Structure Refinement: LMO, ECHIDNA¶

This example refines an LMO structure with Li/Ni site mixing against constant-wavelength neutron powder diffraction data collected on the ECHIDNA diffractometer at ANSTO. The workflow starts from approximate structural and profile parameters, constrains the coupled site occupancies, and performs a Rietveld refinement.

🛠️ Import Library¶

In [2]:

import easydiffraction as edi

import easydiffraction as edi

📦 Define Project¶

The project manages the structure, experiment, analysis, and saved results used throughout the tutorial.

Create Project¶

In [3]:

project = edi.Project(
    name='lmo_echidna',
    description='LMO refinement using ECHIDNA neutron powder diffraction data.',
)

project = edi.Project( name='lmo_echidna', description='LMO refinement using ECHIDNA neutron powder diffraction data.', )

Save Initial Project¶

Create the project directory before fitting so that analysis results can be written as they are produced.

In [4]:

project.save_as(dir_path='projects/refine-lmo-echidna')

project.save_as(dir_path='projects/refine-lmo-echidna')

Saving project 📦 'lmo_echidna' to '../../../projects/refine-lmo-echidna'

├── 📄 project.edi

├── 📁 structures/

├── 📁 experiments/

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 lmo_echidna.html

🧩 Define Structure¶

The rhombohedral LMO model contains two crystallographic cation sites. Li1 and Ni1 share the site at z = 1/2, while Li2 and Ni2 share the site at z = 0. Their starting occupancies describe a small amount of Li/Ni site mixing.

Create Structure from CIF¶

Define the complete starting structure in a compact inline CIF. The hexagonal setting of space group R-3m is used, with approximate cell dimensions and oxygen z coordinate.

In [5]:

structure_cif = """
data_lmo

_cell.length_a  2.88
_cell.length_b  2.88
_cell.length_c 14.18
_cell.angle_alpha 90.
_cell.angle_beta  90.
_cell.angle_gamma 120.

_space_group.name_h_m "R -3 m"
_space_group.coord_system_code h

loop_
_atom_site.id
_atom_site.type_symbol
_atom_site.fract_x
_atom_site.fract_y
_atom_site.fract_z
_atom_site.occupancy
_atom_site.adp_iso
_atom_site.adp_type
O   O   0. 0. 0.26  1.0000  0.94645 Biso
Ni1 Ni  0. 0. 0.5   0.0184  1.00000 Biso
Li1 Li  0. 0. 0.5   0.9816  1.00000 Biso
Li2 Li  0. 0. 0.0   0.0184  1.00000 Biso
Ni2 Ni  0. 0. 0.0   0.9816  1.00000 Biso
"""

structure_cif = """ data_lmo _cell.length_a 2.88 _cell.length_b 2.88 _cell.length_c 14.18 _cell.angle_alpha 90. _cell.angle_beta 90. _cell.angle_gamma 120. _space_group.name_h_m "R -3 m" _space_group.coord_system_code h loop_ _atom_site.id _atom_site.type_symbol _atom_site.fract_x _atom_site.fract_y _atom_site.fract_z _atom_site.occupancy _atom_site.adp_iso _atom_site.adp_type O O 0. 0. 0.26 1.0000 0.94645 Biso Ni1 Ni 0. 0. 0.5 0.0184 1.00000 Biso Li1 Li 0. 0. 0.5 0.9816 1.00000 Biso Li2 Li 0. 0. 0.0 0.0184 1.00000 Biso Ni2 Ni 0. 0. 0.0 0.9816 1.00000 Biso """

In [6]:

project.structures.add_from_cif_str(structure_cif)

project.structures.add_from_cif_str(structure_cif)

In [7]:

project.structures.show_names()

project.structures.show_names()

Defined structures 🧩

['lmo']

Use a short alias to access the structure parameters below.

In [8]:

structure = project.structures['lmo']

structure = project.structures['lmo']

Display Structure¶

Inspect the structure as text and as an interactive crystal model.

