Structure Refinement: Tb2TiO7, HEiDi¶

Crystal structure refinement of Tb2TiO7 using single crystal neutron diffraction data from HEiDi at FRM II.

Import Library¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Step 1: Define Project¶

In [3]:

# Create minimal project without name and description
project = ed.Project()

# Create minimal project without name and description project = ed.Project()

Step 2: Define Structure¶

In [4]:

# Download CIF file from repository
structure_path = ed.download_data(id=20, destination='data')

# Download CIF file from repository structure_path = ed.download_data(id=20, destination='data')

Getting data...

Data #20: Tb2Ti2O7 (crystal structure)

✅ Data #20 downloaded to 'data/ed-20.cif'

In [5]:

project.structures.add_from_cif_path(structure_path)

project.structures.add_from_cif_path(structure_path)

In [6]:

project.structures.show_names()

project.structures.show_names()

Defined structures 🧩

['tbti']

In [7]:

structure = project.structures['tbti']

structure = project.structures['tbti']

In [8]:

structure.atom_sites['Tb'].b_iso = 0.0
structure.atom_sites['Ti'].b_iso = 0.0
structure.atom_sites['O1'].b_iso = 0.0
structure.atom_sites['O2'].b_iso = 0.0

structure.atom_sites['Tb'].b_iso = 0.0 structure.atom_sites['Ti'].b_iso = 0.0 structure.atom_sites['O1'].b_iso = 0.0 structure.atom_sites['O2'].b_iso = 0.0

In [9]:

structure.show_as_cif()

structure.show_as_cif()

Structure 🧩 'tbti' as cif

	CIF
1	data_tbti
2
3	_cell.length_a 10.13000000
4	_cell.length_b 10.13000000
5	_cell.length_c 10.13000000
6	_cell.angle_alpha 90.00000000
7	_cell.angle_beta 90.00000000
8	_cell.angle_gamma 90.00000000
9
10	_space_group.name_H-M_alt "F d -3 m"
11	_space_group.IT_coordinate_system_code 2
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.B_iso_or_equiv
22	_atom_site.adp_type
23	Tb Tb 0.50000000 0.50000000 0.50000000 d 1.00000000 0.00000000 Biso
24	Ti Ti 0.00000000 0.00000000 0.00000000 c 1.00000000 0.00000000 Biso
25	O1 O 0.32804000 0.12500000 0.12500000 f 1.00000000 0.00000000 Biso
26	O2 O 0.37500000 0.37500000 0.37500000 b 0.97000000 0.00000000 Biso

Step 3: Define Experiment¶

In [10]:

data_path = ed.download_data(id=19, destination='data')

data_path = ed.download_data(id=19, destination='data')

Getting data...

Data #19: Tb2Ti2O7, HEiDi (MLZ)

✅ Data #19 downloaded to 'data/ed-19.xye'

In [11]:

project.experiments.add_from_data_path(
    name='heidi',
    data_path=data_path,
    sample_form='single crystal',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
)

project.experiments.add_from_data_path( name='heidi', data_path=data_path, sample_form='single crystal', beam_mode='constant wavelength', radiation_probe='neutron', )

Data loaded successfully

Experiment 🔬 'heidi'. Number of data points: 220.

In [12]:

experiment = project.experiments['heidi']  # TODO: <heidi (None)>

experiment = project.experiments['heidi'] # TODO: <heidi (None)>

In [13]:

experiment.linked_crystal.id = 'tbti'
experiment.linked_crystal.scale = 1.0

experiment.linked_crystal.id = 'tbti' experiment.linked_crystal.scale = 1.0

In [14]:

experiment.instrument.setup_wavelength = 0.793

experiment.instrument.setup_wavelength = 0.793

In [15]:

experiment.extinction.mosaicity = 29820
experiment.extinction.radius = 30

experiment.extinction.mosaicity = 29820 experiment.extinction.radius = 30

Step 4: Perform Analysis¶

In [16]:

project.plot_meas_vs_calc(expt_name='heidi')

project.plot_meas_vs_calc(expt_name='heidi')

In [17]:

experiment.linked_crystal.scale.free = True
experiment.extinction.radius.free = True

experiment.linked_crystal.scale.free = True experiment.extinction.radius.free = True

In [18]:

experiment.show_as_cif()

experiment.show_as_cif()

