Re: Literature on Rietveld limitations in nano materials

[Frank Girgsdies]

Dear Rietvelders,

Thank you for your numerous replies, which give me a bunch of references 
to read through.
Please take my apologies that I'm not able to reply and say thank you to 
all contributors individually.


With kind regards,
Frank Girgsdies

On 07.06.2019 15:36, Darren Broom wrote:

Dear Frank

With regard to accurately determining the size of small particles or nano-crystallites, 
have you seen this article on "Pitfalls in the characterization of nanoporous and 
nanosized materials" by Claudia Weidenthaler?

https://pubs.rsc.org/en/content/articlelanding/2011/nr/c0nr00561d

Best regards,

Darren


-Original Message-
From: girgs...@fhi-berlin.mpg.de
Sent: Thu, 6 Jun 2019 12:39:29 +0200
To: rietveld_l@ill.fr
Subject: Literature on Rietveld limitations in nano materials

Dear fellow Rietvelders,

Could anyone point me to some nice literature which critically discusses
the limitations of the Rietveld method when it comes to nano-crystalline
materials (specifically in the 1 to 3 nm range)?
As far as I'm aware, the core Rietveld literature seems to touch this
point only in the passing.

Background:
To the best of my knowledge, Rietveld-derived parameters (like lattice
constants or domain sizes) should not be trusted as being "physically
meaningful"  anymore when you fit the powder pattern of a material in
the few nm range with standard Rietveld tools.
My naive understanding of this problem is that the physical principles
of diffraction (or rather the best way to model it) gradually change
when you go from long-range ordered to medium-/short-range ordered
materials.
Being a Rietveld practitioner rather than a theoretician, and having no
first-hand experience with WPPM and PDF methods, I am often confronted
with the problem to explain to my "customers" why I can't extract
trustworthy lattice constants or domain sizes from their
nano-crystalline samples, especially if it seems technically possible to
fit the pattern with a Rietveld program.
I think it would be nice if I could cite some critical discussion, or
overview article with further references, to put my finger on the
problem.
Especially in the catalysis community literature, my impression is that
the applicability of the Rietveld method is sometimes overestimated,
leading to overinterpretation of the results.

Any suggestions?

Best wishes,
Frank Girgsdies



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Re: Literature on Rietveld limitations in nano materials

[Matthew Rowles]

We've seen that asymmetric profile in our graphene simulations.

.

How many 1000s of atoms can debussy/discus reasonably deal with?

Matthew

On Thu, 6 Jun. 2019, 19:39 Reinhard Neder,  wrote:

