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.coord_system_code = '1'

structure.space_group.name_h_m = 'F d -3 m' structure.space_group.coord_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(
    id='Si',
    type_symbol='Si',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    adp_iso=0.5223,
)

structure.atom_sites.create( id='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, adp_iso=0.5223, )

🔬 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('meas-si-sepd', destination='data')

bragg_data_path = download_data('meas-si-sepd', destination='data')

Getting data...

Data 'meas-si-sepd': Si, SEPD (Argonne)

✅ Data 'meas-si-sepd' downloaded to '../../../data/meas-si-sepd.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' )

Set Instrument¶

In [9]:

bragg_expt.instrument.setup_twotheta_bank = 144.845
bragg_expt.instrument.calib_d_to_tof_offset = -8.4
bragg_expt.instrument.calib_d_to_tof_linear = 7476.91
bragg_expt.instrument.calib_d_to_tof_quadratic = -1.54

bragg_expt.instrument.setup_twotheta_bank = 144.845 bragg_expt.instrument.calib_d_to_tof_offset = -8.4 bragg_expt.instrument.calib_d_to_tof_linear = 7476.91 bragg_expt.instrument.calib_d_to_tof_quadratic = -1.54

Set Peak Profile¶

In [10]:

bragg_expt.peak.type = 'jorgensen-von-dreele'
bragg_expt.peak.broad_gauss_sigma_0 = 5.61
bragg_expt.peak.broad_gauss_sigma_1 = 33.19
bragg_expt.peak.broad_lorentz_gamma_1 = 2.21
bragg_expt.peak.decay_beta_0 = 0.0406
bragg_expt.peak.decay_beta_1 = 0.0124
bragg_expt.peak.rise_alpha_1 = 0.5971
bragg_expt.peak.cutoff_fwhm = 8.2

bragg_expt.peak.type = 'jorgensen-von-dreele' bragg_expt.peak.broad_gauss_sigma_0 = 5.61 bragg_expt.peak.broad_gauss_sigma_1 = 33.19 bragg_expt.peak.broad_lorentz_gamma_1 = 2.21 bragg_expt.peak.decay_beta_0 = 0.0406 bragg_expt.peak.decay_beta_1 = 0.0124 bragg_expt.peak.rise_alpha_1 = 0.5971 bragg_expt.peak.cutoff_fwhm = 8.2

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • broad_lorentz_gamma_0=0.0                                                                                                    
   • broad_lorentz_gamma_1=0.0                                                                                                    
   • broad_lorentz_gamma_2=0.0                                                                                                    
   • broad_lorentz_size_l=0.0                                                                                                     
   • broad_lorentz_strain_l=0.0                                                                                                   

Peak profile type for experiment 'sepd' changed to

jorgensen-von-dreele

Set Background¶

In [11]:

for idx, (x, y) in enumerate(
    [
        (2000.0, 203.79),
        (9035.0, 103.74),
        (9335.0, 125.12),
        (11915.0, 119.81),
        (12315.0, 127.52),
        (12695.0, 123.16),
        (13745.0, 121.72),
        (14410.0, 140.39),
        (14875.0, 135.11),
        (15660.0, 129.95),
        (23075.0, 143.23),
        (23515.0, 175.48),
        (28100.0, 166.48),
        (29995.0, 203.98),
    ],
    start=1,
):
    bragg_expt.background.create(id=str(idx), position=x, intensity=y)

for idx, (x, y) in enumerate( [ (2000.0, 203.79), (9035.0, 103.74), (9335.0, 125.12), (11915.0, 119.81), (12315.0, 127.52), (12695.0, 123.16), (13745.0, 121.72), (14410.0, 140.39), (14875.0, 135.11), (15660.0, 129.95), (23075.0, 143.23), (23515.0, 175.48), (28100.0, 166.48), (29995.0, 203.98), ], start=1, ): bragg_expt.background.create(id=str(idx), position=x, intensity=y)

Set Linked Structures¶

In [12]:

bragg_expt.linked_structures.create(structure_id='si', scale=634.3132)

bragg_expt.linked_structures.create(structure_id='si', scale=634.3132)

Experiment 2: PDF (NOMAD, TOF)¶

Download Data¶

In [13]:

pdf_data_path = download_data('meas-si-pdf-nomad', destination='data')

pdf_data_path = download_data('meas-si-pdf-nomad', destination='data')

Getting data...

Data 'meas-si-pdf-nomad': Si, NOMAD (SNS), PDF

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

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', )

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

Set Peak Profile (PDF Parameters)¶

In [15]:

pdf_expt.peak.damp_q = 0.02
pdf_expt.peak.broad_q = 0.03
pdf_expt.peak.cutoff_q = 35.0
pdf_expt.peak.sharp_delta_1 = 0.4
pdf_expt.peak.sharp_delta_2 = 3.0
pdf_expt.peak.damp_particle_diameter = 0

pdf_expt.peak.damp_q = 0.02 pdf_expt.peak.broad_q = 0.03 pdf_expt.peak.cutoff_q = 35.0 pdf_expt.peak.sharp_delta_1 = 0.4 pdf_expt.peak.sharp_delta_2 = 3.0 pdf_expt.peak.damp_particle_diameter = 0

Set Linked Structures¶

In [16]:

pdf_expt.linked_structures.create(structure_id='si', scale=1.6)

pdf_expt.linked_structures.create(structure_id='si', scale=1.6)

