Structure Refinement: Si, SEPD¶

This example demonstrates a Rietveld refinement of Si crystal structure using time-of-flight neutron powder diffraction data from SEPD at Argonne.

It also shows how to switch calculation engine and peak profile type.

🛠️ 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¶

This section shows how to add structures and modify their parameters.

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 = '2'

structure.space_group.name_h_m = 'F d -3 m' structure.space_group.it_coordinate_system_code = '2'

Set Unit Cell¶

In [5]:

structure.cell.length_a = 5.431

structure.cell.length_a = 5.431

Set Atom Sites¶

In [6]:

structure.atom_sites.create(
    label='Si',
    type_symbol='Si',
    fract_x=0.125,
    fract_y=0.125,
    fract_z=0.125,
    adp_iso=0.5,
)

structure.atom_sites.create( label='Si', type_symbol='Si', fract_x=0.125, fract_y=0.125, fract_z=0.125, adp_iso=0.5, )

🔬 Define Experiment¶

This section shows how to add experiments, configure their parameters, and link the structures defined in the previous step.

Download Data¶

In [7]:

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

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

Getting data...

Data #7: Si, SEPD (Argonne)

✅ Data #7 already present at '../../../data/ed-7.xye'. Keeping existing.

Create Experiment¶

In [8]:

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

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

Set Instrument¶

In [9]:

expt.instrument.setup_twotheta_bank = 144.845
expt.instrument.calib_d_to_tof_offset = 0.0
expt.instrument.calib_d_to_tof_linear = 7476.91
expt.instrument.calib_d_to_tof_quad = -1.54

expt.instrument.setup_twotheta_bank = 144.845 expt.instrument.calib_d_to_tof_offset = 0.0 expt.instrument.calib_d_to_tof_linear = 7476.91 expt.instrument.calib_d_to_tof_quad = -1.54

Set Peak Profile¶

In [10]:

expt.peak.show_supported()
expt.peak.broad_gauss_sigma_0 = 3.0
expt.peak.broad_gauss_sigma_1 = 40.0
expt.peak.broad_gauss_sigma_2 = 2.0
expt.peak.exp_decay_beta_0 = 0.04221
expt.peak.exp_decay_beta_1 = 0.00946
expt.peak.exp_rise_alpha_0 = 0.0
expt.peak.exp_rise_alpha_1 = 0.5971

expt.peak.show_supported() expt.peak.broad_gauss_sigma_0 = 3.0 expt.peak.broad_gauss_sigma_1 = 40.0 expt.peak.broad_gauss_sigma_2 = 2.0 expt.peak.exp_decay_beta_0 = 0.04221 expt.peak.exp_decay_beta_1 = 0.00946 expt.peak.exp_rise_alpha_0 = 0.0 expt.peak.exp_rise_alpha_1 = 0.5971

Peak types

		Type	Description
1		pseudo-voigt	TOF non-convoluted pseudo-Voigt profile
2	*	jorgensen	TOF Jorgensen profile: back-to-back exponentials ⊗ Gaussian
3		jorgensen-von-dreele	TOF Jorgensen-Von Dreele profile: back-to-back exponentials ⊗ pseudo-Voigt
4		double-jorgensen-von-dreele	TOF Double-Jorgensen-Von Dreele profile: double back-to-back exponentials ⊗ pseudo-Voigt (Z-Rietveld type0m)

Set Background¶

In [11]:

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

expt.background.type = 'line-segment' for x in range(0, 35000, 5000): 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]:

expt.linked_phases.create(id='si', scale=10.0)

expt.linked_phases.create(id='si', scale=10.0)

📦 Define Project¶

The project object is used to manage the structure, experiment, and analysis.

Create Project¶

In [13]:

project = Project(name='si_sepd')

project = Project(name='si_sepd')

Add Structure¶

In [14]:

project.structures.add(structure)

project.structures.add(structure)

Add Experiment¶

In [15]:

project.experiments.add(expt)

project.experiments.add(expt)

🚀 Perform Analysis¶

This section shows the analysis process, including how to set up calculation and fitting engines.

Display Structure¶

In [16]:

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¶

In [17]:

project.display.pattern(expt_name='sepd')
project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd') project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

Loading plot…

Perform Fit 1/5¶

Set parameters to be refined.