Experiment 🔬 'heidi' as cif

	CIF
1	data_heidi
2
3	_expt_type.sample_form "single crystal"
4	_expt_type.beam_mode "constant wavelength"
5	_expt_type.radiation_probe neutron
6	_expt_type.scattering_type bragg
7
8	_diffrn.ambient_temperature None
9	_diffrn.ambient_pressure None
10	_diffrn.ambient_magnetic_field None
11	_diffrn.ambient_electric_field None
12
13	_extinction.mosaicity 29820.00000000
14	_extinction.radius 30.00000000
15
16	_sc_crystal_block.id tbti
17	_sc_crystal_block.scale 1.00000000
18
19	_instr.wavelength 0.79300000
20
21	loop_
22	_refln.id
23	_refln.d_spacing
24	_refln.sin_theta_over_lambda
25	_refln.index_h
26	_refln.index_k
27	_refln.index_l
28	_refln.intensity_meas
29	_refln.intensity_meas_su
30	_refln.intensity_calc
31	_refln.wavelength
32	1 5.84855823 0.08549116 1 1 1 194.56770000 2.32530000 70.70434347 0.00000000
33	2 3.58149585 0.13960647 2 2 0 22.63190000 1.12330000 5.36662412 0.00000000
34	3 3.05430992 0.16370310 3 1 1 99.29170000 2.56200000 34.58237047 0.00000000
35	4 2.92427911 0.17098231 2 2 2 219.28770000 3.25220000 75.59158819 0.00000000
36	5 2.53250000 0.19743337 4 0 0 1366.73770000 31.07660000 525.98535818 0.00000000
37	6 2.32398138 0.21514802 3 3 1 1381.24040000 24.41820000 524.34607512 0.00000000
38	7 2.06777759 0.24180550 4 2 2 272.46650000 4.23510000 102.47071749 0.00000000
39	8 1.94951941 0.25647347 5 1 1 991.50850000 19.20150000 382.60109139 0.00000000
40	9 1.94951941 0.25647347 3 3 3 504.58740000 7.25520000 171.41304211 0.00000000
41	10 1.79074792 0.27921294 4 4 0 2167.68580000 37.96090000 755.00629740 0.00000000
42	...
43	211 0.52241486 0.95709375 18 6 4 59.66740000 9.11170000 42.29620112 0.00000000
44	212 0.52241486 0.95709375 14 12 6 43.38570000 9.20750000 16.56049760 0.00000000
45	213 0.52034315 0.96090436 19 3 3 23.80390000 9.18670000 0.67255365 0.00000000
46	214 0.52034315 0.96090436 17 9 3 48.75870000 7.73330000 15.66868414 0.00000000
47	215 0.51694440 0.96722201 16 8 8 29.30630000 12.65520000 10.49908682 0.00000000
48	216 0.51493684 0.97099287 17 7 7 1601.51540000 628.89150000 979.81259767 0.00000000
49	217 0.51493684 0.97099287 13 13 7 1176.08960000 414.60180000 837.22733156 0.00000000
50	218 0.51493684 0.97099287 19 5 1 0.83340000 20.42070000 1.03428818 0.00000000
51	219 0.51493684 0.97099287 15 9 9 10.98640000 8.06500000 0.70341088 0.00000000
52	220 0.51427283 0.97224657 12 12 10 14.40740000 11.38000000 0.00000000 0.00000000

In [19]:

# Start refinement. All parameters, which have standard uncertainties
# in the input CIF files, are refined by default.
project.analysis.fit()

# Start refinement. All parameters, which have standard uncertainties # in the input CIF files, are refined by default. project.analysis.fit()

Using experiment 🔬 'heidi' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	512.08
2	13	187.71	63.3% ↓
3	23	66.70	64.5% ↓
4	33	13.20	80.2% ↓
5	43	12.84	2.8% ↓
6	74	12.84

🏆 Best goodness-of-fit (reduced χ²) is 12.84 at iteration 73

✅ Fitting complete.

In [20]:

# Show fit results summary
project.analysis.show_fit_results()

# Show fit results summary project.analysis.show_fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 1.76 seconds

📏 Goodness-of-fit (reduced χ²): 12.84

📏 R-factor (Rf): 7.68%

📏 R-factor squared (Rf²): 8.14%

📏 Weighted R-factor (wR): 8.51%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	tbti	atom_site	Tb	b_iso	0.0000	0.5303	0.0222	Ų	N/A
2	tbti	atom_site	Ti	b_iso	0.0000	0.4760	0.0327	Ų	N/A
3	tbti	atom_site	O1	fract_x	0.3280	0.3280	0.0001		0.00 % ↓
4	tbti	atom_site	O1	occupancy	1.0000	1.0015	0.0103		0.15 % ↑
5	tbti	atom_site	O1	b_iso	0.0000	0.4516	0.0196	Ų	N/A
6	tbti	atom_site	O2	occupancy	0.9700	0.9687	0.0183		0.13 % ↓
7	tbti	atom_site	O2	b_iso	0.0000	0.2333	0.0381	Ų	N/A
8	heidi	extinction		radius	30.0000	27.1471	1.0427	µm	9.51 % ↓
9	heidi	linked_crystal		scale	1.0000	2.9210	0.0583		192.10 % ↑

In [21]:

experiment.show_as_cif()

experiment.show_as_cif()

