Tutorial:Qualitative inspection - Revision history

KevinYager: /* Diffuse Scattering */

2015-01-29T21:47:00Z

‎Diffuse Scattering

KevinYager: /* Scattering Contrast */

2015-01-29T21:46:21Z

‎Scattering Contrast

KevinYager: /* Scattering Volume */

2015-01-29T21:43:15Z

‎Scattering Volume

KevinYager: /* Peak Width */

2015-01-29T21:42:31Z

‎Peak Width

KevinYager: /* Peak Width */

2015-01-29T21:42:18Z

‎Peak Width

KevinYager: /* Amount of Order */

2015-01-29T21:35:58Z

‎Amount of Order

KevinYager: /* Diffuse Scattering */

2015-01-29T21:35:36Z

‎Diffuse Scattering

KevinYager: /* Missing Orders */

2014-12-16T18:57:15Z

‎Missing Orders

KevinYager at 19:30, 3 December 2014

2014-12-03T19:30:23Z

KevinYager: /* Multiple Sharp Peaks */

2014-10-16T13:27:51Z

‎Multiple Sharp Peaks

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 ====Diffuse Scattering====
 [[Diffuse scattering]] is the scattering intensity which is spread over a wide range of ''q''-values, and lacks any definite structure (i.e. it is not concentrated into a peak, ring, or even broad halo). This kind of scattering arises from structuring that is not periodic or otherwise well-ordered. Thus, it arises from random ordering, or from disorder. For instance, a nanoporous material (sponge-like, with voids of many different sizes) will give rise to intense low-''q'' diffuse scattering. A rough surface will create substantial diffuse scattering (a broad and bright [[specular rod]]) in [[GISAXS]]. Thus, diffuse scattering is a signature of some kind of random [[realspace]] structure. Unfortunately, quantitative analysis of this kind of scattering is quite difficult (since there are so many models that give rise to essentially the same diffuse scattering signature).
 ====Single Broad Ring (Halo)====

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 ===Scattering Contrast===
-The intensity of scattering scales with the square of the scattering contrast. For x-rays, scattering arises from electron density; i.e. the relevant contrast is the electron-density difference between the two phases. (For neutrons scattering, the nuclear [[Scattering Length Density]] is the relevant contrast.) For instance, [[Material:Gold|gold]] spheres sitting in [[Material:Vacuum|vacuum]] will have extremely large contrast and will lead to very intense scattering. Equivalently-sized [[Material:Polystyrene|polystyrene]] spheres sitting in [[Material:Water|water]] will have much lower scattering contrast. Many soft-matter systems thus have weak contrast: e.g. [[block-copolymer]] mesophases involve two different polymer species, with nearly identical densities. Thus their scattering contrast is comparatively weak (but can still be probed using [[synchrotron]] [[beamlines]]).
+The intensity of scattering scales with the square of the scattering contrast. For x-rays, scattering arises from [[electron-density distribution|electron density]]; i.e. the relevant contrast is the electron-density difference between the two phases. (For neutrons scattering, the nuclear [[Scattering Length Density]] is the relevant contrast.) For instance, [[Material:Gold|gold]] spheres sitting in [[Material:Vacuum|vacuum]] will have extremely large contrast and will lead to very intense scattering. Equivalently-sized [[Material:Polystyrene|polystyrene]] spheres sitting in [[Material:Water|water]] will have much lower scattering contrast. Many soft-matter systems thus have weak contrast: e.g. [[block-copolymer]] mesophases involve two different polymer species, with nearly identical densities. Thus their scattering contrast is comparatively weak (but can still be probed using [[synchrotron]] [[beamlines]]).
 Scattering contrast can be intentionally varied in order to gain additional information about a system. For instance, one can measure a porous system in air, and then with solvent filling the pores. The difference in scattering allows one to assess the structure. For multi-component systems, one can intentionally 'contrast-match' a particular species, making it invisible (to scattering).

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 ===Scattering Volume===
-The scattering intensity (counts on the x-ray detector per unit time) scales with the amount of scattering material. Thus, a bigger sample yields a stronger scattering signal. The truly relevant quantity is the '''scattering volume''': the intersection between the x-ray beam and the sample. (Of course if you try to scatter through a sample that is too thick, [[absorption]] or [[multiple scattering]] will at some point instead reduce the signal.) In [[GISAXS]], the scattering volume can be difficult to estimate accurately: one must account for the beam width, the sample thickness, and the [[beam projection]] along the beam direction (while accounting for whether this projected beam size or the sample dimensions limits the scattering volume in this direction).
+The [[scattering intensity]] (counts on the x-ray detector per unit time) scales with the amount of scattering material. Thus, a bigger sample yields a stronger scattering signal. The truly relevant quantity is the [[scattering volume]]: the intersection between the x-ray beam and the sample. (Of course if you try to scatter through a sample that is too thick, [[absorption]] or [[multiple scattering]] will at some point instead reduce the signal.) In [[GISAXS]], the scattering volume can be difficult to estimate accurately: one must account for the beam width, the sample thickness, and the [[beam projection]] along the beam direction (while accounting for whether this projected beam size or the sample dimensions limits the scattering volume in this direction).
 Note that because real x-ray beams are not not square-waves (i.e. they have a pseudo-Gaussian cross section), and scattering intensity is affected by flux, determining the relevant scattering volume can be subtle (c.f. [[integral breadth]]).

