Talk:Structure factor

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Structure factor proportional to intensity for crystals but amplitude for liquids

I'm asking to clarify something I have noticed. In crystallography (and SAXS) the structure factor is defined in terms of intensity, rather than amplitude of the wave. Looking at the structure factor for liquids it looks like it is proportional to the amplitude. The definition for liquid structure factor I see here looks the same as I see everywhere else, so I'm guessing this could be a difference in nomenclature between fields. If this is the case, this point needs to be clarified somewhere close to the relevant equations so that people coming here looking for information (such as myself) don't wind up spending hours trying to figure out whether I've missed something in the derivation (which I may have) or if $S_{crystallography}(q)$ and $S_{liquids}(q)$ are defined differently. 150.203.179.56 (talk) 00:36, 12 August 2019 (UTC)[reply]

Disambiguation

This page is confusing to many readers because there are two different functions called "structure factor" used by two different groups whose work is closely related -- although they do not talk to each other much. Neither group is 'right' or 'wrong'.

One structure factor (usually S) is as defined here, coming from solid state physics and general diffraction (starting with a gas of identical particles as in the current version of the page). It compares the observed diffraction per atom to that from a single atom.

The other (usually F or $F_{hkl}$ ) comes from crystallography and is defined by IUCR at http://reference.iucr.org/dictionary/Structure_factor. It is defined in terms of amplitude and phase rather than intensity, and since it relates to diffraction from a unit cell (comparing the observed diffraction in allowed directions to that from a single electron at the chosen unit cell vertices) it does not contain the factor 1/N.

To outsiders these groups are more or less identical, so I do not think this deserves a formal disambiguation page. Instead, both definitions need to be stated, along with their preferred range of use -- S for disordered systems, $F_{hkl}$ for crystals, particularly those with many different atoms in a unit cell. Of course there is overlap in partially ordered systems and since there is no error involved, both can be used. I am working on a suitable revision and welcome comments before the fact as well as after. Clavipes (talk) 20:47, 5 September 2016 (UTC)[reply]

Notation

I've changed some of the notation in this article, the most important changes are:

I would like to use $F$ for the structure factor instead of $S$ , since this seems to be the preferred notation of the International Union of Crystallography.

I've introduced the scattering vector $\Delta \mathbf {k}$ to emphasize that we are dealing with a general scattering of the radiation, which only under certain assumptions reduces to scattering vectors equal to a reciprocal lattice vector.

I would also like to change the notation in the last part to use h, k and l as Miller indices. This is consistent with the Miller index article and standard use. Also we should use e.g. ${\hat {x}}^{*}$ for the basis vector of the reciprocal lattice.

O. Prytz 20:17, 31 May 2006 (UTC)[reply]

Notation in solid state physics

Unfortunately the articles uses both at the moment $F$ and $S$ . Considering standard books on Solid State Physics (Ashcroft Mermin^[1], Kittel^[2]), it should probably be $S$ . Kittel uses $F$ for the scattering amplitude both use $f$ for the atomic form factor, like in the article right now. From the solid state physics point of view, $S$ is preferable and very common in experiments like SAXS. $\mathbf {q}$ as momentum exchange is also typical in neutron scattering, etc. But I have to confess that notation throughout literature is inconsistent and basically a mess. Mikuszefski (talk) 12:29, 28 January 2014 (UTC)[reply]

References

^ N. W. Ashcroft, N. D. Mermin, Solid State Physics,Sounders College Publishing, 1976
^ C. Kittel, Introduction to Solid State Physics John Wiley \& Sons, Inc., 1996

Complex Structure Factor

What surprises me, is the fact the structure factor is already squared. To my knowledge it is a factor of the scattering amplitude and, hence, complex. Consequently the intensity should be proportional $\vert S\vert ^{2}$ .Mikuszefski (talk) 12:38, 28 January 2014 (UTC)[reply]

Vector Notation

r_i is a vector representing the position of atom i. However, in the worked examples on body-centered and face-centered cubics, r₀, r₁, r₂ and r₃ weren't represented as vectors in bold. This has been changed as it caused confusion to those not so familiar with the topic.

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Comment(s)

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Silicon does not crystallize in the FCC structure. It is a diamond cubic material.

== Structure Factor - real or complex? ==

The definition of the structure factor is misleading, since a real quantity (the intensity) is equated said to be proportional to the structure factor itself, which is a priori complex. Did I understand the article correctly? — Preceding unsigned comment added by Franciturci (talk • contribs) 16:15, 16 July 2012 (UTC)[reply]

==a mistake?== I think the following part have a mistake, $\delta (\mathbf {r} -\mathbf {R} _{j})$ is not a Dirac delta function here, because it does not fit the properties of the Dirac delta function.

"

\phi (\mathbf {r} )=\sum _{j=1}^{N}f(\mathbf {r} -\mathbf {R} _{j})=f(\mathbf {r} )\ast \sum _{j=1}^{N}\delta (\mathbf {r} -\mathbf {R} _{j})

,

(1)

with $\textstyle \mathbf {R} _{j},j=1,\,\ldots ,\,N$ the particle positions. In the second equality, the field is decomposed as the convolution product $\ast$ of the function $f$ , describing the "form" of the particles, with a sum of Dirac delta functions depending only on their positions.

"

Last edited at 21:00, 20 January 2015 (UTC). Substituted at 07:10, 30 April 2016 (UTC)

This sentence does not make sense

It says " $F_{hkl}$ is thus not a special case of $S(\mathbf {q} )$ ; the observed scattering intensity depends on $S(\mathbf {q} )$ , but on the squared modulus $|F_{hkl}|^{2}$ ." Does it mean the observed scattering intensity does not depend ..., but... Other wise the "but" doesn't make sense.Billlion (talk) 00:20, 17 December 2017 (UTC)[reply]

Super slow response, sorry; rewrote sentence to try to make it clearer Clavipes (talk) 18:09, 17 October 2019 (UTC)[reply]

[1] N. W. Ashcroft, N. D. Mermin, Solid State Physics,Sounders College Publishing, 1976

[2] C. Kittel, Introduction to Solid State Physics John Wiley \& Sons, Inc., 1996

[1]

[2]