In [9]:

structure.show_as_text()

structure.show_as_text()

Structure 🧩 'lmo' as text

	Edi
1	data_lmo
2
3	_cell.length_a 2.88
4	_cell.length_b 2.88
5	_cell.length_c 14.18
6	_cell.angle_alpha 90.
7	_cell.angle_beta 90.
8	_cell.angle_gamma 120.
9
10	_space_group.name_h_m "R -3 m"
11	_space_group.coord_system_code h
12
13	_geom.min_bond_distance_cutoff 0.
14	_geom.bond_distance_inc 0.25
15
16	loop_
17	_atom_site.id
18	_atom_site.type_symbol
19	_atom_site.fract_x
20	_atom_site.fract_y
21	_atom_site.fract_z
22	_atom_site.wyckoff_letter
23	_atom_site.multiplicity
24	_atom_site.occupancy
25	_atom_site.adp_iso
26	_atom_site.adp_type
27	O O 0. 0. 0.26 c 6 1. 0.94645 Biso
28	Ni1 Ni 0. 0. 0.5 b 3 0.0184 1. Biso
29	Li1 Li 0. 0. 0.5 b 3 0.9816 1. Biso
30	Li2 Li 0. 0. 0. a 3 0.0184 1. Biso
31	Ni2 Ni 0. 0. 0. a 3 0.9816 1. Biso

In [10]:

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

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

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

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

🔬 Define Experiment¶

Load the measured pattern, choose the calculation engine, configure the instrument and peak profile, and link the structure to the data.

Download Data¶

Download the LMO pattern from the EasyDiffraction online data repository. The columns contain 2-theta, intensity, and the standard uncertainty of the measured intensity.

In [11]:

data_path = edi.download_data('meas-lmo-echidna', destination='data')

data_path = edi.download_data('meas-lmo-echidna', destination='data')

Getting data...

Data 'meas-lmo-echidna': LMO, ECHIDNA (ANSTO), wavelength 1.6215 A

✅ Data 'meas-lmo-echidna' downloaded to '../../../data/meas-lmo-echidna.dat'

Create Experiment¶

In [12]:

project.experiments.add_from_data_path(
    name='echidna',
    data_path=data_path,
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
)

project.experiments.add_from_data_path( name='echidna', data_path=data_path, sample_form='powder', beam_mode='constant wavelength', radiation_probe='neutron', )

Data loaded successfully

Experiment 🔬 'echidna'. Number of data points: 3200.

Use a short alias to access the experiment parameters below.

In [13]:

experiment = project.experiments['echidna']

experiment = project.experiments['echidna']

Select Calculator¶

Use the CrysFML calculation engine for this refinement.

In [14]:

experiment.calculator.show_supported()

experiment.calculator.show_supported()

Calculator types

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

In [15]:

experiment.calculator.type = 'crysfml'

experiment.calculator.type = 'crysfml'

Calculator for experiment 'echidna' changed to

crysfml

Set Instrument¶

Set the measured neutron wavelength and approximate calibration corrections for the 2-theta zero, sample displacement, and sample transparency.

In [16]:

experiment.instrument.setup_wavelength = 1.6215
experiment.instrument.calib_twotheta_offset = 0.0
experiment.instrument.calib_sample_displacement = 0.03
experiment.instrument.calib_sample_transparency = 0.02

experiment.instrument.setup_wavelength = 1.6215 experiment.instrument.calib_twotheta_offset = 0.0 experiment.instrument.calib_sample_displacement = 0.03 experiment.instrument.calib_sample_transparency = 0.02

Set Peak Profile¶

Select the Thompson-Cox-Hastings pseudo-Voigt profile. U, V, and W define its Gaussian broadening; Y defines its Lorentzian broadening; and the Finger-Cox-Jephcoat terms describe the low-angle asymmetry.

