Critical angle - Revision history

KevinYager: /* See Also */

2019-03-21T20:28:31Z

‎See Also

KevinYager at 20:52, 14 October 2014

2014-10-14T20:52:27Z

KevinYager at 20:50, 14 October 2014

2014-10-14T20:50:35Z

KevinYager at 01:40, 30 September 2014

2014-09-30T01:40:10Z

KevinYager: /* Examples */

2014-06-09T16:40:55Z

‎Examples

KevinYager: /* Energy dependence */

2014-06-06T04:43:05Z

‎Energy dependence

KevinYager: /* Critical q */

2014-06-05T21:21:45Z

‎Critical q

KevinYager: /* Calculating */

2014-06-05T21:20:11Z

‎Calculating

KevinYager: /* Elemental dependence */

2014-06-05T21:13:36Z

‎Elemental dependence

KevinYager: /* Examples */

2014-06-05T21:10:21Z

‎Examples

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 * [[Scattering Length Density]]
 * [[Refractive index]]
 * [http://en.wikipedia.org/wiki/Evanescent_wave Wikipedia: Evanescent wave]

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 In [[GISAXS]], the '''critical angle''' for a thin film is the incident angle below which one gets [[Refractive_index#Total_external_reflection|total external reflection]] of the x-ray beam.
-Below the critical angle, the beam is fully reflected from the film. The x-ray field probes a short distance into the film surface (due to the evanescent wave); on the order of a few nanometers. Thus, a GISAXS measurement below the critical angle is inherently probing only the film surface. A measurement well above the critical angle, by comparison, penetrates through the film and thus measures the average of the structure through the whole film. Close to the critical angle, the [[Refraction distortion|refracted beam]] is nearly parallel to the film interface; in other words the beam is coupled into [[X-ray waveguide|waveguide]] modes. This increases the effective path-length of the beam through the sample, which thereby increases the intensity of the scattering.
+Below the critical angle, the beam is fully reflected from the film. The x-ray field probes a short distance into the film surface (due to the evanescent wave); on the order of a few nanometers. Thus, a GISAXS measurement below the critical angle is inherently probing only the film surface. A measurement well above the critical angle, by comparison, penetrates through the film and thus measures the average of the structure through the whole film. Close to the critical angle, the [[Refraction distortion|refracted beam]] is nearly parallel to the film interface; in other words the beam is coupled into [[X-ray waveguide|waveguide]] modes. This increases the effective path-length of the beam through the sample, which thereby increases the intensity of the [[scattering]].
-Normally in GISAXS experiments, it is useful to do measurements both below and above the critical angle; by comparing the two patterns, you can ascertain whether the structures observed at the surface (e.g. as seen by AFM or SEM) are representative of the entire film. Measurements close to the critical angle are useful because of the intensity enhancement.
+Normally in GISAXS experiments, it is useful to do measurements both below and above the critical angle; by comparing the two patterns, you can ascertain whether the structures observed at the surface (e.g. as seen by AFM or SEM) are representative of the entire film. Measurements close to the critical angle are useful because of the [[GISAXS#Intensity_Enhancement|intensity enhancement]].
 ==Examples==

@@ Line 1: / Line 1: @@
 In [[GISAXS]], the '''critical angle''' for a thin film is the incident angle below which one gets [[Refractive_index#Total_external_reflection|total external reflection]] of the x-ray beam.
-Below the critical angle, the beam is fully reflected from the film. The x-ray field probes a short distance into the film surface (due to the evanescent wave); on the order of a few nanometers. Thus, a GISAXS measurement below the critical angle is inherently probing only the film surface. A measurement well above the critical angle, by comparison, penetrates through the film and thus measures the average of the structure through the whole film. Close to the critical angle, the refracted beam is nearly parallel to the film interface; in other words the beam is coupled into [[X-ray waveguide|waveguide]] modes. This increases the effective path-length of the beam through the sample, which thereby increases the intensity of the scattering.
+Below the critical angle, the beam is fully reflected from the film. The x-ray field probes a short distance into the film surface (due to the evanescent wave); on the order of a few nanometers. Thus, a GISAXS measurement below the critical angle is inherently probing only the film surface. A measurement well above the critical angle, by comparison, penetrates through the film and thus measures the average of the structure through the whole film. Close to the critical angle, the [[Refraction distortion|refracted beam]] is nearly parallel to the film interface; in other words the beam is coupled into [[X-ray waveguide|waveguide]] modes. This increases the effective path-length of the beam through the sample, which thereby increases the intensity of the scattering.
 Normally in GISAXS experiments, it is useful to do measurements both below and above the critical angle; by comparing the two patterns, you can ascertain whether the structures observed at the surface (e.g. as seen by AFM or SEM) are representative of the entire film. Measurements close to the critical angle are useful because of the intensity enhancement.

← Older revision		Revision as of 01:40, 30 September 2014
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	* [[Scattering Length Density]]		* [[Scattering Length Density]]
	* [[Refractive index]]		* [[Refractive index]]
		+	* [http://en.wikipedia.org/wiki/Evanescent_wave Wikipedia: Evanescent wave]

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 ==Examples==
 {| class="wikitable"
 |-

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 [[Image:Gold-crit.png|400px]][[Image:Gold-critq.png|400px]]
 ==See Also==
 * [[Scattering Length Density]]
 * [[Refractive index]]

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 q_c = \frac{4 \pi}{\lambda}\sin\theta_c
 </math>
 ==Calculating==

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 | 130.80
 |}
 ==Calculating==
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 The [[Scattering Length Density]] (SLD) for any given material can be computed using tabulated values. From this, the critical angle can be computed. The critical scattering vector is:
 :<math>q_c = \sqrt{ 16 \pi \mathrm{SLD} }</math>
-In reflection-mode, the scattering vector is:
+So:
 :<math>
 \begin{alignat}{2}

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 ==Elemental dependence==
-[[Image:Elements-crit.png|400px]]
+[[Image:Elements-crit.png|400px]][[Image:Elements-critq.png|400px]]
 ==Energy dependence==