Fundamentals of Rietveld Refinement Additional Examples HSP v3
Crystal structure approximation by Rietveld Refinement ... Refienment... · Using Rietveld...
Transcript of Crystal structure approximation by Rietveld Refinement ... Refienment... · Using Rietveld...
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