Experiment 🔬 'heidi' as cif

	CIF
1	data_heidi
2
3	_expt_type.sample_form "single crystal"
4	_expt_type.beam_mode "constant wavelength"
5	_expt_type.radiation_probe neutron
6	_expt_type.scattering_type bragg
7
8	_diffrn.ambient_temperature None
9	_diffrn.ambient_pressure None
10	_diffrn.ambient_magnetic_field None
11	_diffrn.ambient_electric_field None
12
13	_extinction.mosaicity 29820.00000000
14	_extinction.radius 27.14714199
15
16	_sc_crystal_block.id tbti
17	_sc_crystal_block.scale 2.92102835
18
19	_instr.wavelength 0.79300000
20
21	loop_
22	_refln.id
23	_refln.d_spacing
24	_refln.sin_theta_over_lambda
25	_refln.index_h
26	_refln.index_k
27	_refln.index_l
28	_refln.intensity_meas
29	_refln.intensity_meas_su
30	_refln.intensity_calc
31	_refln.wavelength
32	1 5.84855823 0.08549116 1 1 1 194.56770000 2.32530000 206.33175510 0.00000000
33	2 3.58149585 0.13960647 2 2 0 22.63190000 1.12330000 15.33289341 0.00000000
34	3 3.05430992 0.16370310 3 1 1 99.29170000 2.56200000 97.60574185 0.00000000
35	4 2.92427911 0.17098231 2 2 2 219.28770000 3.25220000 215.52043827 0.00000000
36	5 2.53250000 0.19743337 4 0 0 1366.73770000 31.07660000 1608.99981288 0.00000000
37	6 2.32398138 0.21514802 3 3 1 1381.24040000 24.41820000 1583.81250618 0.00000000
38	7 2.06777759 0.24180550 4 2 2 272.46650000 4.23510000 285.13547112 0.00000000
39	8 1.94951941 0.25647347 5 1 1 991.50850000 19.20150000 1102.20798047 0.00000000
40	9 1.94951941 0.25647347 3 3 3 504.58740000 7.25520000 491.44427626 0.00000000
41	10 1.79074792 0.27921294 4 4 0 2167.68580000 37.96090000 2318.98900610 0.00000000
42	...
43	211 0.52241486 0.95709375 18 6 4 59.66740000 9.11170000 80.13302726 0.00000000
44	212 0.52241486 0.95709375 14 12 6 43.38570000 9.20750000 38.16401987 0.00000000
45	213 0.52034315 0.96090436 19 3 3 23.80390000 9.18670000 7.97474738 0.00000000
46	214 0.52034315 0.96090436 17 9 3 48.75870000 7.73330000 40.45604773 0.00000000
47	215 0.51694440 0.96722201 16 8 8 29.30630000 12.65520000 10.19565915 0.00000000
48	216 0.51493684 0.97099287 17 7 7 1601.51540000 628.89150000 1719.43846073 0.00000000
49	217 0.51493684 0.97099287 13 13 7 1176.08960000 414.60180000 1398.33865452 0.00000000
50	218 0.51493684 0.97099287 19 5 1 0.83340000 20.42070000 0.61943652 0.00000000
51	219 0.51493684 0.97099287 15 9 9 10.98640000 8.06500000 0.34582844 0.00000000
52	220 0.51427283 0.97224657 12 12 10 14.40740000 11.38000000 0.00000000 0.00000000

In [22]:

project.experiments.show_names()

project.experiments.show_names()

Defined experiments 🔬

['heidi']

In [23]:

project.plot_meas_vs_calc(expt_name='heidi')

project.plot_meas_vs_calc(expt_name='heidi')

Step 5: Show Project Summary¶

In [24]:

project.summary.show_report()

project.summary.show_report()

————————————
PROJECT INFO
————————————

Title

Untitled Project

—————————————————————
CRYSTALLOGRAPHIC DATA
—————————————————————

Phase datablock

🧩 tbti

Space group

F d -3 m

Cell parameters

	Parameter	Value
1	a	10.13000
2	b	10.13000
3	c	10.13000
4	alpha	90.00000
5	beta	90.00000
6	gamma	90.00000

Atom sites

	label	type	x	y	z	occ	Biso
1	Tb	Tb	0.50000	0.50000	0.50000	1.00000	0.53035
2	Ti	Ti	0.00000	0.00000	0.00000	1.00000	0.47604
3	O1	O	0.32804	0.12500	0.12500	1.00155	0.45165
4	O2	O	0.37500	0.37500	0.37500	0.96871	0.23334

———————————
EXPERIMENTS
———————————

Experiment datablock

🔬 heidi

Experiment type

single crystal, neutron, constant wavelength

Wavelength

0.79300

———————
FITTING
———————

Calculation engine

  heidi: CalculatorEnum.CRYSPY

Minimization engine

lmfit

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	12.84