In [17]:

experiment.peak.show_supported()

experiment.peak.show_supported()

Peak types

		Type	Description
1	*	pseudo-voigt	CWL pseudo-Voigt profile
2		thompson-cox-hastings	CWL Thompson-Cox-Hastings profile with FCJ asymmetry correction.

In [18]:

experiment.peak.type = 'thompson-cox-hastings'

experiment.peak.type = 'thompson-cox-hastings'

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • asym_fcj_1=0.0                                                                                                               
   • asym_fcj_2=0.0                                                                                                               

Peak profile type for experiment 'echidna' changed to

thompson-cox-hastings

In [19]:

experiment.peak.broad_gauss_u = 0.1
experiment.peak.broad_gauss_v = -0.3
experiment.peak.broad_gauss_w = 0.4
experiment.peak.broad_lorentz_y = 0.1
experiment.peak.asym_fcj_1 = 0.08
experiment.peak.asym_fcj_2 = 0.08

experiment.peak.broad_gauss_u = 0.1 experiment.peak.broad_gauss_v = -0.3 experiment.peak.broad_gauss_w = 0.4 experiment.peak.broad_lorentz_y = 0.1 experiment.peak.asym_fcj_1 = 0.08 experiment.peak.asym_fcj_2 = 0.08

Set Absorption¶

Apply the Hewat cylindrical-sample absorption correction with an approximate value of the dimensionless absorption-radius product.

In [20]:

experiment.absorption.type = 'cylinder-hewat'
experiment.absorption.mu_r = 0.3

experiment.absorption.type = 'cylinder-hewat' experiment.absorption.mu_r = 0.3

Absorption type changed to

cylinder-hewat

Set Excluded Regions¶

Exclude the low- and high-angle regions outside the useful measured range from 12 to 162 degrees.

In [21]:

experiment.excluded_regions.create(id='1', start=0.0, end=12.0)
experiment.excluded_regions.create(id='2', start=162.0, end=180.0)

experiment.excluded_regions.create(id='1', start=0.0, end=12.0) experiment.excluded_regions.create(id='2', start=162.0, end=180.0)

Set Background¶

Estimate initial background points from the measured pattern.

In [22]:

experiment.background.show_supported()

experiment.background.show_supported()

Background types

		Type	Description
1		chebyshev	Chebyshev polynomial background
2	*	line-segment	Linear interpolation between points

In [23]:

experiment.background.auto_estimate()

experiment.background.auto_estimate()

In [24]:

experiment.background.show()

experiment.background.show()

Line-segment background points

	Position	Intensity
1	12.02420	558.74541
2	20.03970	640.62497
3	32.05130	497.74000
4	39.42070	641.87000
5	58.71960	553.94103
6	93.37010	550.51000
7	149.84400	653.58448
8	161.99680	772.38099

Set Linked Structure¶

Link the LMO model to the experiment and provide an initial estimate for its scale factor.

In [25]:

experiment.linked_structures.create(structure_id='lmo', scale=10.0)

experiment.linked_structures.create(structure_id='lmo', scale=10.0)

Inspect Experiment¶

Display the configured experiment as text.

In [26]:

experiment.show_as_text()

experiment.show_as_text()

