OLD THEORIES ARE STILL
VALID
No progress in basic powder
diffraction theories on imperfect materials has really emerged since 1950.
THE MOTHER OF POWDER DIFFRACTION
FORMULAE :
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. H. Gleiter,
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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
Size/Microstrain EFFECTS
REMAINS UNDISPUTED :
This equation, expressed as a Fourier series, provides f for a reflection family :
h3 = 2|a3|sin
q/l
Supposes an homogeneous
material.
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.