OLD THEORIES ARE STILL
No progress in basic powder
diffraction theories on imperfect materials has really emerged since 1950.
THE MOTHER OF POWDER DIFFRACTION
The Debye scattering equation :
k = 4psinq/l
It involves only the magnitude of the distances rmn of each atom from every other atom.
Valid for any form of
matter in which there is a random orientation, including gases, liquids,
amorphous solids and crystalline powders :
From that formula, you can calculate the powder diffraction pattern of any model, homogeneous or inhomogeneous, ordered or disordered.
NOT APPLICABLE TO THE RIETVELD METHOD
Comparison of measured (-+-) and computed (___) interference function. The model system is a boundary structure consisting of four atomic layers in which atoms are displaced in random directions.
The calculated patterns
were probably (?) estimated by using the Debye scatterring formula.
How would such data be
treated by using the Rietveld method ?
(first, I hope that this is really f, not h = f *g
i.e. the instrumental effect was removed or negligible)
One crystalline phase + "diffusive" effects included in the background, or
two phases or more, each
of them described from a crystalline model (the core + some boundary models).
Describing defects by
using the hkl-based approach
THE WARREN EQUATION FOR
REMAINS UNDISPUTED :
This equation, expressed as a Fourier series, provides f for a reflection family :
h3 = 2|a3|sin q/l
Supposes an homogeneous
NOT APPLICABLE AS SUCH TO THE RIETVELD METHOD.
TOO MUCH UNKNOWNS :
n = 20-100 values of Nn and Zn for each reflection family.
The need for few parameters explains why poor restrictive representations of S/M effects were chosen for f (and h) in WPPF as Gaussian, Lorentzian, Pearson VII, Voigt, pseudo-Voigt.