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.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 0.53000000(2000000) Biso
24	Ti Ti 0.00000000 0.00000000 0.00000000 c 1.00000000 0.48000000(3000000) Biso
25	O1 O 0.32804000(9000) 0.12500000 0.12500000 f 1.00000000(1000000) 0.45000000(2000000) Biso
26	O2 O 0.37500000 0.37500000 0.37500000 b 0.97000000(2000000) 0.23000000(4000000) Biso
27

In [9]:

structure.atom_sites['Tb'].adp_type = 'Uiso'
structure.atom_sites['Ti'].adp_type = 'Uiso'
structure.atom_sites['O1'].adp_type = 'Uiso'
structure.atom_sites['O2'].adp_type = 'Uiso'

structure.atom_sites['Tb'].adp_type = 'Uiso' structure.atom_sites['Ti'].adp_type = 'Uiso' structure.atom_sites['O1'].adp_type = 'Uiso' structure.atom_sites['O2'].adp_type = 'Uiso'

In [10]:

print(structure.atom_sites.as_cif)

print(structure.atom_sites.as_cif)

loop_
_atom_site.label
_atom_site.type_symbol
_atom_site.fract_x
_atom_site.fract_y
_atom_site.fract_z
_atom_site.Wyckoff_letter
_atom_site.occupancy
_atom_site.U_iso_or_equiv
_atom_site.adp_type
Tb Tb 0.50000000 0.50000000 0.50000000 d 1.00000000 0.00671253(2000000) Uiso
Ti Ti 0.00000000 0.00000000 0.00000000 c 1.00000000 0.00607927(3000000) Uiso
O1 O 0.32804000(9000) 0.12500000 0.12500000 f 1.00000000(1000000) 0.00569932(2000000) Uiso
O2 O 0.37500000 0.37500000 0.37500000 b 0.97000000(2000000) 0.00291298(4000000) Uiso

In [11]:

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

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

Step 3: Define Experiment¶

In [12]:

# Download data file from repository
data_path = ed.download_data(id=19, destination='data')

# Download data file from repository 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 [13]:

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 [14]:

experiment = project.experiments['heidi']

experiment = project.experiments['heidi']

In [15]:

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

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

In [16]:

experiment.instrument.setup_wavelength = 0.793

experiment.instrument.setup_wavelength = 0.793

In [17]:

experiment.extinction.mosaicity = 35000
experiment.extinction.radius = 10

experiment.extinction.mosaicity = 35000 experiment.extinction.radius = 10

Step 4: Perform Analysis I (ADP iso)¶

In [18]:

project.plotter.plot_meas_vs_calc(expt_name='heidi')

project.plotter.plot_meas_vs_calc(expt_name='heidi')

In [19]:

structure.atom_sites['O1'].fract_x.free = True

structure.atom_sites['Ti'].occupancy.free = True
structure.atom_sites['O1'].occupancy.free = True
structure.atom_sites['O2'].occupancy.free = True

structure.atom_sites['Tb'].adp_iso.free = True
structure.atom_sites['Ti'].adp_iso.free = True
structure.atom_sites['O1'].adp_iso.free = True
structure.atom_sites['O2'].adp_iso.free = True

structure.atom_sites['O1'].fract_x.free = True structure.atom_sites['Ti'].occupancy.free = True structure.atom_sites['O1'].occupancy.free = True structure.atom_sites['O2'].occupancy.free = True structure.atom_sites['Tb'].adp_iso.free = True structure.atom_sites['Ti'].adp_iso.free = True structure.atom_sites['O1'].adp_iso.free = True structure.atom_sites['O2'].adp_iso.free = True

In [20]:

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

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

In [21]:

# 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()

Standard fitting

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

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

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

	iteration	χ²	improvement [%]
1	1	355.79
2	14	186.41	47.6% ↓
3	25	42.28	77.3% ↓
4	36	12.97	69.3% ↓
5	47	12.75	1.6% ↓
6	81	12.75

🏆 Best goodness-of-fit (reduced χ²) is 12.75 at iteration 80

✅ Fitting complete.

