_sigma_1	45.00000		-inf	inf	µs/Å
6	sepd	peak		gauss_sigma_2	1.00000		-inf	inf	µs²/Ų
7	sepd	instrument		d_to_tof_offset	-9.20000		-inf	inf	µs
8	sepd	background	0	y	200.00000		-inf	inf
9	sepd	background	5000	y	200.00000		-inf	inf
10	sepd	background	10000	y	200.00000		-inf	inf
11	sepd	background	15000	y	200.00000		-inf	inf
12	sepd	background	20000	y	200.00000		-inf	inf
13	sepd	background	25000	y	200.00000		-inf	inf
14	sepd	background	30000	y	200.00000		-inf	inf
15	nomad	linked_phases	si	scale	1.00000		-inf	inf
16	nomad	peak		damp_q	0.02000		-inf	inf	Å⁻¹
17	nomad	peak		broad_q	0.02000		-inf	inf	Å⁻²
18	nomad	peak		sharp_delta_1	0.00100		-inf	inf	Å
19	nomad	peak		sharp_delta_2	4.00000		-inf	inf	Ų

Run Fitting¶

In [28]:

project.analysis.fit()
project.analysis.show_fit_results()

project.analysis.fit() project.analysis.show_fit_results()

Using all experiments 🔬 ['sepd', 'nomad'] for 'joint' fitting

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

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

	iteration	χ²	improvement [%]
1	1	3378.13
2	23	844.33	75.0% ↓
3	43	267.01	68.4% ↓
4	63	59.98	77.5% ↓
5	83	52.58	12.3% ↓
6	103	51.89	1.3% ↓
7	170	51.87

🏆 Best goodness-of-fit (reduced χ²) is 51.87 at iteration 153

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 91.78 seconds

📏 Goodness-of-fit (reduced χ²): 51.87

📏 R-factor (Rf): 10.50%

📏 R-factor squared (Rf²): 9.32%

📏 Weighted R-factor (wR): 8.30%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	si	cell		length_a	5.4200	5.4306	0.0000	Å	0.20 % ↑
2	si	atom_site	Si	b_iso	0.2000	0.7041	0.0037	Ų	252.05 % ↑
3	sepd	linked_phases	si	scale	13.0000	16.0569	0.1008		23.51 % ↑
4	sepd	peak		gauss_sigma_0	5.0000	-1.9630	1.2495	µs²	139.26 % ↓
5	sepd	peak		gauss_sigma_1	45.0000	50.3913	2.4601	µs/Å	11.98 % ↑
6	sepd	peak		gauss_sigma_2	1.0000	0.2155	0.4974	µs²/Ų	78.45 % ↓
7	sepd	instrument		d_to_tof_offset	-9.2000	-8.2424	0.0950	µs	10.41 % ↓
8	sepd	background	0	y	200.0000	280.6064	3.2291		40.30 % ↑
9	sepd	background	5000	y	200.0000	148.7236	1.3525		25.64 % ↓
10	sepd	background	10000	y	200.0000	118.2995	1.4191		40.85 % ↓
11	sepd	background	15000	y	200.0000	135.8529	2.7036		32.07 % ↓
12	sepd	background	20000	y	200.0000	132.6849	4.7369		33.66 % ↓
13	sepd	background	25000	y	200.0000	174.9850	9.5201		12.51 % ↓
14	sepd	background	30000	y	200.0000	180.5821	19.3648		9.71 % ↓
15	nomad	linked_phases	si	scale	1.0000	1.2713	0.0010		27.13 % ↑
16	nomad	peak		damp_q	0.0200	0.0250	0.0001	Å⁻¹	25.16 % ↑
17	nomad	peak		broad_q	0.0200	0.0188	0.0002	Å⁻²	5.92 % ↓
18	nomad	peak		sharp_delta_1	0.0010	2.4399	0.0382	Å	243887.89 % ↑
19	nomad	peak		sharp_delta_2	4.0000	-1.5282	0.0898	Ų	138.21 % ↓

Plot Measured vs Calculated (After Fit)¶

In [29]:

project.plot_meas_vs_calc(expt_name='sepd', show_residual=False)

project.plot_meas_vs_calc(expt_name='sepd', show_residual=False)

In [30]:

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)

project.plot_meas_vs_calc(expt_name='nomad', show_residual=False)

In [ ]: