Structure Refinement: LBCO, HRPT¶

This minimalistic example is designed to show how Rietveld refinement of a crystal structure can be performed when both the sample model and experiment are defined using CIF files.

For this example, constant-wavelength neutron powder diffraction data for La0.5Ba0.5CoO3 from HRPT at PSI is used.

It does not contain any advanced features or options, and includes no comments or explanations—these can be found in the other tutorials. Default values are used for all parameters if not specified. Only essential and self-explanatory code is provided.

The example is intended for users who are already familiar with the EasyDiffraction library and want to quickly get started with a simple refinement. It is also useful for those who want to see what a refinement might look like in code. For a more detailed explanation of the code, please refer to the other tutorials.

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 Sample Model¶

In [4]:

# Download CIF file from repository
model_path = ed.download_data(id=1, destination='data')

# Download CIF file from repository model_path = ed.download_data(id=1, destination='data')

Getting data...

Data #1: La0.5Ba0.5CoO3 (crystal structure)

✅ Data #1 downloaded to 'data/ed-1.cif'

In [5]:

project.sample_models.add(cif_path=model_path)

project.sample_models.add(cif_path=model_path)

Step 3: Define Experiment¶

In [6]:

# Download CIF file from repository
expt_path = ed.download_data(id=2, destination='data')

# Download CIF file from repository expt_path = ed.download_data(id=2, destination='data')

Getting data...

Data #2: La0.5Ba0.5CoO3, HRPT (PSI), 300 K

✅ Data #2 downloaded to 'data/ed-2.cif'

In [7]:

project.experiments.add(cif_path=expt_path)

project.experiments.add(cif_path=expt_path)

Step 4: Perform Analysis¶

In [8]:

# 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 🔬 'hrpt' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	165.50
2	28	33.67	79.7% ↓
3	45	10.85	67.8% ↓
4	63	6.43	40.7% ↓
5	81	3.33	48.2% ↓
6	98	2.23	33.2% ↓
7	116	1.91	14.5% ↓
8	133	1.50	21.1% ↓
9	150	1.45	3.6% ↓
10	167	1.34	7.7% ↓
11	185	1.29	3.4% ↓
12	276	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 261

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 16.55 seconds

📏 Goodness-of-fit (reduced χ²): 1.29

📏 R-factor (Rf): 5.64%

📏 R-factor squared (Rf²): 5.29%

📏 Weighted R-factor (wR): 4.45%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8800	3.8909	0.0000	Å	0.28 % ↑
2	lbco	atom_site	La	b_iso	0.5000	0.5051	6011.6004	Ų	1.02 % ↑
3	lbco	atom_site	Ba	b_iso	0.5000	0.5052	9770.5350	Ų	1.04 % ↑
4	lbco	atom_site	Co	b_iso	0.5000	0.2371	0.0611	Ų	52.59 % ↓
5	lbco	atom_site	O	b_iso	0.5000	1.3935	0.0168	Ų	178.70 % ↑
6	hrpt	linked_phases	lbco	scale	10.0000	9.1349	0.0643		8.65 % ↓
7	hrpt	peak		broad_gauss_u	0.1000	0.0816	0.0031	deg²	18.44 % ↓
8	hrpt	peak		broad_gauss_v	-0.1000	-0.1159	0.0067	deg²	15.90 % ↑
9	hrpt	peak		broad_gauss_w	0.1000	0.1204	0.0033	deg²	20.45 % ↑
10	hrpt	peak		broad_lorentz_y	0.1000	0.0844	0.0021	deg	15.57 % ↓
11	hrpt	instrument		twotheta_offset	0.6000	0.6226	0.0010	deg	3.76 % ↑
12	hrpt	background	1	y	170.0000	168.4242	1.3977		0.93 % ↓
13	hrpt	background	2	y	170.0000	164.3715	1.0025		3.31 % ↓
14	hrpt	background	3	y	170.0000	166.8870	0.7391		1.83 % ↓
15	hrpt	background	4	y	170.0000	175.3977	0.6586		3.18 % ↑
16	hrpt	background	5	y	170.0000	174.3027	0.9113		2.53 % ↑

In [9]:

project.experiments.show_names()

project.experiments.show_names()

Defined experiments 🔬

['hrpt']

In [10]:

project.plot_meas_vs_calc(expt_name='hrpt', show_residual=True)

project.plot_meas_vs_calc(expt_name='hrpt', show_residual=True)

Step 5: Show Project Summary¶

In [11]:

project.summary.show_report()

project.summary.show_report()

PROJECT INFO
━━━━━━━━━━━━

Title

Untitled Project

CRYSTALLOGRAPHIC DATA
━━━━━━━━━━━━━━━━━━━━━

Phase datablock

🧩 lbco

Space group

P m -3 m

Cell parameters

	Parameter	Value
1	a	3.89087
2	b	3.89087
3	c	3.89087
4	alpha	90.00000
5	beta	90.00000
6	gamma	90.00000

Atom sites

	label	type	x	y	z	occ	Biso
1	La	La	0.00000	0.00000	0.00000	0.50000	0.50512
2	Ba	Ba	0.00000	0.00000	0.00000	0.50000	0.50518
3	Co	Co	0.50000	0.50000	0.50000	1.00000	0.23706
4	O	O	0.00000	0.50000	0.50000	1.00000	1.39351

EXPERIMENTS
━━━━━━━━━━━

Experiment datablock

🔬 hrpt

Experiment type

powder, neutron, constant wavelength

Wavelength

1.49400

2θ offset

0.62258

Profile type

PeakProfileTypeEnum.PSEUDO_VOIGT

Peak broadening (Gaussian)

	Parameter	Value
1	U	0.08156
2	V	-0.11590
3	W	0.12045

Peak broadening (Lorentzian)

	Parameter	Value
1	X	0.00000
2	Y	0.08443

FITTING
━━━━━━━

Calculation engine

cryspy

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	1.29