In [18]:

structure.cell.length_a.free = True

expt.linked_phases['si'].scale.free = True
expt.instrument.calib_d_to_tof_offset.free = True

structure.cell.length_a.free = True expt.linked_phases['si'].scale.free = True expt.instrument.calib_d_to_tof_offset.free = True

Show free parameters after selection.

In [19]:

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	5.43100		-inf	inf	Å
2	sepd	linked_phases	si	scale	10.00000		-inf	inf
3	sepd	instrument		d_to_tof_offset	0.00000		-inf	inf	μs

Run Fitting¶

In [20]:

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

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

Standard fitting

📋 Using experiment 🔬 'sepd' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.36	113.06
2	7	2.47	72.20	36.1% ↓
3	11	4.19	66.76	7.5% ↓
4	25	9.47	66.72
5	30	11.58	66.72

🏆 Best goodness-of-fit (reduced χ²) is 66.72 at iteration 26

✅ 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)	11.58
4	🔁 Iterations	27
5	📏 Goodness-of-fit (reduced χ²)	66.72
6	📏 R-factor (Rf, %)	23.08
7	📏 R-factor squared (Rf², %)	12.55
8	📏 Weighted R-factor (wR, %)	12.51

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4310	5.4314	0.0002	0.01 % ↑
2	sepd	linked_phases	si	scale		10.0000	13.3619	0.1153	33.62 % ↑
3	sepd	instrument		d_to_tof_offset	μs	0.0000	-9.2543	0.2503	N/A

• 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

Display Pattern¶

In [21]:

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

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

Loading plot…

In [22]:

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

Perform Fit 2/5¶

Set more parameters to be refined.

In [23]:

for point in expt.background:
    point.y.free = True

for point in expt.background: point.y.free = True

Show free parameters after selection.

In [24]:

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	5.43135	0.00018	-inf	inf	Å
2	sepd	linked_phases	si	scale	13.36187	0.11531	-inf	inf
3	sepd	instrument		d_to_tof_offset	-9.25432	0.25033	-inf	inf	μs
4	sepd	background	0	y	200.00000		-inf	inf
5	sepd	background	5000	y	200.00000		-inf	inf
6	sepd	background	10000	y	200.00000		-inf	inf
7	sepd	background	15000	y	200.00000		-inf	inf
8	sepd	background	20000	y	200.00000		-inf	inf
9	sepd	background	25000	y	200.00000		-inf	inf
10	sepd	background	30000	y	200.00000		-inf	inf

Run Fitting¶

In [25]:

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

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

Standard fitting

📋 Using experiment 🔬 'sepd' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.36	66.80
2	13	5.38	66.80
3	14	5.77	3.38	94.9% ↓
4	27	10.81	3.38
5	40	16.29	3.38
6	48	19.22	3.38

🏆 Best goodness-of-fit (reduced χ²) is 3.38 at iteration 47

✅ 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)	19.22
4	🔁 Iterations	45
5	📏 Goodness-of-fit (reduced χ²)	3.38
6	📏 R-factor (Rf, %)	9.29
7	📏 R-factor squared (Rf², %)	6.33
8	📏 Weighted R-factor (wR, %)	5.95

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4314	5.4314	0.0000	0.00 % ↑
2	sepd	linked_phases	si	scale		13.3619	14.6317	0.0265	9.50 % ↑
3	sepd	instrument		d_to_tof_offset	μs	-9.2543	-9.2534	0.0515	0.01 % ↓
4	sepd	background	0	y		200.0000	268.6002	0.9745	34.30 % ↑
5	sepd	background	5000	y		200.0000	144.7589	0.4071	27.62 % ↓
6	sepd	background	10000	y		200.0000	120.0247	0.4282	39.99 % ↓
7	sepd	background	15000	y		200.0000	135.8494	0.8169	32.08 % ↓
8	sepd	background	20000	y		200.0000	132.6887	1.4317	33.66 % ↓
9	sepd	background	25000	y		200.0000	175.1775	2.8755	12.41 % ↓
10	sepd	background	30000	y		200.0000	180.4556	5.8525	9.77 % ↓

• 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

Display Pattern¶

In [26]:

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

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

Loading plot…

In [27]:

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

Perform Fit 3/5¶

Fix background points.

In [28]:

for point in expt.background:
    point.y.free = False

for point in expt.background: point.y.free = False

Set more parameters to be refined.

