Dear Johannnes,
Thank you, too.
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)?
No. The criteria do not rely on the previous knowledge.
Although we gave the value of a_SRM for the initial value of
the lattice parameter, it is refined. (Only Z-value was fixed.)
We just picked up the result of (Σ|Δ2θR|^(sum or all) = Min)
from the several results. That is a^(sum or all).
(We also obtained the same results with the other initial values.)
For computing (Σ|Δ2θR|^(sum or all) = Min), would you please see
the last part of this email? I explained for fluoroapatite.
In short, Z, Ds and Ts are used. We don't use the lattice parameter.
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),
For the SRM sample with a cubic crystal system, it is yes.
i.e., the correction seems to rely
on the known certified value of lattice parameter a_SRM.
This is no. The formula can be generally expressed as:
Δ2θR = Δ2θexp + Δ2θana = Δ2θexp + 2·(arcsin(1/A · sinθ)-θ)
= Δ2θexp + 2·(arcsin(a_true/a_refined · sinθ)-θ)
= Δ2θexp + 2·(arcsin(b_true/b_refined · sinθ)-θ)
= Δ2θexp + 2·(arcsin(c_true/c_refined · sinθ)-θ).
They include no information about a_SRM.
The formula Δ2θana is derived from just rearranging two Bragg's equations
shown on page 2 in the manuscript. (No information about a_SRM is used
to derive Δ2θana.)
If this is correct, how could this criterion be applied to any other
sample? Or is it only meant for standard reference materials?
No. One can apply the proposed criteria for any non-certificated sample.
I'm going to show a step-by-step way how to calculate the criteria
for fluoroapatite with a hexagonal crystal system as another example.
The data collected by Young with Cu K alpha radiation is nowadays
widely distributed with GSAS and RIETAN-FP.
The 2th range of the pattern is from 15.0 deg. to 130.0 deg.
The maximum intensity is about 20000 counts.
As for Σ|Δ2θR|^(sum)...
There are six hundred and fourty six diffraction peaks in the 2th range
from 15 deg. to 130 deg. according to a lst file output by RIETAN-FP.
The peak at minimum 2th of ~16.9 deg. is from {101} reflection.
The peak at maximum 2th of ~129.6 deg. is from {560} and {910} reflections.
By using the peak-shift parameters (Z, Ds and Ts) with Eq. (1),
one can compute 646 points of the peak-shift for each reflection.
Then, sum up them.
This is Σ|Δ2θR|^(sum) for fluoroapatite with Young's data.
As for Σ|Δ2θR|^(all)...
There should be eight hundred and seventy four diffraction peaks
in the 2th range from 15 deg. upto 180 deg.
The peak at minimum 2th of ~16.9 deg. is from {101} reflection.
The peak at maximum 2th of ~177.4 deg. is from {617} reflection.
By using the peak-shift parameters (Z, Ds and Ts) with Eq. (1),
one can compute 874 points of the peak-shift. Then, sum up them.
This is Σ|Δ2θR|^(all) for fluoroapatite with Cu K alpha radiation.
You don't need to sum over up to 2th = 180 deg.
But the point is that the larger 2th is better as shown in Fig. 3e.
Hope this helps.
All the best,
Masami
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