> Dear Mr Girgsdies,
>
> Off hand I am not aware of any critical discussion. Let me add a few
> thoughts though that may help to explain the issues at hand.
>
> A Rietveld program calculates the diffraction pattern as a sum of all
> Bragg reflections. Initially these Bragg peaks are treated as
> infinitesimally sharp points at a fixed 2Theta position. This hold in
> particular for the calculation of the structure factor, which is calculated
> at the corresponding point in reciprocal space for the integer values
> triplet hkl. In a second step these sharp peaks are widened by a profile
> function to describe the experimentally observed broad peaks. The
> broadening of the profile function has components due to the instrumental
> resolution and sample contributions (size and strain).
>
> The Rietveld treatment implicitly assumes perfect translational
> periodicity, as all calculations in reciprocal space are limited to the
> integer Bragg positions. The sample contribution to the broadening is thus
> a bit of an artificial "trick" to get a good/reasonable agreement.
>
> In the actual diffraction experiment the diffraction pattern arises form
> the sum of all secondary waves emitted by all atoms. This sum of all the
> secondary waves is a continuous function in reciprocal space. Only in the
> limit of a perfect infinite crystal will the sum reduce to the Bragg
> positions, and be zero at all other points in reciprocal space.
>
> For a (very) small nanoparticle this sum of the secondary waves will
> naturally "widen" the Bragg positions compared to those of a large crystal.
> If one looks at a point slightly off the Bragg position, one has to keep in
> mind that this diffraction angle differs from that of the integer Bragg
> reflection. As a consequence, the individual atomic form factors and the
> structure factor will differ from the values at the integer Bragg position.
> This difference is not included in the Rietveld algorithm. This difference
> can lead to an asymmetric profile function. This profile may be asymmetric
> enough to have its maximum off the Bragg position and one must be super
> careful not to mistake the location of the maximum intensity of such an
> asymmetric profile with the actual Bragg position. This is described nicely
> in Tchoubar & Drits X-ray Diffraction by disordered lamellar structures.
> There are a bunch of "lovely" papers that do misinterpret this.
>
> The small nanoparticles below 3 nm diameter will add two more
> complications to the situation.
>
> A) The (irregular) surface will likely truncate the average bulk unit cell
> at different positions around the nanoparticle. Thus the Rietveld
> assumption that the crystal consists of identical unit cells is no longer
> absolutely correct. This may change the relative intensities.
>
> B) The surface is bound to be subject to
> distortions/reconstructions/different surface chemistry compared to the
> interior of the nanoparticle and will in many cases cause an appreciable
> strain across the particle, which again is not part of the Rietveld
> algorithm.
>
> All in all I would recommend to calculate the diffraction pattern of such
> small nanoparticles by use of the Debye-Scattering-Equation. This algorithm
> adds up the diffraction pattern from the contribution of all atom (pairs)
> and gives a direct diffraction pattern without the need of a sample related
> profile function. The Debussy program by Antonio Cervellino J.Appl.Cryst
> 48, 2026 (2015) and my own DISCUS program JAC 32, 838 (1999)
> "https://github.com/tproffen/DiffuseCode;
>  are two examples of such
> programs.
>
> The special issue of Acta Crystallographica A72 (2016) has several papers
> related to the Deby-Scattering-Equation, Paolo Scardi and Matteo Leoni have
> written several papers on the sample related profile function.
>
> Sincerely
>
> Reinhard Neder
> Am 06.06.19 um 12:39 schrieb Frank Girgsdies:
>
> Dear fellow Rietvelders,
>
> Could anyone point me to some nice literature which critically discusses
> the limitations of the Rietveld method when it comes to nano-crystalline
> materials (specifically in the 1 to 3 nm range)?
> As far as I'm aware, the core Rietveld literature seems to touch this
> point only in the passing.
>
> Background:
> To the best of my knowledge, Rietveld-derived parameters (like lattice
> constants or domain sizes) should not be trusted as being "physically
> meaningful"  anymore when you fit the powder pattern of a material in the
> few nm range with standard Rietveld tools.
> My naive understanding of this problem is that the physical principles of
> diffraction (or rather the best way to model it) gradually change when you
> go from long-range ordered to medium-/short-range ordered materials.
> 

Re: Literature on Rietveld limitations in nano materials

[Jonathan WRIGHT]

Hello,

I think it would be nice if I could cite some critical discussion, or 


There are a couple of comments in the current issue of J.Appl.Cryst that 
might be interesting for you:


https://doi.org/10.1107/S1600576719006575

Best,

Jon

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Re: Literature on Rietveld limitations in nano materials

[Reinhard Neder]

Dear Mr Girgsdies,

Off hand I am not aware of any critical discussion. Let me add a few 
thoughts though that may help to explain the issues at hand.


A Rietveld program calculates the diffraction pattern as a sum of all 
Bragg reflections. Initially these Bragg peaks are treated as 
infinitesimally sharp points at a fixed 2Theta position. This hold in 
particular for the calculation of the structure factor, which is 
calculated at the corresponding point in reciprocal space for the 
integer values triplet hkl. In a second step these sharp peaks are 
widened by a profile function to describe the experimentally observed 
broad peaks. The broadening of the profile function has components due 
to the instrumental resolution and sample contributions (size and strain).


The Rietveld treatment implicitly assumes perfect translational 
periodicity, as all calculations in reciprocal space are limited to the 
integer Bragg positions. The sample contribution to the broadening is 
thus a bit of an artificial "trick" to get a good/reasonable agreement.


In the actual diffraction experiment the diffraction pattern arises form 
the sum of all secondary waves emitted by all atoms. This sum of all the 
secondary waves is a continuous function in reciprocal space. Only in 
the limit of a perfect infinite crystal will the sum reduce to the Bragg 
positions, and be zero at all other points in reciprocal space.