In [29]:

expt.peak.broad_gauss_sigma_0.free = True
expt.peak.broad_gauss_sigma_1.free = True
expt.peak.broad_gauss_sigma_2.free = True

expt.peak.broad_gauss_sigma_0.free = True expt.peak.broad_gauss_sigma_1.free = True expt.peak.broad_gauss_sigma_2.free = True

Show free parameters after selection.

In [30]:

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	5.43137	0.00004	-inf	inf	Å
2	sepd	linked_phases	si	scale	14.63167	0.02651	-inf	inf
3	sepd	peak		gauss_sigma_0	3.00000		-inf	inf	μs²
4	sepd	peak		gauss_sigma_1	40.00000		-inf	inf	μs/Å
5	sepd	peak		gauss_sigma_2	2.00000		-inf	inf	μs²/Ų
6	sepd	instrument		d_to_tof_offset	-9.25336	0.05153	-inf	inf	μs

Run Fitting¶

In [31]:

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

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

Standard fitting

📋 Using experiment 🔬 'sepd' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.36	3.38
2	10	3.92	3.21	5.0% ↓
3	24	9.28	3.21
4	36	14.30	3.21
5	39	15.42	3.21

🏆 Best goodness-of-fit (reduced χ²) is 3.21 at iteration 38

✅ 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)	15.42
4	🔁 Iterations	36
5	📏 Goodness-of-fit (reduced χ²)	3.21
6	📏 R-factor (Rf, %)	8.99
7	📏 R-factor squared (Rf², %)	5.52
8	📏 Weighted R-factor (wR, %)	4.88

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4314	5.4314	0.0000	0.00 % ↑
2	sepd	linked_phases	si	scale		14.6317	14.7057	0.0257	0.51 % ↑
3	sepd	peak		gauss_sigma_0	μs²	3.0000	5.7727	0.4206	92.42 % ↑
4	sepd	peak		gauss_sigma_1	μs/Å	40.0000	44.2827	0.7966	10.71 % ↑
5	sepd	peak		gauss_sigma_2	μs²/Ų	2.0000	1.2962	0.1680	35.19 % ↓
6	sepd	instrument		d_to_tof_offset	μs	-9.2534	-9.2506	0.0546	0.03 % ↓

• 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

Display Pattern¶

In [32]:

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

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

Loading plot…

In [33]:

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

Perform Fit 4/5¶

Set more parameters to be refined.

In [34]:

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

expt.peak.exp_decay_beta_0.free = True
expt.peak.exp_decay_beta_1.free = True
expt.peak.exp_rise_alpha_1.free = True

structure.atom_sites['Si'].adp_iso.free = True expt.peak.exp_decay_beta_0.free = True expt.peak.exp_decay_beta_1.free = True expt.peak.exp_rise_alpha_1.free = True

Show free parameters after selection.

In [35]:

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	5.43143	0.00004	-inf	inf	Å
2	si	atom_site	Si	adp_iso	0.50000		-inf	inf	Ų
3	sepd	linked_phases	si	scale	14.70568	0.02567	-inf	inf
4	sepd	peak		rise_alpha_1	0.59710		-inf	inf	μs/Å
5	sepd	peak		decay_beta_0	0.04221		-inf	inf	μs
6	sepd	peak		decay_beta_1	0.00946		-inf	inf	μs/Å
7	sepd	peak		gauss_sigma_0	5.77274	0.42055	-inf	inf	μs²
8	sepd	peak		gauss_sigma_1	44.28265	0.79664	-inf	inf	μs/Å
9	sepd	peak		gauss_sigma_2	1.29621	0.16795	-inf	inf	μs²/Ų
10	sepd	instrument		d_to_tof_offset	-9.25065	0.05458	-inf	inf	μs

Run Fitting¶

In [36]:

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

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

Standard fitting

📋 Using experiment 🔬 'sepd' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.37	3.21
2	13	5.37	3.21
3	15	6.10	3.17	1.2% ↓
4	16	6.47	3.13	1.5% ↓
5	26	10.43	3.01	3.7% ↓
6	38	15.14	2.96	1.7% ↓
7	50	20.27	2.93
8	60	24.27	2.93	1.1% ↓
9	73	29.40	2.93
10	86	34.94	2.93
11	99	40.00	2.93
12	105	42.61	2.93