Experiment 🔬 'echidna' as text

	Edi
1	data_echidna
2
3	_experiment_type.sample_form powder
4	_experiment_type.beam_mode "constant wavelength"
5	_experiment_type.radiation_probe neutron
6	_experiment_type.scattering_type bragg
7
8	_diffrn.ambient_temperature ?
9	_diffrn.ambient_pressure ?
10	_diffrn.ambient_magnetic_field ?
11	_diffrn.ambient_electric_field ?
12
13	_calculator.type crysfml
14
15	_peak.asym_fcj_1 0.08
16	_peak.asym_fcj_2 0.08
17	_peak.broad_gauss_u 0.1
18	_peak.broad_gauss_v -0.3
19	_peak.broad_gauss_w 0.4
20	_peak.broad_lorentz_x 0.
21	_peak.broad_lorentz_y 0.1
22	_peak.cutoff_fwhm 0.
23	_peak.type cwl-thompson-cox-hastings
24
25	_instrument.setup_wavelength 1.6215
26	_instrument.setup_wavelength_2 0.
27	_instrument.setup_wavelength_2_to_1_ratio 0.
28	_instrument.calib_twotheta_offset 0.
29	_instrument.calib_sample_displacement 0.03
30	_instrument.calib_sample_transparency 0.02
31
32	_absorption.type cylinder-hewat
33	_absorption.mu_r 0.3
34
35	loop_
36	_linked_structure.structure_id
37	_linked_structure.scale
38	lmo 10.
39
40	loop_
41	_excluded_region.id
42	_excluded_region.start
43	_excluded_region.end
44	1 0. 12.
45	2 162. 180.
46
47	_background.type line-segment
48
49	loop_
50	_background.id
51	_background.position
52	_background.intensity
53	1 12.0242 558.74540525
54	2 20.0397 640.62496987
55	3 32.0513 497.74
56	4 39.4207 641.87
57	5 58.7196 553.94102828
58	6 93.3701 550.51
59	7 149.844 653.58448376
60	8 161.9968 772.38098901
61
62	loop_
63	_data.two_theta
64	_data.id
65	_data.d_spacing
66	_data.intensity_meas
67	_data.intensity_meas_su
68	_data.intensity_calc
69	_data.intensity_bkg
70	_data.calc_status
71	4.0138 1 0. 73.54 11.06927 0. 0. excl
72	4.0639 2 0. 76.08 11.30158 0. 0. excl
73	4.1139 3 0. 69.48 10.74801 0. 0. excl
74	4.164 4 0. 73.23 11.00793 0. 0. excl
75	4.2139 5 0. 87.95 12.11325 0. 0. excl
76	4.2638 6 0. 103.51 13.09452 0. 0. excl
77	4.3139 7 0. 134.34 14.94499 0. 0. excl
78	4.3639 8 0. 158.84 16.27419 0. 0. excl
79	4.4139 9 0. 157.33 16.2141 0. 0. excl
80	4.4639 10 0. 185.27 17.68956 0. 0. excl
81	...
82	163.4564 3191 0. 1063.71 69.45311 0. 0. excl
83	163.5065 3192 0. 981.95 66.61054 0. 0. excl
84	163.5566 3193 0. 959.97 65.18457 0. 0. excl
85	163.6065 3194 0. 1116.65 71.63894 0. 0. excl
86	163.6565 3195 0. 1014.94 67.92402 0. 0. excl
87	163.7066 3196 0. 1106.06 70.89243 0. 0. excl
88	163.7566 3197 0. 1219.54 75.04669 0. 0. excl
89	163.8065 3198 0. 1272.44 76.11867 0. 0. excl
90	163.8565 3199 0. 1239.6 75.53265 0. 0. excl
91	163.9066 3200 0. 1262.89 76.04648 0. 0. excl

🚀 Perform Analysis¶

Inspect the starting calculation, constrain the coupled site-mixing parameters, select the independent refinement parameters, and fit the model to the measured pattern.

Display Initial Pattern¶

In [27]:

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

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

Loading plot…

Set Constraints¶

First create readable aliases for the displacement and occupancy parameters involved in the constraints.