For a (very) small nanoparticle this sum of the secondary waves will 
naturally "widen" the Bragg positions compared to those of a large 
crystal. If one looks at a point slightly off the Bragg position, one 
has to keep in mind that this diffraction angle differs from that of the 
integer Bragg reflection. As a consequence, the individual atomic form 
factors and the structure factor will differ from the values at the 
integer Bragg position. This difference is not included in the Rietveld 
algorithm. This difference can lead to an asymmetric profile function. 
This profile may be asymmetric enough to have its maximum off the Bragg 
position and one must be super careful not to mistake the location of 
the maximum intensity of such an asymmetric profile with the actual 
Bragg position. This is described nicely in Tchoubar & Drits X-ray 
Diffraction by disordered lamellar structures.  There are a bunch of 
"lovely" papers that do misinterpret this.


The small nanoparticles below 3 nm diameter will add two more 
complications to the situation.


A) The (irregular) surface will likely truncate the average bulk unit 
cell at different positions around the nanoparticle. Thus the Rietveld 
assumption that the crystal consists of identical unit cells is no 
longer absolutely correct. This may change the relative intensities.


B) The surface is bound to be subject to 
distortions/reconstructions/different surface chemistry compared to the 
interior of the nanoparticle and will in many cases cause an appreciable 
strain across the particle, which again is not part of the Rietveld 
algorithm.


All in all I would recommend to calculate the diffraction pattern of 
such small nanoparticles by use of the Debye-Scattering-Equation. This 
algorithm adds up the diffraction pattern from the contribution of all 
atom (pairs) and gives a direct diffraction pattern without the need of 
a sample related profile function. The Debussy program by Antonio 
Cervellino J.Appl.Cryst 48, 2026 (2015) and my own DISCUS program JAC 
32, 838 (1999) "https://github.com/tproffen/DiffuseCode; are two 
examples of such programs.


The special issue of Acta Crystallographica A72 (2016) has several 
papers related to the Deby-Scattering-Equation, Paolo Scardi and Matteo 
Leoni have written several papers on the sample related profile function.


Sincerely

Reinhard Neder

Am 06.06.19 um 12:39 schrieb Frank Girgsdies:

Dear fellow Rietvelders,

Could anyone point me to some nice literature which critically 
discusses the limitations of the Rietveld method when it comes to 
nano-crystalline materials (specifically in the 1 to 3 nm range)?
As far as I'm aware, the core Rietveld literature seems to touch this 
point only in the passing.


Background:
To the best of my knowledge, Rietveld-derived parameters (like lattice 
constants or domain sizes) should not be trusted as being "physically 
meaningful"  anymore when you fit the powder pattern of a material in 
the few nm range with standard Rietveld tools.
My naive understanding of this problem is that the physical principles 
of diffraction (or rather the best way to model it) gradually change 
when you go from long-range ordered to medium-/short-range ordered 
materials.
Being a Rietveld practitioner rather than a theoretician, and having 
no first-hand experience with WPPM and PDF methods, I am often 
confronted with the problem to explain to my "customers" why I can't 
extract trustworthy lattice constants or domain sizes from their 
nano-crystalline samples, especially if it seems technically 

Literature on Rietveld limitations in nano materials

[Frank Girgsdies]

Dear fellow Rietvelders,

Could anyone point me to some nice literature which critically discusses 
the limitations of the Rietveld method when it comes to nano-crystalline 
materials (specifically in the 1 to 3 nm range)?
As far as I'm aware, the core Rietveld literature seems to touch this 
point only in the passing.


Background:
To the best of my knowledge, Rietveld-derived parameters (like lattice 
constants or domain sizes) should not be trusted as being "physically 
meaningful"  anymore when you fit the powder pattern of a material in 
the few nm range with standard Rietveld tools.
My naive understanding of this problem is that the physical principles 
of diffraction (or rather the best way to model it) gradually change 
when you go from long-range ordered to medium-/short-range ordered 
materials.
Being a Rietveld practitioner rather than a theoretician, and having no 
first-hand experience with WPPM and PDF methods, I am often confronted 
with the problem to explain to my "customers" why I can't extract 
trustworthy lattice constants or domain sizes from their 
nano-crystalline samples, especially if it seems technically possible to 
fit the pattern with a Rietveld program.
I think it would be nice if I could cite some critical discussion, or 
overview article with further references, to put my finger on the problem.
Especially in the catalysis community literature, my impression is that 
the applicability of the Rietveld method is sometimes overestimated, 
leading to overinterpretation of the results.


Any suggestions?

Best wishes,
Frank Girgsdies



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Please do NOT attach files to the whole list 
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