🏆 Best goodness-of-fit (reduced χ²) is 2.93 at iteration 104

✅ 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)	42.61
4	🔁 Iterations	102
5	📏 Goodness-of-fit (reduced χ²)	2.93
6	📏 R-factor (Rf, %)	8.39
7	📏 R-factor squared (Rf², %)	4.16
8	📏 Weighted R-factor (wR, %)	2.48

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4314	5.4325	0.0001	0.02 % ↑
2	si	atom_site	Si	adp_iso	Ų	0.5000	0.5240	0.0033	4.80 % ↑
3	sepd	linked_phases	si	scale		14.7057	14.9693	0.0355	1.79 % ↑
4	sepd	peak		rise_alpha_1	μs/Å	0.5971	0.2370	0.0043	60.31 % ↓
5	sepd	peak		decay_beta_0	μs	0.0422	0.0386	0.0002	8.65 % ↓
6	sepd	peak		decay_beta_1	μs/Å	0.0095	0.0106	0.0002	11.67 % ↑
7	sepd	peak		gauss_sigma_0	μs²	5.7727	6.9657	0.4577	20.67 % ↑
8	sepd	peak		gauss_sigma_1	μs/Å	44.2827	25.6509	1.0250	42.07 % ↓
9	sepd	peak		gauss_sigma_2	μs²/Ų	1.2962	1.1001	0.1584	15.13 % ↓
10	sepd	instrument		d_to_tof_offset	μs	-9.2506	-8.7248	0.0740	5.68 % ↓

• 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

Display Correlations¶

In [37]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

Display Pattern¶

In [38]:

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

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

Loading plot…

In [39]:

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

In [40]:

project.display.pattern(expt_name='sepd', x='d_spacing')

project.display.pattern(expt_name='sepd', x='d_spacing')

Loading plot…

Perform Fit 5/5¶

Switch calculator engine¶

In [41]:

expt.calculator.show_supported()

expt.calculator.show_supported()

Calculator types

		Type	Description
1		crysfml	CrysFML library for crystallographic calculations
2	*	cryspy	CrysPy library for crystallographic calculations

In [42]:

expt.calculator.type = 'crysfml'

expt.calculator.type = 'crysfml'

Calculator for experiment 'sepd' changed to

crysfml

Change peak profile type¶

In [43]:

expt.peak.show_supported()

expt.peak.show_supported()

Peak types

		Type	Description
1	*	jorgensen	TOF Jorgensen profile: back-to-back exponentials ⊗ Gaussian
2		jorgensen-von-dreele	TOF Jorgensen-Von Dreele profile: back-to-back exponentials ⊗ pseudo-Voigt

In [44]:

expt.peak.type = 'jorgensen-von-dreele'

expt.peak.type = 'jorgensen-von-dreele'

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • lorentz_gamma_0=0.0                                                                                                          
   • lorentz_gamma_1=0.0                                                                                                          
   • lorentz_gamma_2=0.0                                                                                                          

⚠️ Switching peak profile type resets these settings to defaults:                                                                 
   • decay_beta_0: 0.03855828522823083 -> 0.04                                                                                    
   • decay_beta_1: 0.010563672401281192 -> 0.0                                                                                    
   • gauss_sigma_0: 6.965738091176624 -> 7.0                                                                                      
   • gauss_sigma_1: 25.650869859687543 -> 0.0                                                                                     
   • gauss_sigma_2: 1.1000945752526443 -> 0.0                                                                                     
   • rise_alpha_1: 0.2370115284481651 -> 0.2                                                                                      

Peak profile type for experiment 'sepd' changed to

jorgensen-von-dreele

In [45]:

expt.peak.broad_gauss_sigma_0 = 3.0148
expt.peak.broad_gauss_sigma_1 = 33.3451
expt.peak.broad_lorentz_gamma_1 = 2.5489
expt.peak.exp_decay_beta_0 = 0.04221
expt.peak.exp_decay_beta_1 = 0.00946
expt.peak.exp_rise_alpha_1 = 0.5971

expt.peak.broad_gauss_sigma_0 = 3.0148 expt.peak.broad_gauss_sigma_1 = 33.3451 expt.peak.broad_lorentz_gamma_1 = 2.5489 expt.peak.exp_decay_beta_0 = 0.04221 expt.peak.exp_decay_beta_1 = 0.00946 expt.peak.exp_rise_alpha_1 = 0.5971

