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,
    adp_iso=0.2,
)

structure.atom_sites.create( label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, adp_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' )

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.type = 'jorgensen'
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.exp_decay_beta_0 = 0.04221
bragg_expt.peak.exp_decay_beta_1 = 0.00946
bragg_expt.peak.exp_rise_alpha_0 = 0.0
bragg_expt.peak.exp_rise_alpha_1 = 0.5971

bragg_expt.peak.type = 'jorgensen' 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.exp_decay_beta_0 = 0.04221 bragg_expt.peak.exp_decay_beta_1 = 0.00946 bragg_expt.peak.exp_rise_alpha_0 = 0.0 bragg_expt.peak.exp_rise_alpha_1 = 0.5971

Peak profile type for experiment 'sepd' changed to

jorgensen

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.

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 = 0.02
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(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=0.7)
project.analysis.joint_fit.create(experiment_id='nomad', weight=0.3)

project.analysis.fitting_mode.type = 'joint' project.analysis.joint_fit.create(experiment_id='sepd', weight=0.7) project.analysis.joint_fit.create(experiment_id='nomad', weight=0.3)

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.atom_sites['Si'].adp_iso.free = True

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

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	si	atom_site	Si	adp_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.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 'lmfit (leastsq)'...

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.51	3378.13
2	11	6.01	3378.13
3	20	11.04	3378.11
4	23	12.58	844.33	75.0% ↓
5	32	17.77	844.33
6	41	22.87	844.33
7	43	23.99	267.01	68.4% ↓
8	51	29.09	267.01
9	60	34.83	267.02
10	63	36.57	59.98	77.5% ↓
11	71	41.66	59.98
12	80	46.73	59.98
13	83	48.90	52.58	12.3% ↓
14	91	53.95	52.58
15	100	59.04	52.58
16	103	61.22	51.89	1.3% ↓
17	111	66.26	51.89
18	120	71.41	51.89
19	129	76.97	51.87
20	135	82.28	51.87
21	141	87.91	51.87
22	147	93.00	51.87
23	153	98.72	51.87
24	159	103.82	51.87
25	165	109.55	51.87
26	170	114.02	51.87

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

✅ 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)	114.02
4	🔁 Iterations	167
5	📏 Goodness-of-fit (reduced χ²)	51.87
6	📏 R-factor (Rf, %)	10.50
7	📏 R-factor squared (Rf², %)	9.32
8	📏 Weighted R-factor (wR, %)	8.30

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4200	5.4306	0.0000	0.20 % ↑
2	si	atom_site	Si	adp_iso	Ų	0.2000	0.7041	0.0037	252.05 % ↑
3	sepd	linked_phases	si	scale		13.0000	16.0569	0.1008	23.51 % ↑
4	sepd	peak		gauss_sigma_0	μs²	5.0000	-1.9630	1.2495	139.26 % ↓
5	sepd	peak		gauss_sigma_1	μs/Å	45.0000	50.3913	2.4601	11.98 % ↑
6	sepd	peak		gauss_sigma_2	μs²/Ų	1.0000	0.2155	0.4974	78.45 % ↓
7	sepd	instrument		d_to_tof_offset	μs	-9.2000	-8.2424	0.0950	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	Å⁻¹	0.0200	0.0250	0.0001	25.16 % ↑
17	nomad	peak		broad_q	Å⁻²	0.0200	0.0188	0.0002	5.92 % ↓
18	nomad	peak		sharp_delta_1	Å	0.0010	2.4399	0.0382	243887.89 % ↑
19	nomad	peak		sharp_delta_2	Ų	4.0000	-1.5282	0.0898	138.21 % ↓

• 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

⚠️ Red s.u.: exceeds the refined value (consider adding constraints)

Loading plot…

Display Pattern (After Fit)¶

In [29]:

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

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

Loading plot…

In [30]:

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

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

Loading plot…

💾 Save Project¶

In [31]:

project.save_as(dir_path='projects/ed_16_si_bragg_pdf')

project.save_as(dir_path='projects/ed_16_si_bragg_pdf')

Saving project 📦 'si_bragg_pdf' to '../../../projects/ed_16_si_bragg_pdf'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 si.cif

├── 📁 experiments/

│   └── 📄 sepd.cif

│   └── 📄 nomad.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 si_bragg_pdf.html