Obtaining Sensible Starting Parameters
Pre-amble
Rietveld novices usually require some guidance on the setting of initial parameters. First and foremost, don't obtain these from a mate without knowing the provenance of the information and also having a good feel for the information quality. Are you using the best information available?
Crystal Structure Parameters
Background Parameters
I assume here that you will be fitting the pattern background with a polynomial of the type
B = B0 + B1 (2?) + B2 (2?)2 + etc.
If so, set B0 = the average background level and set the others initially to zero. Do not include an excessive number of polynomial terms. Thus, if the background is fairly flat, but with a gently rolling background, then include B0, B1 and B2 , but not any of the higher order terms.
Peak Profile Parameters
The following analysis of your measured pattern will give sensible starting parameters. Here I will assume that we are using a pseudo-Voigt function for which the full-width-half-maximum H in radians is modelled by
H2 = U tan2? + V tan? + W
Brian O'Connor
Department of Applied Physics,
Curtin University of Technology,
PO Box U1987 Perth, WA 6845. Australia.
Rietveld novices usually require some guidance on the setting of initial parameters. First and foremost, don't obtain these from a mate without knowing the provenance of the information and also having a good feel for the information quality. Are you using the best information available?
Crystal Structure Parameters
- Obtain a set of high quality crystal structure parameters (atom positions, site occupancies and thermal parameters; and lattice parameters) for each phase.
- The best compilation of crystal structure parameters for inorganic materials is the Inorganic Crystal Structure Database (ICSD) which is available via http://icsd.ill.fr/icsd/
- You need to know how to extract the best information for a given phase, eg for ?-Al2O3, I use the ICSD reference collection # 73725 from a high quality single crystal structure refinement by Maslen et al conducted with synchrotron data.
- Published thermal parameters from XRD studies are largely useless. Experienced Rietveld users often do better by making an informed guess as to the starting values, eg for a metal oxide, I would start with a B value of 0.5 for metal sites and 1.0 for the oxygen sites.
- There are other sources of crystal structure information, notably the Cambridge Structural Data base which is excellent for organic and metal-organic phases - see http://www.ccdc.cam.ac.uk/products/csd/
Background Parameters
I assume here that you will be fitting the pattern background with a polynomial of the type
B = B0 + B1 (2?) + B2 (2?)2 + etc.
If so, set B0 = the average background level and set the others initially to zero. Do not include an excessive number of polynomial terms. Thus, if the background is fairly flat, but with a gently rolling background, then include B0, B1 and B2 , but not any of the higher order terms.
Peak Profile Parameters
The following analysis of your measured pattern will give sensible starting parameters. Here I will assume that we are using a pseudo-Voigt function for which the full-width-half-maximum H in radians is modelled by
H2 = U tan2? + V tan? + W
- (1) Select a set of well-resolved peaks for each phase ranging from low-2? to high-2?, and measure the width of each peak by eye-balling a measured plot of the pattern.
- (2) Use your favourite plotting program to graph H2 versus tan?, and then fit a quadratic (3-term polynomial) to the plot. The values for the three quadratic terms give U, Vand W.
Brian O'Connor
Department of Applied Physics,
Curtin University of Technology,
PO Box U1987 Perth, WA 6845. Australia.