In [22]:

# Show fit results summary
project.analysis.display.fit_results()

# Show fit results summary project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 2.03 seconds

📏 Goodness-of-fit (reduced χ²): 12.75

📏 R-factor (Rf): 7.65%

📏 R-factor squared (Rf²): 8.10%

📏 Weighted R-factor (wR): 8.59%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	tbti	atom_site	Tb	adp_iso	0.0000	0.0068	0.0003	Ų	N/A
2	tbti	atom_site	Ti	occupancy	1.0000	0.9730	0.0178		2.70 % ↓
3	tbti	atom_site	Ti	adp_iso	0.0000	0.0054	0.0006	Ų	N/A
4	tbti	atom_site	O1	fract_x	0.3280	0.3280	0.0001		0.00 % ↑
5	tbti	atom_site	O1	occupancy	1.0000	0.9989	0.0104		0.11 % ↓
6	tbti	atom_site	O1	adp_iso	0.0000	0.0057	0.0002	Ų	N/A
7	tbti	atom_site	O2	occupancy	0.9700	0.9688	0.0183		0.12 % ↓
8	tbti	atom_site	O2	adp_iso	0.0000	0.0030	0.0005	Ų	N/A
9	heidi	extinction		radius	10.0000	26.4348	1.0122	μm	164.35 % ↑
10	heidi	linked_crystal		scale	1.0000	2.9329	0.0586		193.29 % ↑

In [23]:

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.U_iso_or_equiv
22	_atom_site.adp_type
23	Tb Tb 0.50000000 0.50000000 0.50000000 d 1.00000000 0.00681683(28758) Uiso
24	Ti Ti 0.00000000 0.00000000 0.00000000 c 0.97299648(1780992) 0.00539742(59789) Uiso
25	O1 O 0.32804378(9395) 0.12500000 0.12500000 f 0.99893142(1039031) 0.00572628(24749) Uiso
26	O2 O 0.37500000 0.37500000 0.37500000 b 0.96880340(1827132) 0.00302999(48336) Uiso
27

In [24]:

project.experiments.show_names()

project.experiments.show_names()

Defined experiments 🔬

['heidi']

In [25]:

project.plotter.plot_meas_vs_calc(expt_name='heidi')

project.plotter.plot_meas_vs_calc(expt_name='heidi')

Step 5: Perform Analysis (ADP aniso)¶

In [26]:

structure.atom_sites['Tb'].adp_type = 'Uani'
structure.atom_sites['Ti'].adp_type = 'Uani'
structure.atom_sites['O1'].adp_type = 'Uani'
# structure.atom_sites['O2'].adp_type = 'Uani'

structure.atom_sites['Tb'].adp_type = 'Uani' structure.atom_sites['Ti'].adp_type = 'Uani' structure.atom_sites['O1'].adp_type = 'Uani' # structure.atom_sites['O2'].adp_type = 'Uani'

In [27]:

print(structure.atom_site_aniso.as_cif)

print(structure.atom_site_aniso.as_cif)

loop_
_atom_site_aniso.label
_atom_site_aniso.U_11
_atom_site_aniso.U_22
_atom_site_aniso.U_33
_atom_site_aniso.U_12
_atom_site_aniso.U_13
_atom_site_aniso.U_23
Tb 0.00681683 0.00681683 0.00681683 0.00000000 0.00000000 0.00000000
Ti 0.00539742 0.00539742 0.00539742 0.00000000 0.00000000 0.00000000
O1 0.00572628 0.00572628 0.00572628 0.00000000 0.00000000 0.00000000
O2 ? ? ? ? ? ?

In [28]:

structure.atom_site_aniso['Tb'].adp_11.free = True
structure.atom_site_aniso['Tb'].adp_12.free = True
structure.atom_site_aniso['Ti'].adp_11.free = True
structure.atom_site_aniso['Ti'].adp_12.free = True
structure.atom_site_aniso['O1'].adp_11.free = True
structure.atom_site_aniso['O1'].adp_22.free = True
structure.atom_site_aniso['O1'].adp_23.free = True
# structure.atom_site_aniso['O2'].adp_11.free = True

structure.atom_site_aniso['Tb'].adp_11.free = True structure.atom_site_aniso['Tb'].adp_12.free = True structure.atom_site_aniso['Ti'].adp_11.free = True structure.atom_site_aniso['Ti'].adp_12.free = True structure.atom_site_aniso['O1'].adp_11.free = True structure.atom_site_aniso['O1'].adp_22.free = True structure.atom_site_aniso['O1'].adp_23.free = True # structure.atom_site_aniso['O2'].adp_11.free = True