In [28]:

project.analysis.aliases.create(
    id='biso_Li1',
    param=structure.atom_sites['Li1'].adp_iso,
)
project.analysis.aliases.create(
    id='biso_Li2',
    param=structure.atom_sites['Li2'].adp_iso,
)
project.analysis.aliases.create(
    id='biso_Ni1',
    param=structure.atom_sites['Ni1'].adp_iso,
)
project.analysis.aliases.create(
    id='biso_Ni2',
    param=structure.atom_sites['Ni2'].adp_iso,
)

project.analysis.aliases.create(
    id='occ_Li1',
    param=structure.atom_sites['Li1'].occupancy,
)
project.analysis.aliases.create(
    id='occ_Li2',
    param=structure.atom_sites['Li2'].occupancy,
)
project.analysis.aliases.create(
    id='occ_Ni1',
    param=structure.atom_sites['Ni1'].occupancy,
)
project.analysis.aliases.create(
    id='occ_Ni2',
    param=structure.atom_sites['Ni2'].occupancy,
)

project.analysis.aliases.create( id='biso_Li1', param=structure.atom_sites['Li1'].adp_iso, ) project.analysis.aliases.create( id='biso_Li2', param=structure.atom_sites['Li2'].adp_iso, ) project.analysis.aliases.create( id='biso_Ni1', param=structure.atom_sites['Ni1'].adp_iso, ) project.analysis.aliases.create( id='biso_Ni2', param=structure.atom_sites['Ni2'].adp_iso, ) project.analysis.aliases.create( id='occ_Li1', param=structure.atom_sites['Li1'].occupancy, ) project.analysis.aliases.create( id='occ_Li2', param=structure.atom_sites['Li2'].occupancy, ) project.analysis.aliases.create( id='occ_Ni1', param=structure.atom_sites['Ni1'].occupancy, ) project.analysis.aliases.create( id='occ_Ni2', param=structure.atom_sites['Ni2'].occupancy, )

Atoms sharing a crystallographic site use the same Biso value. The occupancy constraints keep each shared site fully occupied and couple the same Li/Ni exchange fraction across both sites. Consequently, occ_Li1 is the only independent occupancy parameter.

In [29]:

project.analysis.constraints.create(
    id='1',
    expression='biso_Ni1 = biso_Li1',
)
project.analysis.constraints.create(
    id='2',
    expression='biso_Li2 = biso_Ni2',
)
project.analysis.constraints.create(
    id='3',
    expression='occ_Ni1 = 1 - occ_Li1',
)
project.analysis.constraints.create(
    id='4',
    expression='occ_Li2 = 1 - occ_Li1',
)
project.analysis.constraints.create(
    id='5',
    expression='occ_Ni2 = occ_Li1',
)

project.analysis.constraints.create( id='1', expression='biso_Ni1 = biso_Li1', ) project.analysis.constraints.create( id='2', expression='biso_Li2 = biso_Ni2', ) project.analysis.constraints.create( id='3', expression='occ_Ni1 = 1 - occ_Li1', ) project.analysis.constraints.create( id='4', expression='occ_Li2 = 1 - occ_Li1', ) project.analysis.constraints.create( id='5', expression='occ_Ni2 = occ_Li1', )

In [30]:

project.analysis.constraints.show()

project.analysis.constraints.show()

User defined constraints

	id	expression
1	1	biso_Ni1 = biso_Li1
2	2	biso_Li2 = biso_Ni2
3	3	occ_Ni1 = 1 - occ_Li1
4	4	occ_Li2 = 1 - occ_Li1
5	5	occ_Ni2 = occ_Li1

Constraints enabled: True

Set Free Parameters¶

Refine the two independent cell lengths, oxygen z coordinate, the two independent cation Biso values, and the independent Li occupancy.

In [31]:

structure.cell.length_a.free = True
structure.cell.length_c.free = True

structure.atom_sites['O'].fract_z.free = True
structure.atom_sites['Li1'].adp_iso.free = True
structure.atom_sites['Ni2'].adp_iso.free = True
structure.atom_sites['Li1'].occupancy.free = True

structure.cell.length_a.free = True structure.cell.length_c.free = True structure.atom_sites['O'].fract_z.free = True structure.atom_sites['Li1'].adp_iso.free = True structure.atom_sites['Ni2'].adp_iso.free = True structure.atom_sites['Li1'].occupancy.free = True

Refine the scale, instrument calibration terms, U/V/W/Y profile terms, and active background-point intensities. The asymmetry and absorption parameters remain fixed at their approximate values.