Add new free parameters¶

In [46]:

expt.peak.broad_gauss_sigma_0.free = True
expt.peak.broad_gauss_sigma_1.free = True
expt.peak.broad_lorentz_gamma_1.free = True
expt.peak.exp_decay_beta_0.free = True
expt.peak.exp_decay_beta_1.free = True
expt.peak.exp_rise_alpha_1.free = True

expt.peak.broad_gauss_sigma_0.free = True expt.peak.broad_gauss_sigma_1.free = True expt.peak.broad_lorentz_gamma_1.free = True expt.peak.exp_decay_beta_0.free = True expt.peak.exp_decay_beta_1.free = True expt.peak.exp_rise_alpha_1.free = True

Run Fitting¶

In [47]:

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

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

Standard fitting

📋 Using experiment 🔬 'sepd' for 'single' fitting

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.31	190.52
2	15	13.52	nan
3	17	22.48	nan
4	35	27.57	189.33
5	40	28.96	187.77	1.4% ↓
6	51	31.91	185.01	1.5% ↓
7	62	34.80	180.22	2.6% ↓
8	73	37.66	172.36	4.4% ↓
9	84	40.49	160.47	6.9% ↓
10	95	43.35	141.18	12.0% ↓
11	106	46.29	107.78	23.7% ↓
12	117	49.43	62.69	41.8% ↓
13	128	52.83	17.06	72.8% ↓
14	140	56.59	10.03	41.2% ↓
15	151	60.07	4.43	55.9% ↓
16	163	63.91	3.80	14.1% ↓
17	174	67.36	3.25	14.4% ↓
18	175	67.70	3.22	1.0% ↓
19	186	71.12	3.06	4.9% ↓
20	198	74.79	3.01	1.6% ↓
21	215	79.94	3.00
22	232	85.12	2.98	1.0% ↓
23	249	90.22	2.98
24	266	95.31	2.98
25	283	100.40	2.98
26	286	101.35	2.98

🏆 Best goodness-of-fit (reduced χ²) is 2.98 at iteration 275

✅ 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)	101.35
4	🔁 Iterations	283
5	📏 Goodness-of-fit (reduced χ²)	2.98
6	📏 R-factor (Rf, %)	8.65
7	📏 R-factor squared (Rf², %)	5.01
8	📏 Weighted R-factor (wR, %)	4.16

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	cell		length_a	Å	5.4325	5.4326	0.0001	0.00 % ↑
2	si	atom_site	Si	adp_iso	Ų	0.5240	0.5243	0.0033	0.05 % ↑
3	sepd	linked_phases	si	scale		14.9693	1113.8694	2.6270	7341.04 % ↑
4	sepd	peak		rise_alpha_1	μs/Å	0.5971	0.2385	0.0044	60.05 % ↓
5	sepd	peak		decay_beta_0	μs	0.0422	0.0388	0.0002	8.20 % ↓
6	sepd	peak		decay_beta_1	μs/Å	0.0095	0.0101	0.0001	7.23 % ↑
7	sepd	peak		lorentz_gamma_1	μs/Å	2.5489	-0.0335	0.0222	101.32 % ↓
8	sepd	peak		gauss_sigma_0	μs²	3.0148	5.2457	0.3644	74.00 % ↑
9	sepd	peak		gauss_sigma_1	μs/Å	33.3451	30.2975	0.8410	9.14 % ↓
10	sepd	instrument		d_to_tof_offset	μs	-8.7248	-8.9036	0.0084	2.05 % ↑

• 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

Display Correlations¶

In [48]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

Display Pattern¶

In [49]:

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

project.display.pattern(expt_name='sepd', x_min=23200, x_max=23700)

Loading plot…

In [50]:

project.display.pattern(expt_name='sepd', x='d_spacing')

project.display.pattern(expt_name='sepd', x='d_spacing')

Loading plot…

💾 Save Project¶

In [51]:

project.save_as(dir_path='projects/ed_7_si_sepd')

project.save_as(dir_path='projects/ed_7_si_sepd')

Saving project 📦 'si_sepd' to '../../../projects/ed_7_si_sepd'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 si.cif

├── 📁 experiments/

│   └── 📄 sepd.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 si_sepd.html