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 ==Peak Width==
 In scattering, sharp peaks correspond to large grain sizes, whereas broad peaks correspond to small grain sizes. This can be quantified through a [[Scherrer grain size analysis]]. Even qualitatively, however, it is usually easy to judge how well-ordered a material is based purely on peak widths. Consider a highly disordered system, such as an amorphous polymer. The polymer chains likely have some preferred chain-packing distance, but the '[[lattice]]' only repeats once or twice before decorrelating; i.e. there isn't a well-defined crystal with well defined grain boundaries. In such a case one would see a very broad halo. In even more disordered systems, only [[diffuse scattering]] would be seen (this can be thought of as the ultimate limit of a broad peak).
 On the other hand, extremely sharp peaks indicate that the [[lattice]] repeats in a well-correlated way over very large distances. Thus, sharp peaks arise when one has well-defined crystals.
 ==Scattering Intensity==

← Older revision		Revision as of 21:42, 29 January 2015
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	On the other hand, extremely sharp peaks indicate that the [[lattice]] repeats in a well-correlated way over very large distances. Thus, sharp peaks arise when one has well-defined crystals.		On the other hand, extremely sharp peaks indicate that the [[lattice]] repeats in a well-correlated way over very large distances. Thus, sharp peaks arise when one has well-defined crystals.
		+
		+	[[Image:BCP example SAXS.png\|200px\|thumb\|right\|Example [[GISAXS]] data for a [[block-copolymer]] thin film. The peak is fairly sharp along ''q<sub>y</sub>'' (horizontal), indicating reasonably large grains. However, the peaks are stretched along ''q<sub>z</sub>'' (vertical), indicating only short-range coherence in the vertical (film normal) direction. This is to be expected for a thin film, since the finite thickness truncates ordering in this direction.]]

	==Scattering Intensity==		==Scattering Intensity==

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 [[Diffuse scattering]] is the scattering intensity which is spread over a wide range of ''q''-values, and lacks any definite structure (i.e. it is not concentrated into a peak, ring, or even broad halo). This kind of scattering arises from structuring that is not periodic or otherwise well-ordered. Thus, it arises from random ordering, or from disorder. For instance, a nanoporous material (sponge-like, with voids of many different sizes) will give rise to intense low-''q'' diffuse scattering. A rough surface will create substantial diffuse scattering (a broad and bright [[specular rod]]) in [[GISAXS]]. Thus, diffuse scattering is a signature of some kind of random [[realspace]] structure. Unfortunately, quantitative analysis of this kind of scattering is quite difficult (since there are so many models that give rise to essentially the same diffuse scattering signature).
-[[Image:Diffuse scattering example SAXS.png|300px|thumb|right|Example [[SAXS]] of a disordered composite, which generates [[diffuse scattering]] at low ''[[q]]''.]]
+[[Image:Diffuse scattering example SAXS.png|200px|thumb|right|Example [[SAXS]] of a disordered composite, which generates [[diffuse scattering]] at low ''[[q]]''.]]
 ====Single Broad Ring (Halo)====

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 ==Missing Orders==
-The intensities of higher-order peaks are affected by the exact shape of the structures sitting on the realspace [[lattice]]; i.e. the realspace lattice determines the peak positions, while the electron-density distribution within the [[unit cell]] controls the peak heights. This modulation of peak heights can be extreme: e.g. an appropriate electron-density distribution can entirely extinguish a particular peak.
+The intensities of higher-order peaks are affected by the exact shape of the structures sitting on the realspace [[lattice]]; i.e. the realspace lattice determines the peak positions, while the [[electron-density distribution]] within the [[unit cell]] controls the peak heights. This modulation of peak heights can be extreme: e.g. an appropriate electron-density distribution can entirely extinguish a particular peak.
 This effect can be understood in terms of the [[form factor]] modulating the [[structure factor]] peak heights. Thus, if a given particle shape (or, more generally, density distribution in the unit cell) has a form-factor minimum at a particular ''q'', then any structural peak at this ''q'' will not appear.

← Older revision		Revision as of 19:30, 3 December 2014
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−	When analyzing data, the first thing one should do is get an overall sense of data. By applying a few simple rules-of-thumb, one can interpret a 2D x-ray scattering image, and infer quite a bit about the structure of the sample.	+	When analyzing data, the first thing one should do is get an overall sense of data. By applying a few simple rules-of-thumb, one can interpret a 2D x-ray scattering image, understanding the origin of various [[scattering features\|features]], and infer quite a bit about the structure of the sample.

	==Amount of Order==		==Amount of Order==

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 ====Multiple Sharp Peaks====
-[[Image:Rubrene GIWAXS example.png|200px|right|thumb|GIWAXS example with many sharp peaks (Rubrene).]]
+[[Image:Rubrene GIWAXS example.png|200px|right|thumb|Example [[GIWAXS]] with many sharp peaks (Rubrene).]]
 When scattering patterns exhibit distinct peaks, rather than rings, this indicates that the material is well-ordered, and well-oriented. Thus, the sample's structure is not isotropic: there is a preferred orientation for the material.