In [32]:

experiment.linked_structures['lmo'].scale.free = True

experiment.instrument.calib_twotheta_offset.free = True
experiment.instrument.calib_sample_displacement.free = True
experiment.instrument.calib_sample_transparency.free = True

experiment.peak.broad_gauss_u.free = True
experiment.peak.broad_gauss_v.free = True
experiment.peak.broad_gauss_w.free = True
experiment.peak.broad_lorentz_y.free = True

for point in experiment.background:
    point.intensity.free = True

experiment.linked_structures['lmo'].scale.free = True experiment.instrument.calib_twotheta_offset.free = True experiment.instrument.calib_sample_displacement.free = True experiment.instrument.calib_sample_transparency.free = True experiment.peak.broad_gauss_u.free = True experiment.peak.broad_gauss_v.free = True experiment.peak.broad_gauss_w.free = True experiment.peak.broad_lorentz_y.free = True for point in experiment.background: point.intensity.free = True

Display all parameters selected for refinement.

In [33]:

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	lmo	cell		length_a	2.88000		-inf	inf	Å
2	lmo	cell		length_c	14.18000		-inf	inf	Å
3	lmo	atom_site	O	fract_z	0.26000		-inf	inf
4	lmo	atom_site	Li1	occupancy	0.98160		-inf	inf
5	lmo	atom_site	Li1	adp_iso	1.00000		-inf	inf	Ų
6	lmo	atom_site	Ni2	adp_iso	1.00000		-inf	inf	Ų
7	echidna	linked_structure	lmo	scale	10.00000		-inf	inf
8	echidna	peak		broad_gauss_u	0.10000		-inf	inf	deg²
9	echidna	peak		broad_gauss_v	-0.30000		-inf	inf	deg²
10	echidna	peak		broad_gauss_w	0.40000		-inf	inf	deg²
11	echidna	peak		broad_lorentz_y	0.10000		-inf	inf	deg
12	echidna	instrument		twotheta_offset	0.00000		-inf	inf	deg
13	echidna	instrument		sample_displacement	0.03000		-inf	inf	deg
14	echidna	instrument		sample_transparency	0.02000		-inf	inf	deg
15	echidna	background	1	intensity	558.74541		-inf	inf
16	echidna	background	2	intensity	640.62497		-inf	inf
17	echidna	background	3	intensity	497.74000		-inf	inf
18	echidna	background	4	intensity	641.87000		-inf	inf
19	echidna	background	5	intensity	553.94103		-inf	inf
20	echidna	background	6	intensity	550.51000		-inf	inf
21	echidna	background	7	intensity	653.58448		-inf	inf
22	echidna	background	8	intensity	772.38099		-inf	inf

Select Minimizer¶

Use the Levenberg-Marquardt optimizer provided by Bumps.

In [34]:

project.analysis.minimizer.show_supported()

project.analysis.minimizer.show_supported()

Minimizer types

		Type	Description
1		bumps	BUMPS library using the default Levenberg-Marquardt method
2		bumps (amoeba)	BUMPS library with Nelder-Mead simplex method
3		bumps (de)	BUMPS library with differential evolution method
4		bumps (dream)	BUMPS library with DREAM Bayesian sampling
5		bumps (lm)	BUMPS library with Levenberg-Marquardt method
6		dfols	DFO-LS library for derivative-free least-squares optimization
7		emcee	emcee affine-invariant ensemble Bayesian sampling
8		lmfit	LMFIT library using the default Levenberg-Marquardt method
9		lmfit (least_squares)	LMFIT library with SciPy's trust region reflective algorithm
10	*	lmfit (leastsq)	LMFIT library with Levenberg-Marquardt least squares method

In [35]:

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

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

Current minimizer changed to

bumps (lm)

Fit Model¶

In [36]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.37	84.57
2	24	6.38	57.98	31.4% ↓
3	47	11.63	6.22	89.3% ↓
4	70	16.50	2.89	53.5% ↓
5	93	21.35	2.44	15.5% ↓
6	116	26.14	2.41	1.2% ↓
7	162	35.73	2.41
8	208	45.32	2.41
9	232	50.34	2.41
10	278	59.94	2.41
11	302	65.06	2.41
12	328	82.74	2.41

🏆 Best goodness-of-fit (reduced χ²) is 2.41 at iteration 302

✅ Fitting complete.