In [29]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

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

	iteration	χ²	improvement [%]
1	1	13.00
2	18	3.02	76.8% ↓
3	33	2.94	2.5% ↓
4	79	2.94

🏆 Best goodness-of-fit (reduced χ²) is 2.94 at iteration 78

✅ Fitting complete.

In [30]:

project.analysis.display.fit_results()

project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 2.57 seconds

📏 Goodness-of-fit (reduced χ²): 2.94

📏 R-factor (Rf): 4.21%

📏 R-factor squared (Rf²): 6.61%

📏 Weighted R-factor (wR): 13.29%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	tbti	atom_site	Ti	occupancy	0.9730	0.9661	0.0085		0.71 % ↓
2	tbti	atom_site	O1	fract_x	0.3280	0.3280	0.0000		0.01 % ↓
3	tbti	atom_site	O1	occupancy	0.9989	0.9940	0.0050		0.50 % ↓
4	tbti	atom_site	O2	occupancy	0.9688	0.9718	0.0088		0.31 % ↑
5	tbti	atom_site	O2	adp_iso	0.0030	0.0033	0.0002	Ų	7.87 % ↑
6	tbti	atom_site_aniso	Tb	adp_11	0.0068	0.0066	0.0001	Ų	3.45 % ↓
7	tbti	atom_site_aniso	Tb	adp_12	0.0000	-0.0023	0.0001	Ų	N/A
8	tbti	atom_site_aniso	Ti	adp_11	0.0054	0.0049	0.0003	Ų	9.56 % ↓
9	tbti	atom_site_aniso	Ti	adp_12	0.0000	-0.0005	0.0002	Ų	N/A
10	tbti	atom_site_aniso	O1	adp_11	0.0057	0.0067	0.0002	Ų	17.67 % ↑
11	tbti	atom_site_aniso	O1	adp_22	0.0057	0.0049	0.0001	Ų	14.61 % ↓
12	tbti	atom_site_aniso	O1	adp_23	0.0000	0.0019	0.0001	Ų	N/A
13	heidi	extinction		radius	26.4348	24.8317	0.4931	μm	6.06 % ↓
14	heidi	linked_crystal		scale	2.9329	2.8744	0.0274		1.99 % ↓

In [31]:

project.plotter.plot_param_correlations()

project.plotter.plot_param_correlations()

In [32]:

project.plotter.plot_meas_vs_calc(expt_name='heidi')

project.plotter.plot_meas_vs_calc(expt_name='heidi')

In [33]:

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.U_iso_or_equiv
22	_atom_site.adp_type
23	Tb Tb 0.50000000 0.50000000 0.50000000 d 1.00000000 0.00658189 Uani
24	Ti Ti 0.00000000 0.00000000 0.00000000 c 0.96606424(850635) 0.00488144 Uani
25	O1 O 0.32799582(4713) 0.12500000 0.12500000 f 0.99395914(497554) 0.00550586 Uani
26	O2 O 0.37500000 0.37500000 0.37500000 b 0.97182102(883817) 0.00326851(23641) Uiso
27
28	loop_
29	_atom_site_aniso.label
30	_atom_site_aniso.U_11
31	_atom_site_aniso.U_22
32	_atom_site_aniso.U_33
33	_atom_site_aniso.U_12
34	_atom_site_aniso.U_13
35	_atom_site_aniso.U_23
36	Tb 0.00658189(13905) 0.00658189 0.00658189 -0.00228459(11215) -0.00228459 -0.00228459
37	Ti 0.00488144(28692) 0.00488144 0.00488144 -0.00048176(24537) -0.00048176 -0.00048176
38	O1 0.00673797(18380) 0.00488980(13460) 0.00488980 0.00000000 0.00000000 0.00188994(12724)
39	O2 ? ? ? ? ? ?