Dear Leandro Bravo,
some comments below:
Leandro Bravo schrieb:
In the refinement of chlorite minerals with well defined disordering
(layers shifting by exactly b/3 along the three pseudohexagonal Y
axis), you separate the peaks into k = 3.n (relative sharp, less
intensive peak) and k  3.n (broadened or disappeared
reflections). How did you determined this value k = 3.n and n =
0,1,2,3..., right?
The occurence of stacking faults along the pseudohexagonal Y axes causes
broadening of all reflections hkl with k unequal 3n (for example 110,
020, 111..) whereas the reflections with k equal 3n remain unaffected
(001, 131, 060, 331...). This is clear from geometric conditions, and
can be seen in single crystal XRD (oscillation photographs, Weissenberg
photographs) as well in selected area electron diffraction patterns. The
fact is known for a long time, and published and discussed in standard
textbooks, for example *Brindley, G.W., Brown, G.: Crystal Structures
of Clay Minerals and their X-ray Identification. Mineralogical Society,
London, 1980.*
First, the chlorite refinement.
In the first refinement of chlorite you used no disordering models and
used ´´cell parameters`` and ´´occupation of octahedra``. So you
refined the lattice parameters and the occupancy of all atoms?
Yes, the lattice parameters.
Only the occupation/substitution of atoms with significant difference in
scattering power can be refined in powder diffraction. In case of
chlorites, the substitution Fe-Mg at the 4 octahedral positions can be
refined.
In the second refinement, you use na anisotropic line broadening ´´in
the traditional way``. So you used a simple ellipsoidal model and/or
spherical harmonics?
Simple ellipsoidal model, assuming very thiny platy crystals. But it was
clear that this model must fail, see above the known fact of disorder in
layer stacking. And from microscopy it is clear that the "crystals" are
much too large to produce significant line broadening from size effects.
You can see this for a lot of clay minerals: If the "ellipsoidal
crystallite shape" model would be ok, the 00l reflections would have the
broadest lines, and the 110, 020 and so on should be the sharpest ones.
But this is not true in practice, mostly the hkl are terribly broadenend
and smeared, but the 00l are still sharp.
The last refinement, describing a real structure. You used for the
reflections k  3.n (broadened peaks) a ´´rod-like intensity
distribution``, with the rod being projected by the cosine of the
direction on the diffractogram. You used also the lenghts of the rods
as a parameter, so as the dimension of the rods for 0k0 with k
 3.n. I would like to know how did you ´´project`` these rods
and use them in the refinement.
For the k = 3.n reflections, you used an anisotropic broadening model
(aniso crystallyte size) and and isotropic broadening model
(microstrain broadening). But you said that crystallite size is an
isotropic line broadening in my kaolinite refinement and I should not
use it. So I use or not the cry size?
Yes, we used an "additional" ellipsoidal broadening in order to describe
any potential "thinning" of the crystals. But this broadening model was
not significant because the broadening was dominated by the stacking
faults. A "microstrain" makes sense because of natural chlorits are
sometimes zoned in their chemical composition and a distribution of the
lattice constants may occur.
In one of your mails you mentioned "crysize gave reasonable numbers with
low error", and from that I assumed you looked only on the errors of the
isotropic crysize as defined in Topas. You must know what model you did
apply. But it is clear that any "crysize" model is inadequate to
describe the line broadening of kaolinite.
Now the kaolinite refinement.
In the first refinement was used fixed atomic positions and a
conventional anisotropic peak broadening. This conventional
anisotropic peak broadening would be the simple ellipsoidal model
and/or spherical harmonics?!
Only ellipsoidal model, assuming a platy crystal shape, see above. Only
for comparision.
After that you use the introduced model of disorfering. Is this model
the same of the chlorite (rods for k  3.n and microstrain
broadening and anisotropic crystallite size?
Not exactly the same like in chlorite, because the disorder in kaolinite
is much more complicated like in chlorites. See also the textbook cited
above, and extensive works of Plancon and Tchoubar. Thus, most of the
natural kaolinites show stacking faults along b/3 as well as along a,
and additional random faults. Thus, more broadening parameters had to be
defined, and this is not completely perfect until now. See the
presentation I sent you last week.
Best regards
Reinhard Kleeberg