Saving project 📦 'lmo_echidna' to '../../../projects/refine-lmo-echidna'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 lmo.edi

├── 📁 experiments/

│   └── 📄 echidna.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 lmo_echidna.html

Inspect Results¶

Review the fit statistics, refined parameters, and parameter correlations, then compare the refined calculation with the data.

In [37]:

project.display.fit.results()

project.display.fit.results()

⚙️ 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)	82.74
4	📏 Goodness-of-fit (reduced χ²)	2.41
5	📏 R-factor (Rf, %)	3.94
6	📏 R-factor squared (Rf², %)	4.50
7	📏 Weighted R-factor (wR, %)	4.29

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	lmo	cell		length_a	Å	2.8800	2.8752	0.0001	0.17 % ↓
2	lmo	cell		length_c	Å	14.1800	14.1835	0.0004	0.02 % ↑
3	lmo	atom_site	O	fract_z		0.2600	0.2591	0.0001	0.36 % ↓
4	lmo	atom_site	Li1	occupancy		0.9816	0.9804	0.0018	0.12 % ↓
5	lmo	atom_site	Li1	adp_iso	Ų	1.0000	1.9540	0.1093	95.40 % ↑
6	lmo	atom_site	Ni2	adp_iso	Ų	1.0000	0.2274	0.0118	77.26 % ↓
7	echidna	linked_structure	lmo	scale		10.0000	15.9990	0.0841	59.99 % ↑
8	echidna	peak		broad_gauss_u	deg²	0.1000	0.0972	0.0023	2.84 % ↓
9	echidna	peak		broad_gauss_v	deg²	-0.3000	-0.2842	0.0066	5.26 % ↓
10	echidna	peak		broad_gauss_w	deg²	0.4000	0.4036	0.0052	0.91 % ↑
11	echidna	peak		broad_lorentz_y	deg	0.1000	0.0806	0.0021	19.35 % ↓
12	echidna	instrument		twotheta_offset	deg	0.0000	-0.0640	0.0072	N/A
13	echidna	instrument		sample_displacement	deg	0.0300	0.0270	0.0042	10.07 % ↓
14	echidna	instrument		sample_transparency	deg	0.0200	0.0176	0.0054	12.24 % ↓
15	echidna	background	1	intensity		558.7454	548.6774	5.5305	1.80 % ↓
16	echidna	background	2	intensity		640.6250	564.8788	4.4804	11.82 % ↓
17	echidna	background	3	intensity		497.7400	528.5260	3.8135	6.19 % ↑
18	echidna	background	4	intensity		641.8700	584.0418	3.5967	9.01 % ↓
19	echidna	background	5	intensity		553.9410	568.5889	2.4646	2.64 % ↑
20	echidna	background	6	intensity		550.5100	574.2245	1.9936	4.31 % ↑
21	echidna	background	7	intensity		653.5845	644.2330	2.7590	1.43 % ↓
22	echidna	background	8	intensity		772.3810	631.4711	6.2037	18.24 % ↓

• 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

In [38]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

In [39]:

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

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

Loading plot…

💾 Save Project¶

Save the refined parameters and analysis results in the project directory created near the beginning of the tutorial.

In [40]:

project.save()

project.save()

Saving project 📦 'lmo_echidna' to '../../../projects/refine-lmo-echidna'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 lmo.edi

├── 📁 experiments/

│   └── 📄 echidna.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 lmo_echidna.html