ASHISH KUMAR MALLPhD

Materials Science Programme IIT Kanpur

Crystal Structure Approximation Using Rietveld Refinement

Technique

Information hidden in X-ray spectrum

Extracting information from X-ray data

• Search and match– ICDD or JCPDS– High Score Plus– Pearson crystal database

• Indexing• Structural refinement

Rietveld refinement

Rietveld refinement is a technique devised by Hugo Rietveld for crystalline materials. Uses a least squares approach to refine a theoretical line profile until it matches the observed profile. Very useful in case of overlapped reflection, multiple phases and complex structures. Function,

Where, Wi is the statistical weight and c is an overall scale factor such that

being the variance of the “observation”

𝑀𝑀 = �𝑊𝑊𝑖𝑖𝑖𝑖

�𝑦𝑦𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜 − 1𝑐𝑐 𝑦𝑦𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 �

2

Useful software's

X’Pert High score plus GSAS (http://www.ccp14.ac.uk/solution/gsas/ ) RIETANMAUD Programe FullProf (www.ill.eu/sites/fullprof/ )

Bilbao Crystallographic Server (http://www.cryst.ehu.es/)

Space Group Diagrams and Tables http://img.chem.ucl.ac.uk/sgp/large/sgp.htm

Juan Rodríguez-Carvajal

In the FullProf Suite toolbar, select ED PCR tab

Following window pops up on clicking ED PCR tab. Note all the tabs on the right hand side are inactive

Click new data to make a new data file and all tabs get activated.

Press the General tab and fill in the sample name at the given space for title

Click on patterns tab to fill information related to diffraction pattern

Click the Data file/Peak shape tab to enter the data file and peak profile parameters

Browse for diffraction data file which should be in .dat format

To make a data file, copy the intensity column into notepad. At the top, enter the value of the start angle, press space, enter the step, space and then enter the final angle. Save the file with .dat extension.

Click on the Refinement/simulation tab to inform the software what you intend to do

For refinement

For simulation

Target material can be changed as applicable

Click the pattern calculation/peak shape tab to select the peak shape function

It is a combination of Lorentzian and Gaussian function and holds good for most of the profiles

Click on background tab to estimate the background

Select one of the background functions from the list

Holds good only if the background is linear. For sloppy background, choose linear interpolation

Click on Phases tab to enter the phase and space group of the material

Orthorhombic

Structural model (Rietveld method)

X Ray

Pseudo-Voigt

Press symmetry tab and fill the space group and press OK.

Each descriptor separated by a space

P n m a

Press the refinement tab and the following window appears

Press the background tab. Insert background parameters

Contd….

Press profile to input profile parameters

Press atoms to fill atomic information

Label: IUPAC symbol of the element with a suffix if more than one atoms are present of the same type.Ntyp: Simply IUPAC symbol or oxidation state if the same atom is present with different oxidation states.B: Isotropic thermal parametersOcc: No of atoms of a particular type in the unit cell

Save the file in the same folder containing the .dat file

Click on this to Save the file

Select the parameters to vary and run the program

Click on this icon to run the program. It will promptly ask for the data file. Browse for it and select to open it. You will see the refinement taking place.

Sequence for varying the parameters

• Scale factor• Background and instrumental parameters• Lattice parameters and more background parameters• Atomic positions • Peak shape parameters• Atomic occupancies• Thermal parameters• Microstructural parameters

Crystal structure Refinement

Quality of the Refinement

Weighted Profile Factor: n = total number of points in the pattern minus total number of excluded points

Expected Weighted Profile Factor: P=number of parameters

being the variance of the “observation”

Goodness of fit indicator: Reduced chi-square:

In the VESTA Toolbar