Scattering models - Revision history

KevinYager: /* Other Solutions Equations */

2015-04-10T17:42:59Z

‎Other Solutions Equations

KevinYager: /* Other Solutions Equations */

2015-04-10T17:40:11Z

‎Other Solutions Equations

KevinYager at 17:39, 10 April 2015

2015-04-10T17:39:13Z

KevinYager at 17:39, 10 April 2015

2015-04-10T17:39:05Z

KevinYager: /* Other Solutions Equations */

2015-04-10T17:33:44Z

‎Other Solutions Equations

KevinYager: Created page with "Unfortunately, x-ray and neutron scattering data cannot be simply inverted to yield a realspace structure. Instead, the experimental scattering intensity m..."

2015-04-10T17:33:23Z

Created page with "Unfortunately, x-ray and neutron scattering data cannot be simply inverted to yield a realspace structure. Instead, the experimental scattering intensity m..."

New page

Unfortunately, [[x-ray]] and [[neutron]] [[scattering]] data cannot be simply inverted to yield a [[realspace]] structure. Instead, the experimental [[scattering intensity]] must be fit to a candidate model, which in turn should be selected based on known physical constraints. Concordance between experimental data and a particular scattering model gives confidence that the selected model is correct. However, this is not absolute: scattering is an ill-posed problem ([[phase problem]]), so a variety of different models may all fit the data. Again, the experimenter must use their knowledge and judgment to select plausible models. (It is very helpful to have secondary measurements, such as electron microscopy, to guide model selection.)

Once a particular model has been selected and validated, fitting scattering data is a robust way to extract precise values of a variety of structural parameters (size, size distribution, shape, orientation, aggregation, etc.). There are a wide variety of literature models available.

==[[Form factor]]==
Any given object shape has a particular form factor ([[reciprocal-space]]). If the objects are randomly ordered (e.g. in solution), then the scattering is dominated by this form factor. Thus, one can fit solution-phase data using form factor equations.
* Refer to [[form factor]] for a list of equations for different shapes.

===Other Solutions Equations===
* Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst. '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]

==[[Structure Factor]]==
The [[structure factor]] is the scattering contribution from the organization of constituents (atomic crystal lattice, aggregation state in solution, etc.). In order to fit data to a given structure factor, one must disentangle the contributions from the form factor. (Or fit the data at the level of the total [[scattering intensity]].) A variety of structure factor equations have been documented.
* Refer to [[structure factor]] for a list of equations.

===[[Lattices of nano-objects]]===
* [[Lattices_of_nano-objects#Specific_models|Specific models]]
* [[Lattices_of_nano-objects#General_models|General models]]

@@ Line 16: / Line 16: @@
 ===Other Solutions Equations===
-* [[Polymer clustering]]
+* [[Example:Polymer clustering|Polymer clustering]]
 * Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst.'' '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]

← Older revision		Revision as of 17:40, 10 April 2015
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	===Other Solutions Equations===		===Other Solutions Equations===
		+	* [[Polymer clustering]]
	* Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst.'' '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]		* Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst.'' '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]

@@ Line 10: / Line 10: @@
 * [[Guinier plot]] (<math>\scriptstyle \ln(I) \sim 1 - (R_g^2/3)q^{2} </math>)
 * [[Zimm plot]]
 ==[[Form factor]]==

← Older revision		Revision as of 17:39, 10 April 2015
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	Once a particular model has been selected and validated, fitting scattering data is a robust way to extract precise values of a variety of structural parameters (size, size distribution, shape, orientation, aggregation, etc.). There are a wide variety of literature models available.		Once a particular model has been selected and validated, fitting scattering data is a robust way to extract precise values of a variety of structural parameters (size, size distribution, shape, orientation, aggregation, etc.). There are a wide variety of literature models available.
		+
		+	==Scaling Analysis==
		+	The scaling of scattering intensity can sometimes be fit with a very general and abstract model, from which one can measure a property of the size or shape of the structuring.
		+	* [[Porod plot]] (<math>\scriptstyle I \sim q^{-4}</math>)
		+	* [[Fresnel plot]] (<math>\scriptstyle R \sim q^{-4}</math>)
		+	* [[Kratky plot]] (<math>\scriptstyle I \sim q^{-2}</math>)
		+	* [[Guinier plot]] (<math>\scriptstyle \ln(I) \sim 1 - (R_g^2/3)q^{2} </math>)
		+	* [[Zimm plot]]
		+

	==[[Form factor]]==		==[[Form factor]]==

@@ Line 8: / Line 8: @@
 ===Other Solutions Equations===
-* Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst. '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]
+* Cylinders vs. ribbons in solution: Y. Su, C. Burger, B. S. Hsiao and B. Chu [http://journals.iucr.org/j/issues/2014/02/00/fs5073/stdsup.html Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering] ''J. Appl. Cryst.'' '''2014''', 47, 788. [http://dx.doi.org/10.1107/S1600576714005020 doi: 10.1107/S1600576714005020]
 ==[[Structure Factor]]==