1. Basics of Rietveld Refinement
Scott A Speakman A
x3-6887

2. Uses of the Rietveld Method
The Rietveld method refines user-selected parameters to minimize the difference between an experimental pattern (observed data) and a model based on the hypothesized crystal structure and instrumental parameters (calculated pattern)
can refine information about a single crystal structure
confirm/disprove a hypothetical crystal structure
refine lattice parameters
refine atomic positions, fractional occupancy, and thermal parameter
refine information about a single sample
preferred orientation
refine information about a multiphase sample
determine the relative amounts of each phase

3. Requirements of Rietveld Method
High quality experimental diffraction pattern
a structure model that makes physical and chemical sense
suitable peak and background functions

4. Obtaining High Quality Data
issues to consider
aligned and calibrated instrument
beam overflow problems
thin specimen error
good counting statistics
appropriate step size
sample transparency
surface roughness
preferred orientation
particle size
go to XRD Basics pg 102

5. Describing the Crystal Structure
space group
lattice parameters
atomic positions
atomic site occupancies
atomic thermal parameters
isotropic or anisotropic

6. The Crystal Structure of LaB6
Space Group Pm-3m (221)
Lattice Parameter a= A
Atom
Wyckoff Site x y z B
occ. La 1a 1 6f
0.1993
0.5
0.0027

7. Where to get crystal structure information
check if the structure is already solved
websites
Inorganic Crystal Structure Database (ICSD)
4% is available for free online as a demo
Crystallography Open Database
Mincryst
American Mineralogist
WebMineral
databases
PDF4 from the ICDD
Linus Pauling File from ASM International
Cambridge Structure Database
literature
use the PDF to search ICSD listings and follow the references
look for similar, hopefully isostructural, materials
index the cell, and then try direct methods or ab-initio solutions
beyond the scope of today’s class

8. Instrumental Parameters
background
peak profile parameters
cagliotti parameters u, v, w
pseudo-voigt or other profile parameters
asymmetry correction
anisotropic broadening
error correcting parameters
zero shift
specimen displacement
absorption
extinction
roughness
porosity

9. How many parameters can we refine?
Each diffraction peak acts as an observation
theoretically, refine n-1 parameters
refining a tetragonal LaNi4.85Sn0.15 crystal structure, there might be:
scale factor
2nd order polynomial background: 3 parameters
2 lattice parameters
no atomic positions (all atoms are fixed)
3 or 5 thermal parameters
2 or 4 occupancy factors
zero shift and specimen displacement
5 profile shape parameters
22 parameters maximum with 43 peaks (20 to 120 deg 2theta)
does this mean we can refine all parameters?

10. background functions manually fit background polynomial chebyshev
shifte chebyshev
amorphous sinc function
many others for different programs

11. profile functions vary significantly with programs
almost all programs use Cagglioti U, V, and W
HSP uses pseudo-voigt, Pearson VII, Voigt, or pseudo-voigt 3 (FJC asymmetry)
GSAS uses functions derived more from neutron and synchrotron beamlines

12. go to parameters_calc_pattern.pdf

13. How do you know if a fit is good?
difference pattern
Residuals R
R is the quantity that is minimized during least-squares or other fitting procedures
Rwp is weighted to emphasize intense peaks over background
Rexp estimates the best value R for a data set
an evaluation of how good the data are
RBragg tries to modify the R for a specific phase
GOF (aka X2)

14. Refinement Strategy
Rietveld methods fit a multivarialbe structure-background- profile model to experimental data
lots of potential for false minima, diverging solutions, etc
need to refine the most important variables first, then add more until an adequate solution is realized
a correct solution may not result …

15. Ray Young’s Refinement Strategy
scale factor
zero shift or specimen displacement (not both)
linear background
lattice parameters
more background
peak width, w
atom positions
preferred orientation
isotropic temperature factor B
u, v, and other profile parameters
anisotropic temperature factors

16. HSP Automatic Refinement Strategy
Very similar to Prof Young’s recommendations
a good choice for beginners
you can set limits on any of these parameters

17. Additional Files XRD_Basics_HSP_2006.pdf
large collection of information about X-ray diffraction, instrumentation, and different techniques
X’Pert HighScore Plus Tutorial.pdf
overview of the different functionality available in HighScore Plus
Introduction.pdf
overview of Rietveld
parameters_calc_patterns.pdf
overview of parameters involved in calculating a diffraction pattern

18. further reading
“Rietveld refinement guidelines”, J. Appl.Cryst. 32 (1999) 36-50
R.A. Young (ed), The Rietveld Method, IUCr 1993
V.K. Pecharsky and P.Y. Zavalij, Fundamentals of Powder Diffraction and Structural Characterization of Materials, Kluwer Academic 2003.
DL Bish and JE Post (eds), Modern Powder Diffraction, Reviews in Mineralogy vol 20, Min. Soc. Amer
CCP14 website
prism.mit.edu/xray/resources.htm

19. Rietveld Programs Free Commercial GSAS + ExpGUI Fullprof Rietica
PSSP (polymers)
Maud (not very good)
PowderCell (mostly for calculating patterns and transforming crystal structures, limited refinement)
Commercial
PANalytical HighScore Plus
Bruker TOPAS (also an academic)
MDI Jade or Ruby

20. Examples
Silicon
LaB6
intermetallic LaNi4.85Sn0.15

21. Silicon Open the datafile in HSP Add the structure model
insert the structure manually
import (insert) a struture file
usually use the CIF format– the ubiquitous standard for crystal structures
HSP can also import ICSD *.cry files and structures from other refinement programs
GSAS can import CIF or PowderCell files
try the automatic refinement
manually improve the fit

22. Silicon Crystal Structure
Fd3m
which setting? (2)
a=5.43 A
Si at 0.125, 0.125, 0.125

23. Lanthanum hexaboride LaB6
Open the datafile
insert the crystal structure CIF file
Note that boron (z=5) makes little difference in the XRD pattern compared to the lanthanum (z=57)
what can we do to improve the fit

24. LaNi4.85Sn0.15
The data was taken from Chapter 6 of Fundamentals of Powder Diffraction and Structural Characterization of Materials, by Pecharsky and Zavalij
The structure is a bit more complex that our earlier example, which allows us to explore more features of HighScore Plus
The data (Ch6_1.raw) is in GSAS format, which can be read into HighScore Plus
I have also included a CIF file from the ICSD (#104685) with all the main features of the structure described

25. How can I work without knowledge of the structure?
Issue to Consider
How can I work without knowledge of the structure?
Use LeBail or Pawley method to determine lattice parameters
Try indexing and solving the structure using the HighScore Plus tools
You will find that there are 16 possible space groups for this material, but picking the most common (and simplest) choice, P6/mmm, is the right way to go
Where do I put the atoms?
You can use a Fourier map to find out wherein the structure the electron densities are greatest. Put the heaviest atoms (La) at these sites, then work your way through the chemistry
What variables do I refine and in what sequence?
Take a look at the “automatic” option in HSP - this is not a bad strategy to use. We will go through these in detail…