Dear Masami Tsubota,
thanks for pointing to the paper. To be honest I'm not completely clear
about the meaning of some termini used in the summary, and about the
value of this new criterion. My questions:
1) What does "peak shift" really mean in this context? Obviously you
discuss any difference between a "measured" or "refined" angular peak
position and the theoretical Bragg angle calculated from referenced or
refined lattice parameters, plotted in fig. 1. Ok, the reference Bragg
position is clear. It is also known (since Klug & Alexander, Wilson etc.
in the 1950ies) that numerous geometrical effects complicate the peak
shape, apparently "shift" the peak maximum from its theoretical value,
and that these effects are strongly angular dependent (Jenkins,
Schreiner in the 1980ies, textbooks...). Btw this is how the trends in
fig 1 and 3 look like. Of course, if not taken into account correctly,
these effects will bias the lattice parameters systematically.
Basically, the primary question is how accurate we can
model/calculate/correct all these effects in our Rietveld refinement
procedure.
Let us assume that our peak shape model (no matter if in Rietveld,
LeBail or local unconstrained profile fitting) includes these well-known
geometrical aberrations of the maximum positions by any "fundamental
parameter" or "ray tracing" approach, and the wavelength profile used in
the convolution fits to the instrument correctly. Such approach includes
besides the asymmetry also the instrumental/geometrical aberrations of
the angular peak position, but of course not the unknowns related to the
individual sample preparation (transparency Ts) and the individual
instruments alignment (zero point Z and sample displacement Ds). As I
understood, the latter 3 unknowns are included/refined in the model in
this paper too (equation 1) and should be well refineable in all
Rietveld programs when the pattern is good and measured up to high
2theta. So, what additional kind of "peak shifts" else are discussed
her? Or, do you rely only on the systematic, geometrically caused
deviations of peak maximum positions when fitted "traditionally" (by
analytical functions) in your Rietveld program? If yes, is your
criterion maybe obsolete in refinements applying good FPA models?
2) What does "reproducibility of the peak shift" mean? How good a peak
position (or shift from the reference value) can be reproduced by
repetition of the measurement (including preparation), as I would expect
from the usual meaning of the word "reproducibility" in analytical work?
Or do you simply mean "how good your refinement model can fit the peak
positions of the measured pattern"? If you mean the latter, we are back
to the discussion above that an incorrect (or oversimplified) peak shape
model in a Rietveld analysis may bias the refined lattice parameters. In
my understanding, such kind of bias is a systematic error, simply caused
by an incorrect model, and the term "reproducibility" sounds a bit
misleading in this context.
3) It is clear that systematically wrong (fixed) lattice parameters will
enhance the number of the proposed criterion (fig. 2 e,f). But what will
happen in a practical refinement when the angular range is smaller, Z,
Ts and Ds become more correlated, and maybe additional nonsense profile
parameters are started to refine and compensate each other, e.g. for
more broadened peak profiles? Will the values of this criterion still
give a clear indication of any systematic error, or will they maybe
masked by such correlation effects?
A few cents from a personal view: Of course I agree that the observation
of any systematic misfit in the peak positions in Rietveld refinement is
a valuable information, e.g. for identification of instrumental
misalignment, or pointing to erroneous peak profile description in a FPA
model. However, to get reliable lattice parameters in Rietveld
refinement with a FPA model it is a recommended strategy to admix
silicon SRM640c to a powder sample, fix the lattice parameters of this
internal standard to the theoretical value during the refinement, and
refine/adjust for example sample transparency parameters (a typical
unknown in practice) in the peak profile model, until the profile and
the peak position of the standard peaks are well fitted. So we can
"anchor" the correlated angular effects by the standard peaks. But this
is possible to do without this new criterion, so I'm not convinced of
the necessity of the criterion proposed, at the moment.
Best regards
Reinhard
Am 14/11/2017 um 16:55 schrieb Johannes Birkenstock:
Dear Masami Tsubota,
thanks for directing us to your interesting, free access article.
However, it is not stated in the article whether and how the new
criterion could be applied in usual Rietveld refinements of
non-certified samples.
Am I right that your new criterion (Σ|Δ2θR|(sum or all) = Min) relies
on the previous knowledge of the true, correct lattice parameter
(which was certified for LaB6 in case of the NIST material SRM 660a
treated in the article)?
I conclude that from combining the relations given in the paper: Δ2θR
= Δ2θexp + Δ2θana = Δ2θexp + 2·(arcsin(1/A · sinθ)-θ) = Δ2θexp +
2·(arcsin(a_SRM/a_refined · sinθ)-θ), i.e., the correction seems to
rely on the known certified value of lattice parameter a_SRM.
If this is correct, how could this criterion be applied to any other
sample? Or is it only meant for standard reference materials?
With best regards,
Johannes
Am 14.11.2017 um 06:15 schrieb TSUBOTA Masami:
Dear Larry,
Thank you for your comments.
The reasons why we showed the results applying the Howard's method
for the asymmetry function in our manuscript are:
1) the peaks were fairly symmetric for the in-house data,
2) no detailed information about the apparatus such as the goniometer
radius,
3) one cannot reproduce the diffraction peak asymmetry completely
even for
the Finger's method,
4) The effect of the asymmmetry on 2th angle affects in the low 2th
region,
however, the peak-shift in the high 2th region is much more important
to obtain the true lattice parameters,
5) the number of the parameters is smaller than the Finger's method,
6) we have confirmed that there is no difference of our findings between
the Howard's and Finger's methods.
You can also try the Finger's method as well. Prof. Le Bail shares
his high quality data with us on the Internet.
http://www.cristal.org/powdif/low_fwhm_and_rp.html
Best regards,
Masami
On 2017/11/14 12:22, Larry Finger wrote:
On 11/13/2017 08:54 PM, TSUBOTA Masami wrote:
Dear Rietvelters,
I'd like to introduce our following article.
https://www.nature.com/articles/s41598-017-15766-y
Accuracy of refinement parameters in the Rietveld method is not so
good.
We have carefully investigated the reason, focusing on the peak-shift.
Our results show that a proportional unit-cell compared to the true
one
is obtained in the conventional Rietveld method. We propose an
additional
criterion to obtain the true lattice parameters accurately.
Hope this might be useful or interesting to you.
Masami,
The manuscript is very interesting, and appears to provide useful
information regarding the accuracy of lattice constants.
That said, why did you choose the ad-hoc method of Howard for
compensating for peak asymmetry, which is largely due to axial
divergence? The method of Finger, Cox and Jephcoat ("A correction for
powder diffraction peak asymmetry due to axial divergence", J. Appl.
Cryst. (1994). 27, 892-900) applies the optics of the diffractometer to
describe the asymmetry, AND the associated peak shift. Yes, the method
is computationally intensive, but it is physically superior to merely
adding sums of Gaussians. For most studies using small aperture slits
with minimal asymmetry, it probably does not matter; however, your
study
in which a great deal is made of peak shifts, should use the best
methodology.
Sincerely,
Larry
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