[sdpd] Defending the true Warren-Averbach method, and more

[Armel Le Bail <alb...@cristal.org>]

Comments on
"Line Profile Analysis: pattern modelling versus profile fitting",
P. Scardi & M. Leoni,
J. Appl. Cryst. 39, 2006, 24-31.

This paper can be considered as a post-deadline contribution to the 
size/strain ceria round robin (2004). The study is limited to the Le Mans 
data (not using the best quality synchrotron data, nor the neutron data, 
etc...).

The claim in the abstract that a "traditional whole powder pattern fitting 
followed by Warren-Averbach analysis...tends to overestimate the domain 
size effect, providing size values about 20% smaller", is misleading.

A comparison (not found in the paper) gives :

- Results in the Round Robin paper (J. Appl. Cryst. 2004, 37, 911-924), 
page 923:
"In the first part of this paper, domain sizes were calculated using three 
approaches: an assumed lognormal size distribution of spherical 
crystallites, the Warren-Averbach method, and Rietveld refinement. An 
average of all the results (...) gives the following values:
                                      DV = (231 ± 5) Å       DA = (179 ± 5) Å
Thus, both the volume-weighted and area-weighted apparent domain sizes 
agree within a single standard uncertainty."

So that the true WA method does not give size values 20% smaller, if 
correctly applied.

I do not see how a reader, if newcomer about such methods, can understand 
why a WPPF followed by WA was necessary to test with the ceria case when a 
real traditional WA can be done and give the correct result in the round robin.

W & A never applied any WPPF before using their method, they used the real 
profiles. I think they would dislike the use of the name "Warren-Averbach 
analysis" as it is made inappropriately in the Sardi & Leoni paper.

- Results in the Scardi and Leoni paper
in Table 1, WPPM using a lognormal size distribution of spherical domains:
                                      DV = 228(4) Å       DA = 180(2) Å
or WPPM using a generic histogram instead of a lognormal distribution:
"Most of the refinement parameters remain unchanged with respect to those 
reported in Table I".


Comparing these results from the RR and the Scardi and Leoni paper, one 
obtains :
           RR :                                  DV = (231 ± 5) Å       DA 
= (179 ± 5) Å
           WPPM - Scardi & Leoni :   DV = 228(4) Å           DA = 180(2) Å.
It is thus clear that WPPM either with an empirical approach using a 
lognormal distribution of spherical domains, or a generic histogram, gives 
the same results (within the error) as those obtained in the RR paper, 
using an assumed lognormal size distribution of spherical crystallites, or 
using the (true) Warren-Averbach method, or using Rietveld refinements.

But the Scardi & Leoni conclusion is :
"Only full pattern modelling provides a correct, accurate analysis of 
disperse nanocrystalline systems"
or
"the fundamental parameter microstructural approach inherent in WPPM is 
more appropriate and accurate for reliable line profile analysis than WPPF 
that uses empirical functions."

Pretending that a method is better, without any argument, when the results 
are in fact equal to those from all other methods (if correctly applied)... 
this is misleading the reader, and adding more confusion to size-strain 
analysis techniques.

Armel Le Bail



 
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