What Are the Exact Scherrer Shape Factors for Different Crystallite Structures?

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Discussion Overview

The discussion revolves around the Scherrer equation and the shape factors used to determine crystallite sizes from X-ray diffraction (XRD) spectra. Participants seek to clarify the exact values of shape factors for different crystallite structures, such as monoclinic and cubic, and the relationship between crystallite shape and unit cell structure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that the Scherrer equation includes a shape factor K, which varies based on crystallite shape, suggesting values of 0.89 for spherical and 0.94 for cubic particles, but seeks a table with exact published values for various crystallite structures.
  • Another participant argues that there is a distinction between crystallite shape and unit cell structure, indicating that while there may be a relationship, it is not unique or well-defined.
  • A third participant provides a reference to a table from the International Union of Crystallography that lists shape factors for cubic systems based on crystal shape, highlighting that most literature defaults to a value of 0.9 when the shape is unknown.
  • One participant expresses a desire for references to support the commonly used value of 0.9 and questions the sources of information in existing literature.
  • A later reply presents specific XRD data and requests assistance in calculating crystallite size, indicating a practical application of the discussed concepts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact shape factors for different crystallite structures, and there are competing views regarding the relationship between crystallite shape and unit cell structure. The discussion remains unresolved regarding the availability of a definitive reference table.

Contextual Notes

Limitations include the lack of consensus on the shape factors and the dependence on specific crystallite shapes and milling conditions, which may affect the resulting particle shapes.

Salish99
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The Scherrer equation is used to determine crystallite sizes from XRD spectra.
they contain K, a shape factor, that varies from 0.89 for spherical to 0.94 for cubic particles. Usually, this is set to 0.9 for particles of unknown size.
Does anyone know where we could find a table with the exact, published values for different crystallites (e.g. monoclinic, cubic, etc.)?

Scherrer's original papers are published here
http://gdz.sub.uni-goettingen.de/dm...]=scherrer&tx_goobit3_search[squery]=scherrer
but a) in German, and b) do not contain such a table.

thanks.

The discussions in
https://www.physicsforums.com/showthread.php?t=122682&page=2
and
https://www.physicsforums.com/showthread.php?t=322033
simply assume it's 0.9. No reference is given there. I need the exact table, and a reference.
 
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I think you are mixing the crystallite shape with the unit cell of the crystal.
As you say yourself, K depends on the shape of the crystallite and not that of the unit cell.
There may be a realtion between unit cell and crystallite shape (NaCl has cubic unit cell and may crystalize in cubic crystallites) but is not unique and not well determined.

If you take cubic crystallites and grind them in a mill you may end up with spherical particles or irregularly shaped particles, depending on the milling conditions.
There are also crystals with cubic unit cell (ferrites for example) that may crystallize in elongated (needle-like) crystals.
 
Attached a table from the International Union of Crystallography, Vol 3 Section 5.2, 1986 pp.318-323. It shows some shape factors to be used for the cubic system, depending on the reflection plane, and the shape (octahedron, cube, tetrahedron) of the actual crystal.
Interesting to see is that only one value is below 1, whereas is all this forum, as well as in many published papers, 0.9 is usually used "when the shape is unknown".
I would like to have someone tell me where that information comes from, with reference please.
thanks!

(and, no, outdated student pages like http://www.d.umn.edu/~bhar0022/dpcalculator/index.php and http://www.eng.uc.edu/~gbeaucag/Classes/XRD/SathishScherrerhtml/SathishScherrerEqn.html do not have any references either - maybe people don't think about that factor usually)
 

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I have value of 2 theta 35.546 deg, d spacing 2.5235 A, fwhm (2 th) 0.148 deg, can someone use it to get size of crystallite. after getting data analysed by a program expertplus i have got this, thankyou
 

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