Introduction: Rietveld refinement of X-ray powder diffraction data can yield
considerable amount of crystallographic information, in addition to
quantitative phase estimation. The Rietveld method is a whole pattern
fitting least squares technique and uses the entire pattern rather than a
limited number of reflections to extract required information. In this method,
the observed pattern for each phase is compared with the calculated
one(modeled using single crystal structural data), and any differences
between the two are minimized by refining structural as well as profile
related parameters. Since the method uses all lines, severely overlapping
reflections are not a problem. The method can obtain the following
crystallographic information from data collected on any type of X-ray

Lattice parameters
Since systematic errors (for example, sample displacement) are refined
during the refinement, accurate values up to one part in 1000 can be
obtained on solid samples without an internal standard. Additionally,
accurate cell dimensions can be computed on low symmetry materials.

Accurate phase quantification
Scale factors are refined and are related to weight percentage of each
phase. Complex mixtures with phases containing overlapping reflections
are quantified with a high degree of accuracy (~2 wt.%)

Crystallite size and strain
A mathematical function is used to model the profiles and to separate
diffraction peak broadening due to size from that due to strain. Size and
microstrain values are derived simultaneously from the XRD pattern.

Site occupancies
Yields quantitative information as to the extent of solid solution or
isomorphous substitution (Zr to Ti).

Preferred orientation
Since preferred orientation on a unique axis can be refined, a relative
measure of degree of orientation can be obtained.

Technology of Materials
Rietveld Analysis