New strategies using old formulae sometimes lead to efficient algorithms.
Every user of the Rietveld method has worked with the so-called "Iobs"
(or "|Fobs|") either by the simple presentation of the Bragg R factor or
by Fourier difference calculation or so on. Some special uses of the Rietveld's
formula for "|Fobs|" extraction were made (to be classified among the two
stages alternatives to the Rietveld method), however the starting |F|s
were always the |Fcalc|s corresponding to a (complete or partial) structure
model (Toraya, Marumo and Yamase, Acta Cryst., 1984, **B40**, 145-150
; Taylor, Miller and Bibby, Z. Kristallogr., 1986, **176**, 183-192
; Taylor, Z. Kristallogr., 1987, **181**, 151-160).

In the original Rietveld's work, the "|Fobs|" are estimated by partitioning
among reflections contributing to each profile point of the pattern according
to the |Fcalc|, thus they are biased. However, it will be shown that iterating
the Rietveld's formula provides a nice and simple way to extract |Fobs|
as accurately as possible, starting from initial |F|s arbitrarily set to
have the same value. The first study applying such an algorithm for structure
determination purpose (using the unpublished program ARITB) was from Le
Bail, Duroy and Fourquet, *Mater. Res. Bull*., 1988, **23**, 447-452.
Near 20 ab initio structure determinations have been now performed in this
way, either from conventional or synchrotron X-ray powder data. The algorithm
has been implemented as an option in two other programs (FULLPROF, GSAS)
; any Rietveld program can be easily modified to accommodate this possibility
to extract structure factors. The strategy necessary for success will be
exposed. The best results are from cell and space group constrained conditions
; only all equal starting |F|s can ensure that the structure factors of
strictly overlapping reflections are undifferentiated : they keep the same
value after each iteration ; lt is strongly recommended to start from very
precise cell parameters (not approximated ones) in order to avoid false
minima in case of complicated patterns with strong overlapping ; some iterations
are necessary without modifying cell and profile parameters in order to
start their least-squares refinement at further cycles in good conditions.
A definite advantage of the procedure is the very low number of parameters
to be refined (15 maximum in ARITB) allowing it to handie problems of any
size. Extracting in one run the several thousand |F|s (for instance from
synchrotron powder data with 0.020° 2-theta-FWHM) implicit for large
and/or low symmetrical cells is not utopia.

**Accuracy in Powder Diffraction II**

Proceedings of the International Conference, May 26-29, 1992

NIST Special Publication 846, E. Prince and J.K. Stalick, Editors

page 213.