📦 Define Project¶

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

Create Project¶

In [17]:

project = Project(name='si_bragg_pdf')

project = Project(name='si_bragg_pdf')

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.fitting_mode.type = 'joint'
project.analysis.joint_fit.create(experiment_id='sepd', weight=0.75)
project.analysis.joint_fit.create(experiment_id='nomad', weight=0.25)

project.analysis.fitting_mode.type = 'joint' project.analysis.joint_fit.create(experiment_id='sepd', weight=0.75) project.analysis.joint_fit.create(experiment_id='nomad', weight=0.25)

Fitting mode changed to

joint

Display Structure¶

In [21]:

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

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

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

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Display Pattern (Before Fit)¶

In [22]:

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

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

Loading plot…

In [23]:

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

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

Loading plot…

Set Free Parameters¶

Shared structural parameters are refined against both datasets simultaneously.

In [24]:

structure.cell.length_a.free = True

structure.cell.length_a.free = True

Bragg experiment parameters.

In [25]:

bragg_expt.linked_structures['si'].scale.free = True
bragg_expt.instrument.calib_d_to_tof_offset.free = True
bragg_expt.peak.broad_gauss_sigma_1.free = True
bragg_expt.peak.broad_lorentz_gamma_1.free = True

bragg_expt.linked_structures['si'].scale.free = True bragg_expt.instrument.calib_d_to_tof_offset.free = True bragg_expt.peak.broad_gauss_sigma_1.free = True bragg_expt.peak.broad_lorentz_gamma_1.free = True

PDF experiment parameters.

In [26]:

pdf_expt.linked_structures['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_structures['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

Display Free Parameters¶

In [27]:

project.display.parameters.free()

project.display.parameters.free()

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	sepd	linked_structure	si	scale	634.31320		-inf	inf
3	sepd	peak		broad_lorentz_gamma_1	2.21000		-inf	inf	μs/Å
4	sepd	peak		broad_gauss_sigma_1	33.19000		-inf	inf	μs/Å
5	sepd	instrument		d_to_tof_offset	-8.40000		-inf	inf	μs
6	nomad	linked_structure	si	scale	1.60000		-inf	inf
7	nomad	peak		damp_q	0.02000		-inf	inf	Å⁻¹
8	nomad	peak		broad_q	0.03000		-inf	inf	Å⁻²
9	nomad	peak		sharp_delta_1	0.40000		-inf	inf	Å
10	nomad	peak		sharp_delta_2	3.00000		-inf	inf	Ų

Run Fitting¶

In [28]:

project.analysis.minimizer.type = 'bumps (lm)'

project.analysis.minimizer.type = 'bumps (lm)'

Current minimizer changed to

bumps (lm)

In [29]:

project.analysis.fit()
project.display.fit.results()
project.display.fit.correlations()

project.analysis.fit() project.display.fit.results() project.display.fit.correlations()

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

🚀 Starting fit process with 'bumps (lm)'...

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.55	988.58
2	12	7.03	135.11	86.3% ↓
3	23	13.61	59.07	56.3% ↓
4	34	20.08	54.00	8.6% ↓
5	45	26.59	53.03	1.8% ↓
6	56	32.90	53.00
7	69	40.46	53.00
8	82	54.92	53.00

🏆 Best goodness-of-fit (reduced χ²) is 53.00 at iteration 82

✅ Fitting complete.

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	bumps (lm)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	54.92
4	📏 Goodness-of-fit (reduced χ²)	53.00
5	📏 R-factor (Rf, %)	8.64
6	📏 R-factor squared (Rf², %)	5.05
7	📏 Weighted R-factor (wR, %)	4.16

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4200	5.4306	0.0001	0.20 % ↑
2	sepd	linked_structure	si	scale		634.3132	634.2327	3.9384	0.01 % ↓
3	sepd	peak		broad_lorentz_gamma_1	μs/Å	2.2100	2.2337	0.2271	1.07 % ↑
4	sepd	peak		broad_gauss_sigma_1	μs/Å	33.1900	32.6348	1.8571	1.67 % ↓
5	sepd	instrument		d_to_tof_offset	μs	-8.4000	-8.0616	0.1768	4.03 % ↓
6	nomad	linked_structure	si	scale		1.6000	1.5668	0.0026	2.08 % ↓
7	nomad	peak		damp_q	Å⁻¹	0.0200	0.0235	0.0001	17.67 % ↑
8	nomad	peak		broad_q	Å⁻²	0.0300	0.0276	0.0001	8.14 % ↓
9	nomad	peak		sharp_delta_1	Å	0.4000	0.3848	0.0340	3.80 % ↓
10	nomad	peak		sharp_delta_2	Ų	3.0000	3.0514	0.0849	1.71 % ↑

• 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 (After Fit)¶

In [30]:

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

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

Loading plot…

In [31]:

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

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

Loading plot…

💾 Save Project¶

In [32]:

project.save_as(dir_path='projects/joint-si-bragg-pdf')

project.save_as(dir_path='projects/joint-si-bragg-pdf')

Saving project 📦 'si_bragg_pdf' to '../../../projects/joint-si-bragg-pdf'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 si.edi

├── 📁 experiments/

│   └── 📄 sepd.edi

│   └── 📄 nomad.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 si_bragg_pdf.html