Circular orientation distribution function - Revision history

KevinYager: /* References */

2022-04-15T19:22:20Z

‎References

KevinYager: /* \eta function */

2021-02-08T16:57:54Z

‎\eta function

KevinYager: /* References */

2016-01-03T17:32:21Z

‎References

KevinYager: /* \scriptstyle \eta function */

2015-12-21T19:38:33Z

‎\scriptstyle \eta function

KevinYager: /* Maier-Saupe distribution parameter */

2015-12-21T19:38:04Z

‎Maier-Saupe distribution parameter

KevinYager at 19:33, 21 December 2015

2015-12-21T19:33:44Z

KevinYager at 22:12, 29 October 2015

2015-10-29T22:12:55Z

KevinYager: Created page with "In assessing the orientation of aligned materials, one can use the orientation order parameter to quantify order. Another possibility is to fit scattering data using a..."

2015-10-29T21:55:18Z

Created page with "In assessing the orientation of aligned materials, one can use the orientation order parameter to quantify order. Another possibility is to fit scattering data using a..."

New page

In assessing the orientation of aligned materials, one can use the [[orientation order parameter]] to quantify order. Another possibility is to fit [[scattering]] data using an equation that has 'circular wrapping' (i.e. periodic along <math>\scriptstyle 2 \pi</math>). Ruland ''et al.'' present such an equation:

:<math>
I (\chi) = \frac{1 - \eta^2}{(1+\eta)^2 - 4 \eta \cos^2 \chi}
</math>

Where <math>\scriptstyle \chi </math> is the angle along the arc of the [[scattering features|scattering ring/feature]]. The single fit parameter (<math>\scriptstyle \eta </math>) is convenient in that it behaves in a similar way to an order parameter: a value close to 1.0 indicates strong alignment, while progressively smaller values indicate lesser alignment. For a random sample, the scattering is isotropic and <math>\scriptstyle \eta = 0</math>.

==See Also==
* Ruland, W.; Tompa, H., The Effect of Preferred Orientation on the Intensity Distribution of (Hk) Interferences. Acta Crystallographica Section A 1968, 24, 93-99.
* Ruland, W.; Smarsly, B., Saxs of Self-Assembled Oriented Lamellar Nanocomposite Films: An Advanced Method of Evaluation. J. Appl. Crystallogr. 2004, 37, 575-584.

@@ Line 22: / Line 22: @@
 * Ruland, W.; Smarsly, B., Saxs of Self-Assembled Oriented Lamellar Nanocomposite Films: An Advanced Method of Evaluation. J. Appl. Crystallogr. 2004, 37, 575-584. [http://dx.doi.org/10.1107/S0021889804011288 doi: 10.1107/S0021889804011288]
 * [[Kevin G. Yager]], Christopher Forrey, Gurpreet Singh, Sushil K. Satija, Kirt A. Page, Derek L. Patton, Jack F. Douglas, Ronald L. Jones and Alamgir Karim [http://pubs.rsc.org/en/Content/ArticleLanding/2015/SM/C5SM00896D#!divAbstract Thermally-induced transition of lamellae orientation in block-copolymer films on ‘neutral’ nanoparticle-coated substrates] ''Soft Matter'' '''2015''' [http://dx.doi.org/10.1039/C5SM00896D doi: 10.1039/C5SM00896D]
 =Maier-Saupe distribution parameter=

← Older revision		Revision as of 16:57, 8 February 2021
Line 11:		Line 11:

	[[Image:Eta func-I chi.png\|500px]]		[[Image:Eta func-I chi.png\|500px]]
		+
		+	==Normalized==
		+	The function normalized so that the maximum is always at 1 would be:
		+	:<math>
		+	I_{\mathrm{norm}} (\chi) = \frac{(1+\eta)^2 - 4 \eta}{(1+\eta)^2 - 4 \eta \cos^2 \chi}
		+	</math>

	==References==		==References==

@@ Line 13: / Line 13: @@
 ==References==
-* Ruland, W.; Tompa, H., The Effect of Preferred Orientation on the Intensity Distribution of (Hk) Interferences. Acta Crystallographica Section A 1968, 24, 93-99.
+* Ruland, W.; Tompa, H., The Effect of Preferred Orientation on the Intensity Distribution of (Hk) Interferences. Acta Crystallographica Section A 1968, 24, 93-99. [http://dx.doi.org/10.1107/S0567739468000112 10.1107/S0567739468000112]
-* Ruland, W.; Smarsly, B., Saxs of Self-Assembled Oriented Lamellar Nanocomposite Films: An Advanced Method of Evaluation. J. Appl. Crystallogr. 2004, 37, 575-584.
+* Ruland, W.; Smarsly, B., Saxs of Self-Assembled Oriented Lamellar Nanocomposite Films: An Advanced Method of Evaluation. J. Appl. Crystallogr. 2004, 37, 575-584. [http://dx.doi.org/10.1107/S0021889804011288 doi: 10.1107/S0021889804011288]
 =Maier-Saupe distribution parameter=

@@ Line 1: / Line 1: @@
 In assessing the orientation of aligned materials, one can use the [[orientation order parameter]] to quantify order. Another possibility is to fit [[scattering]] data using an equation that has 'circular wrapping' (i.e. periodic along <math>\scriptstyle 2 \pi</math>).
-=<math>\scriptstyle \eta </math> function=
+=<math>\eta </math> function=
 Ruland ''et al.'' present such an equation:

← Older revision		Revision as of 19:38, 21 December 2015
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	[[Image:MaierSaupe-ODF-01.png\|500px]]		[[Image:MaierSaupe-ODF-01.png\|500px]]
	[[Image:MaierSaupe-ODF-021.png\|500px]]		[[Image:MaierSaupe-ODF-021.png\|500px]]
		+
		+	The parameter ''c'' can be used to normalize:
		+
		+	[[Image:MaierSaupe-ODF-01b.png\|500px]]
		+	[[Image:MaierSaupe-ODF-02b.png\|500px]]

← Older revision		Revision as of 22:12, 29 October 2015
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	Where <math>\scriptstyle \chi </math> is the angle along the arc of the [[scattering features\|scattering ring/feature]]. The single fit parameter (<math>\scriptstyle \eta </math>) is convenient in that it behaves in a similar way to an order parameter: a value close to 1.0 indicates strong alignment, while progressively smaller values indicate lesser alignment. For a random sample, the scattering is isotropic and <math>\scriptstyle \eta = 0</math>.		Where <math>\scriptstyle \chi </math> is the angle along the arc of the [[scattering features\|scattering ring/feature]]. The single fit parameter (<math>\scriptstyle \eta </math>) is convenient in that it behaves in a similar way to an order parameter: a value close to 1.0 indicates strong alignment, while progressively smaller values indicate lesser alignment. For a random sample, the scattering is isotropic and <math>\scriptstyle \eta = 0</math>.

−		+	[[Image:Eta func-I chi.png\|500px]]